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Message #01386
[Merge] lp:~gang65/ubuntu-calculator-app/reboot-do-not-modify-sourcecode-during-translation-generation into lp:ubuntu-calculator-app
Bartosz Kosiorek has proposed merging lp:~gang65/ubuntu-calculator-app/reboot-do-not-modify-sourcecode-during-translation-generation into lp:ubuntu-calculator-app.
Commit message:
Do not modify source code during generating pot translation template file
Requested reviews:
Ubuntu Calculator Developers (ubuntu-calculator-dev)
For more details, see:
https://code.launchpad.net/~gang65/ubuntu-calculator-app/reboot-do-not-modify-sourcecode-during-translation-generation/+merge/255425
Do not modify source code during generating pot translation template file.
It is very ugly and dirty to modify source code with scripts to generate translation template, without user permission/knowledge.
It is visible especially during using Ubuntu-SDK.
--
The attached diff has been truncated due to its size.
Your team Ubuntu Calculator Developers is requested to review the proposed merge of lp:~gang65/ubuntu-calculator-app/reboot-do-not-modify-sourcecode-during-translation-generation into lp:ubuntu-calculator-app.
=== added file 'CMakeLists.txt'
--- CMakeLists.txt 1970-01-01 00:00:00 +0000
+++ CMakeLists.txt 2015-04-07 21:05:21 +0000
@@ -0,0 +1,103 @@
+project(com.ubuntu.calculator)
+cmake_minimum_required(VERSION 2.8.9)
+
+find_program(INTLTOOL_MERGE intltool-merge)
+if(NOT INTLTOOL_MERGE)
+ message(FATAL_ERROR "Could not find intltool-merge, please install the intltool package")
+endif(NOT INTLTOOL_MERGE)
+
+find_program(INTLTOOL_EXTRACT intltool-extract)
+if(NOT INTLTOOL_EXTRACT)
+ message(FATAL_ERROR "Could not find intltool-extract, please install the intltool package")
+endif(NOT INTLTOOL_EXTRACT)
+
+set(UBUNTU_MANIFEST_PATH "manifest.json.in" CACHE INTERNAL "Tells QtCreator location and name of the manifest file")
+
+find_package(Qt5Core REQUIRED)
+find_package(Qt5Qml REQUIRED)
+find_package(Qt5Quick REQUIRED)
+# Find_package(ubuntu-sdk-libs)
+
+#automatically create moc files
+set(CMAKE_AUTOMOC ON)
+
+
+option(INSTALL_TESTS "Install the tests on make install" on)
+option(CLICK_MODE "Installs to a contained location" on)
+
+include(GNUInstallDirs)
+
+set(APP_NAME ubuntu-calculator-app)
+set(APP_HARDCODE ubuntu-calculator-app)
+set(AUTOPILOT_DIR ubuntu_calculator_app)
+set(MAIN_QML ${APP_HARDCODE}.qml)
+set(ICON "${APP_HARDCODE}.png")
+set(DESKTOP_FILE "${APP_HARDCODE}.desktop")
+set(AUTOPILOT_DIR ubuntu_calculator_app)
+set(APP_VERSION 2.0)
+
+if(CLICK_MODE)
+ set(CMAKE_INSTALL_PREFIX "/")
+ set(UBUNTU-CALCULATOR-APP_DIR "${CMAKE_INSTALL_DATADIR}/qml")
+
+ set(QT_IMPORTS_DIR "${CMAKE_INSTALL_LIBDIR}")
+ set(EXEC "qmlscene $@ ${UBUNTU-CALCULATOR-APP_DIR}/${MAIN_QML}")
+ set(MODULE_PATH ${QT_IMPORTS_DIR})
+ if(NOT BZR_REVNO)
+ execute_process(
+ COMMAND bzr revno
+ OUTPUT_VARIABLE BZR_REVNO
+ WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}
+ OUTPUT_STRIP_TRAILING_WHITESPACE
+ )
+ endif(NOT BZR_REVNO)
+ if(NOT BZR_SOURCE)
+ set(BZR_SOURCE lp:${APP_HARDCODE})
+ message("-- Setting BZR_SOURCE to ${BZR_SOURCE}")
+ endif(NOT BZR_SOURCE)
+else(CLICK_MODE)
+ set(UBUNTU-CALCULATOR-APP_DIR "${CMAKE_INSTALL_DATADIR}/${APP_HARDCODE}")
+ execute_process(
+ COMMAND qmake -query QT_INSTALL_QML
+ OUTPUT_VARIABLE QT_IMPORTS_DIR
+ OUTPUT_STRIP_TRAILING_WHITESPACE
+ )
+endif(CLICK_MODE)
+
+if(CLICK_MODE)
+ message("-- Configuring manifest.json")
+
+ execute_process(
+ COMMAND dpkg-architecture -qDEB_HOST_ARCH
+ OUTPUT_VARIABLE CLICK_ARCH
+ OUTPUT_STRIP_TRAILING_WHITESPACE
+ )
+
+ configure_file(${UBUNTU_MANIFEST_PATH} ${CMAKE_CURRENT_BINARY_DIR}/manifest.json)
+ install(FILES ${CMAKE_CURRENT_BINARY_DIR}/manifest.json DESTINATION ${CMAKE_INSTALL_PREFIX})
+ install(FILES "${APP_HARDCODE}.apparmor" DESTINATION ${CMAKE_INSTALL_PREFIX})
+else(CLICK_MODE)
+ set(EXEC "qmlscene $@ -I ${MODULE_PATH} ${CMAKE_INSTALL_PREFIX}/${UBUNTU-CALCULATOR-APP_DIR}/${MAIN_QML}")
+endif(CLICK_MODE)
+
+file(GLOB_RECURSE I18N_SRC_FILES
+ RELATIVE ${CMAKE_CURRENT_SOURCE_DIR}/po
+ *.qml *.js)
+list(APPEND I18N_SRC_FILES ${CMAKE_CURRENT_BINARY_DIR}/po/${DESKTOP_FILE}.in.in.h)
+list(SORT I18N_SRC_FILES)
+
+configure_file(app/${DESKTOP_FILE}.in.in ${DESKTOP_FILE}.in)
+
+add_custom_target(${DESKTOP_FILE} ALL
+ COMMENT "Merging translations into ${DESKTOP_FILE}"
+ COMMAND LC_ALL=C ${INTLTOOL_MERGE} -d -u ${CMAKE_SOURCE_DIR}/po ${DESKTOP_FILE}.in ${DESKTOP_FILE}
+)
+
+install(FILES ${CMAKE_CURRENT_BINARY_DIR}/${DESKTOP_FILE}
+ DESTINATION ${CMAKE_INSTALL_DATADIR}/applications)
+
+# Tests
+enable_testing()
+
+add_subdirectory(app)
+add_subdirectory(po)
=== renamed file 'CMakeLists.txt' => 'CMakeLists.txt.moved'
=== added file 'README'
--- README 1970-01-01 00:00:00 +0000
+++ README 2015-04-07 21:05:21 +0000
@@ -0,0 +1,52 @@
+# Ubuntu Calculator App
+Default Calculator application for Ubuntu devices.
+
+# Useful links
+- Project page: https://launchpad.net/ubuntu-calculator-app
+- Design page:
+ https://docs.google.com/presentation/d/1EiIELGizPHrd0TY7JdNwULbiqPYfOyEEI5CS87n7QlY/edit
+
+
+# How to develop
+
+## Calculation engine.
+
+Current calculation engine is math.js version 1.1.0.
+You could download latest version from webpage:
+ http://mathjs.org
+
+The engine was sligtly modified to properly work with Ubuntu-Calculator-App.
+
+## Style guide
+
+General idea above style guide is:
+"All code in any code-base should look like a single person typed it, no matter how many people contributed."
+
+If you're editing code, take a few minutes to look at the code around you and determine its style. If they use spaces around all their arithmetic operators, you should too. If their comments have little boxes of hash marks around them, make your comments have little boxes of hash marks around them too.
+
+The point of having style guidelines is to have a common vocabulary of coding so people can concentrate on what you're saying rather than on how you're saying it. If code you add to a file looks drastically different from the existing code around it, it throws readers out of their rhythm when they go to read it. Avoid this.
+
+More information about style guides, and why we need it:
+ http://addyosmani.com/blog/javascript-style-guides-and-beautifiers/
+
+Curent style guide for ubuntu-calculator-app is:
+ https://google-styleguide.googlecode.com/svn/trunk/javascriptguide.xml
+
+## Clean/Beautiful Code
+
+When you creating code, every function/variable name should be meaningful and has easy to understand form. The names should reveal intent of creator. With good names you even do not need an comments. The code is documentting itself. We should avoid comments if it is not necessary.
+If someone during review, ask you to add comment then you should check if names are reveal your intent.
+
+More information about clean/beautiful code is available in books:
+ * Clean Code: A Handbook of Agile Software Craftsmanship Paperback, by Robert C. Martin
+ * Beautiful Code: Leading Programmers Explain How They Think, by Andy Oram
+
+## Run the autopilot tests
+
+Prerequisites:
+ sudo apt-get install ubuntu-ui-toolkit-autopilot
+
+Once the app has been built, you can go to the build directory and run:
+
+ cd tests/autopilot
+ autopilot run ubuntu_calculator_app
=== renamed file 'README' => 'README.moved'
=== added file 'README.translations'
--- README.translations 1970-01-01 00:00:00 +0000
+++ README.translations 2015-04-07 21:05:21 +0000
@@ -0,0 +1,40 @@
+# Updating translations
+
+Translations for the Calculator app happen in [Launchpad Translations] and
+are automatically committed daily on the trunk branch in the po/ folder.
+
+They are then built and installed as part of the package build, so that
+developers don't really need to worry about them.
+
+However, there is one task that needs to be taken care of: exposing new
+translatable messages to translators. So whenever you add new translatable
+messages in the code, make sure to follow these steps:
+
+ 1. Run click-buddy retaining the build directory:
+ $ click-buddy --dir . --no-clean
+ 2. Copy the .pot file from the <build dir> mentioned in the output to your
+ original source:
+ $ cp <build dir>/po/*.pot po/
+ 2. Commit the generated .pot file:
+ $ bzr commit -m"Updated translation template"
+ 3. Push the branch and send a merge proposal as usual
+
+And that's it, once the branch lands Launchpad should take care of all the rest!
+
+# Behind the scenes
+
+Behind the scenes, whenever the po/*.pot file (also known as translations template)
+is committed to trunk Launchpad reads it and updates the translatable strings
+exposed in the web UI. This will enable translators to work on the new strings.
+The translations template contains all translatable strings that have been
+extracted from the source code files.
+
+Launchpad will then store translations in its database and will commit them daily
+in the form of textual po/*.po files to trunk. The PO files are also usually
+referred to as the translations files. You'll find a translation file for each
+language the app has got at least a translated message available for.
+
+Translations for core apps follow the standard [gettext format].
+
+ [Launchpad Translations]: https://translations.launchpad.net/ubuntu-calculator-app
+ [gettext format]: https://www.gnu.org/software/gettext/
=== renamed file 'README.translations' => 'README.translations.moved'
=== added directory 'app'
=== added file 'app/CMakeLists.txt'
--- app/CMakeLists.txt 1970-01-01 00:00:00 +0000
+++ app/CMakeLists.txt 2015-04-07 21:05:21 +0000
@@ -0,0 +1,17 @@
+if(NOT "${CMAKE_CURRENT_SOURCE_DIR}" STREQUAL "${CMAKE_CURRENT_BINARY_DIR}")
+ file(GLOB QML_JS_FILES *.qml *.js)
+ add_custom_target(ubuntu-calculator-app_QMlFiles ALL SOURCES ${QML_JS_FILES})
+endif(NOT "${CMAKE_CURRENT_SOURCE_DIR}" STREQUAL "${CMAKE_CURRENT_BINARY_DIR}")
+
+if(CLICK_MODE)
+ set(ICON ${ICON})
+ install(FILES graphics/${ICON} DESTINATION ${CMAKE_INSTALL_PREFIX})
+endif(CLICK_MODE)
+
+install(FILES ${MAIN_QML} DESTINATION ${UBUNTU-CALCULATOR-APP_DIR})
+
+add_subdirectory(engine)
+add_subdirectory(graphics)
+add_subdirectory(ui)
+add_subdirectory(upstreamcomponents)
+add_subdirectory(tests)
=== added directory 'app/engine'
=== added file 'app/engine/CMakeLists.txt'
--- app/engine/CMakeLists.txt 1970-01-01 00:00:00 +0000
+++ app/engine/CMakeLists.txt 2015-04-07 21:05:21 +0000
@@ -0,0 +1,7 @@
+file(GLOB ENGINE_QML_JS_FILES *.qml *.js)
+
+# Make the files visible in the qtcreator tree
+add_custom_target(ubuntu-calculator-app_engine_QMlFiles ALL SOURCES ${ENGINE_QML_JS_FILES})
+
+install(FILES ${ENGINE_QML_JS_FILES} DESTINATION ${UBUNTU-CALCULATOR-APP_DIR}/engine)
+
=== added file 'app/engine/CalculationHistory.qml'
--- app/engine/CalculationHistory.qml 1970-01-01 00:00:00 +0000
+++ app/engine/CalculationHistory.qml 2015-04-07 21:05:21 +0000
@@ -0,0 +1,220 @@
+/*
+ * Copyright (C) 2014 Canonical, Ltd.
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; version 3.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program. If not, see <http://www.gnu.org/licenses/>.
+ */
+import QtQuick 2.3
+import QtQuick.LocalStorage 2.0
+
+Item {
+ property var calculationHistoryDatabase: null
+ readonly property int lastDatabaseVersion: 1
+ property int numberOfFavourites: 0
+
+ ListModel {
+ id: history
+
+ Component.onCompleted: {
+ getCalculations(function(calc) {
+ // Also if isFavourite is set as BOOL, LocalStorage saves it as
+ // int, so we need to convert it before adding the calc to
+ // the history
+ if (calc.isFavourite === 1) {
+ calc.isFavourite = true;
+ numberOfFavourites++;
+ } else {
+ calc.isFavourite = false;
+ }
+ history.append(calc);
+ });
+ }
+
+ ListElement {
+ dbId: -1
+ formula: ''
+ result: ''
+ date: 0
+ isFavourite: false
+ favouriteText: ''
+ }
+ }
+
+ Timer {
+ id: timer
+ interval: 500
+ property var execute: []
+ onTriggered: {
+ for (var i = 0; i < execute.length; i++) {
+ execute[i]();
+ }
+ execute = [];
+ }
+ }
+
+ function openDatabase() {
+ // Check if the database was already opened
+ if (calculationHistoryDatabase !== null) return;
+
+ calculationHistoryDatabase = LocalStorage.openDatabaseSync(
+ "com.ubuntu.calculator_reboot", "", "", 5000);
+
+ // Update (or create) the database if needed
+ if (calculationHistoryDatabase.version !== lastDatabaseVersion) {
+ upgradeDatabase(calculationHistoryDatabase.version);
+ }
+ }
+
+ function upgradeDatabase(currentDatabaseVersion) {
+ // Array with all the SQL needed to create database and update versions
+ var sqlcode = [
+ 'CREATE TABLE IF NOT EXISTS Calculations(
+ dbId INTEGER PRIMARY KEY,
+ formula TEXT NOT NULL,
+ result TEXT NOT NULL,
+ date INTEGER NOT NULL DEFAULT 0,
+ isFavourite BOOL DEFAULT false,
+ favouriteText TEXT
+ )'
+ ];
+
+ // Start the upgrade
+ calculationHistoryDatabase.changeVersion(currentDatabaseVersion,
+ lastDatabaseVersion, function(tx) {
+ // Create the database
+ if (currentDatabaseVersion < lastDatabaseVersion) {
+ tx.executeSql(sqlcode[0]);
+ console.log("Database upgraded to " + lastDatabaseVersion.toString());
+ }
+ }
+ );
+ }
+
+ function getCalculations(callback) {
+ openDatabase();
+
+ // Do a transaction to take all calculations
+ calculationHistoryDatabase.transaction(
+ function (tx) {
+ var results = tx.executeSql('SELECT * FROM Calculations');
+
+ for (var i = 0; i < results.rows.length; i++) {
+ callback(results.rows.item(i));
+ }
+ }
+ );
+ }
+
+ function addCalculationToScreen(formula, result, isFavourite, favouriteText) {
+ // The function add the last formula to the model, and leave to
+ // addCalculationToDatabase the job to add it to the database
+ // that is called only after the element has been added to the
+ // model
+ if (isFavourite) {
+ numberOfFavourites++;
+ }
+ var date = Date.now();
+ history.append({"formula": formula,
+ "result": result,
+ "date": date,
+ "isFavourite": isFavourite,
+ "favouriteText": favouriteText});
+ var index = history.count - 1;
+ // TODO: move this function to a plave that retards the execution to
+ // improve performances
+ timer.execute.push(function() {
+ calculationHistory.addCalculationToDatabase(formula, result, date, index, isFavourite, favouriteText);
+ });
+ timer.start();
+ }
+
+ function addCalculationToDatabase(formula, result, date, index, isFavourite, favouriteText) {
+ openDatabase();
+ calculationHistoryDatabase.transaction(
+ function (tx) {
+ var results = tx.executeSql('INSERT INTO Calculations (
+ formula, result, date, isFavourite, favouriteText) VALUES(
+ ?, ?, ?, ?, ?)',
+ [formula, result, date, isFavourite, favouriteText]
+ );
+ // we need to update the listmodel unless we would have dbId = 0 on the
+ // last inserted item
+ history.setProperty(index, "dbId", parseInt(results.insertId));
+ }
+ );
+ }
+
+ function updateCalculationInDatabase(listIndex, dbId, isFavourite, favouriteText) {
+ openDatabase();
+ calculationHistoryDatabase.transaction(
+ function (tx) {
+ var results = tx.executeSql('UPDATE Calculations
+ SET isFavourite=?, favouriteText=?
+ WHERE dbId=?',
+ [isFavourite, favouriteText, dbId]
+ );
+ if (!history.get(listIndex).isFavourite && isFavourite) {
+ numberOfFavourites++;
+ }
+ if (history.get(listIndex).isFavourite && !isFavourite) {
+ numberOfFavourites--;
+ }
+ history.setProperty(listIndex, "isFavourite", isFavourite);
+ history.setProperty(listIndex, "favouriteText", favouriteText);
+ }
+ );
+ }
+
+ function getContents() {
+ return history;
+ }
+
+ function deleteCalc(dbId, id) {
+ openDatabase();
+ if (history.get(id).isFavourite) {
+ numberOfFavourites--;
+ }
+ history.setProperty(id, "dbId", -1);
+
+ timer.execute.push(function () {
+ calculationHistoryDatabase.transaction(
+ function (tx) {
+ tx.executeSql('DELETE FROM Calculations WHERE dbId = ?', [dbId]);
+ }
+ );
+ });
+ timer.start();
+ }
+
+ function removeFavourites(removedFavourites) {
+ openDatabase();
+ var sql = "UPDATE Calculations SET isFavourite = 'false' WHERE dbId IN (";
+ var removed = removedFavourites[0];
+ history.setProperty(removedFavourites[0], "isFavourite", false);
+ removedFavourites.splice(0, 1);
+ numberOfFavourites--;
+
+ for (var index in removedFavourites) {
+ numberOfFavourites--;
+ history.setProperty(removedFavourites[index], "isFavourite", false);
+ removed += "," + removedFavourites[index];
+ }
+
+ sql += removed + ")";
+
+ calculationHistoryDatabase.transaction(
+ function (tx) {
+ var result = tx.executeSql(sql);
+ }
+ );
+ }
+}
=== added file 'app/engine/formula.js'
--- app/engine/formula.js 1970-01-01 00:00:00 +0000
+++ app/engine/formula.js 2015-04-07 21:05:21 +0000
@@ -0,0 +1,257 @@
+/*
+ * Copyright (C) 2014 Canonical Ltd
+ *
+ * This file is part of Ubuntu Calculator App
+ *
+ * Ubuntu Calculator App is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License version 3 as
+ * published by the Free Software Foundation.
+ *
+ * Ubuntu Calculator App is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program. If not, see <http://www.gnu.org/licenses/>.
+ */
+
+/**
+ * Function which will delete last element in the formula
+ * It could be literal, operator, const (eg. "pi") or function (eg. "sin(" )
+ *
+ * @param bool isLastCalculate: if in the textfield there is the result of a
+ * calc this is true and the function delete all
+ * @param string formulaToCheck: the formula in the textfield
+ * @return a string with the new formula
+ */
+function deleteLastFormulaElement(isLastCalculate, formulaToCheck) {
+ if (isLastCalculate === true) {
+ return '';
+ }
+
+ if (formulaToCheck !== '') {
+ // We choose how many chars remove checking if in the end of the string
+ // there is a special operation. Default: 1
+ var removeSize = 1;
+
+ // 5 chars: sqrt(, asin(, acos(, atan(
+ if (formulaToCheck.slice(-5) === 'sqrt(' ||
+ formulaToCheck.slice(-5) === 'asin(' ||
+ formulaToCheck.slice(-5) === 'acos(' ||
+ formulaToCheck.slice(-5) === 'atan(') {
+ removeSize = 5;
+ }
+ // 4 chars: log(, exp(, sin(, cos(, tan(, abs(
+ else if (formulaToCheck.slice(-4) === 'log(' ||
+ formulaToCheck.slice(-4) === 'exp(' ||
+ formulaToCheck.slice(-4) === 'sin(' ||
+ formulaToCheck.slice(-4) === 'cos(' ||
+ formulaToCheck.slice(-4) === 'tan(' ||
+ formulaToCheck.slice(-4) === 'abs(') {
+ removeSize = 4;
+
+ }
+ // 2 chars: pi
+ else if (formulaToCheck.slice(-2) === 'pi') {
+ removeSize = 2;
+ }
+ formulaToCheck = formulaToCheck.substring(0, formulaToCheck.length - removeSize);
+ }
+
+ return formulaToCheck;
+}
+
+
+/**
+ * Function to check if a char is an operator
+ *
+ * @param char digit: the digit to check if is a valid operator
+ * @return bool that indicates if the digit is a valid operator
+ */
+function isOperator(digit) {
+ switch(digit) {
+ case "+":
+ case "-":
+ case "*":
+ case "/":
+ case "%":
+ case "^":
+ case "!":
+ return true;
+ default:
+ return false;
+ }
+}
+
+function validateStringForAddingToFormula(formula, stringToAddToFormula) {
+ // We are checking first character to validate strings with number eg. "^3"
+ if (isOperator(stringToAddToFormula[0])) {
+ return couldAddOperator(formula, stringToAddToFormula[0]);
+ }
+
+ if (stringToAddToFormula === ".") {
+ return couldAddDot(formula);
+ }
+
+ if (stringToAddToFormula === ")") {
+ return couldAddCloseBracket(formula);
+ }
+
+ // Validate complex numbers
+ if ((stringToAddToFormula === "i") || (!isNaN(stringToAddToFormula))){
+ if (formula.slice(-1) === "i") {
+ return false;
+ }
+ }
+ return true;
+}
+
+/**
+ * Function to check if could be add a close bracket at the end of a formula
+ *
+ * @param string formulaToCheck: the formula where we have to add the close bracket
+ * @return bool: true if the close bracket could be added, false otherwhise
+ */
+function couldAddCloseBracket(formulaToCheck) {
+ // Don't close a bracket just after opened it
+ if (formulaToCheck.slice(-1) === "(") {
+ return false;
+ }
+
+ // Calculate how many brackets are opened
+ var numberOfOpenedBrackets = (longFormula.match(/\(/g) || []).length -
+ (longFormula.match(/\)/g) || []).length;
+
+ if (numberOfOpenedBrackets < 1) {
+ return false;
+ }
+
+ return true;
+}
+
+/**
+ * Function to determine what bracket needs to be added after press
+ * universal bracket
+ * @param string formulaToCheck: formula which will be analysed
+ * @return a string contains bracket to add
+ */
+function determineBracketTypeToAdd(formulaToCheck) {
+ if (formulaToCheck === '') {
+ return "(";
+ }
+ var lastChar = longFormula.substring(formulaToCheck.length - 1, formulaToCheck.length);
+
+ if (isNaN(lastChar) && lastChar !== ")" && lastChar !== "i" && lastChar !== "E" && lastChar !== "!") {
+ return "(";
+ } else if (couldAddCloseBracket(formulaToCheck) === true) {
+ return ")";
+ }
+
+ return "*("
+}
+
+/**
+ * Function to replace some chars in the visual textfield
+ *
+ * @param string engineFormulaToConvert: the string where we have to replace chars
+ * @return a string based on param with changes in chars
+ */
+function returnFormulaToDisplay(engineFormulaToConvert) {
+ // The deletion of " is necessary for MathJs.format function - it returns a
+ // string surrounded by ", and they're useless, so we remove them
+ var engineToVisualMap = {
+ '-': '−',
+ '\\/': '÷',
+ '\\*': '×',
+ '\\.': decimalPoint,
+ 'NaN': i18n.tr("NaN"),
+ 'E': 'ℯ',
+ 'Infinity': '∞',
+ '"': '',
+ ' ': ''
+ }
+
+ if (engineFormulaToConvert !== undefined) {
+ for (var engineElement in engineToVisualMap) {
+ var regExp = new RegExp(engineElement, 'g');
+ engineFormulaToConvert = engineFormulaToConvert.replace(regExp, engineToVisualMap[engineElement]);
+ }
+ } else {
+ engineFormulaToConvert = '';
+ }
+
+ return engineFormulaToConvert;
+}
+
+/**
+ * Function to check if an operator could be added to the formula
+ *
+ * @param char operatorToAdd: the operator that will be added to the formula
+ * @param string formulaToCheck: the actual formula
+ * @return bool: true if the operator could be added, false otherwise
+ */
+function couldAddOperator(formulaToCheck, operatorToAdd) {
+ // No two operators one after other, except factorial operator
+ if (isOperator(formulaToCheck.slice(-1)) && formulaToCheck.slice(-1) !== "!") {
+ // But a minus after a * or a / is allowed
+ if (!(operatorToAdd === "-" && (formulaToCheck.slice(-1) === "*" ||
+ formulaToCheck.slice(-1) === "/"))) {
+ return false;
+ }
+ }
+
+ // No operator after a dot
+ if (formulaToCheck.slice(-1) === ".") {
+ return false;
+ }
+
+ // No operator after an open brackets, but minus
+ if (formulaToCheck.slice(-1) === "(" && operatorToAdd !== "-") {
+ return false;
+ }
+
+ // No operator at beginning (but minus)
+ if (formulaToCheck === "" && operatorToAdd !== "-") {
+ return false;
+ }
+
+ return true;
+}
+
+/**
+ * Function to check if could be add a dot at the end of a formula
+ *
+ * @param string formulaToCheck: the formula where we have to add the dot
+ * @return bool: true if the dot could be added, false otherwhise
+ */
+function couldAddDot(formulaToCheck) {
+ // A dot could be only after a number
+ if ((isNaN(formulaToCheck.slice(-1))) || (formulaToCheck === "")) {
+ return false;
+ }
+
+ // If is after a number and it's the first dot of the calc it could be added
+ if (formulaToCheck.indexOf('.') === -1) {
+ return true;
+ }
+
+ // If there is already a dot we have to check if it isn't in the same operation
+ // So we take all the string since the last occurence of dot to the end
+ var lastOperation = formulaToCheck.substring(formulaToCheck.lastIndexOf('.') + 1);
+
+ // If there isn't something different from a number we can't add a dot
+ if (!isNaN(lastOperation)) {
+ return false;
+ }
+
+ // If the only thing different from a number is a pi we cannot add a dot
+ if (lastOperation.indexOf('pi') !== -1) {
+ if (!isNaN(lastOperation.replace('pi', ''))) {
+ return false;
+ }
+ }
+
+ return true;
+}
+
=== added file 'app/engine/math.js'
--- app/engine/math.js 1970-01-01 00:00:00 +0000
+++ app/engine/math.js 2015-04-07 21:05:21 +0000
@@ -0,0 +1,32477 @@
+// All edits done for the Ubuntu Calculator App are preceded by a comment that
+// starts with 'UCA:' and describes the edit
+
+// UCA: add a var to which we will refer to when we include the code in qml
+// in app/ubuntu-calculator-app.qml with import "engine/math.js" as MathJs and
+// then property var mathJs: MathJs.mathJs;
+var mathJs;
+
+/**
+ * math.js
+ * https://github.com/josdejong/mathjs
+ *
+ * Math.js is an extensive math library for JavaScript and Node.js,
+ * It features real and complex numbers, units, matrices, a large set of
+ * mathematical functions, and a flexible expression parser.
+ *
+ * @version 1.2.0
+ * @date 2014-12-25
+ *
+ * @license
+ * Copyright (C) 2013-2014 Jos de Jong <wjosdejong@xxxxxxxxx>
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License"); you may not
+ * use this file except in compliance with the License. You may obtain a copy
+ * of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+ * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
+ * License for the specific language governing permissions and limitations under
+ * the License.
+ */
+
+(function webpackUniversalModuleDefinition(root, factory) {
+ // UCA: we delete all exports, we don't need them, and we keep only our var
+ mathJs = factory();
+})(this, function() {
+return /******/ (function(modules) { // webpackBootstrap
+/******/ // The module cache
+/******/ var installedModules = {};
+/******/
+/******/ // The require function
+/******/ function __webpack_require__(moduleId) {
+/******/
+/******/ // Check if module is in cache
+/******/ if(installedModules[moduleId])
+/******/ return installedModules[moduleId].exports;
+/******/
+/******/ // Create a new module (and put it into the cache)
+/******/ var module = installedModules[moduleId] = {
+/******/ exports: {},
+/******/ id: moduleId,
+/******/ loaded: false
+/******/ };
+/******/
+/******/ // Execute the module function
+/******/ modules[moduleId].call(module.exports, module, module.exports, __webpack_require__);
+/******/
+/******/ // Flag the module as loaded
+/******/ module.loaded = true;
+/******/
+/******/ // Return the exports of the module
+/******/ return module.exports;
+/******/ }
+/******/
+/******/
+/******/ // expose the modules object (__webpack_modules__)
+/******/ __webpack_require__.m = modules;
+/******/
+/******/ // expose the module cache
+/******/ __webpack_require__.c = installedModules;
+/******/
+/******/ // __webpack_public_path__
+/******/ __webpack_require__.p = "";
+/******/
+/******/ // Load entry module and return exports
+/******/ return __webpack_require__(0);
+/******/ })
+/************************************************************************/
+/******/ ([
+/* 0 */
+/***/ function(module, exports, __webpack_require__) {
+
+ module.exports = __webpack_require__(1);
+
+
+/***/ },
+/* 1 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var object = __webpack_require__(2);
+ var digits = __webpack_require__(3).digits;
+
+ /**
+ * math.js factory function.
+ *
+ * @param {Object} [config] Available configuration options:
+ * {String} matrix
+ * A string 'matrix' (default) or 'array'.
+ * {String} number
+ * A string 'number' (default) or 'bignumber'
+ * {Number} precision
+ * The number of significant digits for BigNumbers.
+ * Not applicable for Numbers.
+ */
+ function create (config) {
+ // simple test for ES5 support
+ if (typeof Object.create !== 'function') {
+ throw new Error('ES5 not supported by this JavaScript engine. ' +
+ 'Please load the es5-shim and es5-sham library for compatibility.');
+ }
+
+ // create namespace
+ var math = {};
+
+ // create configuration options. These are private
+ var _config = {
+ // type of default matrix output. Choose 'matrix' (default) or 'array'
+ matrix: 'matrix',
+
+ // type of default number output. Choose 'number' (default) or 'bignumber'
+ number: 'number',
+
+ // number of significant digits in BigNumbers
+ precision: 64,
+
+ // minimum relative difference between two compared values,
+ // used by all comparison functions
+ epsilon: 1e-14
+ };
+
+ /**
+ * Set configuration options for math.js, and get current options
+ * @param {Object} [options] Available options:
+ * {String} matrix
+ * A string 'matrix' (default) or 'array'.
+ * {String} number
+ * A string 'number' (default) or 'bignumber'
+ * {Number} precision
+ * The number of significant digits for BigNumbers.
+ * Not applicable for Numbers.
+ * @return {Object} Returns the current configuration
+ */
+ math.config = function(options) {
+ if (options) {
+ // merge options
+ object.deepExtend(_config, options);
+
+ if (options.precision) {
+ math.type.BigNumber.config({
+ precision: options.precision
+ });
+ }
+
+ // reload the constants (they depend on option number and precision)
+ // this must be done after math.type.BigNumber.config is applied
+ __webpack_require__(4)(math, _config);
+
+ // TODO: remove deprecated setting some day (deprecated since version 0.17.0)
+ if (options.number && options.number.defaultType) {
+ throw new Error('setting `number.defaultType` is deprecated. Use `number` instead.')
+ }
+
+ // TODO: remove deprecated setting some day (deprecated since version 0.17.0)
+ if (options.number && options.number.precision) {
+ throw new Error('setting `number.precision` is deprecated. Use `precision` instead.')
+ }
+
+ // TODO: remove deprecated setting some day (deprecated since version 0.17.0)
+ if (options.matrix && options.matrix.defaultType) {
+ throw new Error('setting `matrix.defaultType` is deprecated. Use `matrix` instead.')
+ }
+
+ // TODO: remove deprecated setting some day (deprecated since version 0.15.0)
+ if (options.matrix && options.matrix['default']) {
+ throw new Error('setting `matrix.default` is deprecated. Use `matrix` instead.')
+ }
+
+ // TODO: remove deprecated setting some day (deprecated since version 0.20.0)
+ if (options.decimals) {
+ throw new Error('setting `decimals` is deprecated. Use `precision` instead.')
+ }
+ }
+
+ // return a clone of the settings
+ return object.clone(_config);
+ };
+
+ /**
+ * math.js factory function. Creates a new instance of math.js
+ *
+ * @param {Object} [config] Available configuration options:
+ * {String} matrix
+ * A string 'matrix' (default) or 'array'.
+ * {String} number
+ * A string 'number' (default) or 'bignumber'
+ * {Number} precision
+ * The number of significant digits for BigNumbers.
+ * Not applicable for Numbers.
+ */
+ math.create = create;
+
+ // create a new BigNumber factory for this instance of math.js
+ var BigNumber = __webpack_require__(5).constructor();
+
+ // extend BigNumber with a function clone
+ if (typeof BigNumber.prototype.clone !== 'function') {
+ /**
+ * Clone a bignumber
+ * @return {BigNumber} clone
+ */
+ BigNumber.prototype.clone = function() {
+ return this; // just return itself (a BigNumber is immutable)
+ };
+ }
+
+ // extend BigNumber with a function convert
+ if (typeof BigNumber.convert !== 'function') {
+ /**
+ * Try to convert a Number in to a BigNumber.
+ * If the number has 15 or mor significant digits, the Number cannot be
+ * converted to BigNumber and will return the original number.
+ * @param {Number} number
+ * @return {BigNumber | Number} bignumber
+ */
+ BigNumber.convert = function(number) {
+ if (digits(number) > 15) {
+ return number;
+ }
+ else {
+ return new BigNumber(number);
+ }
+ };
+ }
+ else {
+ throw new Error('Cannot add function convert to BigNumber: function already exists');
+ }
+
+ // errors
+ math.error = __webpack_require__(6);
+
+ // types (Matrix, Complex, Unit, ...)
+ math.type = {};
+ math.type.Complex = __webpack_require__(7);
+ math.type.Range = __webpack_require__(8);
+ math.type.Index = __webpack_require__(9);
+ math.type.Matrix = __webpack_require__(10);
+ math.type.Unit = __webpack_require__(11);
+ math.type.Help = __webpack_require__(12);
+ math.type.ResultSet = __webpack_require__(13);
+ math.type.BigNumber = BigNumber;
+
+ math.collection = __webpack_require__(14);
+
+ // expression (parse, Parser, nodes, docs)
+ math.expression = {};
+ math.expression.node = __webpack_require__(15);
+ math.expression.parse = __webpack_require__(16);
+ math.expression.Parser = __webpack_require__(17);
+ math.expression.docs = __webpack_require__(18);
+
+ // serialization utilities
+ math.json = {
+ reviver: __webpack_require__(19)
+ };
+
+ // expression parser
+ __webpack_require__(31)(math, _config);
+ __webpack_require__(32)(math, _config);
+ __webpack_require__(33)(math, _config);
+ __webpack_require__(34)(math, _config);
+
+ // functions - arithmetic
+ __webpack_require__(35)(math, _config);
+ __webpack_require__(36)(math, _config);
+ __webpack_require__(37)(math, _config);
+ __webpack_require__(38)(math, _config);
+ __webpack_require__(39)(math, _config);
+ __webpack_require__(40)(math, _config);
+ __webpack_require__(41)(math, _config);
+ __webpack_require__(42)(math, _config);
+ __webpack_require__(43)(math, _config);
+ __webpack_require__(44)(math, _config);
+ __webpack_require__(45)(math, _config);
+ __webpack_require__(46)(math, _config);
+ __webpack_require__(47)(math, _config);
+ __webpack_require__(48)(math, _config);
+ __webpack_require__(49)(math, _config);
+ __webpack_require__(50)(math, _config);
+ __webpack_require__(51)(math, _config);
+ __webpack_require__(52)(math, _config);
+ __webpack_require__(53)(math, _config);
+ __webpack_require__(54)(math, _config);
+ __webpack_require__(55)(math, _config);
+ __webpack_require__(56)(math, _config);
+ __webpack_require__(57)(math, _config);
+ __webpack_require__(58)(math, _config);
+ __webpack_require__(59)(math, _config);
+ __webpack_require__(60)(math, _config);
+ __webpack_require__(61)(math, _config);
+ __webpack_require__(62)(math, _config);
+ __webpack_require__(63)(math, _config);
+
+ // functions - bitwise
+ __webpack_require__(64)(math, _config);
+ __webpack_require__(65)(math, _config);
+ __webpack_require__(66)(math, _config);
+ __webpack_require__(67)(math, _config);
+ __webpack_require__(68)(math, _config);
+ __webpack_require__(69)(math, _config);
+ __webpack_require__(70)(math, _config);
+
+ // functions - complex
+ __webpack_require__(71)(math, _config);
+ __webpack_require__(72)(math, _config);
+ __webpack_require__(73)(math, _config);
+ __webpack_require__(74)(math, _config);
+
+ // functions - construction
+ __webpack_require__(75)(math, _config);
+ __webpack_require__(76)(math, _config);
+ __webpack_require__(77)(math, _config);
+ __webpack_require__(78)(math, _config);
+ __webpack_require__(79)(math, _config);
+ __webpack_require__(80)(math, _config);
+ __webpack_require__(81)(math, _config);
+ __webpack_require__(82)(math, _config);
+ __webpack_require__(83)(math, _config);
+ __webpack_require__(84)(math, _config);
+
+ // functions - logical
+ __webpack_require__(85)(math, _config);
+ __webpack_require__(86)(math, _config);
+ __webpack_require__(87)(math, _config);
+ __webpack_require__(88)(math, _config);
+
+ // functions - matrix
+ __webpack_require__(89)(math, _config);
+ __webpack_require__(90)(math, _config);
+ __webpack_require__(91)(math, _config);
+ __webpack_require__(92)(math, _config);
+ __webpack_require__(93)(math, _config);
+ __webpack_require__(94)(math, _config);
+ __webpack_require__(95)(math, _config);
+ __webpack_require__(96)(math, _config);
+ __webpack_require__(97)(math, _config);
+ __webpack_require__(98)(math, _config);
+ __webpack_require__(99)(math, _config);
+ __webpack_require__(100)(math, _config);
+ __webpack_require__(101)(math, _config);
+ __webpack_require__(102)(math, _config);
+ __webpack_require__(103)(math, _config);
+ __webpack_require__(104)(math, _config);
+ __webpack_require__(105)(math, _config);
+
+ // functions - probability
+ //require('./function/probability/distribution')(math, _config); // TODO: rethink math.distribution
+ __webpack_require__(106)(math, _config);
+ __webpack_require__(107)(math, _config);
+ __webpack_require__(108)(math, _config);
+ __webpack_require__(109)(math, _config);
+ __webpack_require__(110)(math, _config);
+ __webpack_require__(111)(math, _config);
+ __webpack_require__(112)(math, _config);
+
+ // functions - relational
+ __webpack_require__(113)(math, _config);
+ __webpack_require__(114)(math, _config);
+ __webpack_require__(115)(math, _config);
+ __webpack_require__(116)(math, _config);
+ __webpack_require__(117)(math, _config);
+ __webpack_require__(118)(math, _config);
+ __webpack_require__(119)(math, _config);
+ __webpack_require__(120)(math, _config);
+
+ // functions - statistics
+ __webpack_require__(121)(math, _config);
+ __webpack_require__(122)(math, _config);
+ __webpack_require__(123)(math, _config);
+ __webpack_require__(124)(math, _config);
+ __webpack_require__(125)(math, _config);
+ __webpack_require__(126)(math, _config);
+ __webpack_require__(127)(math, _config);
+ __webpack_require__(128)(math, _config);
+
+ // functions - trigonometry
+ __webpack_require__(129)(math, _config);
+ __webpack_require__(130)(math, _config);
+ __webpack_require__(131)(math, _config);
+ __webpack_require__(132)(math, _config);
+ __webpack_require__(133)(math, _config);
+ __webpack_require__(134)(math, _config);
+ __webpack_require__(135)(math, _config);
+ __webpack_require__(136)(math, _config);
+ __webpack_require__(137)(math, _config);
+ __webpack_require__(138)(math, _config);
+ __webpack_require__(139)(math, _config);
+ __webpack_require__(140)(math, _config);
+ __webpack_require__(141)(math, _config);
+ __webpack_require__(142)(math, _config);
+ __webpack_require__(143)(math, _config);
+ __webpack_require__(144)(math, _config);
+ __webpack_require__(145)(math, _config);
+ __webpack_require__(146)(math, _config);
+ __webpack_require__(147)(math, _config);
+ __webpack_require__(148)(math, _config);
+ __webpack_require__(149)(math, _config);
+ __webpack_require__(150)(math, _config);
+ __webpack_require__(151)(math, _config);
+ __webpack_require__(152)(math, _config);
+ __webpack_require__(153)(math, _config);
+
+ // functions - units
+ __webpack_require__(154)(math, _config);
+
+ // functions - utils
+ __webpack_require__(155)(math, _config);
+ __webpack_require__(156)(math, _config);
+ __webpack_require__(157)(math, _config);
+ __webpack_require__(158)(math, _config);
+ __webpack_require__(159)(math, _config);
+ __webpack_require__(160)(math, _config);
+ __webpack_require__(161)(math, _config);
+ __webpack_require__(162)(math, _config);
+ __webpack_require__(163)(math, _config);
+
+ // TODO: deprecated since version 0.25.0, remove some day.
+ math.ifElse = function () {
+ throw new Error('Function ifElse is deprecated. Use the conditional operator instead.');
+ };
+
+ // constants
+ __webpack_require__(4)(math, _config);
+
+ // attach transform functions (for converting one-based indices to zero-based)
+ math.expression.transform = {
+ concat: __webpack_require__(20)(math, _config),
+ filter: __webpack_require__(21)(math, _config),
+ forEach:__webpack_require__(22)(math, _config),
+ index: __webpack_require__(23)(math, _config),
+ map: __webpack_require__(24)(math, _config),
+ max: __webpack_require__(25)(math, _config),
+ mean: __webpack_require__(26)(math, _config),
+ min: __webpack_require__(27)(math, _config),
+ range: __webpack_require__(28)(math, _config),
+ subset: __webpack_require__(29)(math, _config)
+ };
+
+ // selector (we initialize after all functions are loaded)
+ math.chaining = {};
+ math.chaining.Chain = __webpack_require__(30)(math, _config);
+ math.chaining.Selector = math.chaining.Chain; // TODO: deprecate in v2.0
+
+ // apply provided configuration options
+ math.config(_config); // apply the default options
+ math.config(config); // apply custom options
+
+ // return the new instance
+ return math;
+ }
+
+ // create a default instance of math.js
+ var math = create();
+
+ if (typeof window !== 'undefined') {
+ window.mathjs = math; // TODO: deprecate the mathjs namespace some day (replaced with 'math' since version 0.25.0)
+ }
+
+ // export the default instance
+ module.exports = math;
+
+
+
+/***/ },
+/* 2 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ /**
+ * Clone an object
+ *
+ * clone(x)
+ *
+ * Can clone any primitive type, array, and object.
+ * If x has a function clone, this function will be invoked to clone the object.
+ *
+ * @param {*} x
+ * @return {*} clone
+ */
+ exports.clone = function clone(x) {
+ var type = typeof x;
+
+ // immutable primitive types
+ if (type === 'number' || type === 'string' || type === 'boolean' ||
+ x === null || x === undefined) {
+ return x;
+ }
+
+ // use clone function of the object when available
+ if (typeof x.clone === 'function') {
+ return x.clone();
+ }
+
+ // array
+ if (Array.isArray(x)) {
+ return x.map(function (value) {
+ return clone(value);
+ });
+ }
+
+ if (x instanceof Number) return new Number(x.valueOf());
+ if (x instanceof String) return new String(x.valueOf());
+ if (x instanceof Boolean) return new Boolean(x.valueOf());
+ if (x instanceof Date) return new Date(x.valueOf());
+ if (x instanceof RegExp) throw new TypeError('Cannot clone ' + x); // TODO: clone a RegExp
+
+ // object
+ var m = {};
+ for (var key in x) {
+ if (x.hasOwnProperty(key)) {
+ m[key] = clone(x[key]);
+ }
+ }
+ return m;
+ };
+
+ /**
+ * Extend object a with the properties of object b
+ * @param {Object} a
+ * @param {Object} b
+ * @return {Object} a
+ */
+ exports.extend = function(a, b) {
+ for (var prop in b) {
+ if (b.hasOwnProperty(prop)) {
+ a[prop] = b[prop];
+ }
+ }
+ return a;
+ };
+
+ /**
+ * Deep extend an object a with the properties of object b
+ * @param {Object} a
+ * @param {Object} b
+ * @returns {Object}
+ */
+ exports.deepExtend = function deepExtend (a, b) {
+ // TODO: add support for Arrays to deepExtend
+ if (Array.isArray(b)) {
+ throw new TypeError('Arrays are not supported by deepExtend');
+ }
+
+ for (var prop in b) {
+ if (b.hasOwnProperty(prop)) {
+ if (b[prop] && b[prop].constructor === Object) {
+ if (a[prop] === undefined) {
+ a[prop] = {};
+ }
+ if (a[prop].constructor === Object) {
+ deepExtend(a[prop], b[prop]);
+ }
+ else {
+ a[prop] = b[prop];
+ }
+ } else if (Array.isArray(b[prop])) {
+ throw new TypeError('Arrays are not supported by deepExtend');
+ } else {
+ a[prop] = b[prop];
+ }
+ }
+ }
+ return a;
+ };
+
+ /**
+ * Deep test equality of all fields in two pairs of arrays or objects.
+ * @param {Array | Object} a
+ * @param {Array | Object} b
+ * @returns {boolean}
+ */
+ exports.deepEqual = function deepEqual (a, b) {
+ var prop, i, len;
+ if (Array.isArray(a)) {
+ if (!Array.isArray(b)) {
+ return false;
+ }
+
+ if (a.length != b.length) {
+ return false;
+ }
+
+ for (i = 0, len = a.length; i < len; i++) {
+ if (!exports.deepEqual(a[i], b[i])) {
+ return false;
+ }
+ }
+ return true;
+ }
+ else if (a instanceof Object) {
+ if (Array.isArray(b) || !(b instanceof Object)) {
+ return false;
+ }
+
+ for (prop in a) {
+ //noinspection JSUnfilteredForInLoop
+ if (!exports.deepEqual(a[prop], b[prop])) {
+ return false;
+ }
+ }
+ for (prop in b) {
+ //noinspection JSUnfilteredForInLoop
+ if (!exports.deepEqual(a[prop], b[prop])) {
+ return false;
+ }
+ }
+ return true;
+ }
+ else {
+ return (typeof a === typeof b) && (a == b);
+ }
+ };
+
+ /**
+ * Test whether the current JavaScript engine supports Object.defineProperty
+ * @returns {boolean} returns true if supported
+ */
+ exports.canDefineProperty = function () {
+ // test needed for broken IE8 implementation
+ try {
+ if (Object.defineProperty) {
+ Object.defineProperty({}, 'x', {});
+ return true;
+ }
+ } catch (e) {}
+
+ return false;
+ };
+
+ /**
+ * Attach a lazy loading property to a constant.
+ * The given function `fn` is called once when the property is first requested.
+ * On older browsers (<IE8), the function will fall back to direct evaluation
+ * of the properties value.
+ * @param {Object} object Object where to add the property
+ * @param {string} prop Property name
+ * @param {function} fn Function returning the property value. Called
+ * without arguments.
+ */
+ exports.lazy = function (object, prop, fn) {
+ if (exports.canDefineProperty()) {
+ var _uninitialized = true;
+ var _value;
+ Object.defineProperty(object, prop, {
+ get: function () {
+ if (_uninitialized) {
+ _value = fn();
+ _uninitialized = false;
+ }
+ return _value;
+ },
+
+ set: function (value) {
+ _value = value;
+ _uninitialized = false;
+ }
+ });
+ }
+ else {
+ // fall back to immediate evaluation
+ object[prop] = fn();
+ }
+ };
+
+
+/***/ },
+/* 3 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ /**
+ * Test whether value is a Number
+ * @param {*} value
+ * @return {Boolean} isNumber
+ */
+ exports.isNumber = function(value) {
+ return (value instanceof Number) || (typeof value == 'number');
+ };
+
+ /**
+ * Check if a number is integer
+ * @param {Number | Boolean} value
+ * @return {Boolean} isInteger
+ */
+ exports.isInteger = function(value) {
+ return (value == Math.round(value));
+ // Note: we use ==, not ===, as we can have Booleans as well
+ };
+
+ /**
+ * Calculate the sign of a number
+ * @param {Number} x
+ * @returns {*}
+ */
+ exports.sign = function(x) {
+ if (x > 0) {
+ return 1;
+ }
+ else if (x < 0) {
+ return -1;
+ }
+ else {
+ return 0;
+ }
+ };
+
+ /**
+ * Convert a number to a formatted string representation.
+ *
+ * Syntax:
+ *
+ * format(value)
+ * format(value, options)
+ * format(value, precision)
+ * format(value, fn)
+ *
+ * Where:
+ *
+ * {Number} value The value to be formatted
+ * {Object} options An object with formatting options. Available options:
+ * {String} notation
+ * Number notation. Choose from:
+ * 'fixed' Always use regular number notation.
+ * For example '123.40' and '14000000'
+ * 'exponential' Always use exponential notation.
+ * For example '1.234e+2' and '1.4e+7'
+ * 'auto' (default) Regular number notation for numbers
+ * having an absolute value between
+ * `lower` and `upper` bounds, and uses
+ * exponential notation elsewhere.
+ * Lower bound is included, upper bound
+ * is excluded.
+ * For example '123.4' and '1.4e7'.
+ * {Number} precision A number between 0 and 16 to round
+ * the digits of the number.
+ * In case of notations 'exponential' and
+ * 'auto', `precision` defines the total
+ * number of significant digits returned
+ * and is undefined by default.
+ * In case of notation 'fixed',
+ * `precision` defines the number of
+ * significant digits after the decimal
+ * point, and is 0 by default.
+ * {Object} exponential An object containing two parameters,
+ * {Number} lower and {Number} upper,
+ * used by notation 'auto' to determine
+ * when to return exponential notation.
+ * Default values are `lower=1e-3` and
+ * `upper=1e5`.
+ * Only applicable for notation `auto`.
+ * {Function} fn A custom formatting function. Can be used to override the
+ * built-in notations. Function `fn` is called with `value` as
+ * parameter and must return a string. Is useful for example to
+ * format all values inside a matrix in a particular way.
+ *
+ * Examples:
+ *
+ * format(6.4); // '6.4'
+ * format(1240000); // '1.24e6'
+ * format(1/3); // '0.3333333333333333'
+ * format(1/3, 3); // '0.333'
+ * format(21385, 2); // '21000'
+ * format(12.071, {notation: 'fixed'}); // '12'
+ * format(2.3, {notation: 'fixed', precision: 2}); // '2.30'
+ * format(52.8, {notation: 'exponential'}); // '5.28e+1'
+ *
+ * @param {Number} value
+ * @param {Object | Function | Number} [options]
+ * @return {String} str The formatted value
+ */
+ exports.format = function(value, options) {
+ if (typeof options === 'function') {
+ // handle format(value, fn)
+ return options(value);
+ }
+
+ // handle special cases
+ if (value === Infinity) {
+ return 'Infinity';
+ }
+ else if (value === -Infinity) {
+ return '-Infinity';
+ }
+ else if (isNaN(value)) {
+ return 'NaN';
+ }
+
+ // default values for options
+ var notation = 'auto';
+ var precision = undefined;
+
+ if (options) {
+ // determine notation from options
+ if (options.notation) {
+ notation = options.notation;
+ }
+
+ // determine precision from options
+ if (exports.isNumber(options)) {
+ precision = options;
+ }
+ else if (options.precision) {
+ precision = options.precision;
+ }
+ }
+
+ // handle the various notations
+ switch (notation) {
+ case 'fixed':
+ return exports.toFixed(value, precision);
+
+ case 'exponential':
+ return exports.toExponential(value, precision);
+
+ case 'auto':
+ // determine lower and upper bound for exponential notation.
+ // TODO: implement support for upper and lower to be BigNumbers themselves
+ var lower = 1e-3;
+ var upper = 1e5;
+ if (options && options.exponential) {
+ if (options.exponential.lower !== undefined) {
+ lower = options.exponential.lower;
+ }
+ if (options.exponential.upper !== undefined) {
+ upper = options.exponential.upper;
+ }
+ }
+
+ // handle special case zero
+ if (value === 0) return '0';
+
+ // determine whether or not to output exponential notation
+ var str;
+ var abs = Math.abs(value);
+ if (abs >= lower && abs < upper) {
+ // normal number notation
+ // Note: IE7 does not allow value.toPrecision(undefined)
+ var valueStr = precision ?
+ value.toPrecision(Math.min(precision, 21)) :
+ value.toPrecision();
+ str = parseFloat(valueStr) + '';
+ }
+ else {
+ // exponential notation
+ str = exports.toExponential(value, precision);
+ }
+
+ // remove trailing zeros after the decimal point
+ return str.replace(/((\.\d*?)(0+))($|e)/, function () {
+ var digits = arguments[2];
+ var e = arguments[4];
+ return (digits !== '.') ? digits + e : e;
+ });
+
+ default:
+ throw new Error('Unknown notation "' + notation + '". ' +
+ 'Choose "auto", "exponential", or "fixed".');
+ }
+ };
+
+ /**
+ * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'
+ * @param {Number} value
+ * @param {Number} [precision] Number of digits in formatted output.
+ * If not provided, the maximum available digits
+ * is used.
+ * @returns {string} str
+ */
+ exports.toExponential = function(value, precision) {
+ if (precision !== undefined) {
+ return value.toExponential(Math.min(precision - 1, 20));
+ }
+ else {
+ return value.toExponential();
+ }
+ };
+
+ /**
+ * Format a number with fixed notation.
+ * @param {Number} value
+ * @param {Number} [precision=0] Optional number of decimals after the
+ * decimal point. Zero by default.
+ */
+ exports.toFixed = function(value, precision) {
+ return value.toFixed(Math.min(precision, 20));
+ };
+
+ /**
+ * Count the number of significant digits of a number.
+ *
+ * For example:
+ * 2.34 returns 3
+ * 0.0034 returns 2
+ * 120.5e+30 returns 4
+ *
+ * @param {Number} value
+ * @return {Number} digits Number of significant digits
+ */
+ exports.digits = function(value) {
+ return value
+ .toExponential()
+ .replace(/e.*$/, '') // remove exponential notation
+ .replace( /^0\.?0*|\./, '') // remove decimal point and leading zeros
+ .length
+ };
+
+ /**
+ * Minimum number added to one that makes the result different than one
+ */
+ exports.DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16;
+
+ /**
+ * Compares two floating point numbers.
+ * @param {Number} x First value to compare
+ * @param {Number} y Second value to compare
+ * @param {Number} [epsilon] The maximum relative difference between x and y
+ * If epsilon is undefined or null, the function will
+ * test whether x and y are exactly equal.
+ * @return {boolean} whether the two numbers are equal
+ */
+ exports.nearlyEqual = function(x, y, epsilon) {
+ // if epsilon is null or undefined, test whether x and y are exactly equal
+ if (epsilon == null) return x == y;
+
+ // use "==" operator, handles infinities
+ if (x == y) return true;
+
+ // NaN
+ if (isNaN(x) || isNaN(y)) return false;
+
+ // at this point x and y should be finite
+ if(isFinite(x) && isFinite(y)) {
+ // check numbers are very close, needed when comparing numbers near zero
+ var diff = Math.abs(x - y);
+ if (diff < exports.DBL_EPSILON) {
+ return true;
+ }
+ else {
+ // use relative error
+ return diff <= Math.max(Math.abs(x), Math.abs(y)) * epsilon;
+ }
+ }
+
+ // Infinite and Number or negative Infinite and positive Infinite cases
+ return false;
+ };
+
+
+/***/ },
+/* 4 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var object = __webpack_require__(2);
+ var bignumber = __webpack_require__(164);
+ var Complex = __webpack_require__(7);
+ var BigNumber = math.type.BigNumber;
+
+ math['true'] = true;
+ math['false'] = false;
+ math['null'] = null;
+ math['uninitialized'] = __webpack_require__(165).UNINITIALIZED;
+
+ if (config.number === 'bignumber') {
+ math['Infinity'] = new BigNumber(Infinity);
+ math['NaN'] = new BigNumber(NaN);
+
+ object.lazy(math, 'pi', function () {return bignumber.pi(config.precision)});
+ object.lazy(math, 'tau', function () {return bignumber.tau(config.precision)});
+ object.lazy(math, 'e', function () {return bignumber.e(config.precision)});
+ object.lazy(math, 'phi', function () {return bignumber.phi(config.precision)}); // golden ratio, (1+sqrt(5))/2
+
+ // uppercase constants (for compatibility with built-in Math)
+ object.lazy(math, 'E', function () {return math.e;});
+ object.lazy(math, 'LN2', function () {return new BigNumber(2).ln();});
+ object.lazy(math, 'LN10', function () {return new BigNumber(10).ln()});
+ object.lazy(math, 'LOG2E', function () {return new BigNumber(1).div(new BigNumber(2).ln());});
+ object.lazy(math, 'LOG10E', function () {return new BigNumber(1).div(new BigNumber(10).ln())});
+ object.lazy(math, 'PI', function () {return math.pi});
+ object.lazy(math, 'SQRT1_2', function () {return new BigNumber('0.5').sqrt()});
+ object.lazy(math, 'SQRT2', function () {return new BigNumber(2).sqrt()});
+ }
+ else {
+ math['Infinity'] = Infinity;
+ math['NaN'] = NaN;
+
+ math.pi = Math.PI;
+ math.tau = Math.PI * 2;
+ math.e = Math.E;
+ math.phi = 1.61803398874989484820458683436563811772030917980576286213545; // golden ratio, (1+sqrt(5))/2
+
+ // uppercase constants (for compatibility with built-in Math)
+ math.E = math.e;
+ math.LN2 = Math.LN2;
+ math.LN10 = Math.LN10;
+ math.LOG2E = Math.LOG2E;
+ math.LOG10E = Math.LOG10E;
+ math.PI = math.pi;
+ math.SQRT1_2 = Math.SQRT1_2;
+ math.SQRT2 = Math.SQRT2;
+ }
+
+ // complex i
+ math.i = new Complex(0, 1);
+
+ // meta information
+ math.version = __webpack_require__(166);
+ };
+
+
+/***/ },
+/* 5 */
+/***/ function(module, exports, __webpack_require__) {
+
+ var BigNumber = __webpack_require__(336);
+
+ // FIXME: replace all require('decimal.js') with require('./BigNumber').
+
+ /**
+ * Get a JSON representation of a BigNumber containing
+ * type information
+ * @returns {Object} Returns a JSON object structured as:
+ * `{"mathjs": "BigNumber", "value": "0.2"}`
+ */
+ BigNumber.prototype.toJSON = function () {
+ return {
+ mathjs: 'BigNumber',
+ value: this.toString()
+ };
+ };
+
+ /**
+ * Instantiate a BigNumber from a JSON object
+ * @param {Object} json a JSON object structured as:
+ * `{"mathjs": "BigNumber", "value": "0.2"}`
+ * @return {BigNumber}
+ */
+ BigNumber.fromJSON = function (json) {
+ return new BigNumber(json.value);
+ };
+
+ module.exports = BigNumber;
+
+
+/***/ },
+/* 6 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ exports.ArgumentsError = __webpack_require__(167);
+ exports.DimensionError = __webpack_require__(168);
+ exports.IndexError = __webpack_require__(169);
+ exports.UnsupportedTypeError = __webpack_require__(170);
+
+ // TODO: implement an InvalidValueError?
+
+
+/***/ },
+/* 7 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171),
+ Unit = __webpack_require__(11),
+ number = util.number,
+
+ isNumber = util.number.isNumber,
+ isUnit = Unit.isUnit,
+ isString = util.string.isString;
+
+ /**
+ * @constructor Complex
+ *
+ * A complex value can be constructed in the following ways:
+ * var a = new Complex();
+ * var b = new Complex(re, im);
+ * var c = Complex.parse(str);
+ *
+ * Example usage:
+ * var a = new Complex(3, -4); // 3 - 4i
+ * a.re = 5; // a = 5 - 4i
+ * var i = a.im; // -4;
+ * var b = Complex.parse('2 + 6i'); // 2 + 6i
+ * var c = new Complex(); // 0 + 0i
+ * var d = math.add(a, b); // 5 + 2i
+ *
+ * @param {Number} re The real part of the complex value
+ * @param {Number} [im] The imaginary part of the complex value
+ */
+ function Complex(re, im) {
+ if (!(this instanceof Complex)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ switch (arguments.length) {
+ case 0:
+ this.re = 0;
+ this.im = 0;
+ break;
+
+ case 1:
+ var arg = arguments[0];
+ if (typeof arg === 'object') {
+ if('re' in arg && 'im' in arg) {
+ var construct = new Complex(arg.re, arg.im); // pass on input validation
+ this.re = construct.re;
+ this.im = construct.im;
+ break;
+ } else if ('r' in arg && 'phi' in arg) {
+ var construct = Complex.fromPolar(arg.r, arg.phi);
+ this.re = construct.re;
+ this.im = construct.im;
+ break;
+ }
+ }
+ throw new SyntaxError('Object with the re and im or r and phi properties expected.');
+
+ case 2:
+ if (!isNumber(re) || !isNumber(im)) {
+ throw new TypeError('Two numbers expected in Complex constructor');
+ }
+ this.re = re;
+ this.im = im;
+ break;
+
+ default:
+ throw new SyntaxError('One, two or three arguments expected in Complex constructor');
+ }
+ }
+
+ /**
+ * Test whether value is a Complex value
+ * @param {*} value
+ * @return {Boolean} isComplex
+ */
+ Complex.isComplex = function (value) {
+ return (value instanceof Complex);
+ };
+
+ // private variables and functions for the parser
+ var text, index, c;
+
+ function skipWhitespace() {
+ while (c == ' ' || c == '\t') {
+ next();
+ }
+ }
+
+ function isDigitDot (c) {
+ return ((c >= '0' && c <= '9') || c == '.');
+ }
+
+ function isDigit (c) {
+ return ((c >= '0' && c <= '9'));
+ }
+
+ function next() {
+ index++;
+ c = text.charAt(index);
+ }
+
+ function revert(oldIndex) {
+ index = oldIndex;
+ c = text.charAt(index);
+ }
+
+ function parseNumber () {
+ var number = '';
+ var oldIndex;
+ oldIndex = index;
+
+ if (c == '+') {
+ next();
+ }
+ else if (c == '-') {
+ number += c;
+ next();
+ }
+
+ if (!isDigitDot(c)) {
+ // a + or - must be followed by a digit
+ revert(oldIndex);
+ return null;
+ }
+
+ // get number, can have a single dot
+ if (c == '.') {
+ number += c;
+ next();
+ if (!isDigit(c)) {
+ // this is no legal number, it is just a dot
+ revert(oldIndex);
+ return null;
+ }
+ }
+ else {
+ while (isDigit(c)) {
+ number += c;
+ next();
+ }
+ if (c == '.') {
+ number += c;
+ next();
+ }
+ }
+ while (isDigit(c)) {
+ number += c;
+ next();
+ }
+
+ // check for exponential notation like "2.3e-4" or "1.23e50"
+ if (c == 'E' || c == 'e') {
+ number += c;
+ next();
+
+ if (c == '+' || c == '-') {
+ number += c;
+ next();
+ }
+
+ // Scientific notation MUST be followed by an exponent
+ if (!isDigit(c)) {
+ // this is no legal number, exponent is missing.
+ revert(oldIndex);
+ return null;
+ }
+
+ while (isDigit(c)) {
+ number += c;
+ next();
+ }
+ }
+
+ return number;
+ }
+
+ function parseComplex () {
+ // check for 'i', '-i', '+i'
+ var cnext = text.charAt(index + 1);
+ if (c == 'I' || c == 'i') {
+ next();
+ return '1';
+ }
+ else if ((c == '+' || c == '-') && (cnext == 'I' || cnext == 'i')) {
+ var number = (c == '+') ? '1' : '-1';
+ next();
+ next();
+ return number;
+ }
+
+ return null;
+ }
+
+ /**
+ * Parse a complex number from a string. For example Complex.parse("2 + 3i")
+ * will return a Complex value where re = 2, im = 3.
+ * Returns null if provided string does not contain a valid complex number.
+ * @param {String} str
+ * @returns {Complex | null} complex
+ */
+ Complex.parse = function (str) {
+ text = str;
+ index = -1;
+ c = '';
+
+ if (!isString(text)) {
+ return null;
+ }
+
+ next();
+ skipWhitespace();
+ var first = parseNumber();
+ if (first) {
+ if (c == 'I' || c == 'i') {
+ // pure imaginary number
+ next();
+ skipWhitespace();
+ if (c) {
+ // garbage at the end. not good.
+ return null;
+ }
+
+ return new Complex(0, Number(first));
+ }
+ else {
+ // complex and real part
+ skipWhitespace();
+ var separator = c;
+ if (separator != '+' && separator != '-') {
+ // pure real number
+ skipWhitespace();
+ if (c) {
+ // garbage at the end. not good.
+ return null;
+ }
+
+ return new Complex(Number(first), 0);
+ }
+ else {
+ // complex and real part
+ next();
+ skipWhitespace();
+ var second = parseNumber();
+ if (second) {
+ if (c != 'I' && c != 'i') {
+ // 'i' missing at the end of the complex number
+ return null;
+ }
+ next();
+ }
+ else {
+ second = parseComplex();
+ if (!second) {
+ // imaginary number missing after separator
+ return null;
+ }
+ }
+
+ if (separator == '-') {
+ if (second[0] == '-') {
+ second = '+' + second.substring(1);
+ }
+ else {
+ second = '-' + second;
+ }
+ }
+
+ next();
+ skipWhitespace();
+ if (c) {
+ // garbage at the end. not good.
+ return null;
+ }
+
+ return new Complex(Number(first), Number(second));
+ }
+ }
+ }
+ else {
+ // check for 'i', '-i', '+i'
+ first = parseComplex();
+ if (first) {
+ skipWhitespace();
+ if (c) {
+ // garbage at the end. not good.
+ return null;
+ }
+
+ return new Complex(0, Number(first));
+ }
+ }
+
+ return null;
+ };
+
+ /**
+ * Create a complex number from polar coordinates
+ *
+ * Usage:
+ *
+ * Complex.fromPolar(r: Number, phi: Number) : Complex
+ * Complex.fromPolar({r: Number, phi: Number}) : Complex
+ *
+ * @param {*} args...
+ * @return {Complex}
+ */
+ Complex.fromPolar = function (args) {
+ switch (arguments.length) {
+ case 1:
+ var arg = arguments[0];
+ if(typeof arg === 'object') {
+ return Complex.fromPolar(arg.r, arg.phi);
+ }
+ throw new TypeError('Input has to be an object with r and phi keys.');
+
+ case 2:
+ var r = arguments[0],
+ phi = arguments[1];
+ if(isNumber(r)) {
+ if (isUnit(phi) && phi.hasBase(Unit.BASE_UNITS.ANGLE)) {
+ // convert unit to a number in radians
+ phi = phi.toNumber('rad');
+ }
+
+ if(isNumber(phi)) {
+ return new Complex(r * Math.cos(phi), r * Math.sin(phi));
+ }
+
+ throw new TypeError('Phi is not a number nor an angle unit.');
+ } else {
+ throw new TypeError('Radius r is not a number.');
+ }
+
+ default:
+ throw new SyntaxError('Wrong number of arguments in function fromPolar');
+ }
+ };
+
+ /*
+ * Return the value of the complex number in polar notation
+ * The angle phi will be set in the interval of [-pi, pi].
+ * @return {{r: number, phi: number}} Returns and object with properties r and phi.
+ */
+ Complex.prototype.toPolar = function() {
+ return {
+ r: Math.sqrt(this.re * this.re + this.im * this.im),
+ phi: Math.atan2(this.im, this.re)
+ };
+ };
+
+ /**
+ * Create a copy of the complex value
+ * @return {Complex} clone
+ */
+ Complex.prototype.clone = function () {
+ return new Complex(this.re, this.im);
+ };
+
+ /**
+ * Test whether this complex number equals an other complex value.
+ * Two complex numbers are equal when both their real and imaginary parts
+ * are equal.
+ * @param {Complex} other
+ * @return {boolean} isEqual
+ */
+ Complex.prototype.equals = function (other) {
+ return (this.re === other.re) && (this.im === other.im);
+ };
+
+ /**
+ * Get a string representation of the complex number,
+ * with optional formatting options.
+ * @param {Object | Number | Function} [options] Formatting options. See
+ * lib/util/number:format for a
+ * description of the available
+ * options.
+ * @return {String} str
+ */
+ Complex.prototype.format = function (options) {
+ var str = '';
+ var im = this.im;
+ var re = this.re;
+ var strRe = number.format(this.re, options);
+ var strIm = number.format(this.im, options);
+
+ // round either re or im when smaller than the configured precision
+ var precision = isNumber(options) ? options : options ? options.precision : null;
+ if (precision !== null) {
+ var epsilon = Math.pow(10, -precision);
+ if (Math.abs(re / im) < epsilon) {re = 0;}
+ if (Math.abs(im / re) < epsilon) {im = 0;}
+ }
+
+ if (im == 0) {
+ // real value
+ str = strRe;
+ }
+ else if (re == 0) {
+ // purely complex value
+ if (im == 1) {
+ str = 'i';
+ }
+ else if (im == -1) {
+ str = '-i';
+ }
+ else {
+ str = strIm + 'i';
+ }
+ }
+ else {
+ // complex value
+ if (im > 0) {
+ if (im == 1) {
+ str = strRe + ' + i';
+ }
+ else {
+ str = strRe + ' + ' + strIm + 'i';
+ }
+ }
+ else {
+ if (im == -1) {
+ str = strRe + ' - i';
+ }
+ else {
+ str = strRe + ' - ' + strIm.substring(1) + 'i';
+ }
+ }
+ }
+
+ return str;
+ };
+
+ /**
+ * Get a string representation of the complex number.
+ * @return {String} str
+ */
+ Complex.prototype.toString = function () {
+ return this.format();
+ };
+
+ /**
+ * Get a JSON representation of the complex number
+ * @returns {Object} Returns a JSON object structured as:
+ * `{"mathjs": "Complex", "re": 2, "im": 3}`
+ */
+ Complex.prototype.toJSON = function () {
+ return {
+ mathjs: 'Complex',
+ re: this.re,
+ im: this.im
+ };
+ };
+
+ /**
+ * Create a Complex number from a JSON object
+ * @param {Object} json A JSON Object structured as
+ * {"mathjs": "Complex", "re": 2, "im": 3}
+ * All properties are optional, default values
+ * for `re` and `im` are 0.
+ * @return {Complex} Returns a new Complex number
+ */
+ Complex.fromJSON = function (json) {
+ return new Complex(json);
+ };
+
+ /**
+ * Returns a string representation of the complex number.
+ * @return {String} str
+ */
+ Complex.prototype.valueOf = Complex.prototype.toString;
+
+ // exports
+ module.exports = Complex;
+
+
+/***/ },
+/* 8 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171);
+
+ var number = util.number;
+ var string = util.string;
+ var array = util.array;
+
+ /**
+ * @constructor Range
+ * Create a range. A range has a start, step, and end, and contains functions
+ * to iterate over the range.
+ *
+ * A range can be constructed as:
+ * var range = new Range(start, end);
+ * var range = new Range(start, end, step);
+ *
+ * To get the result of the range:
+ * range.forEach(function (x) {
+ * console.log(x);
+ * });
+ * range.map(function (x) {
+ * return math.sin(x);
+ * });
+ * range.toArray();
+ *
+ * Example usage:
+ * var c = new Range(2, 6); // 2:1:5
+ * c.toArray(); // [2, 3, 4, 5]
+ * var d = new Range(2, -3, -1); // 2:-1:-2
+ * d.toArray(); // [2, 1, 0, -1, -2]
+ *
+ * @param {Number} start included lower bound
+ * @param {Number} end excluded upper bound
+ * @param {Number} [step] step size, default value is 1
+ */
+ function Range(start, end, step) {
+ if (!(this instanceof Range)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ if (start != null && !number.isNumber(start)) {
+ throw new TypeError('Parameter start must be a number');
+ }
+ if (end != null && !number.isNumber(end)) {
+ throw new TypeError('Parameter end must be a number');
+ }
+ if (step != null && !number.isNumber(step)) {
+ throw new TypeError('Parameter step must be a number');
+ }
+
+ this.start = (start != null) ? parseFloat(start) : 0;
+ this.end = (end != null) ? parseFloat(end) : 0;
+ this.step = (step != null) ? parseFloat(step) : 1;
+ }
+
+ /**
+ * Parse a string into a range,
+ * The string contains the start, optional step, and end, separated by a colon.
+ * If the string does not contain a valid range, null is returned.
+ * For example str='0:2:11'.
+ * @param {String} str
+ * @return {Range | null} range
+ */
+ Range.parse = function (str) {
+ if (!string.isString(str)) {
+ return null;
+ }
+
+ var args = str.split(':');
+ var nums = args.map(function (arg) {
+ return parseFloat(arg);
+ });
+
+ var invalid = nums.some(function (num) {
+ return isNaN(num);
+ });
+ if(invalid) {
+ return null;
+ }
+
+ switch (nums.length) {
+ case 2: return new Range(nums[0], nums[1]);
+ case 3: return new Range(nums[0], nums[2], nums[1]);
+ default: return null;
+ }
+ };
+
+ /**
+ * Create a clone of the range
+ * @return {Range} clone
+ */
+ Range.prototype.clone = function () {
+ return new Range(this.start, this.end, this.step);
+ };
+
+ /**
+ * Test whether an object is a Range
+ * @param {*} object
+ * @return {Boolean} isRange
+ */
+ Range.isRange = function (object) {
+ return (object instanceof Range);
+ };
+
+ /**
+ * Retrieve the size of the range.
+ * Returns an array containing one number, the number of elements in the range.
+ * @returns {Number[]} size
+ */
+ Range.prototype.size = function () {
+ var len = 0,
+ start = this.start,
+ step = this.step,
+ end = this.end,
+ diff = end - start;
+
+ if (number.sign(step) == number.sign(diff)) {
+ len = Math.ceil((diff) / step);
+ }
+ else if (diff == 0) {
+ len = 0;
+ }
+
+ if (isNaN(len)) {
+ len = 0;
+ }
+ return [len];
+ };
+
+ /**
+ * Calculate the minimum value in the range
+ * @return {Number | undefined} min
+ */
+ Range.prototype.min = function () {
+ var size = this.size()[0];
+
+ if (size > 0) {
+ if (this.step > 0) {
+ // positive step
+ return this.start;
+ }
+ else {
+ // negative step
+ return this.start + (size - 1) * this.step;
+ }
+ }
+ else {
+ return undefined;
+ }
+ };
+
+ /**
+ * Calculate the maximum value in the range
+ * @return {Number | undefined} max
+ */
+ Range.prototype.max = function () {
+ var size = this.size()[0];
+
+ if (size > 0) {
+ if (this.step > 0) {
+ // positive step
+ return this.start + (size - 1) * this.step;
+ }
+ else {
+ // negative step
+ return this.start;
+ }
+ }
+ else {
+ return undefined;
+ }
+ };
+
+
+ /**
+ * Execute a callback function for each value in the range.
+ * @param {function} callback The callback method is invoked with three
+ * parameters: the value of the element, the index
+ * of the element, and the Matrix being traversed.
+ */
+ Range.prototype.forEach = function (callback) {
+ var x = this.start;
+ var step = this.step;
+ var end = this.end;
+ var i = 0;
+
+ if (step > 0) {
+ while (x < end) {
+ callback(x, i, this);
+ x += step;
+ i++;
+ }
+ }
+ else if (step < 0) {
+ while (x > end) {
+ callback(x, i, this);
+ x += step;
+ i++;
+ }
+ }
+ };
+
+ /**
+ * Execute a callback function for each value in the Range, and return the
+ * results as an array
+ * @param {function} callback The callback method is invoked with three
+ * parameters: the value of the element, the index
+ * of the element, and the Matrix being traversed.
+ * @returns {Array} array
+ */
+ Range.prototype.map = function (callback) {
+ var array = [];
+ this.forEach(function (value, index, obj) {
+ array[index] = callback(value, index, obj);
+ });
+ return array;
+ };
+
+ /**
+ * Create an Array with a copy of the Ranges data
+ * @returns {Array} array
+ */
+ Range.prototype.toArray = function () {
+ var array = [];
+ this.forEach(function (value, index) {
+ array[index] = value;
+ });
+ return array;
+ };
+
+ /**
+ * Get the primitive value of the Range, a one dimensional array
+ * @returns {Array} array
+ */
+ Range.prototype.valueOf = function () {
+ // TODO: implement a caching mechanism for range.valueOf()
+ return this.toArray();
+ };
+
+ /**
+ * Get a string representation of the range, with optional formatting options.
+ * Output is formatted as 'start:step:end', for example '2:6' or '0:0.2:11'
+ * @param {Object | Number | Function} [options] Formatting options. See
+ * lib/util/number:format for a
+ * description of the available
+ * options.
+ * @returns {String} str
+ */
+ Range.prototype.format = function (options) {
+ var str = number.format(this.start, options);
+
+ if (this.step != 1) {
+ str += ':' + number.format(this.step, options);
+ }
+ str += ':' + number.format(this.end, options);
+ return str;
+ };
+
+ /**
+ * Get a string representation of the range.
+ * @returns {String}
+ */
+ Range.prototype.toString = function () {
+ return this.format();
+ };
+
+ /**
+ * Get a JSON representation of the range
+ * @returns {Object} Returns a JSON object structured as:
+ * `{"mathjs": "Range", "start": 2, "end": 4, "step": 1}`
+ */
+ Range.prototype.toJSON = function () {
+ return {
+ mathjs: 'Range',
+ start: this.start,
+ end: this.end,
+ step: this.step
+ };
+ };
+
+ /**
+ * Instantiate a Range from a JSON object
+ * @param {Object} json A JSON object structured as:
+ * `{"mathjs": "Range", "start": 2, "end": 4, "step": 1}`
+ * @return {Range}
+ */
+ Range.fromJSON = function (json) {
+ return new Range(json.start, json.end, json.step);
+ };
+
+ // exports
+ module.exports = Range;
+
+
+/***/ },
+/* 9 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171),
+
+ Range = __webpack_require__(8),
+
+ number = util.number,
+
+ isNumber = number.isNumber,
+ isInteger = number.isInteger,
+ isArray = Array.isArray;
+
+ /**
+ * @Constructor Index
+ * Create an index. An Index can store ranges having start, step, and end
+ * for multiple dimensions.
+ * Matrix.get, Matrix.set, and math.subset accept an Index as input.
+ *
+ * Usage:
+ * var index = new Index(range1, range2, ...);
+ *
+ * Where each range can be any of:
+ * An array [start, end]
+ * An array [start, end, step]
+ * A number
+ * An instance of Range
+ *
+ * The parameters start, end, and step must be integer numbers.
+ *
+ * @param {...*} ranges
+ */
+ function Index(ranges) {
+ if (!(this instanceof Index)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ this._ranges = [];
+ this._isScalar = true;
+
+ for (var i = 0, ii = arguments.length; i < ii; i++) {
+ var arg = arguments[i];
+
+ if (arg instanceof Range) {
+ this._ranges.push(arg);
+ this._isScalar = false;
+ }
+ else if (isArray(arg)) {
+ this._ranges.push(_createRange(arg));
+ this._isScalar = false;
+ }
+ else if (isNumber(arg)) {
+ this._ranges.push(_createRange([arg, arg + 1]));
+ }
+ // TODO: implement support for wildcard '*'
+ else {
+ var primitive = arg.valueOf(); // for example turn a Matrix into an Array
+ if (isArray(primitive)) {
+ this._ranges.push(_createRange(primitive));
+ this._isScalar = false;
+ }
+ else {
+ throw new TypeError('Ranges must be an Array, Number, or Range');
+ }
+ }
+ }
+ }
+
+ /**
+ * Parse an argument into a range and validate the range
+ * @param {Array} arg An array with [start: Number, end: Number] and
+ * optional a third element step:Number
+ * @return {Range} range
+ * @private
+ */
+ function _createRange(arg) {
+ // TODO: make function _createRange simpler/faster
+
+ // test whether all arguments are integers
+ var num = arg.length;
+ for (var i = 0; i < num; i++) {
+ if (!isNumber(arg[i]) || !isInteger(arg[i])) {
+ throw new TypeError('Index parameters must be integer numbers');
+ }
+ }
+
+ switch (arg.length) {
+ case 2:
+ return new Range(arg[0], arg[1]); // start, end
+ case 3:
+ return new Range(arg[0], arg[1], arg[2]); // start, end, step
+ default:
+ // TODO: improve error message
+ throw new SyntaxError('Wrong number of arguments in Index (2 or 3 expected)');
+ }
+ }
+
+ /**
+ * Create a clone of the index
+ * @return {Index} clone
+ */
+ Index.prototype.clone = function () {
+ var index = new Index();
+ index._ranges = util.object.clone(this._ranges);
+ index._isScalar = this._isScalar;
+ return index;
+ };
+
+ /**
+ * Test whether an object is an Index
+ * @param {*} object
+ * @return {Boolean} isIndex
+ */
+ Index.isIndex = function (object) {
+ return (object instanceof Index);
+ };
+
+ /**
+ * Create an index from an array with ranges/numbers
+ * @param {Array.<Array | Number>} ranges
+ * @return {Index} index
+ * @private
+ */
+ Index.create = function (ranges) {
+ var index = new Index();
+ Index.apply(index, ranges);
+ return index;
+ };
+
+ /**
+ * Retrieve the size of the index, the number of elements for each dimension.
+ * @returns {Number[]} size
+ */
+ Index.prototype.size = function () {
+ var size = [];
+
+ for (var i = 0, ii = this._ranges.length; i < ii; i++) {
+ var range = this._ranges[i];
+
+ size[i] = range.size()[0];
+ }
+
+ return size;
+ };
+
+ /**
+ * Get the maximum value for each of the indexes ranges.
+ * @returns {Number[]} max
+ */
+ Index.prototype.max = function () {
+ var values = [];
+
+ for (var i = 0, ii = this._ranges.length; i < ii; i++) {
+ var range = this._ranges[i];
+ values[i] = range.max();
+ }
+
+ return values;
+ };
+
+ /**
+ * Get the minimum value for each of the indexes ranges.
+ * @returns {Number[]} min
+ */
+ Index.prototype.min = function () {
+ var values = [];
+
+ for (var i = 0, ii = this._ranges.length; i < ii; i++) {
+ var range = this._ranges[i];
+
+ values[i] = range.min();
+ }
+
+ return values;
+ };
+
+ /**
+ * Loop over each of the ranges of the index
+ * @param {function} callback Called for each range with a Range as first
+ * argument, the dimension as second, and the
+ * index object as third.
+ */
+ Index.prototype.forEach = function (callback) {
+ for (var i = 0, ii = this._ranges.length; i < ii; i++) {
+ callback(this._ranges[i], i, this);
+ }
+ };
+
+ /**
+ * Retrieve the range for a given dimension number from the index
+ * @param {Number} dim Number of the dimension
+ * @returns {Range | null} range
+ */
+ Index.prototype.range = function(dim) {
+ return this._ranges[dim] || null;
+ };
+
+ /**
+ * Test whether this index contains only a single value.
+ *
+ * This is the case when the index is created with only scalar values as ranges,
+ * not for ranges resolving into a single value.
+ * @return {boolean} isScalar
+ */
+ Index.prototype.isScalar = function () {
+ return this._isScalar;
+ };
+
+ /**
+ * Expand the Index into an array.
+ * For example new Index([0,3], [2,7]) returns [[0,1,2], [2,3,4,5,6]]
+ * @returns {Array} array
+ */
+ Index.prototype.toArray = function () {
+ var array = [];
+ for (var i = 0, ii = this._ranges.length; i < ii; i++) {
+ var range = this._ranges[i],
+ row = [],
+ x = range.start,
+ end = range.end,
+ step = range.step;
+
+ if (step > 0) {
+ while (x < end) {
+ row.push(x);
+ x += step;
+ }
+ }
+ else if (step < 0) {
+ while (x > end) {
+ row.push(x);
+ x += step;
+ }
+ }
+
+ array.push(row);
+ }
+
+ return array;
+ };
+
+ /**
+ * Get the primitive value of the Index, a two dimensional array.
+ * Equivalent to Index.toArray().
+ * @returns {Array} array
+ */
+ Index.prototype.valueOf = Index.prototype.toArray;
+
+ /**
+ * Get the string representation of the index, for example '[2:6]' or '[0:2:10, 4:7]'
+ * @returns {String} str
+ */
+ Index.prototype.toString = function () {
+ var strings = [];
+
+ for (var i = 0, ii = this._ranges.length; i < ii; i++) {
+ var range = this._ranges[i];
+ var str = number.format(range.start);
+ if (range.step != 1) {
+ str += ':' + number.format(range.step);
+ }
+ str += ':' + number.format(range.end);
+ strings.push(str);
+ }
+
+ return '[' + strings.join(', ') + ']';
+ };
+
+ /**
+ * Get a JSON representation of the Index
+ * @returns {Object} Returns a JSON object structured as:
+ * `{"mathjs": "Index", "ranges": [{"mathjs": "Range", start: 0, end: 10, step:1}, ...]}`
+ */
+ Index.prototype.toJSON = function () {
+ return {
+ mathjs: 'Index',
+ ranges: this._ranges
+ };
+ };
+
+ /**
+ * Instantiate an Index from a JSON object
+ * @param {Object} json A JSON object structured as:
+ * `{"mathjs": "Index", "ranges": [{"mathjs": "Range", start: 0, end: 10, step:1}, ...]}`
+ * @return {Index}
+ */
+ Index.fromJSON = function (json) {
+ return Index.create(json.ranges);
+ };
+
+ // exports
+ module.exports = Index;
+
+
+/***/ },
+/* 10 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171);
+ var DimensionError = __webpack_require__(168);
+
+ var Index = __webpack_require__(9);
+
+ var number = util.number;
+ var string = util.string;
+ var array = util.array;
+ var object = util.object;
+
+ var isArray = Array.isArray;
+ var validateIndex = array.validateIndex;
+
+ /**
+ * @constructor Matrix
+ *
+ * A Matrix is a wrapper around an Array. A matrix can hold a multi dimensional
+ * array. A matrix can be constructed as:
+ * var matrix = new Matrix(data)
+ *
+ * Matrix contains the functions to resize, get and set values, get the size,
+ * clone the matrix and to convert the matrix to a vector, array, or scalar.
+ * Furthermore, one can iterate over the matrix using map and forEach.
+ * The internal Array of the Matrix can be accessed using the function valueOf.
+ *
+ * Example usage:
+ * var matrix = new Matrix([[1, 2], [3, 4]);
+ * matix.size(); // [2, 2]
+ * matrix.resize([3, 2], 5);
+ * matrix.valueOf(); // [[1, 2], [3, 4], [5, 5]]
+ * matrix.subset([1,2]) // 3 (indexes are zero-based)
+ *
+ * @param {Array | Matrix} [data] A multi dimensional array
+ */
+ function Matrix(data) {
+ if (!(this instanceof Matrix)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ if (data instanceof Matrix) {
+ // clone data from a Matrix
+ this._data = data.clone()._data;
+ }
+ else if (isArray(data)) {
+ // use array
+ // replace nested Matrices with Arrays
+ this._data = preprocess(data);
+ }
+ else if (data != null) {
+ // unsupported type
+ throw new TypeError('Unsupported type of data (' + util.types.type(data) + ')');
+ }
+ else {
+ // nothing provided
+ this._data = [];
+ }
+
+ // verify the size of the array
+ this._size = array.size(this._data);
+ }
+
+ /**
+ * Test whether an object is a Matrix
+ * @param {*} object
+ * @return {Boolean} isMatrix
+ */
+ Matrix.isMatrix = function (object) {
+ return (object instanceof Matrix);
+ };
+
+ /**
+ * Get a subset of the matrix, or replace a subset of the matrix.
+ *
+ * Usage:
+ * var subset = matrix.subset(index) // retrieve subset
+ * var value = matrix.subset(index, replacement) // replace subset
+ *
+ * @param {Index} index
+ * @param {Array | Matrix | *} [replacement]
+ * @param {*} [defaultValue=0] Default value, filled in on new entries when
+ * the matrix is resized. If not provided,
+ * new matrix elements will be filled with zeros.
+ */
+ Matrix.prototype.subset = function (index, replacement, defaultValue) {
+ switch (arguments.length) {
+ case 1:
+ return _get(this, index);
+
+ // intentional fall through
+ case 2:
+ case 3:
+ return _set(this, index, replacement, defaultValue);
+
+ default:
+ throw new SyntaxError('Wrong number of arguments');
+ }
+ };
+
+ /**
+ * Get a single element from the matrix.
+ * @param {Number[]} index Zero-based index
+ * @return {*} value
+ */
+ Matrix.prototype.get = function (index) {
+ if (!isArray(index)) {
+ throw new TypeError('Array expected');
+ }
+ if (index.length != this._size.length) {
+ throw new DimensionError(index.length, this._size.length);
+ }
+
+ var data = this._data;
+ for (var i = 0, ii = index.length; i < ii; i++) {
+ var index_i = index[i];
+ validateIndex(index_i, data.length);
+ data = data[index_i];
+ }
+
+ return object.clone(data);
+ };
+
+ /**
+ * Replace a single element in the matrix.
+ * @param {Number[]} index Zero-based index
+ * @param {*} value
+ * @param {*} [defaultValue] Default value, filled in on new entries when
+ * the matrix is resized. If not provided,
+ * new matrix elements will be left undefined.
+ * @return {Matrix} self
+ */
+ Matrix.prototype.set = function (index, value, defaultValue) {
+ var i, ii;
+
+ // validate input type and dimensions
+ if (!isArray(index)) {
+ throw new Error('Array expected');
+ }
+ if (index.length < this._size.length) {
+ throw new DimensionError(index.length, this._size.length, '<');
+ }
+
+ // enlarge matrix when needed
+ var size = index.map(function (i) {
+ return i + 1;
+ });
+ _fit(this, size, defaultValue);
+
+ // traverse over the dimensions
+ var data = this._data;
+ for (i = 0, ii = index.length - 1; i < ii; i++) {
+ var index_i = index[i];
+ validateIndex(index_i, data.length);
+ data = data[index_i];
+ }
+
+ // set new value
+ index_i = index[index.length - 1];
+ validateIndex(index_i, data.length);
+ data[index_i] = value;
+
+ return this;
+ };
+
+ /**
+ * Get a submatrix of this matrix
+ * @param {Matrix} matrix
+ * @param {Index} index Zero-based index
+ * @private
+ */
+ function _get (matrix, index) {
+ if (!(index instanceof Index)) {
+ throw new TypeError('Invalid index');
+ }
+
+ var isScalar = index.isScalar();
+ if (isScalar) {
+ // return a scalar
+ return matrix.get(index.min());
+ }
+ else {
+ // validate dimensions
+ var size = index.size();
+ if (size.length != matrix._size.length) {
+ throw new DimensionError(size.length, matrix._size.length);
+ }
+
+ // validate if any of the ranges in the index is out of range
+ var min = index.min();
+ var max = index.max();
+ for (var i = 0, ii = matrix._size.length; i < ii; i++) {
+ validateIndex(min[i], matrix._size[i]);
+ validateIndex(max[i], matrix._size[i]);
+ }
+
+ // retrieve submatrix
+ // TODO: more efficient when creating an empty matrix and setting _data and _size manually
+ return new Matrix(_getSubmatrix(matrix._data, index, size.length, 0));
+ }
+ }
+
+ /**
+ * Recursively get a submatrix of a multi dimensional matrix.
+ * Index is not checked for correct number or length of dimensions.
+ * @param {Array} data
+ * @param {Index} index
+ * @param {number} dims Total number of dimensions
+ * @param {number} dim Current dimension
+ * @return {Array} submatrix
+ * @private
+ */
+ function _getSubmatrix (data, index, dims, dim) {
+ var last = (dim == dims - 1);
+ var range = index.range(dim);
+
+ if (last) {
+ return range.map(function (i) {
+ return data[i];
+ });
+ }
+ else {
+ return range.map(function (i) {
+ var child = data[i];
+ return _getSubmatrix(child, index, dims, dim + 1);
+ });
+ }
+ }
+
+ /**
+ * Replace a submatrix in this matrix
+ * Indexes are zero-based.
+ * @param {Matrix} matrix
+ * @param {Index} index
+ * @param {Matrix | Array | *} submatrix
+ * @param {*} defaultValue Default value, filled in on new entries when
+ * the matrix is resized.
+ * @return {Matrix} matrix
+ * @private
+ */
+ function _set (matrix, index, submatrix, defaultValue) {
+ if (!(index instanceof Index)) {
+ throw new TypeError('Invalid index');
+ }
+
+ // get index size and check whether the index contains a single value
+ var iSize = index.size(),
+ isScalar = index.isScalar();
+
+ // calculate the size of the submatrix, and convert it into an Array if needed
+ var sSize;
+ if (submatrix instanceof Matrix) {
+ sSize = submatrix.size();
+ submatrix = submatrix.valueOf();
+ }
+ else {
+ sSize = array.size(submatrix);
+ }
+
+ if (isScalar) {
+ // set a scalar
+
+ // check whether submatrix is a scalar
+ if (sSize.length != 0) {
+ throw new TypeError('Scalar expected');
+ }
+
+ matrix.set(index.min(), submatrix, defaultValue);
+ }
+ else {
+ // set a submatrix
+
+ // validate dimensions
+ if (iSize.length < matrix._size.length) {
+ throw new DimensionError(iSize.length, matrix._size.length, '<');
+ }
+
+ if (sSize.length < iSize.length) {
+ // calculate number of missing outer dimensions
+ var i = 0;
+ var outer = 0;
+ while (iSize[i] === 1 && sSize[i] === 1) {
+ i++;
+ }
+ while (iSize[i] === 1) {
+ outer++;
+ i++;
+ }
+
+ // unsqueeze both outer and inner dimensions
+ submatrix = array.unsqueeze(submatrix, iSize.length, outer, sSize);
+ }
+
+ // check whether the size of the submatrix matches the index size
+ if (!object.deepEqual(iSize, sSize)) {
+ throw new DimensionError(iSize, sSize, '>');
+ }
+
+ // enlarge matrix when needed
+ var size = index.max().map(function (i) {
+ return i + 1;
+ });
+ _fit(matrix, size, defaultValue);
+
+ // insert the sub matrix
+ var dims = iSize.length,
+ dim = 0;
+ _setSubmatrix (matrix._data, index, submatrix, dims, dim);
+ }
+
+ return matrix;
+ }
+
+ /**
+ * Replace a submatrix of a multi dimensional matrix.
+ * @param {Array} data
+ * @param {Index} index
+ * @param {Array} submatrix
+ * @param {number} dims Total number of dimensions
+ * @param {number} dim
+ * @private
+ */
+ function _setSubmatrix (data, index, submatrix, dims, dim) {
+ var last = (dim == dims - 1),
+ range = index.range(dim);
+
+ if (last) {
+ range.forEach(function (dataIndex, subIndex) {
+ validateIndex(dataIndex);
+ data[dataIndex] = submatrix[subIndex];
+ });
+ }
+ else {
+ range.forEach(function (dataIndex, subIndex) {
+ validateIndex(dataIndex);
+ _setSubmatrix(data[dataIndex], index, submatrix[subIndex], dims, dim + 1);
+ });
+ }
+ }
+
+ /**
+ * Resize the matrix
+ * @param {Number[]} size
+ * @param {*} [defaultValue=0] Default value, filled in on new entries.
+ * If not provided, the matrix elements will
+ * be filled with zeros.
+ * @return {Matrix} self The matrix itself is returned
+ */
+ Matrix.prototype.resize = function (size, defaultValue) {
+ this._size = object.clone(size);
+ this._data = array.resize(this._data, this._size, defaultValue);
+
+ // return the matrix itself
+ return this;
+ };
+
+ /**
+ * Enlarge the matrix when it is smaller than given size.
+ * If the matrix is larger or equal sized, nothing is done.
+ * @param {Matrix} matrix The matrix to be resized
+ * @param {Number[]} size
+ * @param {*} defaultValue Default value, filled in on new entries.
+ * @private
+ */
+ function _fit(matrix, size, defaultValue) {
+ var newSize = object.clone(matrix._size),
+ changed = false;
+
+ // add dimensions when needed
+ while (newSize.length < size.length) {
+ newSize.push(0);
+ changed = true;
+ }
+
+ // enlarge size when needed
+ for (var i = 0, ii = size.length; i < ii; i++) {
+ if (size[i] > newSize[i]) {
+ newSize[i] = size[i];
+ changed = true;
+ }
+ }
+
+ if (changed) {
+ // resize only when size is changed
+ matrix.resize(newSize, defaultValue);
+ }
+ }
+
+ /**
+ * Create a clone of the matrix
+ * @return {Matrix} clone
+ */
+ Matrix.prototype.clone = function () {
+ var matrix = new Matrix();
+ matrix._data = object.clone(this._data);
+ matrix._size = object.clone(this._size);
+ return matrix;
+ };
+
+ /**
+ * Retrieve the size of the matrix.
+ * @returns {Number[]} size
+ */
+ Matrix.prototype.size = function() {
+ return this._size;
+ };
+
+ /**
+ * Create a new matrix with the results of the callback function executed on
+ * each entry of the matrix.
+ * @param {function} callback The callback function is invoked with three
+ * parameters: the value of the element, the index
+ * of the element, and the Matrix being traversed.
+ * @return {Matrix} matrix
+ */
+ Matrix.prototype.map = function (callback) {
+ var me = this;
+ var matrix = new Matrix();
+
+ var recurse = function (value, index) {
+ if (isArray(value)) {
+ return value.map(function (child, i) {
+ return recurse(child, index.concat(i));
+ });
+ }
+ else {
+ return callback(value, index, me);
+ }
+ };
+ matrix._data = recurse(this._data, []);
+ matrix._size = object.clone(this._size);
+
+ return matrix;
+ };
+
+ /**
+ * Execute a callback function on each entry of the matrix.
+ * @param {function} callback The callback function is invoked with three
+ * parameters: the value of the element, the index
+ * of the element, and the Matrix being traversed.
+ */
+ Matrix.prototype.forEach = function (callback) {
+ var me = this;
+
+ var recurse = function (value, index) {
+ if (isArray(value)) {
+ value.forEach(function (child, i) {
+ recurse(child, index.concat(i));
+ });
+ }
+ else {
+ callback(value, index, me);
+ }
+ };
+ recurse(this._data, []);
+ };
+
+ /**
+ * Create an Array with a copy of the data of the Matrix
+ * @returns {Array} array
+ */
+ Matrix.prototype.toArray = function () {
+ return object.clone(this._data);
+ };
+
+ /**
+ * Get the primitive value of the Matrix: a multidimensional array
+ * @returns {Array} array
+ */
+ Matrix.prototype.valueOf = function () {
+ return this._data;
+ };
+
+ /**
+ * Get a string representation of the matrix, with optional formatting options.
+ * @param {Object | Number | Function} [options] Formatting options. See
+ * lib/util/number:format for a
+ * description of the available
+ * options.
+ * @returns {String} str
+ */
+ Matrix.prototype.format = function (options) {
+ return string.format(this._data, options);
+ };
+
+ /**
+ * Get a string representation of the matrix
+ * @returns {String} str
+ */
+ Matrix.prototype.toString = function () {
+ return string.format(this._data);
+ };
+
+ /**
+ * Get a JSON representation of the matrix
+ * @returns {Object}
+ */
+ Matrix.prototype.toJSON = function () {
+ return {
+ mathjs: 'Matrix',
+ data: this._data
+ }
+ };
+
+ /**
+ * Generate a matrix from a JSON object
+ * @param {Object} json An object structured like
+ * `{"mathjs": "Matrix", data: []}`,
+ * where mathjs is optional
+ * @returns {Matrix}
+ */
+ Matrix.fromJSON = function (json) {
+ return new Matrix(json.data);
+ };
+
+ /**
+ * Preprocess data, which can be an Array or Matrix with nested Arrays and
+ * Matrices. Replaces all nested Matrices with Arrays
+ * @param {Array} data
+ * @return {Array} data
+ */
+ function preprocess(data) {
+ for (var i = 0, ii = data.length; i < ii; i++) {
+ var elem = data[i];
+ if (isArray(elem)) {
+ data[i] = preprocess(elem);
+ }
+ else if (elem instanceof Matrix) {
+ data[i] = preprocess(elem._data);
+ }
+ }
+
+ return data;
+ }
+
+ // exports
+ module.exports = Matrix;
+
+
+/***/ },
+/* 11 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171),
+
+ number = util.number,
+ string = util.string,
+ isNumber = util.number.isNumber,
+ isString = util.string.isString;
+
+ /**
+ * @constructor Unit
+ *
+ * A unit can be constructed in the following ways:
+ * var a = new Unit(value, name);
+ * var b = new Unit(null, name);
+ * var c = Unit.parse(str);
+ *
+ * Example usage:
+ * var a = new Unit(5, 'cm'); // 50 mm
+ * var b = Unit.parse('23 kg'); // 23 kg
+ * var c = math.in(a, new Unit(null, 'm'); // 0.05 m
+ *
+ * @param {Number} [value] A value like 5.2
+ * @param {String} [name] A unit name like "cm" or "inch". Can include a prefix
+ */
+ function Unit(value, name) {
+ if (!(this instanceof Unit)) {
+ throw new Error('Constructor must be called with the new operator');
+ }
+
+ if (value != undefined && !isNumber(value)) {
+ throw new TypeError('First parameter in Unit constructor must be a number');
+ }
+ if (name != undefined && (!isString(name) || name == '')) {
+ throw new TypeError('Second parameter in Unit constructor must be a string');
+ }
+
+ if (name != undefined) {
+ // find the unit and prefix from the string
+ var res = _findUnit(name);
+ if (!res) {
+ throw new SyntaxError('Unknown unit "' + name + '"');
+ }
+ this.unit = res.unit;
+ this.prefix = res.prefix;
+ }
+ else {
+ this.unit = UNIT_NONE;
+ this.prefix = PREFIX_NONE; // link to a list with supported prefixes
+ }
+
+ this.value = (value != undefined) ? this._normalize(value) : null;
+ this.fixPrefix = false; // if true, function format will not search for the
+ // best prefix but leave it as initially provided.
+ // fixPrefix is set true by the method Unit.to
+ }
+
+ // private variables and functions for the Unit parser
+ var text, index, c;
+
+ function skipWhitespace() {
+ while (c == ' ' || c == '\t') {
+ next();
+ }
+ }
+
+ function isDigitDot (c) {
+ return ((c >= '0' && c <= '9') || c == '.');
+ }
+
+ function isDigit (c) {
+ return ((c >= '0' && c <= '9'));
+ }
+
+ function next() {
+ index++;
+ c = text.charAt(index);
+ }
+
+ function revert(oldIndex) {
+ index = oldIndex;
+ c = text.charAt(index);
+ }
+
+ function parseNumber () {
+ var number = '';
+ var oldIndex;
+ oldIndex = index;
+
+ if (c == '+') {
+ next();
+ }
+ else if (c == '-') {
+ number += c;
+ next();
+ }
+
+ if (!isDigitDot(c)) {
+ // a + or - must be followed by a digit
+ revert(oldIndex);
+ return null;
+ }
+
+ // get number, can have a single dot
+ if (c == '.') {
+ number += c;
+ next();
+ if (!isDigit(c)) {
+ // this is no legal number, it is just a dot
+ revert(oldIndex);
+ return null;
+ }
+ }
+ else {
+ while (isDigit(c)) {
+ number += c;
+ next();
+ }
+ if (c == '.') {
+ number += c;
+ next();
+ }
+ }
+ while (isDigit(c)) {
+ number += c;
+ next();
+ }
+
+ // check for exponential notation like "2.3e-4" or "1.23e50"
+ if (c == 'E' || c == 'e') {
+ number += c;
+ next();
+
+ if (c == '+' || c == '-') {
+ number += c;
+ next();
+ }
+
+ // Scientific notation MUST be followed by an exponent
+ if (!isDigit(c)) {
+ // this is no legal number, exponent is missing.
+ revert(oldIndex);
+ return null;
+ }
+
+ while (isDigit(c)) {
+ number += c;
+ next();
+ }
+ }
+
+ return number;
+ }
+
+ function parseUnit() {
+ var unitName = '';
+
+ skipWhitespace();
+ while (c && c != ' ' && c != '\t') {
+ unitName += c;
+ next();
+ }
+
+ return unitName || null;
+ }
+
+ /**
+ * Parse a string into a unit. Returns null if the provided string does not
+ * contain a valid unit.
+ * @param {String} str A string like "5.2 inch", "4e2 kg"
+ * @return {Unit | null} unit
+ */
+ Unit.parse = function(str) {
+ text = str;
+ index = -1;
+ c = '';
+
+ if (!isString(text)) {
+ return null;
+ }
+
+ next();
+ skipWhitespace();
+ var value = parseNumber();
+ var name;
+ if (value) {
+ name = parseUnit();
+
+ next();
+ skipWhitespace();
+ if (c) {
+ // garbage at the end. not good.
+ return null;
+ }
+
+ if (value && name) {
+ try {
+ // constructor will throw an error when unit is not found
+ return new Unit(Number(value), name);
+ }
+ catch (err) {}
+ }
+ }
+ else {
+ name = parseUnit();
+
+ next();
+ skipWhitespace();
+ if (c) {
+ // garbage at the end. not good.
+ return null;
+ }
+
+ if (name) {
+ try {
+ // constructor will throw an error when unit is not found
+ return new Unit(null, name);
+ }
+ catch (err) {}
+ }
+ }
+
+ return null;
+ };
+
+ /**
+ * Test whether value is of type Unit
+ * @param {*} value
+ * @return {Boolean} isUnit
+ */
+ Unit.isUnit = function(value) {
+ return (value instanceof Unit);
+ };
+
+ /**
+ * create a copy of this unit
+ * @return {Unit} clone
+ */
+ Unit.prototype.clone = function () {
+ var clone = new Unit();
+
+ for (var p in this) {
+ if (this.hasOwnProperty(p)) {
+ clone[p] = this[p];
+ }
+ }
+
+ return clone;
+ };
+
+ /**
+ * Normalize a value, based on its currently set unit
+ * @param {Number} value
+ * @return {Number} normalized value
+ * @private
+ */
+ Unit.prototype._normalize = function(value) {
+ return (value + this.unit.offset) * this.unit.value * this.prefix.value;
+ };
+
+ /**
+ * Denormalize a value, based on its currently set unit
+ * @param {Number} value
+ * @param {Number} [prefixValue] Optional prefix value to be used
+ * @return {Number} denormalized value
+ * @private
+ */
+ Unit.prototype._denormalize = function (value, prefixValue) {
+ if (prefixValue == undefined) {
+ return value / this.unit.value / this.prefix.value - this.unit.offset;
+ }
+ else {
+ return value / this.unit.value / prefixValue - this.unit.offset;
+ }
+ };
+
+ /**
+ * Find a unit from a string
+ * @param {String} str A string like 'cm' or 'inch'
+ * @returns {Object | null} result When found, an object with fields unit and
+ * prefix is returned. Else, null is returned.
+ * @private
+ */
+ function _findUnit(str) {
+ for (var name in UNITS) {
+ if (UNITS.hasOwnProperty(name)) {
+ if (string.endsWith(str, name) ) {
+ var unit = UNITS[name];
+ var prefixLen = (str.length - name.length);
+ var prefixName = str.substring(0, prefixLen);
+ var prefix = unit.prefixes[prefixName];
+ if (prefix !== undefined) {
+ // store unit, prefix, and value
+ return {
+ unit: unit,
+ prefix: prefix
+ };
+ }
+ }
+ }
+ }
+
+ return null;
+ }
+
+ /**
+ * Test if the given expression is a unit.
+ * The unit can have a prefix but cannot have a value.
+ * @param {String} name A string to be tested whether it is a value less unit.
+ * The unit can have prefix, like "cm"
+ * @return {Boolean} true if the given string is a unit
+ */
+ Unit.isValuelessUnit = function (name) {
+ return (_findUnit(name) != null);
+ };
+
+ /**
+ * check if this unit has given base unit
+ * @param {BASE_UNITS | undefined} base
+ */
+ Unit.prototype.hasBase = function(base) {
+ return (this.unit.base === base);
+ };
+
+ /**
+ * Check if this unit has a base equal to another base
+ * @param {Unit} other
+ * @return {Boolean} true if equal base
+ */
+ Unit.prototype.equalBase = function(other) {
+ return (this.unit.base === other.unit.base);
+ };
+
+ /**
+ * Check if this unit equals another unit
+ * @param {Unit} other
+ * @return {Boolean} true if both units are equal
+ */
+ Unit.prototype.equals = function(other) {
+ return (this.equalBase(other) && this.value == other.value);
+ };
+
+ /**
+ * Create a clone of this unit with a representation
+ * @param {String | Unit} valuelessUnit A unit without value. Can have prefix, like "cm"
+ * @returns {Unit} unit having fixed, specified unit
+ */
+ Unit.prototype.to = function (valuelessUnit) {
+ var other;
+ var value = this.value == null ? this._normalize(1) : this.value;
+ if (isString(valuelessUnit)) {
+ other = new Unit(null, valuelessUnit);
+
+ if (!this.equalBase(other)) {
+ throw new Error('Units do not match');
+ }
+
+ other.value = value;
+ other.fixPrefix = true;
+ return other;
+ }
+ else if (valuelessUnit instanceof Unit) {
+ if (!this.equalBase(valuelessUnit)) {
+ throw new Error('Units do not match');
+ }
+ if (valuelessUnit.value !== null) {
+ throw new Error('Cannot convert to a unit with a value');
+ }
+
+ other = valuelessUnit.clone();
+ other.value = value;
+ other.fixPrefix = true;
+ return other;
+ }
+ else {
+ throw new Error('String or Unit expected as parameter');
+ }
+ };
+
+ /**
+ * Return the value of the unit when represented with given valueless unit
+ * @param {String | Unit} valuelessUnit For example 'cm' or 'inch'
+ * @return {Number} value
+ */
+ Unit.prototype.toNumber = function (valuelessUnit) {
+ var other = this.to(valuelessUnit);
+ return other._denormalize(other.value, other.prefix.value);
+ };
+
+
+ /**
+ * Get a string representation of the unit.
+ * @return {String}
+ */
+ Unit.prototype.toString = function() {
+ return this.format();
+ };
+
+ /**
+ * Get a JSON representation of the unit
+ * @returns {Object} Returns a JSON object structured as:
+ * `{"mathjs": "Unit", "value": 2, "unit": "cm", "fixPrefix": false}`
+ */
+ Unit.prototype.toJSON = function () {
+ return {
+ mathjs: 'Unit',
+ value: this._denormalize(this.value),
+ unit: this.prefix.name + this.unit.name,
+ fixPrefix: this.fixPrefix
+ };
+ };
+
+ /**
+ * Instantiate a Unit from a JSON object
+ * @param {Object} json A JSON object structured as:
+ * `{"mathjs": "Unit", "value": 2, "unit": "cm", "fixPrefix": false}`
+ * @return {Unit}
+ */
+ Unit.fromJSON = function (json) {
+ var unit = new Unit(json.value, json.unit);
+ unit.fixPrefix = json.fixPrefix || false;
+ return unit;
+ };
+
+ /**
+ * Returns the string representation of the unit.
+ * @return {String}
+ */
+ Unit.prototype.valueOf = Unit.prototype.toString;
+
+ /**
+ * Get a string representation of the Unit, with optional formatting options.
+ * @param {Object | Number | Function} [options] Formatting options. See
+ * lib/util/number:format for a
+ * description of the available
+ * options.
+ * @return {String}
+ */
+ Unit.prototype.format = function(options) {
+ var value,
+ str;
+
+ if (this.value !== null && !this.fixPrefix) {
+ var bestPrefix = this._bestPrefix();
+ value = this._denormalize(this.value, bestPrefix.value);
+ str = number.format(value, options) + ' ';
+ str += bestPrefix.name + this.unit.name;
+ }
+ else {
+ value = this._denormalize(this.value);
+ str = (this.value !== null) ? (number.format(value, options) + ' ') : '';
+ str += this.prefix.name + this.unit.name;
+ }
+
+ return str;
+ };
+
+ /**
+ * Calculate the best prefix using current value.
+ * @returns {Object} prefix
+ * @private
+ */
+ Unit.prototype._bestPrefix = function () {
+ // find the best prefix value (resulting in the value of which
+ // the absolute value of the log10 is closest to zero,
+ // though with a little offset of 1.2 for nicer values: you get a
+ // sequence 1mm 100mm 500mm 0.6m 1m 10m 100m 500m 0.6km 1km ...
+ var absValue = Math.abs(this.value / this.unit.value);
+ var bestPrefix = PREFIX_NONE;
+ var bestDiff = Math.abs(
+ Math.log(absValue / bestPrefix.value) / Math.LN10 - 1.2);
+
+ var prefixes = this.unit.prefixes;
+ for (var p in prefixes) {
+ if (prefixes.hasOwnProperty(p)) {
+ var prefix = prefixes[p];
+ if (prefix.scientific) {
+ var diff = Math.abs(
+ Math.log(absValue / prefix.value) / Math.LN10 - 1.2);
+
+ if (diff < bestDiff) {
+ bestPrefix = prefix;
+ bestDiff = diff;
+ }
+ }
+ }
+ }
+
+ return bestPrefix;
+ };
+
+ var PREFIXES = {
+ NONE: {
+ '': {name: '', value: 1, scientific: true}
+ },
+ SHORT: {
+ '': {name: '', value: 1, scientific: true},
+
+ 'da': {name: 'da', value: 1e1, scientific: false},
+ 'h': {name: 'h', value: 1e2, scientific: false},
+ 'k': {name: 'k', value: 1e3, scientific: true},
+ 'M': {name: 'M', value: 1e6, scientific: true},
+ 'G': {name: 'G', value: 1e9, scientific: true},
+ 'T': {name: 'T', value: 1e12, scientific: true},
+ 'P': {name: 'P', value: 1e15, scientific: true},
+ 'E': {name: 'E', value: 1e18, scientific: true},
+ 'Z': {name: 'Z', value: 1e21, scientific: true},
+ 'Y': {name: 'Y', value: 1e24, scientific: true},
+
+ 'd': {name: 'd', value: 1e-1, scientific: false},
+ 'c': {name: 'c', value: 1e-2, scientific: false},
+ 'm': {name: 'm', value: 1e-3, scientific: true},
+ 'u': {name: 'u', value: 1e-6, scientific: true},
+ 'n': {name: 'n', value: 1e-9, scientific: true},
+ 'p': {name: 'p', value: 1e-12, scientific: true},
+ 'f': {name: 'f', value: 1e-15, scientific: true},
+ 'a': {name: 'a', value: 1e-18, scientific: true},
+ 'z': {name: 'z', value: 1e-21, scientific: true},
+ 'y': {name: 'y', value: 1e-24, scientific: true}
+ },
+ LONG: {
+ '': {name: '', value: 1, scientific: true},
+
+ 'deca': {name: 'deca', value: 1e1, scientific: false},
+ 'hecto': {name: 'hecto', value: 1e2, scientific: false},
+ 'kilo': {name: 'kilo', value: 1e3, scientific: true},
+ 'mega': {name: 'mega', value: 1e6, scientific: true},
+ 'giga': {name: 'giga', value: 1e9, scientific: true},
+ 'tera': {name: 'tera', value: 1e12, scientific: true},
+ 'peta': {name: 'peta', value: 1e15, scientific: true},
+ 'exa': {name: 'exa', value: 1e18, scientific: true},
+ 'zetta': {name: 'zetta', value: 1e21, scientific: true},
+ 'yotta': {name: 'yotta', value: 1e24, scientific: true},
+
+ 'deci': {name: 'deci', value: 1e-1, scientific: false},
+ 'centi': {name: 'centi', value: 1e-2, scientific: false},
+ 'milli': {name: 'milli', value: 1e-3, scientific: true},
+ 'micro': {name: 'micro', value: 1e-6, scientific: true},
+ 'nano': {name: 'nano', value: 1e-9, scientific: true},
+ 'pico': {name: 'pico', value: 1e-12, scientific: true},
+ 'femto': {name: 'femto', value: 1e-15, scientific: true},
+ 'atto': {name: 'atto', value: 1e-18, scientific: true},
+ 'zepto': {name: 'zepto', value: 1e-21, scientific: true},
+ 'yocto': {name: 'yocto', value: 1e-24, scientific: true}
+ },
+ SQUARED: {
+ '': {name: '', value: 1, scientific: true},
+
+ 'da': {name: 'da', value: 1e2, scientific: false},
+ 'h': {name: 'h', value: 1e4, scientific: false},
+ 'k': {name: 'k', value: 1e6, scientific: true},
+ 'M': {name: 'M', value: 1e12, scientific: true},
+ 'G': {name: 'G', value: 1e18, scientific: true},
+ 'T': {name: 'T', value: 1e24, scientific: true},
+ 'P': {name: 'P', value: 1e30, scientific: true},
+ 'E': {name: 'E', value: 1e36, scientific: true},
+ 'Z': {name: 'Z', value: 1e42, scientific: true},
+ 'Y': {name: 'Y', value: 1e48, scientific: true},
+
+ 'd': {name: 'd', value: 1e-2, scientific: false},
+ 'c': {name: 'c', value: 1e-4, scientific: false},
+ 'm': {name: 'm', value: 1e-6, scientific: true},
+ 'u': {name: 'u', value: 1e-12, scientific: true},
+ 'n': {name: 'n', value: 1e-18, scientific: true},
+ 'p': {name: 'p', value: 1e-24, scientific: true},
+ 'f': {name: 'f', value: 1e-30, scientific: true},
+ 'a': {name: 'a', value: 1e-36, scientific: true},
+ 'z': {name: 'z', value: 1e-42, scientific: true},
+ 'y': {name: 'y', value: 1e-42, scientific: true}
+ },
+ CUBIC: {
+ '': {name: '', value: 1, scientific: true},
+
+ 'da': {name: 'da', value: 1e3, scientific: false},
+ 'h': {name: 'h', value: 1e6, scientific: false},
+ 'k': {name: 'k', value: 1e9, scientific: true},
+ 'M': {name: 'M', value: 1e18, scientific: true},
+ 'G': {name: 'G', value: 1e27, scientific: true},
+ 'T': {name: 'T', value: 1e36, scientific: true},
+ 'P': {name: 'P', value: 1e45, scientific: true},
+ 'E': {name: 'E', value: 1e54, scientific: true},
+ 'Z': {name: 'Z', value: 1e63, scientific: true},
+ 'Y': {name: 'Y', value: 1e72, scientific: true},
+
+ 'd': {name: 'd', value: 1e-3, scientific: false},
+ 'c': {name: 'c', value: 1e-6, scientific: false},
+ 'm': {name: 'm', value: 1e-9, scientific: true},
+ 'u': {name: 'u', value: 1e-18, scientific: true},
+ 'n': {name: 'n', value: 1e-27, scientific: true},
+ 'p': {name: 'p', value: 1e-36, scientific: true},
+ 'f': {name: 'f', value: 1e-45, scientific: true},
+ 'a': {name: 'a', value: 1e-54, scientific: true},
+ 'z': {name: 'z', value: 1e-63, scientific: true},
+ 'y': {name: 'y', value: 1e-72, scientific: true}
+ },
+ BINARY_SHORT: {
+ '': {name: '', value: 1, scientific: true},
+ 'k': {name: 'k', value: 1024, scientific: true},
+ 'M': {name: 'M', value: Math.pow(1024, 2), scientific: true},
+ 'G': {name: 'G', value: Math.pow(1024, 3), scientific: true},
+ 'T': {name: 'T', value: Math.pow(1024, 4), scientific: true},
+ 'P': {name: 'P', value: Math.pow(1024, 5), scientific: true},
+ 'E': {name: 'E', value: Math.pow(1024, 6), scientific: true},
+ 'Z': {name: 'Z', value: Math.pow(1024, 7), scientific: true},
+ 'Y': {name: 'Y', value: Math.pow(1024, 8), scientific: true},
+
+ 'Ki': {name: 'Ki', value: 1024, scientific: true},
+ 'Mi': {name: 'Mi', value: Math.pow(1024, 2), scientific: true},
+ 'Gi': {name: 'Gi', value: Math.pow(1024, 3), scientific: true},
+ 'Ti': {name: 'Ti', value: Math.pow(1024, 4), scientific: true},
+ 'Pi': {name: 'Pi', value: Math.pow(1024, 5), scientific: true},
+ 'Ei': {name: 'Ei', value: Math.pow(1024, 6), scientific: true},
+ 'Zi': {name: 'Zi', value: Math.pow(1024, 7), scientific: true},
+ 'Yi': {name: 'Yi', value: Math.pow(1024, 8), scientific: true}
+ },
+ BINARY_LONG: {
+ '': {name: '', value: 1, scientific: true},
+ 'kilo': {name: 'kilo', value: 1024, scientific: true},
+ 'mega': {name: 'mega', value: Math.pow(1024, 2), scientific: true},
+ 'giga': {name: 'giga', value: Math.pow(1024, 3), scientific: true},
+ 'tera': {name: 'tera', value: Math.pow(1024, 4), scientific: true},
+ 'peta': {name: 'peta', value: Math.pow(1024, 5), scientific: true},
+ 'exa': {name: 'exa', value: Math.pow(1024, 6), scientific: true},
+ 'zetta': {name: 'zetta', value: Math.pow(1024, 7), scientific: true},
+ 'yotta': {name: 'yotta', value: Math.pow(1024, 8), scientific: true},
+
+ 'kibi': {name: 'kibi', value: 1024, scientific: true},
+ 'mebi': {name: 'mebi', value: Math.pow(1024, 2), scientific: true},
+ 'gibi': {name: 'gibi', value: Math.pow(1024, 3), scientific: true},
+ 'tebi': {name: 'tebi', value: Math.pow(1024, 4), scientific: true},
+ 'pebi': {name: 'pebi', value: Math.pow(1024, 5), scientific: true},
+ 'exi': {name: 'exi', value: Math.pow(1024, 6), scientific: true},
+ 'zebi': {name: 'zebi', value: Math.pow(1024, 7), scientific: true},
+ 'yobi': {name: 'yobi', value: Math.pow(1024, 8), scientific: true}
+ }
+ };
+
+ var PREFIX_NONE = {name: '', value: 1, scientific: true};
+
+ var BASE_UNITS = {
+ NONE: {},
+
+ LENGTH: {}, // meter
+ MASS: {}, // kilogram
+ TIME: {}, // second
+ CURRENT: {}, // ampere
+ TEMPERATURE: {}, // kelvin
+ LUMINOUS_INTENSITY: {}, // candela
+ AMOUNT_OF_SUBSTANCE: {}, // mole
+
+ FORCE: {}, // Newton
+ SURFACE: {}, // m2
+ VOLUME: {}, // m3
+ ANGLE: {}, // rad
+ BIT: {} // bit (digital)
+ };
+
+ var BASE_UNIT_NONE = {};
+
+ var UNIT_NONE = {name: '', base: BASE_UNIT_NONE, value: 1, offset: 0};
+
+ var UNITS = {
+ // length
+ meter: {name: 'meter', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.LONG, value: 1, offset: 0},
+ inch: {name: 'inch', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.0254, offset: 0},
+ foot: {name: 'foot', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.3048, offset: 0},
+ yard: {name: 'yard', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.9144, offset: 0},
+ mile: {name: 'mile', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 1609.344, offset: 0},
+ link: {name: 'link', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.201168, offset: 0},
+ rod: {name: 'rod', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 5.029210, offset: 0},
+ chain: {name: 'chain', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 20.1168, offset: 0},
+ angstrom: {name: 'angstrom', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 1e-10, offset: 0},
+
+ m: {name: 'm', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.SHORT, value: 1, offset: 0},
+ 'in': {name: 'in', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.0254, offset: 0},
+ ft: {name: 'ft', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.3048, offset: 0},
+ yd: {name: 'yd', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.9144, offset: 0},
+ mi: {name: 'mi', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 1609.344, offset: 0},
+ li: {name: 'li', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.201168, offset: 0},
+ rd: {name: 'rd', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 5.029210, offset: 0},
+ ch: {name: 'ch', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 20.1168, offset: 0},
+ mil: {name: 'mil', base: BASE_UNITS.LENGTH, prefixes: PREFIXES.NONE, value: 0.0000254, offset: 0}, // 1/1000 inch
+
+ // Surface
+ m2: {name: 'm2', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.SQUARED, value: 1, offset: 0},
+ sqin: {name: 'sqin', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 0.00064516, offset: 0}, // 645.16 mm2
+ sqft: {name: 'sqft', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 0.09290304, offset: 0}, // 0.09290304 m2
+ sqyd: {name: 'sqyd', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 0.83612736, offset: 0}, // 0.83612736 m2
+ sqmi: {name: 'sqmi', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 2589988.110336, offset: 0}, // 2.589988110336 km2
+ sqrd: {name: 'sqrd', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 25.29295, offset: 0}, // 25.29295 m2
+ sqch: {name: 'sqch', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 404.6873, offset: 0}, // 404.6873 m2
+ sqmil: {name: 'sqmil', base: BASE_UNITS.SURFACE, prefixes: PREFIXES.NONE, value: 6.4516e-10, offset: 0}, // 6.4516 * 10^-10 m2
+
+ // Volume
+ m3: {name: 'm3', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.CUBIC, value: 1, offset: 0},
+ L: {name: 'L', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.SHORT, value: 0.001, offset: 0}, // litre
+ l: {name: 'l', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.SHORT, value: 0.001, offset: 0}, // litre
+ litre: {name: 'litre', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.LONG, value: 0.001, offset: 0},
+ cuin: {name: 'cuin', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 1.6387064e-5, offset: 0}, // 1.6387064e-5 m3
+ cuft: {name: 'cuft', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.028316846592, offset: 0}, // 28.316 846 592 L
+ cuyd: {name: 'cuyd', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.764554857984, offset: 0}, // 764.554 857 984 L
+ teaspoon: {name: 'teaspoon', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.000005, offset: 0}, // 5 mL
+ tablespoon: {name: 'tablespoon', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.000015, offset: 0}, // 15 mL
+ //{name: 'cup', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.000240, offset: 0}, // 240 mL // not possible, we have already another cup
+ drop: {name: 'drop', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 5e-8, offset: 0}, // 0.05 mL = 5e-8 m3
+ gtt: {name: 'gtt', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 5e-8, offset: 0}, // 0.05 mL = 5e-8 m3
+
+ // Liquid volume
+ minim: {name: 'minim', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00000006161152, offset: 0}, // 0.06161152 mL
+ fluiddram: {name: 'fluiddram', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0000036966911, offset: 0}, // 3.696691 mL
+ fluidounce: {name: 'fluidounce', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00002957353, offset: 0}, // 29.57353 mL
+ gill: {name: 'gill', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0001182941, offset: 0}, // 118.2941 mL
+ cc: {name: 'cc', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 1e-6, offset: 0}, // 1e-6 L
+ cup: {name: 'cup', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0002365882, offset: 0}, // 236.5882 mL
+ pint: {name: 'pint', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0004731765, offset: 0}, // 473.1765 mL
+ quart: {name: 'quart', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0009463529, offset: 0}, // 946.3529 mL
+ gallon: {name: 'gallon', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.003785412, offset: 0}, // 3.785412 L
+ beerbarrel: {name: 'beerbarrel', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.1173478, offset: 0}, // 117.3478 L
+ oilbarrel: {name: 'oilbarrel', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.1589873, offset: 0}, // 158.9873 L
+ hogshead: {name: 'hogshead', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.2384810, offset: 0}, // 238.4810 L
+
+ //{name: 'min', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00000006161152, offset: 0}, // 0.06161152 mL // min is already in use as minute
+ fldr: {name: 'fldr', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0000036966911, offset: 0}, // 3.696691 mL
+ floz: {name: 'floz', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00002957353, offset: 0}, // 29.57353 mL
+ gi: {name: 'gi', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0001182941, offset: 0}, // 118.2941 mL
+ cp: {name: 'cp', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0002365882, offset: 0}, // 236.5882 mL
+ pt: {name: 'pt', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0004731765, offset: 0}, // 473.1765 mL
+ qt: {name: 'qt', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.0009463529, offset: 0}, // 946.3529 mL
+ gal: {name: 'gal', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.003785412, offset: 0}, // 3.785412 L
+ bbl: {name: 'bbl', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.1173478, offset: 0}, // 117.3478 L
+ obl: {name: 'obl', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.1589873, offset: 0}, // 158.9873 L
+ //{name: 'hogshead', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.2384810, offset: 0}, // 238.4810 L // TODO: hh?
+
+ // Mass
+ g: {name: 'g', base: BASE_UNITS.MASS, prefixes: PREFIXES.SHORT, value: 0.001, offset: 0},
+ gram: {name: 'gram', base: BASE_UNITS.MASS, prefixes: PREFIXES.LONG, value: 0.001, offset: 0},
+
+ ton: {name: 'ton', base: BASE_UNITS.MASS, prefixes: PREFIXES.SHORT, value: 907.18474, offset: 0},
+ tonne: {name: 'tonne', base: BASE_UNITS.MASS, prefixes: PREFIXES.SHORT, value: 1000, offset: 0},
+
+ grain: {name: 'grain', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 64.79891e-6, offset: 0},
+ dram: {name: 'dram', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 1.7718451953125e-3, offset: 0},
+ ounce: {name: 'ounce', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 28.349523125e-3, offset: 0},
+ poundmass: {name: 'poundmass', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 453.59237e-3, offset: 0},
+ hundredweight: {name: 'hundredweight', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 45.359237, offset: 0},
+ stick: {name: 'stick', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 115e-3, offset: 0},
+
+ gr: {name: 'gr', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 64.79891e-6, offset: 0},
+ dr: {name: 'dr', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 1.7718451953125e-3, offset: 0},
+ oz: {name: 'oz', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 28.349523125e-3, offset: 0},
+ lbm: {name: 'lbm', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 453.59237e-3, offset: 0},
+ cwt: {name: 'cwt', base: BASE_UNITS.MASS, prefixes: PREFIXES.NONE, value: 45.359237, offset: 0},
+
+ // Time
+ s: {name: 's', base: BASE_UNITS.TIME, prefixes: PREFIXES.SHORT, value: 1, offset: 0},
+ min: {name: 'min', base: BASE_UNITS.TIME, prefixes: PREFIXES.NONE, value: 60, offset: 0},
+ h: {name: 'h', base: BASE_UNITS.TIME, prefixes: PREFIXES.NONE, value: 3600, offset: 0},
+ second: {name: 'second', base: BASE_UNITS.TIME, prefixes: PREFIXES.LONG, value: 1, offset: 0},
+ sec: {name: 'sec', base: BASE_UNITS.TIME, prefixes: PREFIXES.LONG, value: 1, offset: 0},
+ minute: {name: 'minute', base: BASE_UNITS.TIME, prefixes: PREFIXES.NONE, value: 60, offset: 0},
+ hour: {name: 'hour', base: BASE_UNITS.TIME, prefixes: PREFIXES.NONE, value: 3600, offset: 0},
+ day: {name: 'day', base: BASE_UNITS.TIME, prefixes: PREFIXES.NONE, value: 86400, offset: 0},
+
+ // Angle
+ rad: {name: 'rad', base: BASE_UNITS.ANGLE, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ // deg = rad / (2*pi) * 360 = rad / 0.017453292519943295769236907684888
+ deg: {name: 'deg', base: BASE_UNITS.ANGLE, prefixes: PREFIXES.NONE, value: 0.017453292519943295769236907684888, offset: 0},
+ // grad = rad / (2*pi) * 400 = rad / 0.015707963267948966192313216916399
+ grad: {name: 'grad', base: BASE_UNITS.ANGLE, prefixes: PREFIXES.NONE, value: 0.015707963267948966192313216916399, offset: 0},
+ // cycle = rad / (2*pi) = rad / 6.2831853071795864769252867665793
+ cycle: {name: 'cycle', base: BASE_UNITS.ANGLE, prefixes: PREFIXES.NONE, value: 6.2831853071795864769252867665793, offset: 0},
+
+ // Electric current
+ A: {name: 'A', base: BASE_UNITS.CURRENT, prefixes: PREFIXES.SHORT, value: 1, offset: 0},
+ ampere: {name: 'ampere', base: BASE_UNITS.CURRENT, prefixes: PREFIXES.LONG, value: 1, offset: 0},
+
+ // Temperature
+ // K(C) = °C + 273.15
+ // K(F) = (°F + 459.67) / 1.8
+ // K(R) = °R / 1.8
+ K: {name: 'K', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ degC: {name: 'degC', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1, offset: 273.15},
+ degF: {name: 'degF', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1/1.8, offset: 459.67},
+ degR: {name: 'degR', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1/1.8, offset: 0},
+ kelvin: {name: 'kelvin', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ celsius: {name: 'celsius', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1, offset: 273.15},
+ fahrenheit: {name: 'fahrenheit', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1/1.8, offset: 459.67},
+ rankine: {name: 'rankine', base: BASE_UNITS.TEMPERATURE, prefixes: PREFIXES.NONE, value: 1/1.8, offset: 0},
+
+ // amount of substance
+ mol: {name: 'mol', base: BASE_UNITS.AMOUNT_OF_SUBSTANCE, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ mole: {name: 'mole', base: BASE_UNITS.AMOUNT_OF_SUBSTANCE, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+
+ // luminous intensity
+ cd: {name: 'cd', base: BASE_UNITS.LUMINOUS_INTENSITY, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ candela: {name: 'candela', base: BASE_UNITS.LUMINOUS_INTENSITY, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ // TODO: units STERADIAN
+ //{name: 'sr', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+ //{name: 'steradian', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},
+
+ // Force
+ N: {name: 'N', base: BASE_UNITS.FORCE, prefixes: PREFIXES.SHORT, value: 1, offset: 0},
+ newton: {name: 'newton', base: BASE_UNITS.FORCE, prefixes: PREFIXES.LONG, value: 1, offset: 0},
+ lbf: {name: 'lbf', base: BASE_UNITS.FORCE, prefixes: PREFIXES.NONE, value: 4.4482216152605, offset: 0},
+ poundforce: {name: 'poundforce', base: BASE_UNITS.FORCE, prefixes: PREFIXES.NONE, value: 4.4482216152605, offset: 0},
+
+ // Binary
+ b: {name: 'b', base: BASE_UNITS.BIT, prefixes: PREFIXES.BINARY_SHORT, value: 1, offset: 0},
+ bits: {name: 'bits', base: BASE_UNITS.BIT, prefixes: PREFIXES.BINARY_LONG, value: 1, offset: 0},
+ B: {name: 'B', base: BASE_UNITS.BIT, prefixes: PREFIXES.BINARY_SHORT, value: 8, offset: 0},
+ bytes: {name: 'bytes', base: BASE_UNITS.BIT, prefixes: PREFIXES.BINARY_LONG, value: 8, offset: 0}
+ };
+
+ // plurals
+ var PLURALS = {
+ meters: 'meter',
+ inches: 'inch',
+ feet: 'foot',
+ yards: 'yard',
+ miles: 'mile',
+ links: 'link',
+ rods: 'rod',
+ chains: 'chain',
+ angstroms: 'angstrom',
+
+ litres: 'litre',
+ teaspoons: 'teaspoon',
+ tablespoons: 'tablespoon',
+ minims: 'minim',
+ fluiddrams: 'fluiddram',
+ fluidounces: 'fluidounce',
+ gills: 'gill',
+ cups: 'cup',
+ pints: 'pint',
+ quarts: 'quart',
+ gallons: 'gallon',
+ beerbarrels: 'beerbarrel',
+ oilbarrels: 'oilbarrel',
+ hogsheads: 'hogshead',
+ gtts: 'gtt',
+
+ grams: 'gram',
+ tons: 'ton',
+ tonnes: 'tonne',
+ grains: 'grain',
+ drams: 'dram',
+ ounces: 'ounce',
+ poundmasses: 'poundmass',
+ hundredweights: 'hundredweight',
+ sticks: 'stick',
+
+ seconds: 'second',
+ minutes: 'minute',
+ hours: 'hour',
+ days: 'day',
+
+ radians: 'rad',
+ degrees: 'deg',
+ gradients: 'grad',
+ cycles: 'cycle',
+
+ amperes: 'ampere',
+ moles: 'mole'
+ };
+
+ for (var name in PLURALS) {
+ /* istanbul ignore next (we cannot really test next statement) */
+ if (PLURALS.hasOwnProperty(name)) {
+ var unit = UNITS[PLURALS[name]];
+ var plural = Object.create(unit);
+ plural.name = name;
+ UNITS[name] = plural;
+ }
+ }
+
+ // aliases
+ UNITS.lt = UNITS.l;
+ UNITS.liter = UNITS.litre;
+ UNITS.liters = UNITS.litres;
+ UNITS.lb = UNITS.lbm;
+ UNITS.lbs = UNITS.lbm;
+
+
+ Unit.PREFIXES = PREFIXES;
+ Unit.BASE_UNITS = BASE_UNITS;
+ Unit.UNITS = UNITS;
+
+ // end of unit aliases
+
+
+ // exports
+ module.exports = Unit;
+
+
+/***/ },
+/* 12 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171);
+ var object = util.object;
+ var string = util.string;
+
+ /**
+ * Documentation object
+ * @param {Object} doc Object containing properties:
+ * {String} name
+ * {String} category
+ * {String} description
+ * {String[]} syntax
+ * {String[]} examples
+ * {String[]} seealso
+ * @constructor
+ */
+ function Help (doc) {
+ if (!(this instanceof Help)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ if (!doc) throw new Error('Argument "doc" missing');
+
+ this.doc = doc;
+ }
+
+ /**
+ * Test whether a value is an instance of Help
+ * @param {*} value
+ * @return {Boolean} isHelp
+ */
+ Help.isHelp = function (value) {
+ return (value instanceof Help);
+ };
+
+ /**
+ * Generate readable description from a Help object
+ * @param {Object} [math] A math instance, used to evaluate the examples
+ * @return {String} readableDoc
+ * @private
+ */
+ Help.prototype.toText = function (math) {
+ var doc = this.doc || {};
+ var desc = '\n';
+
+ if (doc.name) {
+ desc += 'Name: ' + doc.name + '\n\n';
+ }
+ if (doc.category) {
+ desc += 'Category: ' + doc.category + '\n\n';
+ }
+ if (doc.description) {
+ desc += 'Description:\n ' + doc.description + '\n\n';
+ }
+ if (doc.syntax) {
+ desc += 'Syntax:\n ' + doc.syntax.join('\n ') + '\n\n';
+ }
+ if (doc.examples) {
+ var parser = math && math.parser();
+ desc += 'Examples:\n';
+ for (var i = 0; i < doc.examples.length; i++) {
+ var expr = doc.examples[i];
+ desc += ' ' + expr + '\n';
+
+ if (parser) {
+ var res;
+ try {
+ res = parser.eval(expr);
+ }
+ catch (e) {
+ res = e;
+ }
+ if (res !== undefined && !(res instanceof Help)) {
+ desc += ' ' + string.format(res, {precision: 14}) + '\n';
+ }
+ }
+ }
+ desc += '\n';
+ }
+ if (doc.seealso) {
+ desc += 'See also: ' + doc.seealso.join(', ') + '\n';
+ }
+
+ return desc;
+ };
+
+ /**
+ * Generate a string representation of the Help object
+ * @return {String} Returns a string
+ * @private
+ */
+ Help.prototype.toString = function () {
+ return this.toText();
+ };
+
+ /**
+ * Export the help object to JSON
+ */
+ Help.prototype.toJSON = function () {
+ var obj = object.clone(this.doc);
+ obj.mathjs = 'Help';
+ return obj;
+ };
+
+ /**
+ * Instantiate a Help object from a JSON object
+ * @param {Object} json
+ * @returns {Help} Returns a new Help object
+ */
+ Help.fromJSON = function (json) {
+ var doc = {};
+ for (var prop in json) {
+ if (prop !== 'mathjs') { // ignore mathjs field
+ doc[prop] = json[prop];
+ }
+ }
+ return new Help(doc);
+ };
+
+ /**
+ * Returns a string representation of the Help object
+ */
+ Help.prototype.valueOf = Help.prototype.toString;
+
+ // exports
+ module.exports = Help;
+
+
+/***/ },
+/* 13 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ /**
+ * A ResultSet contains a list or results
+ * @param {Array} entries
+ * @constructor
+ */
+ function ResultSet(entries) {
+ if (!(this instanceof ResultSet)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ this.entries = entries || [];
+ }
+
+ /**
+ * Returns the array with results hold by this ResultSet
+ * @returns {Array} entries
+ */
+ ResultSet.prototype.valueOf = function () {
+ return this.entries;
+ };
+
+ /**
+ * Returns the stringified results of the ResultSet
+ * @returns {String} string
+ */
+ ResultSet.prototype.toString = function () {
+ return '[' + this.entries.join(', ') + ']';
+ };
+
+ /**
+ * Get a JSON representation of the ResultSet
+ * @returns {Object} Returns a JSON object structured as:
+ * `{"mathjs": "ResultSet", "entries": [...]}`
+ */
+ ResultSet.prototype.toJSON = function () {
+ return {
+ mathjs: 'ResultSet',
+ entries: this.entries
+ };
+ };
+
+ /**
+ * Instantiate a ResultSet from a JSON object
+ * @param {Object} json A JSON object structured as:
+ * `{"mathjs": "ResultSet", "entries": [...]}`
+ * @return {ResultSet}
+ */
+ ResultSet.fromJSON = function (json) {
+ return new ResultSet(json.entries);
+ };
+
+ module.exports = ResultSet;
+
+
+/***/ },
+/* 14 */
+/***/ function(module, exports, __webpack_require__) {
+
+ // utility methods for arrays and matrices
+ 'use strict';
+
+ var util = __webpack_require__(171),
+
+ IndexError = __webpack_require__(169),
+ DimensionError = __webpack_require__(168),
+
+ Matrix = __webpack_require__(10),
+
+ array = util.array,
+ isArray = util.array.isArray,
+ isString = util.string.isString;
+
+ /**
+ * Convert function arguments to an array. Arguments can have the following
+ * signature:
+ * fn()
+ * fn(n)
+ * fn(m, n, p, ...)
+ * fn([m, n, p, ...])
+ * @param {...Number | Array | Matrix} args
+ * @returns {Array} array
+ */
+ exports.argsToArray = function(args) {
+ if (args.length == 0) {
+ // fn()
+ return [];
+ }
+ else if (args.length == 1) {
+ // fn(n)
+ // fn([m, n, p, ...])
+ var array = args[0];
+ if (array instanceof Matrix) {
+ array = array.valueOf();
+ }
+ if (!isArray(array)) {
+ array = [array];
+ }
+ return array;
+ }
+ else {
+ // fn(m, n, p, ...)
+ return util.array.argsToArray(args);
+ }
+ };
+
+
+ /**
+ * Test whether a value is a collection: an Array or Matrix
+ * @param {*} x
+ * @returns {boolean} isCollection
+ */
+ exports.isCollection = function(x) {
+ return (isArray(x) || (x instanceof Matrix));
+ };
+
+ /**
+ * Execute the callback function element wise for each element in array and any
+ * nested array
+ * Returns an array with the results
+ * @param {Array | Matrix} array
+ * @param {function} callback The callback is called with two parameters:
+ * value1 and value2, which contain the current
+ * element of both arrays.
+ * @return {Array | Matrix} res
+ */
+ exports.deepMap = function deepMap(array, callback) {
+ if (array && (typeof array.map === 'function')) {
+ return array.map(function (x) {
+ return deepMap(x, callback);
+ });
+ }
+ else {
+ return callback(array);
+ }
+ };
+
+ /**
+ * Execute the callback function element wise for each entry in two given arrays,
+ * and for any nested array. Objects can also be scalar objects.
+ * Returns an array with the results.
+ * @param {Array | Matrix | Object} array1
+ * @param {Array | Matrix | Object} array2
+ * @param {function} callback The callback is called with two parameters:
+ * value1 and value2, which contain the current
+ * element of both arrays.
+ * @return {Array | Matrix} res
+ */
+ exports.deepMap2 = function deepMap2(array1, array2, callback) {
+ var res, len, i;
+
+ if (isArray(array1)) {
+ if (isArray(array2)) {
+ // callback(array, array)
+ if (array1.length != array2.length) {
+ throw new DimensionError(array1.length, array2.length);
+ }
+
+ res = [];
+ len = array1.length;
+ for (i = 0; i < len; i++) {
+ res[i] = deepMap2(array1[i], array2[i], callback);
+ }
+ }
+ else if (array2 instanceof Matrix) {
+ // callback(array, matrix)
+ res = deepMap2(array1, array2.valueOf(), callback);
+ return new Matrix(res);
+ }
+ else {
+ // callback(array, object)
+ res = [];
+ len = array1.length;
+ for (i = 0; i < len; i++) {
+ res[i] = deepMap2(array1[i], array2, callback);
+ }
+ }
+ }
+ else if (array1 instanceof Matrix) {
+ if (array2 instanceof Matrix) {
+ // callback(matrix, matrix)
+ res = deepMap2(array1.valueOf(), array2.valueOf(), callback);
+ return new Matrix(res);
+ }
+ else {
+ // callback(matrix, array)
+ // callback(matrix, object)
+ res = deepMap2(array1.valueOf(), array2, callback);
+ return new Matrix(res);
+ }
+ }
+ else {
+ if (isArray(array2)) {
+ // callback(object, array)
+ res = [];
+ len = array2.length;
+ for (i = 0; i < len; i++) {
+ res[i] = deepMap2(array1, array2[i], callback);
+ }
+ }
+ else if (array2 instanceof Matrix) {
+ // callback(object, matrix)
+ res = deepMap2(array1, array2.valueOf(), callback);
+ return new Matrix(res);
+ }
+ else {
+ // callback(object, object)
+ res = callback(array1, array2);
+ }
+ }
+
+ return res;
+ };
+
+ /**
+ * Reduce a given matrix or array to a new matrix or
+ * array with one less dimension, applying the given
+ * callback in the selected dimension.
+ * @param {Array | Matrix} mat
+ * @param {Number} dim
+ * @param {function} callback
+ * @return {Array | Matrix} res
+ */
+ exports.reduce = function(mat, dim, callback) {
+ var size = isArray(mat) ? array.size(mat) : mat.size();
+ if (dim < 0) {
+ // TODO: would be more clear when throwing a DimensionError here
+ throw new IndexError(dim);
+ }
+ if (dim >= size.length) {
+ // TODO: would be more clear when throwing a DimensionError here
+ throw new IndexError(dim, size.length);
+ }
+
+ if (mat instanceof Matrix) {
+ return new Matrix(_reduce(mat.valueOf(), dim, callback));
+ }else {
+ return _reduce(mat, dim, callback);
+ }
+ };
+
+ /**
+ * Recursively reduce a matrix
+ * @param {Array} mat
+ * @param {Number} dim
+ * @param {Function} callback
+ * @returns {Array} ret
+ * @private
+ */
+ function _reduce(mat, dim, callback){
+ var i, ret, val, tran;
+
+ if(dim<=0){
+ if( !isArray(mat[0]) ){
+ val = mat[0];
+ for(i=1; i<mat.length; i++){
+ val = callback(val, mat[i]);
+ }
+ return val;
+ }else{
+ tran = _switch(mat);
+ ret = [];
+ for(i=0; i<tran.length; i++){
+ ret[i] = _reduce(tran[i], dim-1, callback);
+ }
+ return ret
+ }
+ }else{
+ ret = [];
+ for(i=0; i<mat.length; i++){
+ ret[i] = _reduce(mat[i], dim-1, callback);
+ }
+ return ret;
+ }
+ }
+
+ /**
+ * Transpose a matrix
+ * @param {Array} mat
+ * @returns {Array} ret
+ * @private
+ */
+ function _switch(mat){
+ var I = mat.length;
+ var J = mat[0].length;
+ var i, j;
+ var ret = [];
+ for( j=0; j<J; j++) {
+ var tmp = [];
+ for( i=0; i<I; i++) {
+ tmp.push(mat[i][j]);
+ }
+ ret.push(tmp);
+ }
+ return ret;
+ }
+
+ /**
+ * Recursively loop over all elements in a given multi dimensional array
+ * and invoke the callback on each of the elements.
+ * @param {Array | Matrix} array
+ * @param {function} callback The callback method is invoked with one
+ * parameter: the current element in the array
+ */
+ exports.deepForEach = function deepForEach (array, callback) {
+ if (array instanceof Matrix) {
+ array = array.valueOf();
+ }
+
+ for (var i = 0, ii = array.length; i < ii; i++) {
+ var value = array[i];
+
+ if (isArray(value)) {
+ deepForEach(value, callback);
+ }
+ else {
+ callback(value);
+ }
+ }
+ };
+
+
+/***/ },
+/* 15 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ exports.ArrayNode = __webpack_require__(172);
+ exports.AssignmentNode = __webpack_require__(173);
+ exports.BlockNode = __webpack_require__(174);
+ exports.ConditionalNode = __webpack_require__(175);
+ exports.ConstantNode = __webpack_require__(176);
+ exports.IndexNode = __webpack_require__(177);
+ exports.FunctionAssignmentNode = __webpack_require__(178);
+ exports.FunctionNode = __webpack_require__(179);
+ exports.Node = __webpack_require__(180);
+ exports.OperatorNode = __webpack_require__(181);
+ exports.RangeNode = __webpack_require__(182);
+ exports.SymbolNode = __webpack_require__(183);
+ exports.UpdateNode = __webpack_require__(184);
+
+
+/***/ },
+/* 16 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var util = __webpack_require__(171),
+
+ ArgumentsError = __webpack_require__(167),
+
+ isString = util.string.isString,
+ isArray = Array.isArray,
+ type = util.types.type,
+
+ // types
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ // scope and nodes
+ ArrayNode = __webpack_require__(172),
+ AssignmentNode = __webpack_require__(173),
+ BlockNode = __webpack_require__(174),
+ ConditionalNode = __webpack_require__(175),
+ ConstantNode = __webpack_require__(176),
+ FunctionAssignmentNode = __webpack_require__(178),
+ IndexNode = __webpack_require__(177),
+ OperatorNode = __webpack_require__(181),
+ FunctionNode = __webpack_require__(179),
+ RangeNode = __webpack_require__(182),
+ SymbolNode = __webpack_require__(183),
+ UpdateNode = __webpack_require__(184);
+
+ /**
+ * Parse an expression. Returns a node tree, which can be evaluated by
+ * invoking node.eval();
+ *
+ * Syntax:
+ *
+ * parse(expr)
+ * parse(expr, options)
+ * parse([expr1, expr2, expr3, ...])
+ * parse([expr1, expr2, expr3, ...], options)
+ *
+ * Example:
+ *
+ * var node = parse('sqrt(3^2 + 4^2)');
+ * node.compile(math).eval(); // 5
+ *
+ * var scope = {a:3, b:4}
+ * var node = parse('a * b'); // 12
+ * var code = node.compile(math);
+ * code.eval(scope); // 12
+ * scope.a = 5;
+ * code.eval(scope); // 20
+ *
+ * var nodes = math.parse(['a = 3', 'b = 4', 'a * b']);
+ * nodes[2].compile(math).eval(); // 12
+ *
+ * @param {String | String[] | Matrix} expr
+ * @param {{nodes: Object<String, Node>}} [options] Available options:
+ * - `nodes` a set of custom nodes
+ * @return {Node | Node[]} node
+ * @throws {Error}
+ */
+ function parse (expr, options) {
+ if (arguments.length != 1 && arguments.length != 2) {
+ throw new ArgumentsError('parse', arguments.length, 1, 2);
+ }
+
+ // pass extra nodes
+ extra_nodes = (options && options.nodes) ? options.nodes : {};
+
+ if (isString(expr)) {
+ // parse a single expression
+ expression = expr;
+ return parseStart();
+ }
+ else if (isArray(expr) || expr instanceof Matrix) {
+ // parse an array or matrix with expressions
+ return collection.deepMap(expr, function (elem) {
+ if (!isString(elem)) throw new TypeError('String expected');
+
+ expression = elem;
+ return parseStart();
+ });
+ }
+ else {
+ // oops
+ throw new TypeError('String or matrix expected');
+ }
+ }
+
+ // token types enumeration
+ var TOKENTYPE = {
+ NULL : 0,
+ DELIMITER : 1,
+ NUMBER : 2,
+ SYMBOL : 3,
+ UNKNOWN : 4
+ };
+
+ // map with all delimiters
+ var DELIMITERS = {
+ ',': true,
+ '(': true,
+ ')': true,
+ '[': true,
+ ']': true,
+ '\"': true,
+ ';': true,
+
+ '+': true,
+ '-': true,
+ '*': true,
+ '.*': true,
+ '/': true,
+ './': true,
+ '%': true,
+ '^': true,
+ '.^': true,
+ '~': true,
+ '!': true,
+ '&': true,
+ '|': true,
+ '^|': true,
+ '\'': true,
+ '=': true,
+ ':': true,
+ '?': true,
+
+ '==': true,
+ '!=': true,
+ '<': true,
+ '>': true,
+ '<=': true,
+ '>=': true,
+
+ '<<': true,
+ '>>': true,
+ '>>>': true
+ };
+
+ // map with all named delimiters
+ var NAMED_DELIMITERS = {
+ 'mod': true,
+ 'to': true,
+ 'in': true,
+ 'and': true,
+ 'xor': true,
+ 'or': true,
+ 'not': true
+ };
+
+ var extra_nodes = {}; // current extra nodes
+ var expression = ''; // current expression
+ var index = 0; // current index in expr
+ var c = ''; // current token character in expr
+ var token = ''; // current token
+ var token_type = TOKENTYPE.NULL; // type of the token
+ var nesting_level = 0; // level of nesting inside parameters, used to ignore newline characters
+ var conditional_level = null; // when a conditional is being parsed, the level of the conditional is stored here
+
+ /**
+ * Get the first character from the expression.
+ * The character is stored into the char c. If the end of the expression is
+ * reached, the function puts an empty string in c.
+ * @private
+ */
+ function first() {
+ index = 0;
+ c = expression.charAt(0);
+ nesting_level = 0;
+ conditional_level = null;
+ }
+
+ /**
+ * Get the next character from the expression.
+ * The character is stored into the char c. If the end of the expression is
+ * reached, the function puts an empty string in c.
+ * @private
+ */
+ function next() {
+ index++;
+ c = expression.charAt(index);
+ }
+
+ /**
+ * Preview the next character from the expression.
+ * @return {String} cNext
+ * @private
+ */
+ function nextPreview() {
+ return expression.charAt(index + 1);
+ }
+
+ /**
+ * Preview the second next character from the expression.
+ * @return {String} cNext
+ * @private
+ */
+ function nextNextPreview() {
+ return expression.charAt(index + 2);
+ }
+
+ /**
+ * Get next token in the current string expr.
+ * The token and token type are available as token and token_type
+ * @private
+ */
+ function getToken() {
+ token_type = TOKENTYPE.NULL;
+ token = '';
+
+ // skip over whitespaces
+ // space, tab, and newline when inside parameters
+ while (c == ' ' || c == '\t' || (c == '\n' && nesting_level)) {
+ // TODO: also take '\r' carriage return as newline? Or does that give problems on mac?
+ next();
+ }
+
+ // skip comment
+ if (c == '#') {
+ while (c != '\n' && c != '') {
+ next();
+ }
+ }
+
+ // check for end of expression
+ if (c == '') {
+ // token is still empty
+ token_type = TOKENTYPE.DELIMITER;
+ return;
+ }
+
+ // check for new line character
+ if (c == '\n' && !nesting_level) {
+ token_type = TOKENTYPE.DELIMITER;
+ token = c;
+ next();
+ return;
+ }
+
+ // check for delimiters consisting of 3 characters
+ var c2 = c + nextPreview();
+ var c3 = c2 + nextNextPreview();
+ if (c3.length == 3 && DELIMITERS[c3]) {
+ token_type = TOKENTYPE.DELIMITER;
+ token = c3;
+ next();
+ next();
+ next();
+ return;
+ }
+
+ // check for delimiters consisting of 2 characters
+ if (c2.length == 2 && DELIMITERS[c2]) {
+ token_type = TOKENTYPE.DELIMITER;
+ token = c2;
+ next();
+ next();
+ return;
+ }
+
+ // check for delimiters consisting of 1 character
+ if (DELIMITERS[c]) {
+ token_type = TOKENTYPE.DELIMITER;
+ token = c;
+ next();
+ return;
+ }
+
+ // check for a number
+ if (isDigitDot(c)) {
+ token_type = TOKENTYPE.NUMBER;
+
+ // get number, can have a single dot
+ if (c == '.') {
+ token += c;
+ next();
+
+ if (!isDigit(c)) {
+ // this is no legal number, it is just a dot
+ token_type = TOKENTYPE.UNKNOWN;
+ }
+ }
+ else {
+ while (isDigit(c)) {
+ token += c;
+ next();
+ }
+ if (c == '.') {
+ token += c;
+ next();
+ }
+ }
+ while (isDigit(c)) {
+ token += c;
+ next();
+ }
+
+ // check for exponential notation like "2.3e-4", "1.23e50" or "2e+4"
+ c2 = nextPreview();
+ if ((c == 'E' || c == 'e') && (isDigit(c2) || c2 == '-' || c2 == '+')) {
+ token += c;
+ next();
+
+ if (c == '+' || c == '-') {
+ token += c;
+ next();
+ }
+
+ // Scientific notation MUST be followed by an exponent
+ if (!isDigit(c)) {
+ // this is no legal number, exponent is missing.
+ token_type = TOKENTYPE.UNKNOWN;
+ }
+
+ while (isDigit(c)) {
+ token += c;
+ next();
+ }
+ }
+
+ return;
+ }
+
+ // check for variables, functions, named operators
+ if (isAlpha(c)) {
+ while (isAlpha(c) || isDigit(c)) {
+ token += c;
+ next();
+ }
+
+ if (NAMED_DELIMITERS[token]) {
+ token_type = TOKENTYPE.DELIMITER;
+ }
+ else {
+ token_type = TOKENTYPE.SYMBOL;
+ }
+
+ return;
+ }
+
+ // something unknown is found, wrong characters -> a syntax error
+ token_type = TOKENTYPE.UNKNOWN;
+ while (c != '') {
+ token += c;
+ next();
+ }
+ throw createSyntaxError('Syntax error in part "' + token + '"');
+ }
+
+ /**
+ * Get next token and skip newline tokens
+ */
+ function getTokenSkipNewline () {
+ do {
+ getToken();
+ }
+ while (token == '\n');
+ }
+
+ /**
+ * Open parameters.
+ * New line characters will be ignored until closeParams() is called
+ */
+ function openParams() {
+ nesting_level++;
+ }
+
+ /**
+ * Close parameters.
+ * New line characters will no longer be ignored
+ */
+ function closeParams() {
+ nesting_level--;
+ }
+
+ /**
+ * checks if the given char c is a letter (upper or lower case)
+ * or underscore
+ * @param {String} c a string with one character
+ * @return {Boolean}
+ * @private
+ */
+ function isAlpha (c) {
+ return ((c >= 'a' && c <= 'z') ||
+ (c >= 'A' && c <= 'Z') ||
+ c == '_');
+ }
+
+ /**
+ * checks if the given char c is a digit or dot
+ * @param {String} c a string with one character
+ * @return {Boolean}
+ * @private
+ */
+ function isDigitDot (c) {
+ return ((c >= '0' && c <= '9') ||
+ c == '.');
+ }
+
+ /**
+ * checks if the given char c is a digit
+ * @param {String} c a string with one character
+ * @return {Boolean}
+ * @private
+ */
+ function isDigit (c) {
+ return ((c >= '0' && c <= '9'));
+ }
+
+ /**
+ * Start of the parse levels below, in order of precedence
+ * @return {Node} node
+ * @private
+ */
+ function parseStart () {
+ // get the first character in expression
+ first();
+
+ getToken();
+
+ var node = parseBlock();
+
+ // check for garbage at the end of the expression
+ // an expression ends with a empty character '' and token_type DELIMITER
+ if (token != '') {
+ if (token_type == TOKENTYPE.DELIMITER) {
+ // user entered a not existing operator like "//"
+
+ // TODO: give hints for aliases, for example with "<>" give as hint " did you mean != ?"
+ throw createError('Unexpected operator ' + token);
+ }
+ else {
+ throw createSyntaxError('Unexpected part "' + token + '"');
+ }
+ }
+
+ return node;
+ }
+
+ /**
+ * Parse a block with expressions. Expressions can be separated by a newline
+ * character '\n', or by a semicolon ';'. In case of a semicolon, no output
+ * of the preceding line is returned.
+ * @return {Node} node
+ * @private
+ */
+ function parseBlock () {
+ var node;
+ var blocks = [];
+ var visible;
+
+ if (token == '') {
+ // empty expression
+ return new ConstantNode('undefined', 'undefined');
+ }
+
+ if (token != '\n' && token != ';') {
+ node = parseFunctionAssignment();
+ }
+
+ // TODO: simplify this loop
+ while (token == '\n' || token == ';') {
+ if (blocks.length == 0 && node) {
+ visible = (token != ';');
+ blocks.push({
+ node: node,
+ visible: visible
+ });
+ }
+
+ getToken();
+ if (token != '\n' && token != ';' && token != '') {
+ node = parseFunctionAssignment();
+
+ visible = (token != ';');
+ blocks.push({
+ node: node,
+ visible: visible
+ });
+ }
+ }
+
+ if (blocks.length > 0) {
+ return new BlockNode(blocks);
+ }
+ else {
+ return node;
+ }
+ }
+
+ /**
+ * Parse a function assignment like "function f(a,b) = a*b"
+ * @return {Node} node
+ * @private
+ */
+ function parseFunctionAssignment () {
+ // TODO: function assignment using keyword 'function' is deprecated since version 0.18.0, cleanup some day
+ if (token_type == TOKENTYPE.SYMBOL && token == 'function') {
+ throw createSyntaxError('Deprecated keyword "function". ' +
+ 'Functions can now be assigned without it, like "f(x) = x^2".');
+ }
+
+ return parseAssignment();
+ }
+
+ /**
+ * Assignment of a variable, can be a variable like "a=2.3" or a updating an
+ * existing variable like "matrix(2,3:5)=[6,7,8]"
+ * @return {Node} node
+ * @private
+ */
+ function parseAssignment () {
+ var name, args, expr, valid;
+
+ var node = parseConditional();
+
+ if (token == '=') {
+ if (node instanceof SymbolNode) {
+ // parse a variable assignment like 'a = 2/3'
+ name = node.name;
+ getTokenSkipNewline();
+ expr = parseAssignment();
+ return new AssignmentNode(name, expr);
+ }
+ else if (node instanceof IndexNode) {
+ // parse a matrix subset assignment like 'A[1,2] = 4'
+ getTokenSkipNewline();
+ expr = parseAssignment();
+ return new UpdateNode(node, expr);
+ }
+ else if (node instanceof FunctionNode) {
+ // parse function assignment like 'f(x) = x^2'
+ valid = true;
+ args = [];
+
+ name = node.name;
+ node.args.forEach(function (arg, index) {
+ if (arg instanceof SymbolNode) {
+ args[index] = arg.name;
+ }
+ else {
+ valid = false;
+ }
+ });
+
+ if (valid) {
+ getTokenSkipNewline();
+ expr = parseAssignment();
+ return new FunctionAssignmentNode(name, args, expr);
+ }
+ }
+
+ throw createSyntaxError('Invalid left hand side of assignment operator =');
+ }
+
+ return node;
+ }
+
+ /**
+ * conditional operation
+ *
+ * condition ? truePart : falsePart
+ *
+ * Note: conditional operator is right-associative
+ *
+ * @return {Node} node
+ * @private
+ */
+ function parseConditional () {
+ var node = parseLogicalOr();
+
+ while (token == '?') {
+ // set a conditional level, the range operator will be ignored as long
+ // as conditional_level == nesting_level.
+ var prev = conditional_level;
+ conditional_level = nesting_level;
+ getTokenSkipNewline();
+
+ var condition = node;
+ var trueExpr = parseLogicalOr();
+
+ if (token != ':') throw createSyntaxError('False part of conditional expression expected');
+
+ conditional_level = null;
+ getTokenSkipNewline();
+
+ var falseExpr = parseConditional(); // Note: check for conditional operator again, right associativity
+
+ node = new ConditionalNode(condition, trueExpr, falseExpr);
+
+ // restore the previous conditional level
+ conditional_level = prev;
+ }
+
+ return node;
+ }
+
+ /**
+ * logical or, 'x or y'
+ * @return {Node} node
+ * @private
+ */
+ function parseLogicalOr() {
+ var node = parseLogicalXor();
+
+ while (token == 'or') {
+ getTokenSkipNewline();
+ node = new OperatorNode('or', 'or', [node, parseLogicalXor()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * logical exclusive or, 'x xor y'
+ * @return {Node} node
+ * @private
+ */
+ function parseLogicalXor() {
+ var node = parseLogicalAnd();
+
+ while (token == 'xor') {
+ getTokenSkipNewline();
+ node = new OperatorNode('xor', 'xor', [node, parseLogicalAnd()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * logical and, 'x and y'
+ * @return {Node} node
+ * @private
+ */
+ function parseLogicalAnd() {
+ var node = parseBitwiseOr();
+
+ while (token == 'and') {
+ getTokenSkipNewline();
+ node = new OperatorNode('and', 'and', [node, parseBitwiseOr()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * bitwise or, 'x | y'
+ * @return {Node} node
+ * @private
+ */
+ function parseBitwiseOr() {
+ var node = parseBitwiseXor();
+
+ while (token == '|') {
+ getTokenSkipNewline();
+ node = new OperatorNode('|', 'bitOr', [node, parseBitwiseXor()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * bitwise exclusive or (xor), 'x ^| y'
+ * @return {Node} node
+ * @private
+ */
+ function parseBitwiseXor() {
+ var node = parseBitwiseAnd();
+
+ while (token == '^|') {
+ getTokenSkipNewline();
+ node = new OperatorNode('^|', 'bitXor', [node, parseBitwiseAnd()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * bitwise and, 'x & y'
+ * @return {Node} node
+ * @private
+ */
+ function parseBitwiseAnd () {
+ var node = parseRelational();
+
+ while (token == '&') {
+ getTokenSkipNewline();
+ node = new OperatorNode('&', 'bitAnd', [node, parseRelational()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * relational operators
+ * @return {Node} node
+ * @private
+ */
+ function parseRelational () {
+ var node, operators, name, fn, params;
+
+ node = parseShift();
+
+ operators = {
+ '==': 'equal',
+ '!=': 'unequal',
+ '<': 'smaller',
+ '>': 'larger',
+ '<=': 'smallerEq',
+ '>=': 'largerEq'
+ };
+ while (token in operators) {
+ name = token;
+ fn = operators[name];
+
+ getTokenSkipNewline();
+ params = [node, parseShift()];
+ node = new OperatorNode(name, fn, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * Bitwise left shift, bitwise right arithmetic shift, bitwise right logical shift
+ * @return {Node} node
+ * @private
+ */
+ function parseShift () {
+ var node, operators, name, fn, params;
+
+ node = parseConversion();
+
+ operators = {
+ '<<' : 'leftShift',
+ '>>' : 'rightArithShift',
+ '>>>' : 'rightLogShift'
+ };
+
+ while (token in operators) {
+ name = token;
+ fn = operators[name];
+
+ getTokenSkipNewline();
+ params = [node, parseConversion()];
+ node = new OperatorNode(name, fn, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * conversion operators 'to' and 'in'
+ * @return {Node} node
+ * @private
+ */
+ function parseConversion () {
+ var node, operators, name, fn, params;
+
+ node = parseRange();
+
+ operators = {
+ 'to' : 'to',
+ 'in' : 'to' // alias of 'to'
+ };
+
+ while (token in operators) {
+ name = token;
+ fn = operators[name];
+
+ getTokenSkipNewline();
+ params = [node, parseRange()];
+ node = new OperatorNode(name, fn, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * parse range, "start:end", "start:step:end", ":", "start:", ":end", etc
+ * @return {Node} node
+ * @private
+ */
+ function parseRange () {
+ var node, params = [];
+
+ if (token == ':') {
+ // implicit start=1 (one-based)
+ node = new ConstantNode('1', 'number');
+ }
+ else {
+ // explicit start
+ node = parseAddSubtract();
+ }
+
+ if (token == ':' && (conditional_level !== nesting_level)) {
+ // we ignore the range operator when a conditional operator is being processed on the same level
+ params.push(node);
+
+ // parse step and end
+ while (token == ':' && params.length < 3) {
+ getTokenSkipNewline();
+
+ if (token == ')' || token == ']' || token == ',' || token == '') {
+ // implicit end
+ params.push(new SymbolNode('end'));
+ }
+ else {
+ // explicit end
+ params.push(parseAddSubtract());
+ }
+ }
+
+ if (params.length == 3) {
+ // params = [start, step, end]
+ node = new RangeNode(params[0], params[2], params[1]); // start, end, step
+ }
+ else { // length == 2
+ // params = [start, end]
+ node = new RangeNode(params[0], params[1]); // start, end
+ }
+ }
+
+ return node;
+ }
+
+ /**
+ * add or subtract
+ * @return {Node} node
+ * @private
+ */
+ function parseAddSubtract () {
+ var node, operators, name, fn, params;
+
+ node = parseMultiplyDivide();
+
+ operators = {
+ '+': 'add',
+ '-': 'subtract'
+ };
+ while (token in operators) {
+ name = token;
+ fn = operators[name];
+
+ getTokenSkipNewline();
+ params = [node, parseMultiplyDivide()];
+ node = new OperatorNode(name, fn, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * multiply, divide, modulus
+ * @return {Node} node
+ * @private
+ */
+ function parseMultiplyDivide () {
+ var node, operators, name, fn, params;
+
+ node = parseUnary();
+
+ operators = {
+ '*': 'multiply',
+ '.*': 'dotMultiply',
+ '/': 'divide',
+ './': 'dotDivide',
+ '%': 'mod',
+ 'mod': 'mod'
+ };
+
+ if (token in operators) {
+ while (token in operators) {
+ name = token;
+ fn = operators[name];
+
+ getTokenSkipNewline();
+ params = [node, parseUnary()];
+ node = new OperatorNode(name, fn, params);
+ }
+ }
+
+ // parse implicit multiplication
+ if ((token_type == TOKENTYPE.SYMBOL) ||
+ (token == 'in' && (node instanceof ConstantNode)) ||
+ (token_type == TOKENTYPE.NUMBER && !(node instanceof ConstantNode)) ||
+ (token == '(' || token == '[')) {
+ // symbol: implicit multiplication like '2a', '(2+3)a', 'a b'
+ // number: implicit multiplication like '(2+3)2'
+ // Note: we don't allow implicit multiplication between numbers,
+ // like '2 3'. I'm not sure whether that is a good idea.
+ // parenthesis: implicit multiplication like '2(3+4)', '(3+4)(1+2)', '2[1,2,3]'
+ node = new OperatorNode('*', 'multiply', [node, parseMultiplyDivide()]);
+ }
+
+ return node;
+ }
+
+ /**
+ * Unary plus and minus, and logical and bitwise not
+ * @return {Node} node
+ * @private
+ */
+ function parseUnary () {
+ var name, params;
+ var fn = {
+ '-': 'unaryMinus',
+ '+': 'unaryPlus',
+ '~': 'bitNot',
+ 'not': 'not'
+ }[token];
+
+ if (fn) {
+ name = token;
+
+ getTokenSkipNewline();
+ params = [parseUnary()];
+
+ return new OperatorNode(name, fn, params);
+ }
+
+ return parsePow();
+ }
+
+ /**
+ * power
+ * Note: power operator is right associative
+ * @return {Node} node
+ * @private
+ */
+ function parsePow () {
+ var node, name, fn, params;
+
+ node = parseLeftHandOperators();
+
+ if (token == '^' || token == '.^') {
+ name = token;
+ fn = (name == '^') ? 'pow' : 'dotPow';
+
+ getTokenSkipNewline();
+ params = [node, parseUnary()]; // Go back to unary, we can have '2^-3'
+ node = new OperatorNode(name, fn, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * Left hand operators: factorial x!, transpose x'
+ * @return {Node} node
+ * @private
+ */
+ function parseLeftHandOperators () {
+ var node, operators, name, fn, params;
+
+ node = parseCustomNodes();
+
+ operators = {
+ '!': 'factorial',
+ '\'': 'transpose'
+ };
+
+ while (token in operators) {
+ name = token;
+ fn = operators[name];
+
+ getToken();
+ params = [node];
+
+ node = new OperatorNode(name, fn, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * Parse a custom node handler. A node handler can be used to process
+ * nodes in a custom way, for example for handling a plot.
+ *
+ * A handler must be passed as second argument of the parse function.
+ * - must extend math.expression.node.Node
+ * - must contain a function _compile(defs: Object) : String
+ * - must contain a function find(filter: Object) : Node[]
+ * - must contain a function toString() : String
+ * - the constructor is called with a single argument containing all parameters
+ *
+ * For example:
+ *
+ * nodes = {
+ * 'plot': PlotHandler
+ * };
+ *
+ * The constructor of the handler is called as:
+ *
+ * node = new PlotHandler(params);
+ *
+ * The handler will be invoked when evaluating an expression like:
+ *
+ * node = math.parse('plot(sin(x), x)', nodes);
+ *
+ * @return {Node} node
+ * @private
+ */
+ function parseCustomNodes () {
+ var params = [], handler;
+
+ if (token_type == TOKENTYPE.SYMBOL && extra_nodes[token]) {
+ handler = extra_nodes[token];
+
+ getToken();
+
+ // parse parameters
+ if (token == '(') {
+ params = [];
+
+ openParams();
+ getToken();
+
+ if (token != ')') {
+ params.push(parseConditional());
+
+ // parse a list with parameters
+ while (token == ',') {
+ getToken();
+ params.push(parseConditional());
+ }
+ }
+
+ if (token != ')') {
+ throw createSyntaxError('Parenthesis ) expected');
+ }
+ closeParams();
+ getToken();
+ }
+
+ // create a new node handler
+ //noinspection JSValidateTypes
+ return new handler(params);
+ }
+
+ return parseSymbol();
+ }
+
+ /**
+ * parse symbols: functions, variables, constants, units
+ * @return {Node} node
+ * @private
+ */
+ function parseSymbol () {
+ var node, name;
+
+ if (token_type == TOKENTYPE.SYMBOL ||
+ (token_type == TOKENTYPE.DELIMITER && token in NAMED_DELIMITERS)) {
+ name = token;
+
+ getToken();
+
+ // parse function parameters and matrix index
+ node = parseFunctions(name);
+ node = parseIndex(node);
+ return node;
+ }
+
+ return parseString();
+ }
+
+ /**
+ * parse a function call like fn(a, b, c)
+ * @param {string} name Function name
+ * @return {FunctionNode | SymbolNode} node
+ * @private
+ */
+ function parseFunctions (name) {
+ var params;
+
+ if (token == '(') {
+ params = [];
+
+ openParams();
+ getToken();
+
+ if (token != ')') {
+ params.push(parseConditional());
+
+ // parse a list with parameters
+ while (token == ',') {
+ getToken();
+ params.push(parseConditional());
+ }
+ }
+
+ if (token != ')') {
+ throw createSyntaxError('Parenthesis ) expected');
+ }
+ closeParams();
+ getToken();
+
+ return new FunctionNode(name, params);
+ }
+
+ return new SymbolNode(name);
+ }
+
+ /**
+ * parse index parameters, enclosed in square brackets [...], for example A[2,3]
+ * @param {Node} node Node on which to apply the parameters. If there
+ * are no parameters in the expression, the node
+ * itself is returned
+ * @return {Node} node
+ * @private
+ */
+ function parseIndex (node) {
+ var params;
+
+ while (token == '[') {
+ params = [];
+
+ openParams();
+ getToken();
+
+ if (token != ']') {
+ params.push(parseConditional());
+
+ // parse a list with parameters
+ while (token == ',') {
+ getToken();
+ params.push(parseConditional());
+ }
+ }
+
+ if (token != ']') {
+ throw createSyntaxError('Parenthesis ] expected');
+ }
+ closeParams();
+ getToken();
+
+ node = new IndexNode(node, params);
+ }
+
+ return node;
+ }
+
+ /**
+ * parse a string.
+ * A string is enclosed by double quotes
+ * @return {Node} node
+ * @private
+ */
+ function parseString () {
+ var node, str, tPrev;
+
+ if (token == '"') {
+ // string "..."
+ str = '';
+ tPrev = '';
+ while (c != '' && (c != '\"' || tPrev == '\\')) { // also handle escape character
+ str += c;
+ tPrev = c;
+ next();
+ }
+
+ getToken();
+ if (token != '"') {
+ throw createSyntaxError('End of string " expected');
+ }
+ getToken();
+
+ // create constant
+ node = new ConstantNode(str, 'string');
+
+ // parse index parameters
+ node = parseIndex(node);
+
+ return node;
+ }
+
+ return parseMatrix();
+ }
+
+ /**
+ * parse the matrix
+ * @return {Node} node
+ * @private
+ */
+ function parseMatrix () {
+ var array, params, rows, cols;
+
+ if (token == '[') {
+ // matrix [...]
+ openParams();
+ getToken();
+
+ if (token != ']') {
+ // this is a non-empty matrix
+ var row = parseRow();
+
+ if (token == ';') {
+ // 2 dimensional array
+ rows = 1;
+ params = [row];
+
+ // the rows of the matrix are separated by dot-comma's
+ while (token == ';') {
+ getToken();
+
+ params[rows] = parseRow();
+ rows++;
+ }
+
+ if (token != ']') {
+ throw createSyntaxError('End of matrix ] expected');
+ }
+ closeParams();
+ getToken();
+
+ // check if the number of columns matches in all rows
+ cols = params[0].nodes.length;
+ for (var r = 1; r < rows; r++) {
+ if (params[r].nodes.length != cols) {
+ throw createError('Column dimensions mismatch ' +
+ '(' + params[r].nodes.length + ' != ' + cols + ')');
+ }
+ }
+
+ array = new ArrayNode(params);
+ }
+ else {
+ // 1 dimensional vector
+ if (token != ']') {
+ throw createSyntaxError('End of matrix ] expected');
+ }
+ closeParams();
+ getToken();
+
+ array = row;
+ }
+ }
+ else {
+ // this is an empty matrix "[ ]"
+ closeParams();
+ getToken();
+ array = new ArrayNode([]);
+ }
+
+ return array;
+ }
+
+ return parseNumber();
+ }
+
+ /**
+ * Parse a single comma-separated row from a matrix, like 'a, b, c'
+ * @return {ArrayNode} node
+ */
+ function parseRow () {
+ var params = [parseAssignment()];
+ var len = 1;
+
+ while (token == ',') {
+ getToken();
+
+ // parse expression
+ params[len] = parseAssignment();
+ len++;
+ }
+
+ return new ArrayNode(params);
+ }
+
+ /**
+ * parse a number
+ * @return {Node} node
+ * @private
+ */
+ function parseNumber () {
+ var number;
+
+ if (token_type == TOKENTYPE.NUMBER) {
+ // this is a number
+ number = token;
+ getToken();
+
+ return new ConstantNode(number, 'number');
+ }
+
+ return parseParentheses();
+ }
+
+ /**
+ * parentheses
+ * @return {Node} node
+ * @private
+ */
+ function parseParentheses () {
+ var node;
+
+ // check if it is a parenthesized expression
+ if (token == '(') {
+ // parentheses (...)
+ openParams();
+ getToken();
+
+ node = parseAssignment(); // start again
+
+ if (token != ')') {
+ throw createSyntaxError('Parenthesis ) expected');
+ }
+ closeParams();
+ getToken();
+
+ return node;
+ }
+
+ return parseEnd();
+ }
+
+ /**
+ * Evaluated when the expression is not yet ended but expected to end
+ * @return {Node} res
+ * @private
+ */
+ function parseEnd () {
+ if (token == '') {
+ // syntax error or unexpected end of expression
+ throw createSyntaxError('Unexpected end of expression');
+ } else {
+ throw createSyntaxError('Value expected');
+ }
+ }
+
+ /**
+ * Shortcut for getting the current row value (one based)
+ * Returns the line of the currently handled expression
+ * @private
+ */
+ /* TODO: implement keeping track on the row number
+ function row () {
+ return null;
+ }
+ */
+
+ /**
+ * Shortcut for getting the current col value (one based)
+ * Returns the column (position) where the last token starts
+ * @private
+ */
+ function col () {
+ return index - token.length + 1;
+ }
+
+ /**
+ * Create an error
+ * @param {String} message
+ * @return {SyntaxError} instantiated error
+ * @private
+ */
+ function createSyntaxError (message) {
+ var c = col();
+ var error = new SyntaxError(message + ' (char ' + c + ')');
+ error['char'] = c;
+
+ return error;
+ }
+
+ /**
+ * Create an error
+ * @param {String} message
+ * @return {Error} instantiated error
+ * @private
+ */
+ function createError (message) {
+ var c = col();
+ var error = new Error(message + ' (char ' + c + ')');
+ error['char'] = c;
+
+ return error;
+ }
+
+ module.exports = parse;
+
+
+/***/ },
+/* 17 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var _parse = __webpack_require__(16);
+
+ /**
+ * @constructor Parser
+ * Parser contains methods to evaluate or parse expressions, and has a number
+ * of convenience methods to get, set, and remove variables from memory. Parser
+ * keeps a scope containing variables in memory, which is used for all
+ * evaluations.
+ *
+ * Methods:
+ * var result = parser.eval(expr); // evaluate an expression
+ * var value = parser.get(name); // retrieve a variable from the parser
+ * parser.set(name, value); // set a variable in the parser
+ * parser.remove(name); // clear a variable from the
+ * // parsers scope
+ * parser.clear(); // clear the parsers scope
+ *
+ * Example usage:
+ * var parser = new Parser(math);
+ * // Note: there is a convenience method which can be used instead:
+ * // var parser = new math.parser();
+ *
+ * // evaluate expressions
+ * parser.eval('sqrt(3^2 + 4^2)'); // 5
+ * parser.eval('sqrt(-4)'); // 2i
+ * parser.eval('2 inch in cm'); // 5.08 cm
+ * parser.eval('cos(45 deg)'); // 0.7071067811865476
+ *
+ * // define variables and functions
+ * parser.eval('x = 7 / 2'); // 3.5
+ * parser.eval('x + 3'); // 6.5
+ * parser.eval('function f(x, y) = x^y'); // f(x, y)
+ * parser.eval('f(2, 3)'); // 8
+ *
+ * // get and set variables and functions
+ * var x = parser.get('x'); // 7
+ * var f = parser.get('f'); // function
+ * var g = f(3, 2); // 9
+ * parser.set('h', 500);
+ * var i = parser.eval('h / 2'); // 250
+ * parser.set('hello', function (name) {
+ * return 'hello, ' + name + '!';
+ * });
+ * parser.eval('hello("user")'); // "hello, user!"
+ *
+ * // clear defined functions and variables
+ * parser.clear();
+ *
+ *
+ * @param {Object} math Link to the math.js namespace
+ */
+ function Parser(math) {
+ if (!(this instanceof Parser)) {
+ throw new SyntaxError(
+ 'Constructor must be called with the new operator');
+ }
+
+ if (!(math instanceof Object)) {
+ throw new TypeError('Object expected as parameter math');
+ }
+
+ this.math = math;
+ this.scope = {};
+ }
+
+ /**
+ * Parse an expression and return the parsed function node.
+ * The node tree can be compiled via `code = node.compile(math)`,
+ * and the compiled code can be executed as `code.eval([scope])`
+ * @param {String} expr
+ * @return {Node} node
+ * @throws {Error}
+ */
+ Parser.prototype.parse = function (expr) {
+ throw new Error('Parser.parse is deprecated. Use math.parse instead.');
+ };
+
+ /**
+ * Parse and compile an expression, return the compiled javascript code.
+ * The node can be evaluated via code.eval([scope])
+ * @param {String} expr
+ * @return {{eval: function}} code
+ * @throws {Error}
+ */
+ Parser.prototype.compile = function (expr) {
+ throw new Error('Parser.compile is deprecated. Use math.compile instead.');
+ };
+
+ /**
+ * Parse and evaluate the given expression
+ * @param {String} expr A string containing an expression, for example "2+3"
+ * @return {*} result The result, or undefined when the expression was empty
+ * @throws {Error}
+ */
+ Parser.prototype.eval = function (expr) {
+ // TODO: validate arguments
+ return _parse(expr)
+ .compile(this.math)
+ .eval(this.scope);
+ };
+
+ /**
+ * Get a variable (a function or variable) by name from the parsers scope.
+ * Returns undefined when not found
+ * @param {String} name
+ * @return {* | undefined} value
+ */
+ Parser.prototype.get = function (name) {
+ // TODO: validate arguments
+ return this.scope[name];
+ };
+
+ /**
+ * Set a symbol (a function or variable) by name from the parsers scope.
+ * @param {String} name
+ * @param {* | undefined} value
+ */
+ Parser.prototype.set = function (name, value) {
+ // TODO: validate arguments
+ return this.scope[name] = value;
+ };
+
+ /**
+ * Remove a variable from the parsers scope
+ * @param {String} name
+ */
+ Parser.prototype.remove = function (name) {
+ // TODO: validate arguments
+ delete this.scope[name];
+ };
+
+ /**
+ * Clear the scope with variables and functions
+ */
+ Parser.prototype.clear = function () {
+ for (var name in this.scope) {
+ if (this.scope.hasOwnProperty(name)) {
+ delete this.scope[name];
+ }
+ }
+ };
+
+ module.exports = Parser;
+
+
+/***/ },
+/* 18 */
+/***/ function(module, exports, __webpack_require__) {
+
+ // constants
+ exports.e = __webpack_require__(185);
+ exports.E = __webpack_require__(185);
+ exports['false'] = __webpack_require__(186);
+ exports.i = __webpack_require__(187);
+ exports['Infinity'] = __webpack_require__(188);
+ exports.LN2 = __webpack_require__(189);
+ exports.LN10 = __webpack_require__(190);
+ exports.LOG2E = __webpack_require__(191);
+ exports.LOG10E = __webpack_require__(192);
+ exports.NaN = __webpack_require__(193);
+ exports['null'] = __webpack_require__(194);
+ exports.pi = __webpack_require__(195);
+ exports.PI = __webpack_require__(195);
+ exports.phi = __webpack_require__(196);
+ exports.SQRT1_2 = __webpack_require__(197);
+ exports.SQRT2 = __webpack_require__(198);
+ exports.tau = __webpack_require__(199);
+ exports['true'] = __webpack_require__(200);
+ exports.version = __webpack_require__(201);
+
+ // functions - arithmetic
+ exports.abs = __webpack_require__(206);
+ exports.add = __webpack_require__(207);
+ exports.ceil = __webpack_require__(208);
+ exports.cube = __webpack_require__(209);
+ exports.divide = __webpack_require__(210);
+ exports.dotDivide = __webpack_require__(211);
+ exports.dotMultiply = __webpack_require__(212);
+ exports.dotPow = __webpack_require__(213);
+ exports.exp = __webpack_require__(214);
+ exports.fix = __webpack_require__(215);
+ exports.floor = __webpack_require__(216);
+ exports.gcd = __webpack_require__(217);
+ exports.lcm = __webpack_require__(218);
+ exports.log = __webpack_require__(219);
+ exports.log10 = __webpack_require__(220);
+ exports.mod = __webpack_require__(221);
+ exports.multiply = __webpack_require__(222);
+ exports.norm = __webpack_require__(223);
+ exports.nthRoot = __webpack_require__(224);
+ exports.pow = __webpack_require__(225);
+ exports.round = __webpack_require__(226);
+ exports.sign = __webpack_require__(227);
+ exports.sqrt = __webpack_require__(228);
+ exports.square = __webpack_require__(229);
+ exports.subtract = __webpack_require__(230);
+ exports.unaryMinus = __webpack_require__(231);
+ exports.unaryPlus = __webpack_require__(232);
+ exports.xgcd = __webpack_require__(233);
+
+ // functions - bitwise
+ exports.bitAnd = __webpack_require__(234);
+ exports.bitNot = __webpack_require__(235);
+ exports.bitOr = __webpack_require__(236);
+ exports.bitXor = __webpack_require__(237);
+ exports.leftShift = __webpack_require__(238);
+ exports.rightArithShift = __webpack_require__(239);
+ exports.rightLogShift = __webpack_require__(240);
+
+ // functions - complex
+ exports.arg = __webpack_require__(241);
+ exports.conj = __webpack_require__(242);
+ exports.re = __webpack_require__(243);
+ exports.im = __webpack_require__(244);
+
+ // functions - construction
+ exports.bignumber = __webpack_require__(245);
+ exports['boolean'] = __webpack_require__(246);
+ exports.complex = __webpack_require__(247);
+ exports.index = __webpack_require__(248);
+ exports.matrix = __webpack_require__(249);
+ exports.number = __webpack_require__(250);
+ exports.string = __webpack_require__(251);
+ exports.unit = __webpack_require__(252);
+
+ // functions - expression
+ exports['eval'] = __webpack_require__(253);
+ exports.help = __webpack_require__(254);
+
+ // functions - logical
+ exports['and'] = __webpack_require__(255);
+ exports['not'] = __webpack_require__(256);
+ exports['or'] = __webpack_require__(257);
+ exports['xor'] = __webpack_require__(258);
+
+ // functions - matrix
+ exports['concat'] = __webpack_require__(259);
+ exports.cross = __webpack_require__(260);
+ exports.det = __webpack_require__(261);
+ exports.diag = __webpack_require__(262);
+ exports.dot = __webpack_require__(263);
+ exports.eye = __webpack_require__(264);
+ exports.flatten = __webpack_require__(265);
+ exports.inv = __webpack_require__(266);
+ exports.ones = __webpack_require__(267);
+ exports.range = __webpack_require__(268);
+ exports.resize = __webpack_require__(269);
+ exports.size = __webpack_require__(270);
+ exports.squeeze = __webpack_require__(271);
+ exports.subset = __webpack_require__(272);
+ exports.trace = __webpack_require__(273);
+ exports.transpose = __webpack_require__(274);
+ exports.zeros = __webpack_require__(275);
+
+ // functions - probability
+ exports.combinations = __webpack_require__(276);
+ //exports.distribution = require('./function/probability/distribution');
+ exports.factorial = __webpack_require__(277);
+ exports.gamma = __webpack_require__(278);
+ exports.permutations = __webpack_require__(279);
+ exports.pickRandom = __webpack_require__(280);
+ exports.random = __webpack_require__(281);
+ exports.randomInt = __webpack_require__(282);
+
+ // functions - relational
+ exports.compare = __webpack_require__(283);
+ exports.deepEqual = __webpack_require__(284);
+ exports['equal'] = __webpack_require__(285);
+ exports.larger = __webpack_require__(286);
+ exports.largerEq = __webpack_require__(287);
+ exports.smaller = __webpack_require__(288);
+ exports.smallerEq = __webpack_require__(289);
+ exports.unequal = __webpack_require__(290);
+
+ // functions - statistics
+ exports.max = __webpack_require__(291);
+ exports.mean = __webpack_require__(292);
+ exports.median = __webpack_require__(293);
+ exports.min = __webpack_require__(294);
+ exports.prod = __webpack_require__(295);
+ exports.std = __webpack_require__(296);
+ exports.sum = __webpack_require__(297);
+ exports['var'] = __webpack_require__(298);
+
+ // functions - trigonometry
+ exports.acos = __webpack_require__(299);
+ exports.acosh = __webpack_require__(300);
+ exports.acot = __webpack_require__(301);
+ exports.acoth = __webpack_require__(302);
+ exports.acsc = __webpack_require__(303);
+ exports.acsch = __webpack_require__(304);
+ exports.asec = __webpack_require__(305);
+ exports.asech = __webpack_require__(306);
+ exports.asin = __webpack_require__(307);
+ exports.asinh = __webpack_require__(308);
+ exports.atan = __webpack_require__(309);
+ exports.atanh = __webpack_require__(310);
+ exports.atan2 = __webpack_require__(311);
+ exports.cos = __webpack_require__(312);
+ exports.cosh = __webpack_require__(313);
+ exports.cot = __webpack_require__(314);
+ exports.coth = __webpack_require__(315);
+ exports.csc = __webpack_require__(316);
+ exports.csch = __webpack_require__(317);
+ exports.sec = __webpack_require__(318);
+ exports.sech = __webpack_require__(319);
+ exports.sin = __webpack_require__(320);
+ exports.sinh = __webpack_require__(321);
+ exports.tan = __webpack_require__(322);
+ exports.tanh = __webpack_require__(323);
+
+ // functions - units
+ exports.to = __webpack_require__(324);
+
+ // functions - utils
+ exports.clone = __webpack_require__(325);
+ exports.map = __webpack_require__(326);
+ exports.filter = __webpack_require__(327);
+ exports.forEach = __webpack_require__(328);
+ exports.format = __webpack_require__(329);
+ // exports.print = require('./function/utils/print'); // TODO: add documentation for print as soon as the parser supports objects.
+ exports['import'] = __webpack_require__(330);
+ exports.sort = __webpack_require__(331);
+ exports['typeof'] = __webpack_require__(332);
+
+
+/***/ },
+/* 19 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var BigNumber = __webpack_require__(5);
+ var Complex = __webpack_require__(7);
+ var Help = __webpack_require__(12);
+ var Index = __webpack_require__(9);
+ var Matrix = __webpack_require__(10);
+ var Range = __webpack_require__(8);
+ var ResultSet = __webpack_require__(13);
+ var Unit = __webpack_require__(11);
+
+ /**
+ * Instantiate mathjs data types from their JSON representation
+ * @param {string} key
+ * @param {*} value
+ * @returns {*} Returns the revived object
+ */
+ function reviver(key, value) {
+ var type = value && value.mathjs;
+
+ switch (type) {
+ case 'BigNumber': return BigNumber.fromJSON(value);
+ case 'Complex': return Complex.fromJSON(value);
+ case 'Help': return Help.fromJSON(value);
+ case 'Index': return Index.fromJSON(value);
+ case 'Matrix': return Matrix.fromJSON(value);
+ case 'Range': return Range.fromJSON(value);
+ case 'ResultSet': return ResultSet.fromJSON(value);
+ case 'Unit': return Unit.fromJSON(value);
+ }
+
+ return value;
+ }
+
+ module.exports = reviver;
+
+
+/***/ },
+/* 20 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var BigNumber = __webpack_require__(5);
+ var errorTransform = __webpack_require__(203).transform;
+ var isNumber = __webpack_require__(3).isNumber;
+ var argsToArray = __webpack_require__(165).argsToArray;
+
+ /**
+ * Attach a transform function to math.range
+ * Adds a property transform containing the transform function.
+ *
+ * This transform changed the last `dim` parameter of function concat
+ * from one-based to zero based
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ // copy arguments into an array
+ var args = argsToArray(arguments);
+
+ // change last argument from one-based to zero-based
+ var lastIndex = args.length - 1;
+ var last = args[lastIndex];
+ if (isNumber(last)) {
+ args[lastIndex] = last - 1;
+ }
+ else if (last instanceof BigNumber) {
+ args[lastIndex] = last.minus(1);
+ }
+
+ try {
+ return math.concat.apply(math, args);
+ }
+ catch (err) {
+ throw errorTransform(err);
+ }
+ };
+
+ math.concat.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 21 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var SymbolNode = __webpack_require__(183);
+ var isBoolean = __webpack_require__(204).isBoolean;
+ var argsToArray = __webpack_require__(165).argsToArray;
+ var ArgumentsError = __webpack_require__(167);
+
+ /**
+ * Attach a transform function to math.filter
+ * Adds a property transform containing the transform function.
+ *
+ * This transform adds support for equations as test function for math.filter,
+ * so you can do something like 'filter([3, -2, 5], x > 0)'.
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var _filter = math.filter;
+
+ var transform = function (args, math, scope) {
+ if (args.length !== 2) {
+ throw new ArgumentsError('filter', arguments.length, 2);
+ }
+
+ var x = args[0].compile(math).eval(scope);
+ var test;
+ if (args[1] instanceof SymbolNode) {
+ // a function pointer, like filter([3, -2, 5], myTestFunction);
+ test = args[1].compile(math).eval(scope);
+ }
+ else {
+ // an equation like filter([3, -2, 5], x > 0)
+
+ // find an undefined symbol
+ var _scope = scope || {};
+ var symbol = args[1]
+ .filter(function (node) {
+ return (node instanceof SymbolNode) &&
+ !(node.name in math) &&
+ !(node.name in _scope);
+ })[0];
+
+ // create a test function for this equation
+ var sub = Object.create(_scope);
+ var eq = args[1].compile(math);
+ if (symbol) {
+ var name = symbol.name;
+ test = function (x) {
+ sub[name] = x;
+ return eq.eval(sub);
+ }
+ }
+ else {
+ throw new Error('No undefined variable found in filter equation');
+ }
+ }
+
+ return _filter(x, test);
+ };
+
+ transform.rawArgs = true;
+ math.filter.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 22 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var Matrix = __webpack_require__(10);
+
+ /**
+ * Attach a transform function to math.forEach
+ * Adds a property transform containing the transform function.
+ *
+ * This transform creates a one-based index instead of a zero-based index
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function (x, callback) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('forEach', arguments.length, 2);
+ }
+
+ if (Array.isArray(x)) {
+ _forEachArray(x, callback, x);
+ } else if (x instanceof Matrix) {
+ _forEachArray(x.valueOf(), callback, x);
+ } else {
+ throw new math.error.UnsupportedTypeError('forEach', math['typeof'](x));
+ }
+ };
+
+ function _forEachArray (array, callback, arrayOrig) {
+ var recurse = function (value, index) {
+ if (Array.isArray(value)) {
+ value.forEach(function (child, i) {
+ // we create a copy of the index array and append the new index value
+ recurse(child, index.concat(i + 1)); // one based index, hence i+1
+ });
+ }
+ else {
+ callback(value, index, arrayOrig);
+ }
+ };
+ recurse(array, []);
+ }
+
+ math.forEach.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 23 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var BigNumber = __webpack_require__(5);
+ var Range = __webpack_require__(8);
+ var Index = __webpack_require__(9);
+ var Matrix = __webpack_require__(10);
+ var isNumber = __webpack_require__(3).isNumber;
+ var isArray = Array.isArray;
+
+ /**
+ * Attach a transform function to math.index
+ * Adds a property transform containing the transform function.
+ *
+ * This transform creates a one-based index instead of a zero-based index
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ var args = [];
+ for (var i = 0, ii = arguments.length; i < ii; i++) {
+ var arg = arguments[i];
+
+ // change from one-based to zero based, and convert BigNumber to number
+ if (arg instanceof Range) {
+ arg.start--;
+ arg.end -= (arg.step > 0 ? 0 : 2);
+ }
+ else if (isNumber(arg)) {
+ arg--;
+ }
+ else if (arg instanceof BigNumber) {
+ arg = arg.toNumber() - 1;
+ }
+ else {
+ throw new TypeError('Ranges must be a Number or Range');
+ }
+
+ args[i] = arg;
+ }
+
+ var res = new Index();
+ Index.apply(res, args);
+ return res;
+ };
+
+ math.index.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 24 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var Matrix = __webpack_require__(10);
+ var BigNumber = __webpack_require__(5);
+ var Range = __webpack_require__(8);
+ var Index = __webpack_require__(9);
+ var isNumber = __webpack_require__(3).isNumber;
+ var isArray = Array.isArray;
+
+ /**
+ * Attach a transform function to math.map
+ * Adds a property transform containing the transform function.
+ *
+ * This transform creates a one-based index instead of a zero-based index
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function (x, callback) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('map', arguments.length, 2);
+ }
+
+ if (Array.isArray(x)) {
+ return _mapArray(x, callback, x);
+ } else if (x instanceof Matrix) {
+ return new Matrix(_mapArray(x.valueOf(), callback, x))
+ } else {
+ throw new math.error.UnsupportedTypeError('map', math['typeof'](x));
+ }
+ };
+
+ function _mapArray (arrayIn, callback, arrayOrig) {
+ var recurse = function (value, index) {
+ if (Array.isArray(value)) {
+ return value.map(function (child, i) {
+ // we create a copy of the index array and append the new index value
+ return recurse(child, index.concat(i + 1)); // one based index, hence i + 1
+ });
+ }
+ else {
+ return callback(value, index, arrayOrig);
+ }
+ };
+
+ return recurse(arrayIn, []);
+ }
+
+ math.map.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 25 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var BigNumber = __webpack_require__(5);
+ var errorTransform = __webpack_require__(203).transform;
+ var isNumber = __webpack_require__(3).isNumber;
+ var isCollection = __webpack_require__(14).isCollection;
+ var argsToArray = __webpack_require__(165).argsToArray;
+
+ /**
+ * Attach a transform function to math.max
+ * Adds a property transform containing the transform function.
+ *
+ * This transform changed the last `dim` parameter of function max
+ * from one-based to zero based
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ var args = argsToArray(arguments);
+
+ // change last argument dim from one-based to zero-based
+ if (args.length == 2 && isCollection(args[0])) {
+ var dim = args[1];
+ if (isNumber(dim)) {
+ args[1] = dim - 1;
+ }
+ else if (dim instanceof BigNumber) {
+ args[1] = dim.minus(1);
+ }
+ }
+
+ try {
+ return math.max.apply(math, args);
+ }
+ catch (err) {
+ throw errorTransform(err);
+ }
+ };
+
+ math.max.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 26 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var BigNumber = __webpack_require__(5);
+ var errorTransform = __webpack_require__(203).transform;
+ var isNumber = __webpack_require__(3).isNumber;
+ var isCollection = __webpack_require__(14).isCollection;
+ var argsToArray = __webpack_require__(165).argsToArray;
+
+ /**
+ * Attach a transform function to math.mean
+ * Adds a property transform containing the transform function.
+ *
+ * This transform changed the last `dim` parameter of function mean
+ * from one-based to zero based
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ var args = argsToArray(arguments);
+
+ // change last argument dim from one-based to zero-based
+ if (args.length == 2 && isCollection(args[0])) {
+ var dim = args[1];
+ if (isNumber(dim)) {
+ args[1] = dim - 1;
+ }
+ else if (dim instanceof BigNumber) {
+ args[1] = dim.minus(1);
+ }
+ }
+
+ try {
+ return math.mean.apply(math, args);
+ }
+ catch (err) {
+ throw errorTransform(err);
+ }
+ };
+
+ math.mean.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 27 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var BigNumber = __webpack_require__(5);
+ var errorTransform = __webpack_require__(203).transform;
+ var isNumber = __webpack_require__(3).isNumber;
+ var isCollection = __webpack_require__(14).isCollection;
+ var argsToArray = __webpack_require__(165).argsToArray;
+
+ /**
+ * Attach a transform function to math.min
+ * Adds a property transform containing the transform function.
+ *
+ * This transform changed the last `dim` parameter of function min
+ * from one-based to zero based
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ var args = argsToArray(arguments);
+
+ // change last argument dim from one-based to zero-based
+ if (args.length == 2 && isCollection(args[0])) {
+ var dim = args[1];
+ if (isNumber(dim)) {
+ args[1] = dim - 1;
+ }
+ else if (dim instanceof BigNumber) {
+ args[1] = dim.minus(1);
+ }
+ }
+
+ try {
+ return math.min.apply(math, args);
+ }
+ catch (err) {
+ throw errorTransform(err);
+ }
+ };
+
+ math.min.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 28 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var isBoolean = __webpack_require__(204).isBoolean;
+ var argsToArray = __webpack_require__(165).argsToArray;
+
+ /**
+ * Attach a transform function to math.range
+ * Adds a property transform containing the transform function.
+ *
+ * This transform creates a range which includes the end value
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ var args = argsToArray(arguments);
+
+ var lastIndex = args.length - 1;
+ var last = args[lastIndex];
+ if (!isBoolean(last)) {
+ args.push(true); // append a parameter includeEnd=true
+ }
+
+ return math.range.apply(math, args);
+ };
+
+ math.range.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 29 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ var errorTransform = __webpack_require__(203).transform;
+ var isBoolean = __webpack_require__(204).isBoolean;
+ var argsToArray = __webpack_require__(165).argsToArray;
+
+ /**
+ * Attach a transform function to math.subset
+ * Adds a property transform containing the transform function.
+ *
+ * This transform creates a range which includes the end value
+ * @param {Object} math
+ */
+ module.exports = function (math) {
+ var transform = function () {
+ try {
+ return math.subset.apply(math, argsToArray(arguments));
+ }
+ catch (err) {
+ throw errorTransform(err);
+ }
+ };
+
+ math.subset.transform = transform;
+
+ return transform;
+ };
+
+
+/***/ },
+/* 30 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var string = __webpack_require__(205);
+
+ /**
+ * @constructor Chain
+ * Wrap any value in a chain, allowing to perform chained operations on
+ * the value.
+ *
+ * All methods available in the math.js library can be called upon the chain,
+ * and then will be evaluated with the value itself as first argument.
+ * The chain can be closed by executing chain.done(), which will return
+ * the final value.
+ *
+ * The Chain has a number of special functions:
+ * - done() Finalize the chained operation and return the
+ * chain's value.
+ * - valueOf() The same as done()
+ * - toString() Returns a string representation of the chain's value.
+ *
+ * @param {*} [value]
+ */
+ function Chain (value) {
+ if (!(this instanceof Chain)) {
+ throw new SyntaxError('Constructor must be called with the new operator');
+ }
+
+ if (value instanceof Chain) {
+ this.value = value.value;
+ }
+ else {
+ this.value = value;
+ }
+ }
+
+ /**
+ * Close the chain. Returns the final value.
+ * Does the same as method valueOf()
+ * @returns {*} value
+ */
+ Chain.prototype.done = function () {
+ return this.value;
+ };
+
+ /**
+ * Close the chain. Returns the final value.
+ * Does the same as method done()
+ * @returns {*} value
+ */
+ Chain.prototype.valueOf = function () {
+ return this.value;
+ };
+
+ /**
+ * Get a string representation of the value in the chain
+ * @returns {String}
+ */
+ Chain.prototype.toString = function () {
+ return string.format(this.value);
+ };
+
+ /**
+ * Create a proxy method for the chain
+ * @param {String} name
+ * @param {*} value The value or function to be proxied
+ */
+ function createProxy(name, value) {
+ var slice = Array.prototype.slice;
+ if (typeof value === 'function') {
+ // a function
+ Chain.prototype[name] = function () {
+ var args = [this.value].concat(slice.call(arguments, 0));
+ return new Chain(value.apply(this, args));
+ }
+ }
+ else {
+ // a constant
+ Chain.prototype[name] = new Chain(value);
+ }
+ }
+
+ Chain.createProxy = createProxy;
+
+ /**
+ * initialise the Chain prototype with all functions and constants in math
+ */
+ for (var prop in math) {
+ if (math.hasOwnProperty(prop)) {
+ createProxy(prop, math[prop]);
+ }
+ }
+
+ return Chain;
+ };
+
+
+/***/ },
+/* 31 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+ _parse = __webpack_require__(16),
+
+ collection = __webpack_require__(14),
+
+ isString = util.string.isString,
+ isCollection = collection.isCollection;
+
+ /**
+ * Parse and compile an expression.
+ * Returns a an object with a function `eval([scope])` to evaluate the
+ * compiled expression.
+ *
+ * Syntax:
+ *
+ * math.compile(expr) // returns one node
+ * math.compile([expr1, expr2, expr3, ...]) // returns an array with nodes
+ *
+ * Examples:
+ *
+ * var code = math.compile('sqrt(3^2 + 4^2)');
+ * code.eval(); // 5
+ *
+ * var scope = {a: 3, b: 4}
+ * var code = math.compile('a * b'); // 12
+ * code.eval(scope); // 12
+ * scope.a = 5;
+ * code.eval(scope); // 20
+ *
+ * var nodes = math.compile(['a = 3', 'b = 4', 'a * b']);
+ * nodes[2].eval(); // 12
+ *
+ * See also:
+ *
+ * parse, eval
+ *
+ * @param {String | String[] | Matrix} expr
+ * The expression to be compiled
+ * @return {{eval: Function} | Array.<{eval: Function}>} code
+ * An object with the compiled expression
+ * @throws {Error}
+ */
+ math.compile = function compile (expr) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('compile', arguments.length, 1);
+ }
+
+ if (isString(expr)) {
+ // evaluate a single expression
+ return _parse(expr).compile(math);
+ }
+ else if (isCollection(expr)) {
+ // evaluate an array or matrix with expressions
+ return collection.deepMap(expr, function (elem) {
+ return _parse(elem).compile(math);
+ });
+ }
+ else {
+ // oops
+ throw new TypeError('String, array, or matrix expected');
+ }
+ }
+ };
+
+
+/***/ },
+/* 32 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+ _parse = __webpack_require__(16),
+
+ collection = __webpack_require__(14),
+
+ isString = util.string.isString,
+ isCollection = collection.isCollection;
+
+ /**
+ * Evaluate an expression.
+ *
+ * Syntax:
+ *
+ * math.eval(expr)
+ * math.eval(expr, scope)
+ * math.eval([expr1, expr2, expr3, ...])
+ * math.eval([expr1, expr2, expr3, ...], scope)
+ *
+ * Example:
+ *
+ * math.eval('(2+3)/4'); // 1.25
+ * math.eval('sqrt(3^2 + 4^2)'); // 5
+ * math.eval('sqrt(-4)'); // 2i
+ * math.eval(['a=3', 'b=4', 'a*b']);, // [3, 4, 12]
+ *
+ * var scope = {a:3, b:4};
+ * math.eval('a * b', scope); // 12
+ *
+ * See also:
+ *
+ * parse, compile
+ *
+ * @param {String | String[] | Matrix} expr The expression to be evaluated
+ * @param {Object} [scope] Scope to read/write variables
+ * @return {*} The result of the expression
+ * @throws {Error}
+ */
+ math.eval = function _eval (expr, scope) {
+ if (arguments.length != 1 && arguments.length != 2) {
+ throw new math.error.ArgumentsError('eval', arguments.length, 1, 2);
+ }
+
+ // instantiate a scope
+ scope = scope || {};
+
+ if (isString(expr)) {
+ // evaluate a single expression
+ return _parse(expr)
+ .compile(math)
+ .eval(scope);
+ }
+ else if (isCollection(expr)) {
+ // evaluate an array or matrix with expressions
+ return collection.deepMap(expr, function (elem) {
+ return _parse(elem)
+ .compile(math).eval(scope);
+ });
+ }
+ else {
+ // oops
+ throw new TypeError('String, array, or matrix expected');
+ }
+ };
+ };
+
+
+/***/ },
+/* 33 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Help = __webpack_require__(12);
+
+ /**
+ * Retrieve help on a function or data type.
+ * Help files are retrieved from the documentation in math.expression.docs.
+ *
+ * Syntax:
+ *
+ * math.help(search)
+ *
+ * Examples:
+ *
+ * console.log(math.help('sin').toString());
+ * console.log(math.help(math.add).toString());
+ * console.log(math.help(math.add).toJSON());
+ *
+ * @param {function | string | Object} search A function or function name
+ * for which to get help
+ * @return {Help} A help object
+ */
+ math.help = function help(search) {
+ if (arguments.length != 1) {
+ throw new SyntaxError('Wrong number of arguments in function help ' +
+ '(' + arguments.length + ' provided, 1 expected)');
+ }
+
+ var text = null;
+ if ((search instanceof String) || (typeof(search) === 'string')) {
+ text = search;
+ }
+ else {
+ var prop;
+ for (prop in math) {
+ // search in functions and constants
+ if (math.hasOwnProperty(prop) && (search === math[prop])) {
+ text = prop;
+ break;
+ }
+ }
+
+ /* TODO: implement help for data types
+ if (!text) {
+ // search data type
+ for (prop in math.type) {
+ if (math.type.hasOwnProperty(prop)) {
+ if (search === math.type[prop]) {
+ text = prop;
+ break;
+ }
+ }
+ }
+ }
+ */
+ }
+
+ var doc = math.expression.docs[text];
+ if (!text) {
+ throw new Error('Cannot find "' + search + '" in math.js');
+ } else if (!doc) {
+ throw new Error('No documentation found on "' + text + '"');
+ }
+ return new Help(doc);
+ };
+ };
+
+
+/***/ },
+/* 34 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var _parse = __webpack_require__(16);
+
+ /**
+ * Parse an expression. Returns a node tree, which can be evaluated by
+ * invoking node.eval();
+ *
+ * Syntax:
+ *
+ * parse(expr)
+ * parse(expr, options)
+ * parse([expr1, expr2, expr3, ...])
+ * parse([expr1, expr2, expr3, ...], options)
+ *
+ * Example:
+ *
+ * var node = parse('sqrt(3^2 + 4^2)');
+ * node.compile(math).eval(); // 5
+ *
+ * var scope = {a:3, b:4}
+ * var node = parse('a * b'); // 12
+ * var code = node.compile(math);
+ * code.eval(scope); // 12
+ * scope.a = 5;
+ * code.eval(scope); // 20
+ *
+ * var nodes = math.parse(['a = 3', 'b = 4', 'a * b']);
+ * nodes[2].compile(math).eval(); // 12
+ *
+ * @param {String | String[] | Matrix} expr Expression to be parsed
+ * @param {{nodes: Object<String, Node>}} [options] Available options:
+ * - `nodes` a set of custom nodes
+ * @return {Node | Node[]} node
+ * @throws {Error}
+ */
+ math.parse = function parse (expr, options) {
+ return _parse.apply(_parse, arguments);
+ }
+
+ };
+
+
+/***/ },
+/* 35 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the absolute value of a number. For matrices, the function is
+ * evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.abs(x)
+ *
+ * Examples:
+ *
+ * math.abs(3.5); // returns Number 3.5
+ * math.abs(-4.2); // returns Number 4.2
+ *
+ * math.abs([3, -5, -1, 0, 2]); // returns Array [3, 5, 1, 0, 2]
+ *
+ * See also:
+ *
+ * sign
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x
+ * A number or matrix for which to get the absolute value
+ * @return {Number | BigNumber | Complex | Array | Matrix}
+ * Absolute value of `x`
+ */
+ math.abs = function abs(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('abs', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return Math.abs(x);
+ }
+
+ if (isComplex(x)) {
+ // do not compute sqrt(re * re + im * im) since it will overflow with big numbers!
+ var re = Math.abs(x.re);
+ var im = Math.abs(x.im);
+ if (re >= im) {
+ var x = im / re;
+ return re * Math.sqrt(1 + x * x);
+ }
+ var y = re / im;
+ return im * Math.sqrt(1 + y * y);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.abs();
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, abs);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return Math.abs(x);
+ }
+
+ throw new math.error.UnsupportedTypeError('abs', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 36 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isNumber = util.number.isNumber,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Add two values, `x + y`.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.add(x, y)
+ *
+ * Examples:
+ *
+ * math.add(2, 3); // returns Number 5
+ *
+ * var a = math.complex(2, 3);
+ * var b = math.complex(-4, 1);
+ * math.add(a, b); // returns Complex -2 + 4i
+ *
+ * math.add([1, 2, 3], 4); // returns Array [5, 6, 7]
+ *
+ * var c = math.unit('5 cm');
+ * var d = math.unit('2.1 mm');
+ * math.add(c, d); // returns Unit 52.1 mm
+ *
+ * See also:
+ *
+ * subtract
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | String | Array | Matrix | null} x First value to add
+ * @param {Number | BigNumber | Boolean | Complex | Unit | String | Array | Matrix | null} y Second value to add
+ * @return {Number | BigNumber | Complex | Unit | String | Array | Matrix} Sum of `x` and `y`
+ */
+ math.add = function add(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('add', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ // number + number
+ return x + y;
+ }
+ else if (isComplex(y)) {
+ // number + complex
+ return new Complex(
+ x + y.re,
+ y.im
+ )
+ }
+ }
+
+ if (isComplex(x)) {
+ if (isComplex(y)) {
+ // complex + complex
+ return new Complex(
+ x.re + y.re,
+ x.im + y.im
+ );
+ }
+ else if (isNumber(y)) {
+ // complex + number
+ return new Complex(
+ x.re + y,
+ x.im
+ )
+ }
+ }
+
+ if (isUnit(x)) {
+ if (isUnit(y)) {
+ if (x.value == null) {
+ throw new Error('Parameter x contains a unit with undefined value');
+ }
+
+ if (y.value == null) {
+ throw new Error('Parameter y contains a unit with undefined value');
+ }
+
+ if (!x.equalBase(y)) {
+ throw new Error('Units do not match');
+ }
+
+ var res = x.clone();
+ res.value += y.value;
+ res.fixPrefix = false;
+ return res;
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.plus(y);
+ }
+
+ // downgrade to Number
+ return add(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.plus(y)
+ }
+
+ // downgrade to Number
+ return add(x, y.toNumber());
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, add);
+ }
+
+ if (isString(x) || isString(y)) {
+ return x + y;
+ }
+
+ if (isBoolean(x) || x === null) {
+ return add(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return add(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('add', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 37 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isCollection =collection.isCollection,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Round a value towards plus infinity
+ * If `x` is complex, both real and imaginary part are rounded towards plus infinity.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.ceil(x)
+ *
+ * Examples:
+ *
+ * math.ceil(3.2); // returns Number 4
+ * math.ceil(3.8); // returns Number 4
+ * math.ceil(-4.2); // returns Number -4
+ * math.ceil(-4.7); // returns Number -4
+ *
+ * var c = math.complex(3.2, -2.7);
+ * math.ceil(c); // returns Complex 4 - 2i
+ *
+ * math.ceil([3.2, 3.8, -4.7]); // returns Array [4, 4, -4]
+ *
+ * See also:
+ *
+ * floor, fix, round
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x Number to be rounded
+ * @return {Number | BigNumber | Complex | Array | Matrix} Rounded value
+ */
+ math.ceil = function ceil(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('ceil', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return Math.ceil(x);
+ }
+
+ if (isComplex(x)) {
+ return new Complex (
+ Math.ceil(x.re),
+ Math.ceil(x.im)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.ceil();
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, ceil);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return Math.ceil(x);
+ }
+
+ throw new math.error.UnsupportedTypeError('ceil', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 38 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the cube of a value, `x * x * x`.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.cube(x)
+ *
+ * Examples:
+ *
+ * math.cube(2); // returns Number 8
+ * math.pow(2, 3); // returns Number 8
+ * math.cube(4); // returns Number 64
+ * 4 * 4 * 4; // returns Number 64
+ *
+ * math.cube([1, 2, 3, 4]); // returns Array [1, 8, 27, 64]
+ *
+ * See also:
+ *
+ * multiply, square, pow
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x Number for which to calculate the cube
+ * @return {Number | BigNumber | Complex | Array | Matrix} Cube of x
+ */
+ math.cube = function cube(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('cube', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return x * x * x;
+ }
+
+ if (isComplex(x)) {
+ return math.multiply(math.multiply(x, x), x);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.times(x).times(x);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, cube);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return cube(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('cube', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 39 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function(math) {
+ var util = __webpack_require__(171);
+
+ var BigNumber = math.type.BigNumber;
+ var Complex = __webpack_require__(7);
+ var Matrix = __webpack_require__(10);
+ var Unit = __webpack_require__(11);
+
+ var isNumber = util.number.isNumber;
+ var isBoolean = util['boolean'].isBoolean;
+ var isComplex = Complex.isComplex;
+ var isUnit = Unit.isUnit;
+
+ /**
+ * Divide two scalar values, `x / y`.
+ * This function is meant for internal use: it is used by the public functions
+ * `divide` and `inv`.
+ *
+ * This function does not support collections (Array or Matrix), and does
+ * not validate the number of of inputs.
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | null} x Numerator
+ * @param {Number | BigNumber | Boolean | Complex | null} y Denominator
+ * @return {Number | BigNumber | Complex | Unit} Quotient, `x / y`
+ * @private
+ */
+ math._divide = function _divide(x, y) {
+ // TODO: this is a temporary function, to be removed as soon as the library is modularized (i.e. no dependencies on math from the individual functions)
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ // number / number
+ return x / y;
+ }
+ else if (isComplex(y)) {
+ // number / complex
+ return _divideComplex(new Complex(x, 0), y);
+ }
+ }
+
+ if (isComplex(x)) {
+ if (isComplex(y)) {
+ // complex / complex
+ return _divideComplex(x, y);
+ }
+ else if (isNumber(y)) {
+ // complex / number
+ return _divideComplex(x, new Complex(y, 0));
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.div(y);
+ }
+
+ // downgrade to Number
+ return _divide(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.div(y)
+ }
+
+ // downgrade to Number
+ return _divide(x, y.toNumber());
+ }
+
+ if (isUnit(x)) {
+ if (isNumber(y)) {
+ var res = x.clone();
+ res.value = ((res.value === null) ? res._normalize(1) : res.value) / y;
+ return res;
+ }
+ }
+
+ if (isBoolean(x) || x === null) {
+ return _divide(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return _divide(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('divide', math['typeof'](x), math['typeof'](y));
+ };
+
+ /**
+ * Divide two complex numbers. x / y or divide(x, y)
+ * @param {Complex} x
+ * @param {Complex} y
+ * @return {Complex} res
+ * @private
+ */
+ function _divideComplex (x, y) {
+ var den = y.re * y.re + y.im * y.im;
+ if (den != 0) {
+ return new Complex(
+ (x.re * y.re + x.im * y.im) / den,
+ (x.im * y.re - x.re * y.im) / den
+ );
+ }
+ else {
+ // both y.re and y.im are zero
+ return new Complex(
+ (x.re != 0) ? (x.re / 0) : 0,
+ (x.im != 0) ? (x.im / 0) : 0
+ );
+ }
+ }
+ };
+
+
+/***/ },
+/* 40 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function(math) {
+ var collection = __webpack_require__(14);
+ var isCollection = collection.isCollection;
+
+ /**
+ * Divide two values, `x / y`.
+ * To divide matrices, `x` is multiplied with the inverse of `y`: `x * inv(y)`.
+ *
+ * Syntax:
+ *
+ * math.divide(x, y)
+ *
+ * Examples:
+ *
+ * math.divide(2, 3); // returns Number 0.6666666666666666
+ *
+ * var a = math.complex(5, 14);
+ * var b = math.complex(4, 1);
+ * math.divide(a, b); // returns Complex 2 + 3i
+ *
+ * var c = [[7, -6], [13, -4]];
+ * var d = [[1, 2], [4, 3]];
+ * math.divide(c, d); // returns Array [[-9, 4], [-11, 6]]
+ *
+ * var e = math.unit('18 km');
+ * math.divide(e, 4.5); // returns Unit 4 km
+ *
+ * See also:
+ *
+ * multiply
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x Numerator
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} y Denominator
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix} Quotient, `x / y`
+ */
+ math.divide = function(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('divide', arguments.length, 2);
+ }
+
+ if (isCollection(x)) {
+ if (isCollection(y)) {
+ // TODO: implement matrix right division using pseudo inverse
+ // http://www.mathworks.nl/help/matlab/ref/mrdivide.html
+ // http://www.gnu.org/software/octave/doc/interpreter/Arithmetic-Ops.html
+ // http://stackoverflow.com/questions/12263932/how-does-gnu-octave-matrix-division-work-getting-unexpected-behaviour
+ return math.multiply(x, math.inv(y));
+ }
+ else {
+ // matrix / scalar
+ return collection.deepMap2(x, y, math._divide);
+ }
+ }
+
+ if (isCollection(y)) {
+ // TODO: implement matrix right division using pseudo inverse
+ return math.multiply(x, math.inv(y));
+ }
+
+ // divide two scalars
+ return math._divide(x, y);
+ };
+ };
+
+
+/***/ },
+/* 41 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var collection = __webpack_require__(14);
+
+ /**
+ * Divide two matrices element wise. The function accepts both matrices and
+ * scalar values.
+ *
+ * Syntax:
+ *
+ * math.dotDivide(x, y)
+ *
+ * Examples:
+ *
+ * math.dotDivide(2, 4); // returns 0.5
+ *
+ * a = [[9, 5], [6, 1]];
+ * b = [[3, 2], [5, 2]];
+ *
+ * math.dotDivide(a, b); // returns [[3, 2.5], [1.2, 0.5]]
+ * math.divide(a, b); // returns [[1.75, 0.75], [-1.75, 2.25]]
+ *
+ * See also:
+ *
+ * divide, multiply, dotMultiply
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x Numerator
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Denominator
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix} Quotient, `x ./ y`
+ */
+ math.dotDivide = function dotDivide(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('dotDivide', arguments.length, 2);
+ }
+
+ return collection.deepMap2(x, y, math.divide);
+ };
+
+ // TODO: deprecated since version 0.23.0, clean up some day
+ math.edivide = function () {
+ throw new Error('Function edivide is renamed to dotDivide');
+ }
+ };
+
+
+/***/ },
+/* 42 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+ collection = __webpack_require__(14);
+
+ /**
+ * Multiply two matrices element wise. The function accepts both matrices and
+ * scalar values.
+ *
+ * Syntax:
+ *
+ * math.dotMultiply(x, y)
+ *
+ * Examples:
+ *
+ * math.dotMultiply(2, 4); // returns 8
+ *
+ * a = [[9, 5], [6, 1]];
+ * b = [[3, 2], [5, 2]];
+ *
+ * math.dotMultiply(a, b); // returns [[27, 10], [30, 2]]
+ * math.multiply(a, b); // returns [[52, 28], [23, 14]]
+ *
+ * See also:
+ *
+ * multiply, divide, dotDivide
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x Left hand value
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Right hand value
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`
+ */
+ math.dotMultiply = function dotMultiply(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('dotMultiply', arguments.length, 2);
+ }
+
+ return collection.deepMap2(x, y, math.multiply);
+ };
+
+ // TODO: deprecated since version 0.23.0, clean up some day
+ math.emultiply = function () {
+ throw new Error('Function emultiply is renamed to dotMultiply');
+ }
+ };
+
+
+/***/ },
+/* 43 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+ collection = __webpack_require__(14);
+
+ /**
+ * Calculates the power of x to y element wise.
+ *
+ * Syntax:
+ *
+ * math.dotPow(x, y)
+ *
+ * Examples:
+ *
+ * math.dotPow(2, 3); // returns Number 8
+ *
+ * var a = [[1, 2], [4, 3]];
+ * math.dotPow(a, 2); // returns Array [[1, 4], [16, 9]]
+ * math.pow(a, 2); // returns Array [[9, 8], [16, 17]]
+ *
+ * See also:
+ *
+ * pow, sqrt, multiply
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x The base
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y The exponent
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix} The value of `x` to the power `y`
+ */
+ math.dotPow = function dotPow(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('dotPow', arguments.length, 2);
+ }
+
+ return collection.deepMap2(x, y, math.pow);
+ };
+
+ // TODO: deprecated since version 0.23.0, clean up some day
+ math.epow = function () {
+ throw new Error('Function epow is renamed to dotPow');
+ }
+ };
+
+
+/***/ },
+/* 44 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the exponent of a value.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.exp(x)
+ *
+ * Examples:
+ *
+ * math.exp(2); // returns Number 7.3890560989306495
+ * math.pow(math.e, 2); // returns Number 7.3890560989306495
+ * math.log(math.exp(2)); // returns Number 2
+ *
+ * math.exp([1, 2, 3]);
+ * // returns Array [
+ * // 2.718281828459045,
+ * // 7.3890560989306495,
+ * // 20.085536923187668
+ * // ]
+ *
+ * See also:
+ *
+ * log, pow
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x A number or matrix to exponentiate
+ * @return {Number | BigNumber | Complex | Array | Matrix} Exponent of `x`
+ */
+ math.exp = function exp (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('exp', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return Math.exp(x);
+ }
+
+ if (isComplex(x)) {
+ var r = Math.exp(x.re);
+ return new Complex(
+ r * Math.cos(x.im),
+ r * Math.sin(x.im)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.exp();
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, exp);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return Math.exp(x);
+ }
+
+ throw new math.error.UnsupportedTypeError('exp', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 45 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Round a value towards zero.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.fix(x)
+ *
+ * Examples:
+ *
+ * math.fix(3.2); // returns Number 3
+ * math.fix(3.8); // returns Number 3
+ * math.fix(-4.2); // returns Number -4
+ * math.fix(-4.7); // returns Number -4
+ *
+ * var c = math.complex(3.2, -2.7);
+ * math.fix(c); // returns Complex 3 - 2i
+ *
+ * math.fix([3.2, 3.8, -4.7]); // returns Array [3, 3, -4]
+ *
+ * See also:
+ *
+ * ceil, floor, round
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x Number to be rounded
+ * @return {Number | BigNumber | Complex | Array | Matrix} Rounded value
+ */
+ math.fix = function fix(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('fix', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return (x > 0) ? Math.floor(x) : Math.ceil(x);
+ }
+
+ if (isComplex(x)) {
+ return new Complex(
+ (x.re > 0) ? Math.floor(x.re) : Math.ceil(x.re),
+ (x.im > 0) ? Math.floor(x.im) : Math.ceil(x.im)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.isNegative() ? x.ceil() : x.floor();
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, fix);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return fix(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('fix', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 46 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Round a value towards minus infinity.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.floor(x)
+ *
+ * Examples:
+ *
+ * math.floor(3.2); // returns Number 3
+ * math.floor(3.8); // returns Number 3
+ * math.floor(-4.2); // returns Number -5
+ * math.floor(-4.7); // returns Number -5
+ *
+ * var c = math.complex(3.2, -2.7);
+ * math.floor(c); // returns Complex 3 - 3i
+ *
+ * math.floor([3.2, 3.8, -4.7]); // returns Array [3, 3, -5]
+ *
+ * See also:
+ *
+ * ceil, fix, round
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x Number to be rounded
+ * @return {Number | BigNumber | Complex | Array | Matrix} Rounded value
+ */
+ math.floor = function floor(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('floor', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return Math.floor(x);
+ }
+
+ if (isComplex(x)) {
+ return new Complex (
+ Math.floor(x.re),
+ Math.floor(x.im)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.floor();
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, floor);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return floor(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('floor', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 47 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the greatest common divisor for two or more values or arrays.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.gcd(a, b)
+ * math.gcd(a, b, c, ...)
+ *
+ * Examples:
+ *
+ * math.gcd(8, 12); // returns 4
+ * math.gcd(-4, 6); // returns 2
+ * math.gcd(25, 15, -10); // returns 5
+ *
+ * math.gcd([8, -4], [12, 6]); // returns [4, 2]
+ *
+ * See also:
+ *
+ * lcm, xgcd
+ *
+ * @param {... Number | BigNumber | Boolean | Array | Matrix | null} args Two or more integer numbers
+ * @return {Number | BigNumber | Array | Matrix} The greatest common divisor
+ */
+ math.gcd = function gcd(args) {
+ var a = arguments[0],
+ b = arguments[1],
+ r; // remainder
+
+ if (arguments.length == 2) {
+ // two arguments
+ if (isNumber(a) && isNumber(b)) {
+ if (!isInteger(a) || !isInteger(b)) {
+ throw new Error('Parameters in function gcd must be integer numbers');
+ }
+
+ // http://en.wikipedia.org/wiki/Euclidean_algorithm
+ while (b != 0) {
+ r = a % b;
+ a = b;
+ b = r;
+ }
+ return (a < 0) ? -a : a;
+ }
+
+ // evaluate gcd element wise
+ if (isCollection(a) || isCollection(b)) {
+ return collection.deepMap2(a, b, gcd);
+ }
+
+ if (a instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(b)) {
+ b = BigNumber.convert(b);
+ }
+ else if (isBoolean(b) || b === null) {
+ b = new BigNumber(b ? 1 : 0);
+ }
+
+ if (b instanceof BigNumber) {
+ return _bigGcd(a, b);
+ }
+
+ // downgrade to Number
+ return gcd(a.toNumber(), b);
+ }
+ if (b instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(a)) {
+ a = BigNumber.convert(a);
+ }
+ else if (isBoolean(a) || a === null) {
+ a = new BigNumber(a ? 1 : 0);
+ }
+
+ if (a instanceof BigNumber) {
+ return _bigGcd(a, b);
+ }
+
+ // downgrade to Number
+ return gcd(a.toNumber(), b);
+ }
+
+ if (isBoolean(a) || a === null) {
+ return gcd(+a, b);
+ }
+ if (isBoolean(b) || b === null) {
+ return gcd(a, +b);
+ }
+
+ throw new math.error.UnsupportedTypeError('gcd', math['typeof'](a), math['typeof'](b));
+ }
+
+ if (arguments.length > 2) {
+ // multiple arguments. Evaluate them iteratively
+ for (var i = 1; i < arguments.length; i++) {
+ a = gcd(a, arguments[i]);
+ }
+ return a;
+ }
+
+ // zero or one argument
+ throw new SyntaxError('Function gcd expects two or more arguments');
+ };
+
+ /**
+ * Calculate gcd for BigNumbers
+ * @param {BigNumber} a
+ * @param {BigNumber} b
+ * @returns {BigNumber} greatest common denominator of a and b
+ * @private
+ */
+ function _bigGcd(a, b) {
+ if (!a.isInt() || !b.isInt()) {
+ throw new Error('Parameters in function gcd must be integer numbers');
+ }
+
+ // http://en.wikipedia.org/wiki/Euclidean_algorithm
+ var zero = new BigNumber(0);
+ while (!b.isZero()) {
+ var r = a.mod(b);
+ a = b;
+ b = r;
+ }
+ return a.lt(zero) ? a.neg() : a;
+ }
+ };
+
+
+/***/ },
+/* 48 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the least common multiple for two or more values or arrays.
+ *
+ * lcm is defined as:
+ *
+ * lcm(a, b) = abs(a * b) / gcd(a, b)
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.lcm(a, b)
+ * math.lcm(a, b, c, ...)
+ *
+ * Examples:
+ *
+ * math.lcm(4, 6); // returns 12
+ * math.lcm(6, 21); // returns 42
+ * math.lcm(6, 21, 5); // returns 210
+ *
+ * math.lcm([4, 6], [6, 21]); // returns [12, 42]
+ *
+ * See also:
+ *
+ * gcd, xgcd
+ *
+ * @param {... Number | BigNumber | Boolean | Array | Matrix | null} args Two or more integer numbers
+ * @return {Number | BigNumber | Array | Matrix} The least common multiple
+ */
+ math.lcm = function lcm(args) {
+ var a = arguments[0],
+ b = arguments[1],
+ t;
+
+ if (arguments.length == 2) {
+ // two arguments
+ if (isNumber(a) && isNumber(b)) {
+ if (!isInteger(a) || !isInteger(b)) {
+ throw new Error('Parameters in function lcm must be integer numbers');
+ }
+
+ if (a == 0 || b == 0) {
+ return 0;
+ }
+
+ // http://en.wikipedia.org/wiki/Euclidean_algorithm
+ // evaluate lcm here inline to reduce overhead
+ var prod = a * b;
+ while (b != 0) {
+ t = b;
+ b = a % t;
+ a = t;
+ }
+ return Math.abs(prod / a);
+ }
+
+ // evaluate lcm element wise
+ if (isCollection(a) || isCollection(b)) {
+ return collection.deepMap2(a, b, lcm);
+ }
+
+ if (a instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(b)) {
+ b = BigNumber.convert(b);
+ }
+ else if (isBoolean(b) || b === null) {
+ b = new BigNumber(b ? 1 : 0);
+ }
+
+ if (b instanceof BigNumber) {
+ return _bigLcm(a, b);
+ }
+
+ // downgrade to Number
+ return lcm(a.toNumber(), b);
+ }
+ if (b instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(a)) {
+ a = BigNumber.convert(a);
+ }
+ else if (isBoolean(a) || a === null) {
+ a = new BigNumber(a ? 1 : 0);
+ }
+
+ if (a instanceof BigNumber) {
+ return _bigLcm(a, b);
+ }
+
+ // downgrade to Number
+ return lcm(a.toNumber(), b);
+ }
+
+ if (isBoolean(a) || a === null) {
+ return lcm(+a, b);
+ }
+ if (isBoolean(b) || b === null) {
+ return lcm(a, +b);
+ }
+
+ throw new math.error.UnsupportedTypeError('lcm', math['typeof'](a), math['typeof'](b));
+ }
+
+ if (arguments.length > 2) {
+ // multiple arguments. Evaluate them iteratively
+ for (var i = 1; i < arguments.length; i++) {
+ a = lcm(a, arguments[i]);
+ }
+ return a;
+ }
+
+ // zero or one argument
+ throw new SyntaxError('Function lcm expects two or more arguments');
+ };
+
+ /**
+ * Calculate lcm for BigNumbers
+ * @param {BigNumber} a
+ * @param {BigNumber} b
+ * @returns {BigNumber} the least common multiple of a and b
+ * @private
+ */
+ function _bigLcm(a, b) {
+ if (!a.isInt() || !b.isInt()) {
+ throw new Error('Parameters in function lcm must be integer numbers');
+ }
+
+ if (a.isZero() || b.isZero()) {
+ return new BigNumber(0);
+ }
+
+ // http://en.wikipedia.org/wiki/Euclidean_algorithm
+ // evaluate lcm here inline to reduce overhead
+ var prod = a.times(b);
+ while (!b.isZero()) {
+ var t = b;
+ b = a.mod(t);
+ a = t;
+ }
+ return prod.div(a).abs();
+ }
+ };
+
+
+/***/ },
+/* 49 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the logarithm of a value.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.log(x)
+ * math.log(x, base)
+ *
+ * Examples:
+ *
+ * math.log(3.5); // returns 1.252762968495368
+ * math.exp(math.log(2.4)); // returns 2.4
+ *
+ * math.pow(10, 4); // returns 10000
+ * math.log(10000, 10); // returns 4
+ * math.log(10000) / math.log(10); // returns 4
+ *
+ * math.log(1024, 2); // returns 10
+ * math.pow(2, 10); // returns 1024
+ *
+ * See also:
+ *
+ * exp, log10
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x
+ * Value for which to calculate the logarithm.
+ * @param {Number | BigNumber | Boolean | Complex | null} [base=e]
+ * Optional base for the logarithm. If not provided, the natural
+ * logarithm of `x` is calculated.
+ * @return {Number | BigNumber | Complex | Array | Matrix}
+ * Returns the logarithm of `x`
+ */
+ math.log = function log(x, base) {
+ if (arguments.length == 1) {
+ // calculate natural logarithm, log(x)
+ if (isNumber(x)) {
+ if (x >= 0) {
+ return Math.log(x);
+ }
+ else {
+ // negative value -> complex value computation
+ return log(new Complex(x, 0));
+ }
+ }
+
+ if (isComplex(x)) {
+ return new Complex (
+ Math.log(Math.sqrt(x.re * x.re + x.im * x.im)),
+ Math.atan2(x.im, x.re)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isNegative()) {
+ // negative value -> downgrade to number to do complex value computation
+ return log(x.toNumber());
+ }
+ else {
+ return x.ln();
+ }
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, log);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return log(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('log', math['typeof'](x));
+ }
+ else if (arguments.length == 2) {
+ // calculate logarithm for a specified base, log(x, base)
+ return math.divide(log(x), log(base));
+ }
+ else {
+ throw new math.error.ArgumentsError('log', arguments.length, 1, 2);
+ }
+ };
+ };
+
+
+/***/ },
+/* 50 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the 10-base of a value. This is the same as calculating `log(x, 10)`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.log10(x)
+ *
+ * Examples:
+ *
+ * math.log10(0.00001); // returns -5
+ * math.log10(10000); // returns 4
+ * math.log(10000) / math.log(10); // returns 4
+ * math.pow(10, 4); // returns 10000
+ *
+ * See also:
+ *
+ * exp, log
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x
+ * Value for which to calculate the logarithm.
+ * @return {Number | BigNumber | Complex | Array | Matrix}
+ * Returns the 10-base logarithm of `x`
+ */
+ math.log10 = function log10(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('log10', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ if (x >= 0) {
+ return Math.log(x) / Math.LN10;
+ }
+ else {
+ // negative value -> complex value computation
+ return log10(new Complex(x, 0));
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isNegative()) {
+ // negative value -> downgrade to number to do complex value computation
+ return log10(x.toNumber());
+ }
+ else {
+ return x.log();
+ }
+ }
+
+ if (isComplex(x)) {
+ return new Complex (
+ Math.log(Math.sqrt(x.re * x.re + x.im * x.im)) / Math.LN10,
+ Math.atan2(x.im, x.re) / Math.LN10
+ );
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, log10);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return log10(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('log10', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 51 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculates the modulus, the remainder of an integer division.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * The modulus is defined as:
+ *
+ * x - y * floor(x / y)
+ *
+ * See http://en.wikipedia.org/wiki/Modulo_operation.
+ *
+ * Syntax:
+ *
+ * math.mod(x, y)
+ *
+ * Examples:
+ *
+ * math.mod(8, 3); // returns 2
+ * math.mod(11, 2); // returns 1
+ *
+ * function isOdd(x) {
+ * return math.mod(x, 2) != 0;
+ * }
+ *
+ * isOdd(2); // returns false
+ * isOdd(3); // returns true
+ *
+ * See also:
+ *
+ * divide
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x Dividend
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} y Divisor
+ * @return {Number | BigNumber | Array | Matrix} Returns the remainder of `x` divided by `y`.
+ */
+ math.mod = function mod(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('mod', arguments.length, 2);
+ }
+
+ // see http://functions.wolfram.com/IntegerFunctions/Mod/
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ // number % number
+ return _mod(x, y);
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return y.isZero() ? x : x.mod(y);
+ }
+
+ // downgrade x to Number
+ return mod(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return y.isZero() ? x : x.mod(y);
+ }
+
+ // downgrade y to Number
+ return mod(x, y.toNumber());
+ }
+
+ // TODO: implement mod for complex values
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, mod);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return mod(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return mod(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('mod', math['typeof'](x), math['typeof'](y));
+ };
+
+ /**
+ * Calculate the modulus of two numbers
+ * @param {Number} x
+ * @param {Number} y
+ * @returns {number} res
+ * @private
+ */
+ function _mod(x, y) {
+ if (y > 0) {
+ // We don't use JavaScript's % operator here as this doesn't work
+ // correctly for x < 0 and x == 0
+ // see http://en.wikipedia.org/wiki/Modulo_operation
+ return x - y * Math.floor(x / y);
+ }
+ else if (y == 0) {
+ return x;
+ }
+ else { // y < 0
+ // TODO: implement mod for a negative divisor
+ throw new Error('Cannot calculate mod for a negative divisor');
+ }
+ }
+ };
+
+
+/***/ },
+/* 52 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function(math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ array = util.array,
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isArray = Array.isArray,
+ isUnit = Unit.isUnit;
+
+ /**
+ * Multiply two values, `x * y`. The result is squeezed.
+ * For matrices, the matrix product is calculated.
+ *
+ * Syntax:
+ *
+ * math.multiply(x, y)
+ *
+ * Examples:
+ *
+ * math.multiply(4, 5.2); // returns Number 20.8
+ *
+ * var a = math.complex(2, 3);
+ * var b = math.complex(4, 1);
+ * math.multiply(a, b); // returns Complex 5 + 14i
+ *
+ * var c = [[1, 2], [4, 3]];
+ * var d = [[1, 2, 3], [3, -4, 7]];
+ * math.multiply(c, d); // returns Array [[7, -6, 17], [13, -4, 33]]
+ *
+ * var e = math.unit('2.1 km');
+ * math.multiply(3, e); // returns Unit 6.3 km
+ *
+ * See also:
+ *
+ * divide
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First value to multiply
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Second value to multiply
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`
+ */
+ math.multiply = function multiply(x, y) {
+ var res;
+
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('multiply', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ // number * number
+ return x * y;
+ }
+ else if (isComplex(y)) {
+ // number * complex
+ return _multiplyComplex (new Complex(x, 0), y);
+ }
+ else if (isUnit(y)) {
+ res = y.clone();
+ res.value = (res.value === null) ? res._normalize(x) : (res.value * x);
+ return res;
+ }
+ }
+
+ if (isComplex(x)) {
+ if (isNumber(y)) {
+ // complex * number
+ return _multiplyComplex (x, new Complex(y, 0));
+ }
+ else if (isComplex(y)) {
+ // complex * complex
+ return _multiplyComplex (x, y);
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.times(y);
+ }
+
+ // downgrade to Number
+ return multiply(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.times(y)
+ }
+
+ // downgrade to Number
+ return multiply(x, y.toNumber());
+ }
+
+ if (isUnit(x)) {
+ if (isNumber(y)) {
+ res = x.clone();
+ res.value = (res.value === null) ? res._normalize(y) : (res.value * y);
+ return res;
+ }
+ }
+
+ if (isArray(x)) {
+ if (isArray(y)) {
+ // array * array
+ var sizeX = array.size(x);
+ var sizeY = array.size(y);
+
+ if (sizeX.length == 1) {
+ if (sizeY.length == 1) {
+ // vector * vector
+ if (sizeX[0] != sizeY[0]) {
+ throw new RangeError('Dimension mismatch in multiplication. ' +
+ 'Length of A must match length of B ' +
+ '(A is ' + sizeX[0] +
+ ', B is ' + sizeY[0] + ', ' +
+ sizeX[0] + ' != ' + sizeY[0] + ')');
+ }
+
+ return _multiplyVectorVector(x, y);
+ }
+ else if (sizeY.length == 2) {
+ // vector * matrix
+ if (sizeX[0] != sizeY[0]) {
+ throw new RangeError('Dimension mismatch in multiplication. ' +
+ 'Length of A must match rows of B ' +
+ '(A is ' + sizeX[0] +
+ ', B is ' + sizeY[0] + 'x' + sizeY[1] + ', ' +
+ sizeX[0] + ' != ' + sizeY[0] + ')');
+ }
+
+ return _multiplyVectorMatrix(x, y);
+ }
+ else {
+ throw new Error('Can only multiply a 1 or 2 dimensional matrix ' +
+ '(B has ' + sizeY.length + ' dimensions)');
+ }
+ }
+ else if (sizeX.length == 2) {
+ if (sizeY.length == 1) {
+ // matrix * vector
+ if (sizeX[1] != sizeY[0]) {
+ throw new RangeError('Dimension mismatch in multiplication. ' +
+ 'Columns of A must match length of B ' +
+ '(A is ' + sizeX[0] + 'x' + sizeX[0] +
+ ', B is ' + sizeY[0] + ', ' +
+ sizeX[1] + ' != ' + sizeY[0] + ')');
+ }
+
+ return _multiplyMatrixVector(x, y);
+ }
+ else if (sizeY.length == 2) {
+ // matrix * matrix
+ if (sizeX[1] != sizeY[0]) {
+ throw new RangeError('Dimension mismatch in multiplication. ' +
+ 'Columns of A must match rows of B ' +
+ '(A is ' + sizeX[0] + 'x' + sizeX[1] +
+ ', B is ' + sizeY[0] + 'x' + sizeY[1] + ', ' +
+ sizeX[1] + ' != ' + sizeY[0] + ')');
+ }
+
+ return _multiplyMatrixMatrix(x, y);
+ }
+ else {
+ throw new Error('Can only multiply a 1 or 2 dimensional matrix ' +
+ '(B has ' + sizeY.length + ' dimensions)');
+ }
+ }
+ else {
+ throw new Error('Can only multiply a 1 or 2 dimensional matrix ' +
+ '(A has ' + sizeX.length + ' dimensions)');
+ }
+ }
+ else if (y instanceof Matrix) {
+ // array * matrix
+ res = multiply(x, y.valueOf());
+ return isArray(res) ? new Matrix(res) : res;
+ }
+ else {
+ // array * scalar
+ return collection.deepMap2(x, y, multiply);
+ }
+ }
+
+ if (x instanceof Matrix) {
+ if (y instanceof Matrix) {
+ // matrix * matrix
+ res = multiply(x.valueOf(), y.valueOf());
+ return isArray(res) ? new Matrix(res) : res;
+ }
+ else {
+ // matrix * array
+ // matrix * scalar
+ res = multiply(x.valueOf(), y);
+ return isArray(res) ? new Matrix(res) : res;
+ }
+ }
+
+ if (isArray(y)) {
+ // scalar * array
+ return collection.deepMap2(x, y, multiply);
+ }
+ else if (y instanceof Matrix) {
+ // scalar * matrix
+ return new Matrix(collection.deepMap2(x, y.valueOf(), multiply));
+ }
+
+ if (isBoolean(x) || x === null) {
+ return multiply(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return multiply(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('multiply', math['typeof'](x), math['typeof'](y));
+ };
+
+ /**
+ * Multiply two 2-dimensional matrices.
+ * The size of the matrices is not validated.
+ * @param {Array} x A 2d matrix
+ * @param {Array} y A 2d matrix
+ * @return {Array | Number} result
+ * @private
+ */
+ function _multiplyMatrixMatrix(x, y) {
+ // TODO: performance of matrix multiplication can be improved
+ var res = [],
+ rows = x.length,
+ cols = y[0].length,
+ num = x[0].length;
+
+ for (var r = 0; r < rows; r++) {
+ res[r] = [];
+ for (var c = 0; c < cols; c++) {
+ var result = null;
+ for (var n = 0; n < num; n++) {
+ var p = math.multiply(x[r][n], y[n][c]);
+ result = (result === null) ? p : math.add(result, p);
+ }
+ res[r][c] = result;
+ }
+ }
+
+ var isScalar = rows === 1 && cols === 1;
+ return isScalar ? res[0][0] : res;
+ }
+
+ /**
+ * Multiply a vector with a 2-dimensional matrix
+ * The size of the matrices is not validated.
+ * @param {Array} x A vector
+ * @param {Array} y A 2d matrix
+ * @return {Array | Number} result
+ * @private
+ */
+ function _multiplyVectorMatrix(x, y) {
+ // TODO: performance of matrix multiplication can be improved
+ var res = [],
+ rows = y.length,
+ cols = y[0].length;
+
+ for (var c = 0; c < cols; c++) {
+ var result = null;
+ for (var r = 0; r < rows; r++) {
+ var p = math.multiply(x[r], y[r][c]);
+ result = (r === 0) ? p : math.add(result, p);
+ }
+ res[c] = result;
+ }
+
+ return res.length === 1 ? res[0] : res;
+ }
+
+ /**
+ * Multiply a 2-dimensional matrix with a vector
+ * The size of the matrices is not validated.
+ * @param {Array} x A 2d matrix
+ * @param {Array} y A vector
+ * @return {Array | Number} result
+ * @private
+ */
+ function _multiplyMatrixVector(x, y) {
+ // TODO: performance of matrix multiplication can be improved
+ var res = [],
+ rows = x.length,
+ cols = x[0].length;
+
+ for (var r = 0; r < rows; r++) {
+ var result = null;
+ for (var c = 0; c < cols; c++) {
+ var p = math.multiply(x[r][c], y[c]);
+ result = (c === 0) ? p : math.add(result, p);
+ }
+ res[r] = result;
+ }
+
+ return res.length === 1 ? res[0] : res;
+ }
+
+ /**
+ * Multiply two vectors, calculate the dot product
+ * The size of the matrices is not validated.
+ * @param {Array} x A vector
+ * @param {Array} y A vector
+ * @return {Number} dotProduct
+ * @private
+ */
+ function _multiplyVectorVector(x, y) {
+ // TODO: performance of matrix multiplication can be improved
+ var len = x.length;
+
+ if (!len) {
+ throw new Error('Cannot multiply two empty vectors');
+ }
+
+ var dot = 0;
+ for (var i = 0; i < len; i++) {
+ dot = math.add(dot, math.multiply(x[i], y[i]));
+ }
+ return dot;
+ }
+
+ /**
+ * Multiply two complex numbers. x * y or multiply(x, y)
+ * @param {Complex} x
+ * @param {Complex} y
+ * @return {Complex | Number} res
+ * @private
+ */
+ function _multiplyComplex (x, y) {
+ // Note: we test whether x or y are pure real or pure complex,
+ // to prevent unnecessary NaN values. For example, Infinity*i should
+ // result in Infinity*i, and not in NaN+Infinity*i
+
+ if (x.im == 0) {
+ // x is pure real
+ if (y.im == 0) {
+ // y is pure real
+ return new Complex(x.re * y.re, 0);
+ }
+ else if (y.re == 0) {
+ // y is pure complex
+ return new Complex(
+ 0,
+ x.re * y.im
+ );
+ }
+ else {
+ // y has a real and complex part
+ return new Complex(
+ x.re * y.re,
+ x.re * y.im
+ );
+ }
+ }
+ else if (x.re == 0) {
+ // x is pure complex
+ if (y.im == 0) {
+ // y is pure real
+ return new Complex(
+ 0,
+ x.im * y.re
+ );
+ }
+ else if (y.re == 0) {
+ // y is pure complex
+ return new Complex(-x.im * y.im, 0);
+ }
+ else {
+ // y has a real and complex part
+ return new Complex(
+ -x.im * y.im,
+ x.im * y.re
+ );
+ }
+ }
+ else {
+ // x has a real and complex part
+ if (y.im == 0) {
+ // y is pure real
+ return new Complex(
+ x.re * y.re,
+ x.im * y.re
+ );
+ }
+ else if (y.re == 0) {
+ // y is pure complex
+ return new Complex(
+ -x.im * y.im,
+ x.re * y.im
+ );
+ }
+ else {
+ // y has a real and complex part
+ return new Complex(
+ x.re * y.re - x.im * y.im,
+ x.re * y.im + x.im * y.re
+ );
+ }
+ }
+ }
+ };
+
+
+/***/ },
+/* 53 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ array = __webpack_require__(165),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isArray = Array.isArray;
+
+ /**
+ * Calculate the norm of a number, vector or matrix.
+ *
+ * The second parameter p is optional. If not provided, it defaults to 2.
+ *
+ * Syntax:
+ *
+ * math.norm(x)
+ * math.norm(x, p)
+ *
+ * Examples:
+ *
+ * math.abs(-3.5); // returns 3.5
+ * math.norm(-3.5); // returns 3.5
+ *
+ * math.norm(math.complex(3, -4)); // returns 5
+ *
+ * math.norm([1, 2, -3], Infinity); // returns 3
+ * math.norm([1, 2, -3], -Infinity); // returns 1
+ *
+ * math.norm([3, 4], 2); // returns 5
+ *
+ * math.norm([[1, 2], [3, 4]], 1) // returns 6
+ * math.norm([[1, 2], [3, 4]], 'inf'); // returns 7
+ * math.norm([[1, 2], [3, 4]], 'fro'); // returns 5.477225575051661
+ *
+ * See also:
+ *
+ * abs
+ *
+ * @param {Number | BigNumber | Complex | Boolean | Array | Matrix | null} x
+ * Value for which to calculate the norm
+ * @param {Number | String} [p=2]
+ * Vector space.
+ * Supported numbers include Infinity and -Infinity.
+ * Supported strings are: 'inf', '-inf', and 'fro' (The Frobenius norm)
+ * @return {Number} the p-norm
+ */
+ math.norm = function norm(x, p) {
+ if (arguments.length < 1 || arguments.length > 2) {
+ throw new math.error.ArgumentsError('abs', arguments.length, 1, 2);
+ }
+
+ if (isNumber(x)) {
+ // norm(x) = abs(x)
+ return Math.abs(x);
+ }
+
+ if (isComplex(x)) {
+ // do not compute sqrt(re * re + im * im) since it will overflow with big numbers!
+ var re = Math.abs(x.re);
+ var im = Math.abs(x.im);
+ if (re >= im) {
+ var x = im / re;
+ return re * Math.sqrt(1 + x * x);
+ }
+ var y = re / im;
+ return im * Math.sqrt(1 + y * y);
+ }
+
+ if (x instanceof BigNumber) {
+ // norm(x) = abs(x)
+ return x.abs();
+ }
+
+ if (isBoolean(x) || x === null) {
+ // norm(x) = abs(x)
+ return Math.abs(x);
+ }
+
+ if (isArray(x)) {
+ // size
+ var sizeX = array.size(x);
+ // missing p
+ if (p == null)
+ p = 2;
+ // check it is a Vector
+ if (sizeX.length == 1) {
+ // check p
+ if (p === Number.POSITIVE_INFINITY || p === 'inf') {
+ // norm(x, Infinity) = max(abs(x))
+ var n;
+ math.forEach(x, function (value) {
+ var v = math.abs(value);
+ if (!n || math.larger(v, n))
+ n = v;
+ });
+ return n;
+ }
+ if (p === Number.NEGATIVE_INFINITY || p === '-inf') {
+ // norm(x, -Infinity) = min(abs(x))
+ var n;
+ math.forEach(x, function (value) {
+ var v = math.abs(value);
+ if (!n || math.smaller(v, n))
+ n = v;
+ });
+ return n;
+ }
+ if (p === 'fro')
+ return norm(x);
+ if (isNumber(p) && !isNaN(p)) {
+ // check p != 0
+ if (!math.equal(p, 0)) {
+ // norm(x, p) = sum(abs(xi) ^ p) ^ 1/p
+ var n = 0;
+ math.forEach(x, function (value) {
+ n = math.add(math.pow(math.abs(value), p), n);
+ });
+ return math.pow(n, 1 / p);
+ }
+ return Number.POSITIVE_INFINITY;
+ }
+ // invalid parameter value
+ throw new Error('Unsupported parameter value');
+ }
+ else if (sizeX.length == 2) {
+ // check p
+ if (p == 1) {
+ // norm(x) = the largest column sum
+ var c = [];
+ // loop rows
+ for (var i = 0; i < x.length; i++) {
+ var r = x[i];
+ // loop columns
+ for (var j = 0; j < r.length; j++) {
+ c[j] = math.add(c[j] || 0, math.abs(r[j]));
+ }
+ }
+ return math.max(c);
+ }
+ if (p == Number.POSITIVE_INFINITY || p === 'inf') {
+ // norm(x) = the largest row sum
+ var n = 0;
+ // loop rows
+ for (var i = 0; i < x.length; i++) {
+ var rs = 0;
+ var r = x[i];
+ // loop columns
+ for (var j = 0; j < r.length; j++) {
+ rs = math.add(rs, math.abs(r[j]));
+ }
+ if (math.larger(rs, n))
+ n = rs;
+ }
+ return n;
+ }
+ if (p === 'fro') {
+ // norm(x) = sqrt(sum(diag(x'x)))
+ var d = math.diag(math.multiply(math.transpose(x), x));
+ var s = 0;
+ math.forEach(d, function (value) {
+ s = math.add(value, s);
+ });
+ return math.sqrt(s);
+ }
+ if (p == 2) {
+ // not implemented
+ throw new Error('Unsupported parameter value, missing implementation of matrix singular value decomposition');
+ }
+ // invalid parameter value
+ throw new Error('Unsupported parameter value');
+ }
+ }
+
+ if (x instanceof Matrix) {
+ return norm(x.valueOf(), p);
+ }
+
+ throw new math.error.UnsupportedTypeError('norm', x);
+ };
+ };
+
+
+/***/ },
+/* 54 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171);
+
+ var BigNumber = math.type.BigNumber;
+ var collection = __webpack_require__(14);
+
+ var isNumber = util.number.isNumber;
+ var isBoolean = util['boolean'].isBoolean;
+ var isCollection = collection.isCollection;
+
+ /**
+ * Calculate the nth root of a value.
+ * The principal nth root of a positive real number A, is the positive real
+ * solution of the equation
+ *
+ * x^root = A
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.nthRoot(a, root)
+ *
+ * Examples:
+ *
+ * math.nthRoot(9, 2); // returns 3, as 3^2 == 9
+ * math.sqrt(9); // returns 3, as 3^2 == 9
+ * math.nthRoot(64, 3); // returns 4, as 4^3 == 64
+ *
+ * See also:
+ *
+ * sqrt, pow
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} a
+ * Value for which to calculate the nth root
+ * @param {Number | BigNumber | Boolean | null} [root=2] The root.
+ * @return {Number | Complex | Array | Matrix} Returns the nth root of `a`
+ */
+ math.nthRoot = function nthRoot (a, root) {
+ if (arguments.length != 1 && arguments.length != 2) {
+ throw new math.error.ArgumentsError('nthRoot', arguments.length, 1, 2);
+ }
+
+ switch(arguments.length) {
+ case 1:
+ if (isNumber(a)) {
+ return _nthRoot(a);
+ }
+ else if (a instanceof BigNumber) {
+ return _nthRootBig(a);
+ }
+ else if (isCollection(a)) {
+ return collection.deepMap(x, nthRoot);
+ }
+
+ if (isBoolean(a) || a === null) {
+ return nthRoot(+a);
+ }
+
+ break;
+
+ case 2:
+ if (isNumber(a)) {
+ if (isNumber(root)) {
+ return _nthRoot(a, root);
+ }
+ else if (root instanceof BigNumber) {
+ // try to convert to bignumber
+ a = BigNumber.convert(a);
+
+ if (a instanceof BigNumber) {
+ return _nthRootBig(a, root);
+ }
+ else {
+ // downgrade to number
+ return _nthRoot(a, root.toNumber());
+ }
+ }
+ }
+ else if (a instanceof BigNumber) {
+ // try to convert to bignumber
+ if (isNumber(root)) {
+ root = BigNumber.convert(root);
+ }
+
+ if (root instanceof BigNumber) {
+ return _nthRootBig(a, root);
+ }
+ else {
+ // downgrade to number
+ return _nthRoot(a.toNumber(), root);
+ }
+ }
+ else if (isCollection(a) && !isCollection(root)) {
+ return collection.deepMap2(a, root, nthRoot);
+ }
+
+ if (isBoolean(a) || a === null) {
+ return nthRoot(+a, root);
+ }
+ if (isBoolean(root) || root === null) {
+ return nthRoot(a, +root);
+ }
+
+ break;
+
+ default:
+ throw new math.error.ArgumentsError('nthRoot', arguments.length, 1, 2);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return arguments.length == 2 ? nthRoot(+x, n) : nthRoot(+x);
+ }
+
+
+ throw new math.error.UnsupportedTypeError('nthRoot', math['typeof'](a), math['typeof'](root));
+ };
+
+ /**
+ * Calculate the nth root of a, solve x^root == a
+ * http://rosettacode.org/wiki/Nth_root#JavaScript
+ * @param {number} a
+ * @param {number} [root=2]
+ * @private
+ */
+ function _nthRoot(a, root) {
+ var _root = (root != undefined) ? root : 2;
+ var inv = _root < 0;
+ if (inv) _root = -_root;
+
+ if (_root == 0) throw new Error('Root must be non-zero');
+ if (a < 0 && (Math.abs(_root) % 2 != 1)) throw new Error('Root must be odd when a is negative.');
+
+ // edge cases zero and infinity
+ if (a == 0) return 0;
+ if (!Number.isFinite(a)) {
+ return inv ? 0 : a;
+ }
+
+ var epsilon = 1e-16;
+ var x = 1; // Initial guess
+ var i = 0;
+ var iMax = 100;
+ do {
+ var delta = (a / Math.pow(x, _root - 1) - x) / _root;
+ x = x + delta;
+ i++;
+ }
+ while (Math.abs(delta) > epsilon && i < iMax);
+
+ return inv ? 1 / x : x;
+ }
+
+ /**
+ * Calculate the nth root of a for BigNumbers, solve x^root == a
+ * http://rosettacode.org/wiki/Nth_root#JavaScript
+ * @param {BigNumber} a
+ * @param {BigNumber} [root=2]
+ * @private
+ */
+ function _nthRootBig(a, root) {
+ var _root = (root != undefined) ? root : new BigNumber(2);
+ var zero = new BigNumber(0);
+ var one = new BigNumber(1);
+ var inv = _root.isNegative();
+ if (inv) _root = _root.negated();
+
+ if (_root.isZero()) throw new Error('Root must be non-zero');
+ if (a.isNegative() && !_root.abs().mod(2).equals(1)) throw new Error('Root must be odd when a is negative.');
+
+ // edge cases zero and infinity
+ if (a.isZero()) return zero;
+ if (!a.isFinite())
+ {
+ return inv ? zero : a;
+ }
+
+ var x = one; // Initial guess
+ var i = 0;
+ var iMax = 100;
+ do {
+ var xPrev = x;
+ var delta = a.div(x.pow(_root.minus(1))).minus(x).div(_root);
+ x = x.plus(delta);
+ i++;
+ }
+ while (!x.equals(xPrev) && i < iMax);
+
+ return inv ? one.div(x) : x;
+ }
+ };
+
+
+/***/ },
+/* 55 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ array = util.array,
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isArray = Array.isArray,
+ isInteger = util.number.isInteger,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Calculates the power of x to y, `x ^ y`.
+ * Matrix exponentiation is supported for square matrices `x`, and positive
+ * integer exponents `y`.
+ *
+ * Syntax:
+ *
+ * math.pow(x, y)
+ *
+ * Examples:
+ *
+ * math.pow(2, 3); // returns Number 8
+ *
+ * var a = math.complex(2, 3);
+ * math.pow(a, 2) // returns Complex -5 + 12i
+ *
+ * var b = [[1, 2], [4, 3]];
+ * math.pow(b, 2); // returns Array [[9, 8], [16, 17]]
+ *
+ * See also:
+ *
+ * multiply, sqrt
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x The base
+ * @param {Number | BigNumber | Boolean | Complex | null} y The exponent
+ * @return {Number | BigNumber | Complex | Array | Matrix} The value of `x` to the power `y`
+ */
+ math.pow = function pow(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('pow', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ if (isInteger(y) || x >= 0) {
+ // real value computation
+ return Math.pow(x, y);
+ }
+ else {
+ return powComplex(new Complex(x, 0), new Complex(y, 0));
+ }
+ }
+ else if (isComplex(y)) {
+ return powComplex(new Complex(x, 0), y);
+ }
+ }
+
+ if (isComplex(x)) {
+ if (isNumber(y)) {
+ return powComplex(x, new Complex(y, 0));
+ }
+ else if (isComplex(y)) {
+ return powComplex(x, y);
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to upgrade y to to bignumber
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ if (y.isInteger() || !x.isNegative()) {
+ return x.pow(y);
+ }
+ else {
+ // downgrade to number to do complex valued computation
+ return pow(x.toNumber(), y.toNumber())
+ }
+ }
+ else {
+ // failed to upgrade y to bignumber, lets downgrade x to number
+ return pow(x.toNumber(), y);
+ }
+ }
+
+ if (y instanceof BigNumber) {
+ // try to convert x to bignumber
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ if (y.isInteger() && !x.isNegative()) {
+ return x.pow(y);
+ }
+ else {
+ // downgrade to number to do complex valued computation
+ return pow(x.toNumber(), y.toNumber())
+ }
+ }
+ else {
+ // failed to upgrade x to bignumber, lets downgrade y to number
+ return pow(x, y.toNumber());
+ }
+ }
+
+ if (isArray(x)) {
+ if (!isNumber(y) || !isInteger(y) || y < 0) {
+ throw new TypeError('For A^b, b must be a positive integer ' +
+ '(value is ' + y + ')');
+ }
+ // verify that A is a 2 dimensional square matrix
+ var s = array.size(x);
+ if (s.length != 2) {
+ throw new Error('For A^b, A must be 2 dimensional ' +
+ '(A has ' + s.length + ' dimensions)');
+ }
+ if (s[0] != s[1]) {
+ throw new Error('For A^b, A must be square ' +
+ '(size is ' + s[0] + 'x' + s[1] + ')');
+ }
+
+ // compute power of matrix
+ var res = math.eye(s[0]).valueOf();
+ var px = x;
+ while (y >= 1) {
+ if ((y & 1) == 1) {
+ res = math.multiply(px, res);
+ }
+ y >>= 1;
+ px = math.multiply(px, px);
+ }
+ return res;
+ }
+ else if (x instanceof Matrix) {
+ return new Matrix(pow(x.valueOf(), y));
+ }
+
+ if (isBoolean(x) || x === null) {
+ return pow(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return pow(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('pow', math['typeof'](x), math['typeof'](y));
+ };
+
+ /**
+ * Calculates the power of x to y, x^y, for two complex numbers.
+ * @param {Complex} x
+ * @param {Complex} y
+ * @return {Complex} res
+ * @private
+ */
+ function powComplex (x, y) {
+ // complex computation
+ // x^y = exp(log(x)*y) = exp((abs(x)+i*arg(x))*y)
+ var temp1 = math.log(x);
+ var temp2 = math.multiply(temp1, y);
+ return math.exp(temp2);
+ }
+ };
+
+
+/***/ },
+/* 56 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Round a value towards the nearest integer.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.round(x)
+ * math.round(x, n)
+ *
+ * Examples:
+ *
+ * math.round(3.2); // returns Number 3
+ * math.round(3.8); // returns Number 4
+ * math.round(-4.2); // returns Number -4
+ * math.round(-4.7); // returns Number -5
+ * math.round(math.pi, 3); // returns Number 3.142
+ * math.round(123.45678, 2); // returns Number 123.46
+ *
+ * var c = math.complex(3.2, -2.7);
+ * math.round(c); // returns Complex 3 - 3i
+ *
+ * math.round([3.2, 3.8, -4.7]); // returns Array [3, 4, -5]
+ *
+ * See also:
+ *
+ * ceil, fix, floor
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x Number to be rounded
+ * @param {Number | BigNumber | Boolean | Array | null} [n=0] Number of decimals
+ * @return {Number | BigNumber | Complex | Array | Matrix} Rounded value
+ */
+ math.round = function round(x, n) {
+ if (arguments.length != 1 && arguments.length != 2) {
+ throw new math.error.ArgumentsError('round', arguments.length, 1, 2);
+ }
+
+ if (n == undefined) {
+ // round (x)
+ if (isNumber(x)) {
+ return Math.round(x);
+ }
+
+ if (isComplex(x)) {
+ return new Complex (
+ Math.round(x.re),
+ Math.round(x.im)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.toDecimalPlaces(0);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, round);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return Math.round(x);
+ }
+
+ throw new math.error.UnsupportedTypeError('round', math['typeof'](x));
+ }
+ else {
+ // round (x, n)
+ if (!isNumber(n) || !isInteger(n)) {
+ if (n instanceof BigNumber) {
+ n = parseFloat(n.valueOf());
+ }
+ else if (isBoolean(n) || x === null) {
+ return round(x, +n);
+ }
+ else {
+ throw new TypeError('Number of decimals in function round must be an integer');
+ }
+ }
+ if (n < 0 || n > 15) {
+ throw new Error ('Number of decimals in function round must be in te range of 0-15');
+ }
+
+ if (isNumber(x)) {
+ return roundNumber(x, n);
+ }
+
+ if (isComplex(x)) {
+ return new Complex (
+ roundNumber(x.re, n),
+ roundNumber(x.im, n)
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.toDecimalPlaces(n);
+ }
+
+ if (isCollection(x) || isCollection(n)) {
+ return collection.deepMap2(x, n, round);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return round(+x, n);
+ }
+
+ throw new math.error.UnsupportedTypeError('round', math['typeof'](x), math['typeof'](n));
+ }
+ };
+
+ /**
+ * round a number to the given number of decimals, or to zero if decimals is
+ * not provided
+ * @param {Number} value
+ * @param {Number} decimals number of decimals, between 0 and 15 (0 by default)
+ * @return {Number} roundedValue
+ */
+ function roundNumber (value, decimals) {
+ var p = Math.pow(10, decimals);
+ return Math.round(value * p) / p;
+ }
+ };
+
+
+/***/ },
+/* 57 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ number = util.number,
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the sign of a value. The sign of a value x is:
+ *
+ * - 1 when x > 1
+ * - -1 when x < 0
+ * - 0 when x == 0
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.sign(x)
+ *
+ * Examples:
+ *
+ * math.sign(3.5); // returns 1
+ * math.sign(-4.2); // returns -1
+ * math.sign(0); // returns 0
+ *
+ * math.sign([3, 5, -2, 0, 2]); // returns [1, 1, -1, 0, 1]
+ *
+ * See also:
+ *
+ * abs
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x
+ * The number for which to determine the sign
+ * @return {Number | BigNumber | Complex | Array | Matrix}e
+ * The sign of `x`
+ */
+ math.sign = function sign(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('sign', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return number.sign(x);
+ }
+
+ if (isComplex(x)) {
+ var abs = Math.sqrt(x.re * x.re + x.im * x.im);
+ return new Complex(x.re / abs, x.im / abs);
+ }
+
+ if (x instanceof BigNumber) {
+ return new BigNumber(x.cmp(0));
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, sign);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return number.sign(x);
+ }
+
+ throw new math.error.UnsupportedTypeError('sign', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 58 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Calculate the square root of a value.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.sqrt(x)
+ *
+ * Examples:
+ *
+ * math.sqrt(25); // returns 5
+ * math.square(5); // returns 25
+ * math.sqrt(-4); // returns Complex -2i
+ *
+ * See also:
+ *
+ * square, multiply
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x
+ * Value for which to calculate the square root.
+ * @return {Number | BigNumber | Complex | Array | Matrix}
+ * Returns the square root of `x`
+ */
+ math.sqrt = function sqrt (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('sqrt', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ if (x >= 0) {
+ return Math.sqrt(x);
+ }
+ else {
+ return sqrt(new Complex(x, 0));
+ }
+ }
+
+ if (isComplex(x)) {
+ var r = Math.sqrt(x.re * x.re + x.im * x.im);
+
+ var re, im;
+
+ if (x.re >= 0) {
+ re = 0.5 * Math.sqrt(2.0 * (r + x.re));
+ }
+ else {
+ re = Math.abs(x.im) / Math.sqrt(2 * (r - x.re));
+ }
+
+ if (x.re <= 0) {
+ im = 0.5 * Math.sqrt(2.0 * (r - x.re));
+ }
+ else {
+ im = Math.abs(x.im) / Math.sqrt(2 * (r + x.re));
+ }
+
+ if (x.im >= 0) {
+ return new Complex(re, im);
+ }
+ else {
+ return new Complex(re, -im);
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isNegative()) {
+ // negative value -> downgrade to number to do complex value computation
+ return sqrt(x.toNumber());
+ }
+ else {
+ return x.sqrt();
+ }
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, sqrt);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return sqrt(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('sqrt', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 59 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the square of a value, `x * x`.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.square(x)
+ *
+ * Examples:
+ *
+ * math.square(2); // returns Number 4
+ * math.square(3); // returns Number 9
+ * math.pow(3, 2); // returns Number 9
+ * math.multiply(3, 3); // returns Number 9
+ *
+ * math.square([1, 2, 3, 4]); // returns Array [1, 4, 9, 16]
+ *
+ * See also:
+ *
+ * multiply, cube, sqrt, pow
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x
+ * Number for which to calculate the square
+ * @return {Number | BigNumber | Complex | Array | Matrix}
+ * Squared value
+ */
+ math.square = function square(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('square', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return x * x;
+ }
+
+ if (isComplex(x)) {
+ return math.multiply(x, x);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.times(x);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, square);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return x * x;
+ }
+
+ throw new math.error.UnsupportedTypeError('square', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 60 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isNumber = util.number.isNumber,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Subtract two values, `x - y`.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.subtract(x, y)
+ *
+ * Examples:
+ *
+ * math.subtract(5.3, 2); // returns Number 3.3
+ *
+ * var a = math.complex(2, 3);
+ * var b = math.complex(4, 1);
+ * math.subtract(a, b); // returns Complex -2 + 2i
+ *
+ * math.subtract([5, 7, 4], 4); // returns Array [1, 3, 0]
+ *
+ * var c = math.unit('2.1 km');
+ * var d = math.unit('500m');
+ * math.subtract(c, d); // returns Unit 1.6 km
+ *
+ * See also:
+ *
+ * add
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x
+ * Initial value
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y
+ * Value to subtract from `x`
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix}
+ * Subtraction of `x` and `y`
+ */
+ math.subtract = function subtract(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('subtract', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ // number - number
+ return x - y;
+ }
+ else if (isComplex(y)) {
+ // number - complex
+ return new Complex (
+ x - y.re,
+ - y.im
+ );
+ }
+ }
+ else if (isComplex(x)) {
+ if (isNumber(y)) {
+ // complex - number
+ return new Complex (
+ x.re - y,
+ x.im
+ )
+ }
+ else if (isComplex(y)) {
+ // complex - complex
+ return new Complex (
+ x.re - y.re,
+ x.im - y.im
+ )
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.minus(y);
+ }
+
+ // downgrade to Number
+ return subtract(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.minus(y)
+ }
+
+ // downgrade to Number
+ return subtract(x, y.toNumber());
+ }
+
+ if (isUnit(x)) {
+ if (isUnit(y)) {
+ if (x.value == null) {
+ throw new Error('Parameter x contains a unit with undefined value');
+ }
+
+ if (y.value == null) {
+ throw new Error('Parameter y contains a unit with undefined value');
+ }
+
+ if (!x.equalBase(y)) {
+ throw new Error('Units do not match');
+ }
+
+ var res = x.clone();
+ res.value -= y.value;
+ res.fixPrefix = false;
+
+ return res;
+ }
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, subtract);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return subtract(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return subtract(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('subtract', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 61 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Inverse the sign of a value, apply a unary minus operation.
+ *
+ * For matrices, the function is evaluated element wise. Boolean values and
+ * strings will be converted to a number. For complex numbers, both real and
+ * complex value are inverted.
+ *
+ * Syntax:
+ *
+ * math.unaryMinus(x)
+ *
+ * Examples:
+ *
+ * math.unaryMinus(3.5); // returns -3.5
+ * math.unaryMinus(-4.2); // returns 4.2
+ *
+ * See also:
+ *
+ * add, subtract, unaryPlus
+ *
+ * @param {Number | BigNumber | Boolean | String | Complex | Unit | Array | Matrix | null} x Number to be inverted.
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix} Returns the value with inverted sign.
+ */
+ math.unaryMinus = function unaryMinus(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('unaryMinus', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return -x;
+ }
+
+ if (isComplex(x)) {
+ return new Complex(
+ -x.re,
+ -x.im
+ );
+ }
+
+ if (x instanceof BigNumber) {
+ return x.neg();
+ }
+
+ if (isUnit(x)) {
+ var res = x.clone();
+ res.value = -x.value;
+ return res;
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, unaryMinus);
+ }
+
+ if (isBoolean(x) || isString(x) || x === null) {
+ // convert to a number or bignumber
+ return (config.number == 'bignumber') ? new BigNumber(-x): -x;
+ }
+
+ throw new math.error.UnsupportedTypeError('unaryMinus', math['typeof'](x));
+ };
+
+ // TODO: function unary is renamed to unaryMinus since version 0.23.0. Cleanup some day
+ math.unary = function unary() {
+ throw new Error('Function unary is deprecated. Use unaryMinus instead.');
+ }
+ };
+
+
+/***/ },
+/* 62 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Unary plus operation.
+ * Boolean values and strings will be converted to a number, numeric values will be returned as is.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.unaryPlus(x)
+ *
+ * Examples:
+ *
+ * math.unaryPlus(3.5); // returns 3.5
+ * math.unaryPlus(1); // returns 1
+ *
+ * See also:
+ *
+ * unaryMinus, add, subtract
+ *
+ * @param {Number | BigNumber | Boolean | String | Complex | Unit | Array | Matrix | null} x
+ * Input value
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix}
+ * Returns the input value when numeric, converts to a number when input is non-numeric.
+ */
+ math.unaryPlus = function unaryPlus(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('unaryPlus', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return x;
+ }
+
+ if (isComplex(x)) {
+ return x.clone();
+ }
+
+ if (x instanceof BigNumber) {
+ return x;
+ }
+
+ if (isUnit(x)) {
+ return x.clone();
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, unaryPlus);
+ }
+
+ if (isBoolean(x) || isString(x) || x === null) {
+ // convert to a number or bignumber
+ return (config.number == 'bignumber') ? new BigNumber(+x): +x;
+ }
+
+ throw new math.error.UnsupportedTypeError('unaryPlus', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 63 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+ BigNumber = math.type.BigNumber,
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger;
+
+ /**
+ * Calculate the extended greatest common divisor for two values.
+ * See http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.
+ *
+ * Syntax:
+ *
+ * math.xgcd(a, b)
+ *
+ * Examples:
+ *
+ * math.xgcd(8, 12); // returns [4, -1, 1]
+ * math.gcd(8, 12); // returns 4
+ * math.xgcd(36163, 21199); // returns [1247, -7, 12]
+ *
+ * See also:
+ *
+ * gcd, lcm
+ *
+ * @param {Number | BigNumber | Boolean} a An integer number
+ * @param {Number | BigNumber | Boolean} b An integer number
+ * @return {Array} Returns an array containing 3 integers `[div, m, n]`
+ * where `div = gcd(a, b)` and `a*m + b*n = div`
+ */
+ math.xgcd = function xgcd(a, b) {
+ if (arguments.length == 2) {
+ // two arguments
+ if (isNumber(a) && isNumber(b)) {
+ if (!isInteger(a) || !isInteger(b)) {
+ throw new Error('Parameters in function xgcd must be integer numbers');
+ }
+
+ return _xgcd(a, b);
+ }
+
+ if (a instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(b)) {
+ b = BigNumber.convert(b);
+ }
+ else if (isBoolean(b) || b === null) {
+ b = new BigNumber(b ? 1 : 0);
+ }
+
+ if (b instanceof BigNumber) {
+ return _bigXgcd(a, b);
+ }
+
+ // downgrade to Number
+ return xgcd(a.toNumber(), b);
+ }
+ if (b instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(a)) {
+ a = BigNumber.convert(a);
+ }
+ else if (isBoolean(a) || a === null) {
+ a = new BigNumber(a ? 1 : 0);
+ }
+
+ if (a instanceof BigNumber) {
+ return _bigXgcd(a, b);
+ }
+
+ // downgrade to Number
+ return xgcd(a.toNumber(), b);
+ }
+
+ if (isBoolean(a) || a === null) {
+ return xgcd(+a, b);
+ }
+ if (isBoolean(b) || b === null) {
+ return xgcd(a, +b);
+ }
+
+ throw new math.error.UnsupportedTypeError('xgcd', math['typeof'](a), math['typeof'](b));
+ }
+
+ // zero or one argument
+ throw new SyntaxError('Function xgcd expects two arguments');
+ };
+
+ /**
+ * Calculate xgcd for two numbers
+ * @param {Number} a
+ * @param {Number} b
+ * @return {Number} result
+ * @private
+ */
+ function _xgcd(a, b) {
+ // source: http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
+ var t, // used to swap two variables
+ q, // quotient
+ r, // remainder
+ x = 0, lastx = 1,
+ y = 1, lasty = 0;
+
+ while (b) {
+ q = Math.floor(a / b);
+ r = a % b;
+
+ t = x;
+ x = lastx - q * x;
+ lastx = t;
+
+ t = y;
+ y = lasty - q * y;
+ lasty = t;
+
+ a = b;
+ b = r;
+ }
+
+ var res;
+ if (a < 0) {
+ res = [-a, -lastx, -lasty];
+ }
+ else {
+ res = [a, a ? lastx : 0, lasty];
+ }
+ return (config.matrix === 'array') ? res : new Matrix(res);
+ }
+
+ /**
+ * Calculate xgcd for two BigNumbers
+ * @param {BigNumber} a
+ * @param {BigNumber} b
+ * @return {BigNumber[]} result
+ * @private
+ */
+ function _bigXgcd(a, b) {
+ // source: http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
+ var t, // used to swap two variables
+ q, // quotient
+ r, // remainder
+ zero = new BigNumber(0),
+ x = new BigNumber(0), lastx = new BigNumber(1),
+ y = new BigNumber(1), lasty = new BigNumber(0);
+
+ while (!b.isZero()) {
+ q = a.div(b).floor();
+ r = a.mod(b);
+
+ t = x;
+ x = lastx.minus(q.times(x));
+ lastx = t;
+
+ t = y;
+ y = lasty.minus(q.times(y));
+ lasty = t;
+
+ a = b;
+ b = r;
+ }
+
+ var res;
+ if (a.lt(zero)) {
+ res = [a.neg(), lastx.neg(), lasty.neg()];
+ }
+ else {
+ res = [a, !a.isZero() ? lastx : 0, lasty];
+ }
+ return (config.matrix === 'array') ? res : new Matrix(res);
+ }
+ };
+
+
+/***/ },
+/* 64 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection,
+
+ bigBitAnd = util.bignumber.and;
+
+ /**
+ * Bitwise AND two values, `x & y`.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.bitAnd(x, y)
+ *
+ * Examples:
+ *
+ * math.bitAnd(53, 131); // returns Number 1
+ *
+ * math.bitAnd([1, 12, 31], 42); // returns Array [0, 8, 10]
+ *
+ * See also:
+ *
+ * bitNot, bitOr, bitXor, leftShift, rightArithShift, rightLogShift
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x First value to and
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} y Second value to and
+ * @return {Number | BigNumber | Array | Matrix} AND of `x` and `y`
+ */
+ math.bitAnd = function bitAnd(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('bitAnd', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ if (!isInteger(x) || !isInteger(y)) {
+ throw new Error('Parameters in function bitAnd must be integer numbers');
+ }
+
+ return x & y;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, bitAnd);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return bitAnd(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return bitAnd(x, +y);
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+
+ if (y instanceof BigNumber) {
+ return bigBitAnd(x, y);
+ }
+
+ // downgrade to Number
+ return bitAnd(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+
+ if (x instanceof BigNumber) {
+ return bigBitAnd(x, y);
+ }
+
+ // downgrade to Number
+ return bitAnd(x, y.toNumber());
+ }
+
+ throw new math.error.UnsupportedTypeError('bitAnd', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 65 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection,
+
+ bigBitNot = util.bignumber.not;
+
+ /**
+ * Bitwise NOT value, `~x`.
+ * For matrices, the function is evaluated element wise.
+ * For units, the function is evaluated on the best prefix base.
+ *
+ * Syntax:
+ *
+ * math.bitNot(x)
+ *
+ * Examples:
+ *
+ * math.bitNot(1); // returns Number -2
+ *
+ * math.bitNot([2, -3, 4]); // returns Array [-3, 2, 5]
+ *
+ * See also:
+ *
+ * bitAnd, bitOr, bitXor, leftShift, rightArithShift, rightLogShift
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x Value to not
+ * @return {Number | BigNumber | Array | Matrix} NOT of `x`
+ */
+ math.bitNot = function bitNot(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('bitNot', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ if (!isInteger(x)) {
+ throw new Error('Parameter in function bitNot must be integer numbers');
+ }
+
+ return ~x;
+ }
+
+ if (x instanceof BigNumber) {
+ return bigBitNot(x);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, bitNot);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return bitNot(+x);
+ }
+
+ throw new math.error.UnsupportedTypeError('bitNot', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 66 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection,
+
+ bigBitOr = util.bignumber.or;
+
+ /**
+ * Bitwise OR two values, `x | y`.
+ * For matrices, the function is evaluated element wise.
+ * For units, the function is evaluated on the lowest print base.
+ *
+ * Syntax:
+ *
+ * math.bitOr(x, y)
+ *
+ * Examples:
+ *
+ * math.bitOr(1, 2); // returns Number 3
+ *
+ * math.bitOr([1, 2, 3], 4); // returns Array [5, 6, 7]
+ *
+ * See also:
+ *
+ * bitAnd, bitNot, bitXor, leftShift, rightArithShift, rightLogShift
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x First value to or
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} y Second value to or
+ * @return {Number | BigNumber | Array | Matrix} OR of `x` and `y`
+ */
+ math.bitOr = function bitOr(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('bitOr', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ if (!isInteger(x) || !isInteger(y)) {
+ throw new Error('Parameters in function bitOr must be integer numbers');
+ }
+
+ return x | y;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, bitOr);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return bitOr(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return bitOr(x, +y);
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+
+ if (y instanceof BigNumber) {
+ return bigBitOr(x, y);
+ }
+
+ // downgrade to Number
+ return bitOr(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+
+ if (x instanceof BigNumber) {
+ return bigBitOr(x, y);
+ }
+
+ // downgrade to Number
+ return bitOr(x, y.toNumber());
+ }
+
+ throw new math.error.UnsupportedTypeError('bitOr', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 67 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection,
+
+ bigBitXor = util.bignumber.xor;
+
+ /**
+ * Bitwise XOR two values, `x ^ y`.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.bitXor(x, y)
+ *
+ * Examples:
+ *
+ * math.bitXor(1, 2); // returns Number 3
+ *
+ * math.bitXor([2, 3, 4], 4); // returns Array [6, 7, 0]
+ *
+ * See also:
+ *
+ * bitAnd, bitNot, bitOr, leftShift, rightArithShift, rightLogShift
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x First value to xor
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} y Second value to xor
+ * @return {Number | BigNumber | Array | Matrix} XOR of `x` and `y`
+ */
+ math.bitXor = function bitXor(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('bitXor', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ if (!isInteger(x) || !isInteger(y)) {
+ throw new Error('Parameters in function bitXor must be integer numbers');
+ }
+
+ return x ^ y;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, bitXor);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return bitXor(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return bitXor(x, +y);
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+
+ if (y instanceof BigNumber) {
+ return bigBitXor(x, y);
+ }
+
+ // downgrade to Number
+ return bitXor(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+
+ if (x instanceof BigNumber) {
+ return bigBitXor(x, y);
+ }
+
+ // downgrade to Number
+ return bitXor(x, y.toNumber());
+ }
+
+ throw new math.error.UnsupportedTypeError('bitXor', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 68 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection,
+
+ bigLeftShift = util.bignumber.leftShift;
+
+ /**
+ * Bitwise left logical shift of a value x by y number of bits, `x << y`.
+ * For matrices, the function is evaluated element wise.
+ * For units, the function is evaluated on the best prefix base.
+ *
+ * Syntax:
+ *
+ * math.leftShift(x, y)
+ *
+ * Examples:
+ *
+ * math.leftShift(1, 2); // returns Number 4
+ *
+ * math.leftShift([1, 2, 3], 4); // returns Array [16, 32, 64]
+ *
+ * See also:
+ *
+ * bitAnd, bitNot, bitOr, bitXor, rightArithShift, rightLogShift
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x Value to be shifted
+ * @param {Number | BigNumber | Boolean | null} y Amount of shifts
+ * @return {Number | BigNumber | Array | Matrix} `x` shifted left `y` times
+ */
+ math.leftShift = function leftShift(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('leftShift', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ if (!isInteger(x) || !isInteger(y)) {
+ throw new Error('Parameters in function leftShift must be integer numbers');
+ }
+
+ return x << y;
+ }
+
+ if (y instanceof BigNumber) {
+ return bigLeftShift(BigNumber.convert(x), y);
+ }
+ }
+ if (isNumber(y)) {
+ if (isFinite(y) && !isInteger(y)) {
+ throw new Error('Parameters in function leftShift must be integer numbers');
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isFinite() && !x.isInteger()) {
+ throw new Error('Parameters in function leftShift must be integer numbers');
+ }
+
+ if (x.isNaN() || isNaN(y) || y < 0) {
+ return new BigNumber(NaN);
+ }
+
+ if (y == 0 || x.isZero()) {
+ return x;
+ }
+ if (y == Infinity && !x.isFinite()) {
+ return new BigNumber(NaN);
+ }
+
+ // Math.pow(2, y) is fully precise for y < 55, and fast
+ if (y < 55) {
+ return x.times(Math.pow(2, y) + '');
+ }
+
+ y = BigNumber.convert(y);
+ return bigLeftShift(x, y);
+ }
+ }
+
+ if (isCollection(x) && isNumber(y)) {
+ return collection.deepMap2(x, y, leftShift);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return leftShift(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return leftShift(x, +y);
+ }
+
+ if (x instanceof BigNumber) {
+ if (y instanceof BigNumber) {
+ return bigLeftShift(x, y);
+ }
+
+ // downgrade to Number
+ return leftShift(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // x is probably incompatible with BigNumber
+ return leftShift(x, y.toNumber());
+ }
+
+ throw new math.error.UnsupportedTypeError('leftShift', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 69 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection,
+
+ bigRightShift = util.bignumber.rightShift;
+
+ /**
+ * Bitwise right arithmetic shift of a value x by y number of bits, `x >> y`.
+ * For matrices, the function is evaluated element wise.
+ * For units, the function is evaluated on the best prefix base.
+ *
+ * Syntax:
+ *
+ * math.rightArithShift(x, y)
+ *
+ * Examples:
+ *
+ * math.rightArithShift(4, 2); // returns Number 1
+ *
+ * math.rightArithShift([16, -32, 64], 4); // returns Array [1, -2, 3]
+ *
+ * See also:
+ *
+ * bitAnd, bitNot, bitOr, bitXor, leftShift, rightLogShift
+ *
+ * @param {Number | BigNumber | Boolean | Array | Matrix | null} x Value to be shifted
+ * @param {Number | BigNumber | Boolean | null} y Amount of shifts
+ * @return {Number | BigNumber | Array | Matrix} `x` sign-filled shifted right `y` times
+ */
+ math.rightArithShift = function rightArithShift(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('rightArithShift', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ if (!isInteger(x) || !isInteger(y)) {
+ throw new Error('Parameters in function rightArithShift must be integer numbers');
+ }
+
+ return x >> y;
+ }
+
+ if (y instanceof BigNumber) {
+ return bigRightShift(BigNumber.convert(x), y);
+ }
+ }
+ if (isNumber(y)) {
+ if (isFinite(y) && !isInteger(y)) {
+ throw new Error('Parameters in function rightArithShift must be integer numbers');
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isFinite() && !x.isInteger()) {
+ throw new Error('Parameters in function rightArithShift must be integer numbers');
+ }
+
+ if (x.isNaN() || isNaN(y) || y < 0) {
+ return new BigNumber(NaN);
+ }
+ if (y == Infinity) {
+ if (x.isNegative()) {
+ return new BigNumber(-1);
+ }
+ if (!x.isFinite()) {
+ return new BigNumber(NaN);
+ }
+ return new BigNumber(0);
+ }
+
+ // Math.pow(2, y) is fully precise for y < 55, and fast
+ if (y < 55) {
+ return x.div(Math.pow(2, y) + '').floor();
+ }
+
+ y = BigNumber.convert(y);
+ return bigRightShift(x, y);
+ }
+ }
+
+ if (isCollection(x) && isNumber(y)) {
+ return collection.deepMap2(x, y, rightArithShift);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return rightArithShift(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return rightArithShift(x, +y);
+ }
+
+ if (x instanceof BigNumber) {
+ if (y instanceof BigNumber) {
+ return bigRightShift(x, y);
+ }
+
+ // downgrade to Number
+ return rightArithShift(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // x is probably incompatible with BigNumber
+ return rightArithShift(x, y.toNumber());
+ }
+
+ throw new math.error.UnsupportedTypeError('rightArithShift', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 70 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection;
+
+ /**
+ * Bitwise right logical shift of value x by y number of bits, `x >>> y`.
+ * For matrices, the function is evaluated element wise.
+ * For units, the function is evaluated on the best prefix base.
+ *
+ * Syntax:
+ *
+ * math.rightLogShift(x, y)
+ *
+ * Examples:
+ *
+ * math.rightLogShift(4, 2); // returns Number 1
+ *
+ * math.rightLogShift([16, -32, 64], 4); // returns Array [1, 2, 3]
+ *
+ * See also:
+ *
+ * bitAnd, bitNot, bitOr, bitXor, leftShift, rightArithShift
+ *
+ * @param {Number | Boolean | Array | Matrix | null} x Value to be shifted
+ * @param {Number | Boolean | null} y Amount of shifts
+ * @return {Number | Array | Matrix} `x` zero-filled shifted right `y` times
+ */
+ math.rightLogShift = function rightLogShift(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('rightLogShift', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ if (!isInteger(x) || !isInteger(y)) {
+ throw new Error('Parameters in function rightLogShift must be integer numbers');
+ }
+
+ return x >>> y;
+ }
+
+ if (isCollection(x) && isNumber(y)) {
+ return collection.deepMap2(x, y, rightLogShift);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return rightLogShift(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return rightLogShift(x, +y);
+ }
+
+ throw new math.error.UnsupportedTypeError('rightLogShift', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 71 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isCollection = collection.isCollection,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Compute the argument of a complex value.
+ * For a complex number `a + bi`, the argument is computed as `atan2(b, a)`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.arg(x)
+ *
+ * Examples:
+ *
+ * var a = math.complex(2, 2);
+ * math.arg(a) / math.pi; // returns Number 0.25
+ *
+ * var b = math.complex('2 + 3i');
+ * math.arg(b); // returns Number 0.982793723247329
+ * math.atan2(3, 2); // returns Number 0.982793723247329
+ *
+ * See also:
+ *
+ * re, im, conj, abs
+ *
+ * @param {Number | Complex | Array | Matrix | Boolean | null} x
+ * A complex number or array with complex numbers
+ * @return {Number | Array | Matrix} The argument of x
+ */
+ math.arg = function arg(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('arg', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return Math.atan2(0, x);
+ }
+
+ if (isComplex(x)) {
+ return Math.atan2(x.im, x.re);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, arg);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return arg(+x);
+ }
+
+ if (x instanceof BigNumber) {
+ // downgrade to Number
+ // TODO: implement BigNumber support
+ return arg(x.toNumber());
+ }
+
+ throw new math.error.UnsupportedTypeError('arg', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 72 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ object = util.object,
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isCollection =collection.isCollection,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Compute the complex conjugate of a complex value.
+ * If `x = a+bi`, the complex conjugate of `x` is `a - bi`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.conj(x)
+ *
+ * Examples:
+ *
+ * math.conj(math.complex('2 + 3i')); // returns Complex 2 - 3i
+ * math.conj(math.complex('2 - 3i')); // returns Complex 2 + 3i
+ * math.conj(math.complex('-5.2i')); // returns Complex 5.2i
+ *
+ * See also:
+ *
+ * re, im, arg, abs
+ *
+ * @param {Number | BigNumber | Complex | Array | Matrix | Boolean | null} x
+ * A complex number or array with complex numbers
+ * @return {Number | BigNumber | Complex | Array | Matrix}
+ * The complex conjugate of x
+ */
+ math.conj = function conj(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('conj', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return x;
+ }
+
+ if (x instanceof BigNumber) {
+ return new BigNumber(x);
+ }
+
+ if (isComplex(x)) {
+ return new Complex(x.re, -x.im);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, conj);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return +x;
+ }
+
+ // return a clone of the value for non-complex values
+ return object.clone(x);
+ };
+ };
+
+
+/***/ },
+/* 73 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ object = util.object,
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isCollection = collection.isCollection,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Get the real part of a complex number.
+ * For a complex number `a + bi`, the function returns `a`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.re(x)
+ *
+ * Examples:
+ *
+ * var a = math.complex(2, 3);
+ * math.re(a); // returns Number 2
+ * math.im(a); // returns Number 3
+ *
+ * math.re(math.complex('-5.2i')); // returns Number 0
+ * math.re(math.complex(2.4)); // returns Number 2.4
+ *
+ * See also:
+ *
+ * im, conj, abs, arg
+ *
+ * @param {Number | BigNumber | Complex | Array | Matrix | Boolean | null} x
+ * A complex number or array with complex numbers
+ * @return {Number | BigNumber | Array | Matrix} The real part of x
+ */
+ math.re = function re(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('re', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return x;
+ }
+
+ if (x instanceof BigNumber) {
+ return new BigNumber(x);
+ }
+
+ if (isComplex(x)) {
+ return x.re;
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, re);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return +x;
+ }
+
+ // return a clone of the value itself for all non-complex values
+ return object.clone(x);
+ };
+ };
+
+
+/***/ },
+/* 74 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isCollection =collection.isCollection,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Get the imaginary part of a complex number.
+ * For a complex number `a + bi`, the function returns `b`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.im(x)
+ *
+ * Examples:
+ *
+ * var a = math.complex(2, 3);
+ * math.re(a); // returns Number 2
+ * math.im(a); // returns Number 3
+ *
+ * math.re(math.complex('-5.2i')); // returns Number -5.2
+ * math.re(math.complex(2.4)); // returns Number 0
+ *
+ * See also:
+ *
+ * re, conj, abs, arg
+ *
+ * @param {Number | BigNumber | Complex | Array | Matrix | Boolean | null} x
+ * A complex number or array with complex numbers
+ * @return {Number | BigNumber | Array | Matrix} The imaginary part of x
+ */
+ math.im = function im(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('im', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return 0;
+ }
+
+ if (x instanceof BigNumber) {
+ return new BigNumber(0);
+ }
+
+ if (isComplex(x)) {
+ return x.im;
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, im);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return 0;
+ }
+
+ // return 0 for all non-complex values
+ return 0;
+ };
+ };
+
+
+/***/ },
+/* 75 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ // take the BigNumber instance the provided math.js instance
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+ isNumber = util.number.isNumber,
+ isString = util.string.isString,
+ isBoolean = util['boolean'].isBoolean;
+
+ /**
+ * Create a BigNumber, which can store numbers with arbitrary precision.
+ * When a matrix is provided, all elements will be converted to BigNumber.
+ *
+ * Syntax:
+ *
+ * math.bignumber(x)
+ *
+ * Examples:
+ *
+ * 0.1 + 0.2; // returns Number 0.30000000000000004
+ * math.bignumber(0.1) + math.bignumber(0.2); // returns BigNumber 0.3
+ *
+ *
+ * 7.2e500; // returns Number Infinity
+ * math.bignumber('7.2e500'); // returns BigNumber 7.2e500
+ *
+ * See also:
+ *
+ * boolean, complex, index, matrix, string, unit
+ *
+ * @param {Number | String | Array | Matrix | Boolean | null} [value] Value for the big number,
+ * 0 by default.
+ * @returns {BigNumber} The created bignumber
+ */
+ math.bignumber = function bignumber(value) {
+ if (arguments.length > 1) {
+ throw new math.error.ArgumentsError('bignumber', arguments.length, 0, 1);
+ }
+
+ if ((value instanceof BigNumber) || isNumber(value) || isString(value)) {
+ return new BigNumber(value);
+ }
+
+ if (isBoolean(value) || value === null) {
+ return new BigNumber(+value);
+ }
+
+ if (isCollection(value)) {
+ return collection.deepMap(value, bignumber);
+ }
+
+ if (arguments.length == 0) {
+ return new BigNumber(0);
+ }
+
+ throw new math.error.UnsupportedTypeError('bignumber', math['typeof'](value));
+ };
+ };
+
+
+/***/ },
+/* 76 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+ isNumber = util.number.isNumber,
+ isString = util.string.isString;
+
+ /**
+ * Create a boolean or convert a string or number to a boolean.
+ * In case of a number, `true` is returned for non-zero numbers, and `false` in
+ * case of zero.
+ * Strings can be `'true'` or `'false'`, or can contain a number.
+ * When value is a matrix, all elements will be converted to boolean.
+ *
+ * Syntax:
+ *
+ * math.boolean(x)
+ *
+ * Examples:
+ *
+ * math.boolean(0); // returns false
+ * math.boolean(1); // returns true
+ * math.boolean(-3); // returns true
+ * math.boolean('true'); // returns true
+ * math.boolean('false'); // returns false
+ * math.boolean([1, 0, 1, 1]); // returns [true, false, true, true]
+ *
+ * See also:
+ *
+ * bignumber, complex, index, matrix, string, unit
+ *
+ * @param {String | Number | Boolean | Array | Matrix | null} value A value of any type
+ * @return {Boolean | Array | Matrix} The boolean value
+ */
+ math['boolean'] = function bool (value) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('boolean', arguments.length, 0, 1);
+ }
+
+ if (value === 'true' || value === true) {
+ return true;
+ }
+
+ if (value === 'false' || value === false || value === null) {
+ return false;
+ }
+
+ if (value instanceof Boolean) {
+ return value == true;
+ }
+
+ if (isNumber(value)) {
+ return (value !== 0);
+ }
+
+ if (value instanceof BigNumber) {
+ return !value.isZero();
+ }
+
+ if (isString(value)) {
+ // try case insensitive
+ var lcase = value.toLowerCase();
+ if (lcase === 'true') {
+ return true;
+ }
+ else if (lcase === 'false') {
+ return false;
+ }
+
+ // test whether value is a valid number
+ var num = Number(value);
+ if (value != '' && !isNaN(num)) {
+ return (num !== 0);
+ }
+ }
+
+ if (isCollection(value)) {
+ return collection.deepMap(value, bool);
+ }
+
+ throw new SyntaxError(value.toString() + ' is no valid boolean');
+ };
+ };
+
+
+/***/ },
+/* 77 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+ isNumber = util.number.isNumber,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex;
+
+ /**
+ * Create a complex value or convert a value to a complex value.
+ *
+ * Syntax:
+ *
+ * math.complex() // creates a complex value with zero
+ * // as real and imaginary part.
+ * math.complex(re : number, im : string) // creates a complex value with provided
+ * // values for real and imaginary part.
+ * math.complex(re : number) // creates a complex value with provided
+ * // real value and zero imaginary part.
+ * math.complex(complex : Complex) // clones the provided complex value.
+ * math.complex(arg : string) // parses a string into a complex value.
+ * math.complex(array : Array) // converts the elements of the array
+ * // or matrix element wise into a
+ * // complex value.
+ * math.complex({re: number, im: number}) // creates a complex value with provided
+ * // values for real an imaginary part.
+ * math.complex({r: number, phi: number}) // creates a complex value with provided
+ * // polar coordinates
+ *
+ * Examples:
+ *
+ * var a = math.complex(3, -4); // a = Complex 3 - 4i
+ * a.re = 5; // a = Complex 5 - 4i
+ * var i = a.im; // Number -4;
+ * var b = math.complex('2 + 6i'); // Complex 2 + 6i
+ * var c = math.complex(); // Complex 0 + 0i
+ * var d = math.add(a, b); // Complex 5 + 2i
+ *
+ * See also:
+ *
+ * bignumber, boolean, index, matrix, number, string, unit
+ *
+ * @param {* | Array | Matrix} [args]
+ * Arguments specifying the real and imaginary part of the complex number
+ * @return {Complex | Array | Matrix} Returns a complex value
+ */
+ math.complex = function complex(args) {
+ switch (arguments.length) {
+ case 0:
+ // no parameters. Set re and im zero
+ return new Complex(0, 0);
+
+ case 1:
+ // parse string into a complex number
+ var arg = arguments[0];
+
+ if (isNumber(arg)) {
+ return new Complex(arg, 0);
+ }
+
+ if (arg instanceof BigNumber) {
+ // convert to Number
+ return new Complex(arg.toNumber(), 0);
+ }
+
+ if (isComplex(arg)) {
+ // create a clone
+ return arg.clone();
+ }
+
+ if (isString(arg)) {
+ var c = Complex.parse(arg);
+ if (c) {
+ return c;
+ }
+ else {
+ throw new SyntaxError('String "' + arg + '" is no valid complex number');
+ }
+ }
+
+ if (isCollection(arg)) {
+ return collection.deepMap(arg, complex);
+ }
+
+ if (typeof arg === 'object') {
+ if('re' in arg && 'im' in arg) {
+ return new Complex(arg.re, arg.im);
+ } else if ('r' in arg && 'phi' in arg) {
+ return Complex.fromPolar(arg.r, arg.phi);
+ }
+ }
+
+ throw new TypeError('Two numbers, single string or an fitting object expected in function complex');
+
+ case 2:
+ // re and im provided
+ var re = arguments[0],
+ im = arguments[1];
+
+ // convert re to number
+ if (re instanceof BigNumber) {
+ re = re.toNumber();
+ }
+
+ // convert im to number
+ if (im instanceof BigNumber) {
+ im = im.toNumber();
+ }
+
+ if (isNumber(re) && isNumber(im)) {
+ return new Complex(re, im);
+ }
+ else {
+ throw new TypeError('Two numbers or a single string expected in function complex');
+ }
+
+ default:
+ throw new math.error.ArgumentsError('complex', arguments.length, 0, 2);
+ }
+ };
+ };
+
+
+/***/ },
+/* 78 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Index = __webpack_require__(9);
+
+ /**
+ * Create an index. An Index can store ranges having start, step, and end
+ * for multiple dimensions.
+ * Matrix.get, Matrix.set, and math.subset accept an Index as input.
+ *
+ * Syntax:
+ *
+ * math.index(range1, range2, ...)
+ *
+ * Where:
+ *
+ * Each range can be any of:
+ *
+ * - An array [start, end]
+ * - An array [start, end, step]
+ * - A number
+ * - An instance of `Range`
+ *
+ * The parameters start, end, and step must be integer numbers. Start and end
+ * are zero based. The start of a range is included, the end is excluded.
+ *
+ * Examples:
+ *
+ * var math = math.js
+ *
+ * var b = [1, 2, 3, 4, 5];
+ * math.subset(b, math.index([1, 3])); // returns [2, 3]
+ *
+ * var a = math.matrix([[1, 2], [3, 4]]);
+ * a.subset(math.index(0, 1)); // returns 2
+ * a.subset(math.index(1, null)); // returns [3, 4]
+ *
+ * See also:
+ *
+ * bignumber, boolean, complex, matrix, number, string, unit
+ *
+ * @param {...*} ranges Zero or more ranges or numbers.
+ * @return {Index} Returns the created index
+ */
+ math.index = function(ranges) {
+ // downgrade BigNumber to Number
+ var args = Array.prototype.slice.apply(arguments).map(function (arg) {
+ if (arg instanceof BigNumber) {
+ return arg.toNumber();
+ }
+ else if (Array.isArray(arg)) {
+ return arg.map(function (elem) {
+ return (elem instanceof BigNumber) ? elem.toNumber() : elem;
+ });
+ }
+ else {
+ return arg;
+ }
+ });
+
+ var res = new Index();
+ Index.apply(res, args);
+ return res;
+ };
+ };
+
+
+/***/ },
+/* 79 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+ Matrix = __webpack_require__(10);
+
+ /**
+ * Create a Matrix. The function creates a new `math.type.Matrix` object from
+ * an `Array`. A Matrix has utility functions to manipulate the data in the
+ * matrix, like getting the size and getting or setting values in the matrix.
+ *
+ * Syntax:
+ *
+ * math.matrix() // creates an empty matrix
+ * math.matrix(data) // creates a matrix with initial data.
+ *
+ * Examples:
+ *
+ * var m = math.matrix([[1, 2], [3, 4]]);
+ * m.size(); // Array [2, 2]
+ * m.resize([3, 2], 5);
+ * m.valueOf(); // Array [[1, 2], [3, 4], [5, 5]]
+ * m.get([1, 0]) // number 3
+ *
+ * See also:
+ *
+ * bignumber, boolean, complex, index, number, string, unit
+ *
+ * @param {Array | Matrix} [data] A multi dimensional array
+ * @return {Matrix} The created matrix
+ */
+ math.matrix = function matrix(data) {
+ if (arguments.length > 1) {
+ throw new math.error.ArgumentsError('matrix', arguments.length, 0, 1);
+ }
+
+ return new Matrix(data);
+ };
+ };
+
+
+/***/ },
+/* 80 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171);
+
+ var BigNumber = math.type.BigNumber;
+ var Unit = math.type.Unit;
+ var collection = __webpack_require__(14);
+
+ var isCollection = collection.isCollection;
+ var isNumber = util.number.isNumber;
+ var isBoolean = util['boolean'].isBoolean;
+ var isString = util.string.isString;
+
+ /**
+ * Create a number or convert a string, boolean, or unit to a number.
+ * When value is a matrix, all elements will be converted to number.
+ *
+ * Syntax:
+ *
+ * math.number(value)
+ * math.number(unit, valuelessUnit)
+ *
+ * Examples:
+ *
+ * math.number(2); // returns number 2
+ * math.number('7.2'); // returns number 7.2
+ * math.number(true); // returns number 1
+ * math.number([true, false, true, true]); // returns [1, 0, 1, 1]
+ * math.number(math.unit('52cm'), 'm'); // returns 0.52
+ *
+ * See also:
+ *
+ * bignumber, boolean, complex, index, matrix, string, unit
+ *
+ * @param {String | Number | Boolean | Array | Matrix | Unit | null} [value] Value to be converted
+ * @param {Unit | string} [valuelessUnit] A valueless unit, used to convert a unit to a number
+ * @return {Number | Array | Matrix} The created number
+ */
+ math.number = function number (value, valuelessUnit) {
+ switch (arguments.length) {
+ case 0:
+ return 0;
+
+ case 1:
+ if (isCollection(value)) {
+ return collection.deepMap(value, number);
+ }
+
+ if (value instanceof BigNumber) {
+ return value.toNumber();
+ }
+
+ if (isString(value)) {
+ var num = Number(value);
+ if (isNaN(num)) {
+ num = Number(value.valueOf());
+ }
+ if (isNaN(num)) {
+ throw new SyntaxError(value.toString() + ' is no valid number');
+ }
+ return num;
+ }
+
+ if (isBoolean(value) || value === null) {
+ return +value;
+ }
+
+ if (isNumber(value)) {
+ return value;
+ }
+
+ if (value instanceof Unit) {
+ throw new Error('Second argument with valueless unit expected');
+ }
+
+ throw new math.error.UnsupportedTypeError('number', math['typeof'](value));
+
+ case 2:
+ if (value instanceof Unit && isString(valuelessUnit) || valuelessUnit instanceof Unit) {
+ return value.toNumber(valuelessUnit);
+ }
+
+ throw new math.error.UnsupportedTypeError('number', math['typeof'](value), math['typeof'](valuelessUnit));
+
+
+ default:
+ throw new math.error.ArgumentsError('number', arguments.length, 0, 1);
+ }
+ };
+ };
+
+
+/***/ },
+/* 81 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Parser = __webpack_require__(17);
+
+ /**
+ * Create a parser. The function creates a new `math.expression.Parser` object.
+ *
+ * Syntax:
+ *
+ * math.parser()
+ *
+ * Examples:
+ *
+ * var parser = new math.parser();
+ *
+ * // evaluate expressions
+ * var a = parser.eval('sqrt(3^2 + 4^2)'); // 5
+ * var b = parser.eval('sqrt(-4)'); // 2i
+ * var c = parser.eval('2 inch in cm'); // 5.08 cm
+ * var d = parser.eval('cos(45 deg)'); // 0.7071067811865476
+ *
+ * // define variables and functions
+ * parser.eval('x = 7 / 2'); // 3.5
+ * parser.eval('x + 3'); // 6.5
+ * parser.eval('function f(x, y) = x^y'); // f(x, y)
+ * parser.eval('f(2, 3)'); // 8
+ *
+ * // get and set variables and functions
+ * var x = parser.get('x'); // 7
+ * var f = parser.get('f'); // function
+ * var g = f(3, 2); // 9
+ * parser.set('h', 500);
+ * var i = parser.eval('h / 2'); // 250
+ * parser.set('hello', function (name) {
+ * return 'hello, ' + name + '!';
+ * });
+ * parser.eval('hello("user")'); // "hello, user!"
+ *
+ * // clear defined functions and variables
+ * parser.clear();
+ *
+ * See also:
+ *
+ * eval, compile, parse
+ *
+ * @return {Parser} Parser
+ */
+ math.parser = function parser() {
+ return new Parser(math);
+ };
+ };
+
+
+/***/ },
+/* 82 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ /**
+ * Wrap any value in a chain, allowing to perform chained operations on
+ * the value.
+ *
+ * All methods available in the math.js library can be called upon the chain,
+ * and then will be evaluated with the value itself as first argument.
+ * The chain can be closed by executing `chain.done()`, which returns
+ * the final value.
+ *
+ * The chain has a number of special functions:
+ *
+ * - `done()` Finalize the chain and return the chain's value.
+ * - `valueOf()` The same as `done()`
+ * - `toString()` Executes `math.format()` onto the chain's value, returning
+ * a string representation of the value.
+ *
+ * Syntax:
+ *
+ * math.chain(value)
+ *
+ * Examples:
+ *
+ * math.chain(3)
+ * .add(4)
+ * .subtract(2)
+ * .done(); // 5
+ *
+ * math.chain( [[1, 2], [3, 4]] )
+ * .subset(math.index(0, 0), 8)
+ * .multiply(3)
+ * .done(); // [[24, 6], [9, 12]]
+ *
+ * @param {*} [value] A value of any type on which to start a chained operation.
+ * @return {math.chaining.Chain} The created chain
+ */
+ math.chain = function(value) {
+ // TODO: check number of arguments
+ return new math.chaining.Chain(value);
+ };
+
+ // TODO: deprecate math.select in v2.0
+ math.select = function(value) {
+ // give a warning once.
+ if (console && typeof console.log === 'function') {
+ console.log('WARNING: Function "select" is renamed to "chain". It will be deprecated in v2.0.')
+ }
+
+ // replace warning function with chain function
+ math.select = math.chain;
+ math.chaining.Chain.prototype['select'] = math.select;
+
+ return math.chain(value);
+ }
+ };
+
+
+/***/ },
+/* 83 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ collection = __webpack_require__(14),
+
+ number = util.number,
+ isNumber = util.number.isNumber,
+ isCollection = collection.isCollection;
+
+ /**
+ * Create a string or convert any object into a string.
+ * Elements of Arrays and Matrices are processed element wise.
+ *
+ * Syntax:
+ *
+ * math.string(value)
+ *
+ * Examples:
+ *
+ * math.string(4.2); // returns string '4.2'
+ * math.string(math.complex(3, 2); // returns string '3 + 2i'
+ *
+ * var u = math.unit(5, 'km');
+ * math.string(u.to('m')); // returns string '5000 m'
+ *
+ * math.string([true, false]); // returns ['true', 'false']
+ *
+ * See also:
+ *
+ * bignumber, boolean, complex, index, matrix, number, unit
+ *
+ * @param {* | Array | Matrix | null} [value] A value to convert to a string
+ * @return {String | Array | Matrix} The created string
+ */
+ math.string = function string (value) {
+ switch (arguments.length) {
+ case 0:
+ return '';
+
+ case 1:
+ if (isNumber(value)) {
+ return number.format(value);
+ }
+
+ if (isCollection(value)) {
+ return collection.deepMap(value, string);
+ }
+
+ if (value === null) {
+ return 'null';
+ }
+
+ return value.toString();
+
+ default:
+ throw new math.error.ArgumentsError('string', arguments.length, 0, 1);
+ }
+ };
+ };
+
+
+/***/ },
+/* 84 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+ isString = util.string.isString;
+
+ /**
+ * Create a unit. Depending on the passed arguments, the function
+ * will create and return a new math.type.Unit object.
+ * When a matrix is provided, all elements will be converted to units.
+ *
+ * Syntax:
+ *
+ * math.unit(unit : string)
+ * math.unit(value : number, unit : string)
+ *
+ * Examples:
+ *
+ * var a = math.unit(5, 'cm'); // returns Unit 50 mm
+ * var b = math.unit('23 kg'); // returns Unit 23 kg
+ * a.to('m'); // returns Unit 0.05 m
+ *
+ * See also:
+ *
+ * bignumber, boolean, complex, index, matrix, number, string
+ *
+ * @param {* | Array | Matrix} args A number and unit.
+ * @return {Unit | Array | Matrix} The created unit
+ */
+ math.unit = function unit(args) {
+ switch(arguments.length) {
+ case 1:
+ // parse a string
+ var arg = arguments[0];
+
+ if (arg instanceof Unit) {
+ // create a clone of the unit
+ return arg.clone();
+ }
+
+ if (isString(arg)) {
+ if (Unit.isValuelessUnit(arg)) {
+ return new Unit(null, arg); // a pure unit
+ }
+
+ var u = Unit.parse(arg); // a unit with value, like '5cm'
+ if (u) {
+ return u;
+ }
+
+ throw new SyntaxError('String "' + arg + '" is no valid unit');
+ }
+
+ if (isCollection(args)) {
+ return collection.deepMap(args, unit);
+ }
+
+ throw new TypeError('A string or a number and string expected in function unit');
+
+ case 2:
+ // a number and a unit
+
+ if (arguments[0] instanceof BigNumber) {
+ // convert value to number
+ return new Unit(arguments[0].toNumber(), arguments[1]);
+ }
+ else {
+ return new Unit(arguments[0], arguments[1]);
+ }
+
+ default:
+ throw new math.error.ArgumentsError('unit', arguments.length, 1, 2);
+ }
+ };
+ };
+
+
+/***/ },
+/* 85 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Logical `and`. Test whether two values are both defined with a nonzero/nonempty value.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.and(x, y)
+ *
+ * Examples:
+ *
+ * math.and(2, 4); // returns true
+ *
+ * a = [2, 0, 0];
+ * b = [3, 7, 0];
+ * c = 0;
+ *
+ * math.and(a, b); // returns [true, false, false]
+ * math.and(a, c); // returns [false, false, false]
+ *
+ * See also:
+ *
+ * not, or, xor
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First value to check
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Second value to check
+ * @return {Boolean | Array | Matrix}
+ * Returns true when both inputs are defined with a nonzero/nonempty value.
+ */
+ math.and = function and(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('and', arguments.length, 2);
+ }
+
+ if ((isNumber(x) || isBoolean(x) || x === null) &&
+ (isNumber(y) || isBoolean(y) || y === null)) {
+ return !!(x && y);
+ }
+
+ if (isComplex(x)) {
+ if (x.re == 0 && x.im == 0) {
+ return false;
+ }
+
+ return and(true, y);
+ }
+ if (isComplex(y)) {
+ if (y.re == 0 && y.im == 0) {
+ return false;
+ }
+
+ return and(x, true);
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isZero() || x.isNaN()) {
+ return false;
+ }
+
+ return and(true, y);
+ }
+ if (y instanceof BigNumber) {
+ if (y.isZero() || y.isNaN()) {
+ return false;
+ }
+
+ return and(x, true);
+ }
+
+ if (isUnit(x)) {
+ if (x.value === null || x.value == 0) {
+ return false;
+ }
+
+ return and(true, y);
+ }
+ if (isUnit(y)) {
+ if (y.value === null || y.value == 0) {
+ return false;
+ }
+
+ return and(x, true);
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, and);
+ }
+
+ throw new math.error.UnsupportedTypeError('and', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 86 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Logical `not`. Flips boolean value of a given parameter.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.not(x)
+ *
+ * Examples:
+ *
+ * math.not(2); // returns false
+ * math.not(0); // returns true
+ * math.not(true); // returns false
+ *
+ * a = [2, -7, 0];
+ * math.not(a); // returns [false, false, true]
+ *
+ * See also:
+ *
+ * and, or, xor
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First value to check
+ * @return {Boolean | Array | Matrix}
+ * Returns true when input is a zero or empty value.
+ */
+ math.not = function not(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('not', arguments.length, 1);
+ }
+
+ if (isNumber(x) || isBoolean(x) || x === null) {
+ return !x;
+ }
+
+ if (isComplex(x)) {
+ return x.re == 0 && x.im == 0;
+ }
+
+ if (x instanceof BigNumber) {
+ return x.isZero() || x.isNaN();
+ }
+
+ if (isUnit(x)) {
+ return x.value === null || x.value == 0;
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, not);
+ }
+
+ throw new math.error.UnsupportedTypeError('not', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 87 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Logical `or`. Test if at least one value is defined with a nonzero/nonempty value.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.or(x, y)
+ *
+ * Examples:
+ *
+ * math.or(2, 4); // returns true
+ *
+ * a = [2, 5, 0];
+ * b = [0, 22, 0];
+ * c = 0;
+ *
+ * math.or(a, b); // returns [true, true, false]
+ * math.or(b, c); // returns [false, true, false]
+ *
+ * See also:
+ *
+ * and, not, xor
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First value to check
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Second value to check
+ * @return {Boolean | Array | Matrix}
+ * Returns true when one of the inputs is defined with a nonzero/nonempty value.
+ */
+ math.or = function or(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('or', arguments.length, 2);
+ }
+
+ if ((isNumber(x) || isBoolean(x) || x === null) &&
+ (isNumber(y) || isBoolean(y) || y === null)) {
+ return !!(x || y);
+ }
+
+ if (isComplex(x)) {
+ if (x.re == 0 && x.im == 0) {
+ return or(false, y);
+ }
+ return true;
+ }
+ if (isComplex(y)) {
+ if (y.re == 0 && y.im == 0) {
+ return or(x, false);
+ }
+ return true;
+ }
+
+ if (x instanceof BigNumber) {
+ if (x.isZero() || x.isNaN()) {
+ return or(false, y);
+ }
+ return true;
+ }
+ if (y instanceof BigNumber) {
+ if (y.isZero() || y.isNaN()) {
+ return or(x, false);
+ }
+ return true;
+ }
+
+ if (isUnit(x)) {
+ if (x.value === null || x.value == 0) {
+ return or(false, y);
+ }
+ return true;
+ }
+ if (isUnit(y)) {
+ if (y.value === null || y.value == 0) {
+ return or(x, false);
+ }
+ return true;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, or);
+ }
+
+ throw new math.error.UnsupportedTypeError('or', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 88 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Logical `xor`. Test whether one and only one value is defined with a nonzero/nonempty value.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.xor(x, y)
+ *
+ * Examples:
+ *
+ * math.xor(2, 4); // returns false
+ *
+ * a = [2, 0, 0];
+ * b = [2, 7, 0];
+ * c = 0;
+ *
+ * math.xor(a, b); // returns [false, true, false]
+ * math.xor(a, c); // returns [true, false, false]
+ *
+ * See also:
+ *
+ * and, not, or
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First value to check
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Second value to check
+ * @return {Boolean | Array | Matrix}
+ * Returns true when one and only one input is defined with a nonzero/nonempty value.
+ */
+ math.xor = function xor(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('xor', arguments.length, 2);
+ }
+
+ if ((isNumber(x) || isBoolean(x) || x === null) &&
+ (isNumber(y) || isBoolean(y) || y === null)) {
+ return !!(!!x ^ !!y);
+ }
+
+ if (isComplex(x)) {
+ return xor(!(x.re == 0 && x.im == 0), y);
+ }
+ if (isComplex(y)) {
+ return xor(x, !(y.re == 0 && y.im == 0));
+ }
+
+ if (x instanceof BigNumber) {
+ return xor(!(x.isZero() || x.isNaN()), y);
+ }
+ if (y instanceof BigNumber) {
+ return xor(x, !(y.isZero() || y.isNaN()));
+ }
+
+ if (isUnit(x)) {
+ return xor(!(x.value === null || x.value == 0), y);
+ }
+ if (isUnit(y)) {
+ return xor(x, !(y.value === null || y.value == 0));
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, xor);
+ }
+
+ throw new math.error.UnsupportedTypeError('xor', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 89 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171);
+
+ var BigNumber = __webpack_require__(5);
+ var Matrix = __webpack_require__(10);
+ var collection = __webpack_require__(14);
+
+ var object = util.object;
+ var array = util.array;
+ var isNumber = util.number.isNumber;
+ var isInteger = util.number.isInteger;
+ var isCollection = collection.isCollection;
+
+ /**
+ * Concatenate two or more matrices.
+ *
+ * Syntax:
+ *
+ * math.concat(A, B, C, ...)
+ * math.concat(A, B, C, ..., dim)
+ *
+ * Where:
+ *
+ * - `dim: number` is a zero-based dimension over which to concatenate the matrices.
+ * By default the last dimension of the matrices.
+ *
+ * Examples:
+ *
+ * var A = [[1, 2], [5, 6]];
+ * var B = [[3, 4], [7, 8]];
+ *
+ * math.concat(A, B); // returns [[1, 2, 3, 4], [5, 6, 7, 8]]
+ * math.concat(A, B, 0); // returns [[1, 2], [5, 6], [3, 4], [7, 8]]
+ *
+ * See also:
+ *
+ * size, squeeze, subset, transpose
+ *
+ * @param {... Array | Matrix} args Two or more matrices
+ * @return {Array | Matrix} Concatenated matrix
+ */
+ math.concat = function concat (args) {
+ var i,
+ len = arguments.length,
+ dim = -1, // zero-based dimension
+ prevDim,
+ asMatrix = false,
+ matrices = []; // contains multi dimensional arrays
+
+ for (i = 0; i < len; i++) {
+ var arg = arguments[i];
+
+ // test whether we need to return a Matrix (if not we return an Array)
+ if (arg instanceof Matrix) {
+ asMatrix = true;
+ }
+
+ if ((i == len - 1) && (isNumber(arg) || arg instanceof BigNumber)) {
+ // last argument contains the dimension on which to concatenate
+ prevDim = dim;
+ dim = arg.valueOf(); // change bignumber to number
+
+ if (!isInteger(dim)) {
+ throw new TypeError('Integer number expected for dimension');
+ }
+
+ if (dim < 0) {
+ // TODO: would be more clear when throwing a DimensionError here
+ throw new math.error.IndexError(dim);
+ }
+ if (i > 0 && dim > prevDim) {
+ // TODO: would be more clear when throwing a DimensionError here
+ throw new math.error.IndexError(dim, prevDim + 1);
+ }
+ }
+ else if (isCollection(arg)) {
+ // this is a matrix or array
+ var matrix = object.clone(arg).valueOf();
+ var size = array.size(arg.valueOf());
+ matrices[i] = matrix;
+ prevDim = dim;
+ dim = size.length - 1;
+
+ // verify whether each of the matrices has the same number of dimensions
+ if (i > 0 && dim != prevDim) {
+ throw new math.error.DimensionError(prevDim + 1, dim + 1);
+ }
+ }
+ else {
+ throw new math.error.UnsupportedTypeError('concat', math['typeof'](arg));
+ }
+ }
+
+ if (matrices.length == 0) {
+ throw new SyntaxError('At least one matrix expected');
+ }
+
+ var res = matrices.shift();
+ while (matrices.length) {
+ res = _concat(res, matrices.shift(), dim, 0);
+ }
+
+ return asMatrix ? new Matrix(res) : res;
+ };
+
+ /**
+ * Recursively concatenate two matrices.
+ * The contents of the matrices is not cloned.
+ * @param {Array} a Multi dimensional array
+ * @param {Array} b Multi dimensional array
+ * @param {Number} concatDim The dimension on which to concatenate (zero-based)
+ * @param {Number} dim The current dim (zero-based)
+ * @return {Array} c The concatenated matrix
+ * @private
+ */
+ function _concat(a, b, concatDim, dim) {
+ if (dim < concatDim) {
+ // recurse into next dimension
+ if (a.length != b.length) {
+ throw new math.error.DimensionError(a.length, b.length);
+ }
+
+ var c = [];
+ for (var i = 0; i < a.length; i++) {
+ c[i] = _concat(a[i], b[i], concatDim, dim + 1);
+ }
+ return c;
+ }
+ else {
+ // concatenate this dimension
+ return a.concat(b);
+ }
+ }
+ };
+
+
+/***/ },
+/* 90 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function(math) {
+ var array = __webpack_require__(165);
+ var Matrix = __webpack_require__(10);
+
+ /**
+ * Calculate the cross product for two vectors in three dimensional space.
+ * The cross product of `A = [a1, a2, a3]` and `B =[b1, b2, b3]` is defined
+ * as:
+ *
+ * cross(A, B) = [
+ * a2 * b3 - a3 * b2,
+ * a3 * b1 - a1 * b3,
+ * a1 * b2 - a2 * b1
+ * ]
+ *
+ * Syntax:
+ *
+ * math.cross(x, y)
+ *
+ * Examples:
+ *
+ * math.cross([1, 1, 0], [0, 1, 1]); // Returns [1, -1, 1]
+ * math.cross([3, -3, 1], [4, 9, 2]); // Returns [-15, -2, 39]
+ * math.cross([2, 3, 4], [5, 6, 7]); // Returns [-3, 6, -3]
+ *
+ * See also:
+ *
+ * dot, multiply
+ *
+ * @param {Array | Matrix} x First vector
+ * @param {Array | Matrix} y Second vector
+ * @return {Array | Matrix} Returns the cross product of `x` and `y`
+ */
+ math.cross = function cross(x, y) {
+ if (x instanceof Matrix) {
+ if (y instanceof Matrix) {
+ return new Matrix(_cross(x.toArray(), y.toArray()));
+ }
+ else if (Array.isArray(y)) {
+ return new Matrix(_cross(x.toArray(), y));
+ }
+ }
+ else if (Array.isArray(x)) {
+ if (y instanceof Matrix) {
+ return new Matrix(_cross(x, y.toArray()));
+ }
+ else if (Array.isArray(y)) {
+ return _cross(x, y);
+ }
+ }
+
+ throw new math.error.UnsupportedTypeError('cross', math['typeof'](x), math['typeof'](y));
+ };
+
+ /**
+ * Calculate the cross product for two arrays
+ * @param {Array} x First vector
+ * @param {Array} y Second vector
+ * @returns {Array} Returns the cross product of x and y
+ * @private
+ */
+ function _cross(x, y) {
+ var xSize= array.size(x);
+ var ySize = array.size(y);
+
+ if (xSize.length != 1 || ySize.length != 1 || xSize[0] != 3 || ySize[0] != 3) {
+ throw new RangeError('Vectors with length 3 expected ' +
+ '(Size A = [' + xSize.join(', ') + '], B = [' + ySize.join(', ') + '])');
+ }
+
+ return [
+ math.subtract(math.multiply(x[1], y[2]), math.multiply(x[2], y[1])),
+ math.subtract(math.multiply(x[2], y[0]), math.multiply(x[0], y[2])),
+ math.subtract(math.multiply(x[0], y[1]), math.multiply(x[1], y[0]))
+ ];
+ }
+ };
+
+
+/***/ },
+/* 91 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+
+ object = util.object,
+ string = util.string;
+
+ /**
+ * Calculate the determinant of a matrix.
+ *
+ * Syntax:
+ *
+ * math.det(x)
+ *
+ * Examples:
+ *
+ * math.det([[1, 2], [3, 4]]); // returns -2
+ *
+ * var A = [
+ * [-2, 2, 3],
+ * [-1, 1, 3],
+ * [2, 0, -1]
+ * ]
+ * math.det(A); // returns 6
+ *
+ * See also:
+ *
+ * inv
+ *
+ * @param {Array | Matrix} x A matrix
+ * @return {Number} The determinant of `x`
+ */
+ math.det = function det (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('det', arguments.length, 1);
+ }
+
+ var size;
+ if (x instanceof Matrix) {
+ size = x.size();
+ }
+ else if (x instanceof Array) {
+ x = new Matrix(x);
+ size = x.size();
+ }
+ else {
+ // a scalar
+ size = [];
+ }
+
+ switch (size.length) {
+ case 0:
+ // scalar
+ return object.clone(x);
+
+ case 1:
+ // vector
+ if (size[0] == 1) {
+ return object.clone(x.valueOf()[0]);
+ }
+ else {
+ throw new RangeError('Matrix must be square ' +
+ '(size: ' + string.format(size) + ')');
+ }
+
+ case 2:
+ // two dimensional array
+ var rows = size[0];
+ var cols = size[1];
+ if (rows == cols) {
+ return _det(x.clone().valueOf(), rows, cols);
+ }
+ else {
+ throw new RangeError('Matrix must be square ' +
+ '(size: ' + string.format(size) + ')');
+ }
+
+ default:
+ // multi dimensional array
+ throw new RangeError('Matrix must be two dimensional ' +
+ '(size: ' + string.format(size) + ')');
+ }
+ };
+
+ /**
+ * Calculate the determinant of a matrix
+ * @param {Array[]} matrix A square, two dimensional matrix
+ * @param {Number} rows Number of rows of the matrix (zero-based)
+ * @param {Number} cols Number of columns of the matrix (zero-based)
+ * @returns {Number} det
+ * @private
+ */
+ function _det (matrix, rows, cols) {
+ if (rows == 1) {
+ // this is a 1 x 1 matrix
+ return object.clone(matrix[0][0]);
+ }
+ else if (rows == 2) {
+ // this is a 2 x 2 matrix
+ // the determinant of [a11,a12;a21,a22] is det = a11*a22-a21*a12
+ return math.subtract(
+ math.multiply(matrix[0][0], matrix[1][1]),
+ math.multiply(matrix[1][0], matrix[0][1])
+ );
+ }
+ else {
+ // this is an n x n matrix
+ var compute_mu = function (matrix) {
+ var i, j;
+
+ // Compute the matrix with zero lower triangle, same upper triangle,
+ // and diagonals given by the negated sum of the below diagonal
+ // elements.
+ var mu = new Array(matrix.length);
+ var sum = 0;
+ for (i = 1; i < matrix.length; i++) {
+ sum = math.add(sum, matrix[i][i]);
+ }
+
+ for (i = 0; i < matrix.length; i++) {
+ mu[i] = new Array(matrix.length);
+ mu[i][i] = math.unaryMinus(sum);
+
+ for (j = 0; j < i; j++) {
+ mu[i][j] = 0; // TODO: make bignumber 0 in case of bignumber computation
+ }
+
+ for (j = i + 1; j < matrix.length; j++) {
+ mu[i][j] = matrix[i][j];
+ }
+
+ if (i+1 < matrix.length) {
+ sum = math.subtract(sum, matrix[i + 1][i + 1]);
+ }
+ }
+
+ return mu;
+ };
+
+ var fa = matrix;
+ for (var i = 0; i < rows - 1; i++) {
+ fa = math.multiply(compute_mu(fa), matrix);
+ }
+
+ if (rows % 2 == 0) {
+ return math.unaryMinus(fa[0][0]);
+ } else {
+ return fa[0][0];
+ }
+ }
+ }
+ };
+
+
+/***/ },
+/* 92 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+
+ object = util.object,
+ isArray = util.array.isArray,
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger;
+
+ /**
+ * Create a diagonal matrix or retrieve the diagonal of a matrix
+ *
+ * When `x` is a vector, a matrix with vector `x` on the diagonal will be returned.
+ * When `x` is a two dimensional matrix, the matrixes `k`th diagonal will be returned as vector.
+ * When k is positive, the values are placed on the super diagonal.
+ * When k is negative, the values are placed on the sub diagonal.
+ *
+ * Syntax:
+ *
+ * math.diag(X)
+ * math.diag(X, k)
+ *
+ * Examples:
+ *
+ * // create a diagonal matrix
+ * math.diag([1, 2, 3]); // returns [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
+ * math.diag([1, 2, 3], 1); // returns [[0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]
+ * math.diag([1, 2, 3], -1); // returns [[0, 0, 0], [1, 0, 0], [0, 2, 0], [0, 0, 3]]
+ *
+ * // retrieve the diagonal from a matrix
+ * var a = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];
+ * math.diag(a); // returns [1, 5, 9]
+ *
+ * See also:
+ *
+ * ones, zeros, eye
+ *
+ * @param {Matrix | Array} x A two dimensional matrix or a vector
+ * @param {Number | BigNumber} [k=0] The diagonal where the vector will be filled
+ * in or retrieved.
+ * @returns {Matrix | Array} Diagonal matrix from input vector, or diagonal from input matrix.
+ */
+ math.diag = function diag (x, k) {
+ var data, vector, i, iMax;
+
+ if (arguments.length != 1 && arguments.length != 2) {
+ throw new math.error.ArgumentsError('diag', arguments.length, 1, 2);
+ }
+
+ if (k) {
+ // convert BigNumber to a number
+ if (k instanceof BigNumber) k = k.toNumber();
+
+ if (!isNumber(k) || !isInteger(k)) {
+ throw new TypeError ('Second parameter in function diag must be an integer');
+ }
+ }
+ else {
+ k = 0;
+ }
+ var kSuper = k > 0 ? k : 0;
+ var kSub = k < 0 ? -k : 0;
+
+ // check type of input
+ var asArray;
+ if (x instanceof Matrix) {
+ asArray = false;
+ }
+ else if (isArray(x)) {
+ // convert to matrix
+ x = new Matrix(x);
+ asArray = true;
+ }
+ else {
+ throw new TypeError ('First parameter in function diag must be a Matrix or Array');
+ }
+
+ var s = x.size();
+ switch (s.length) {
+ case 1:
+ // x is a vector. create diagonal matrix
+ vector = x.valueOf();
+ var matrix = new Matrix();
+ var defaultValue = (vector[0] instanceof BigNumber) ? new BigNumber(0) : 0;
+ matrix.resize([vector.length + kSub, vector.length + kSuper], defaultValue);
+ data = matrix.valueOf();
+ iMax = vector.length;
+ for (i = 0; i < iMax; i++) {
+ data[i + kSub][i + kSuper] = object.clone(vector[i]);
+ }
+ return asArray ? matrix.valueOf() : matrix;
+
+ case 2:
+ // x is a matrix get diagonal from matrix
+ vector = [];
+ data = x.valueOf();
+ iMax = Math.min(s[0] - kSub, s[1] - kSuper);
+ for (i = 0; i < iMax; i++) {
+ vector[i] = object.clone(data[i + kSub][i + kSuper]);
+ }
+ return asArray ? vector : new Matrix(vector);
+
+ default:
+ throw new RangeError('Matrix for function diag must be 2 dimensional');
+ }
+ };
+ };
+
+
+/***/ },
+/* 93 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function(math) {
+ var array = __webpack_require__(165);
+ var Matrix = __webpack_require__(10);
+
+ /**
+ * Calculate the dot product of two vectors. The dot product of
+ * `A = [a1, a2, a3, ..., an]` and `B = [b1, b2, b3, ..., bn]` is defined as:
+ *
+ * dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn
+ *
+ * Syntax:
+ *
+ * math.dot(x, y)
+ *
+ * Examples:
+ *
+ * math.dot([2, 4, 1], [2, 2, 3]); // returns Number 15
+ * math.multiply([2, 4, 1], [2, 2, 3]); // returns Number 15
+ *
+ * See also:
+ *
+ * multiply, cross
+ *
+ * @param {Array | Matrix} x First vector
+ * @param {Array | Matrix} y Second vector
+ * @return {Number} Returns the dot product of `x` and `y`
+ */
+ math.dot = function dot(x, y) {
+ if (x instanceof Matrix) {
+ if (y instanceof Matrix) {
+ return _dot(x.toArray(), y.toArray());
+ }
+ else if (Array.isArray(y)) {
+ return _dot(x.toArray(), y);
+ }
+ }
+ else if (Array.isArray(x)) {
+ if (y instanceof Matrix) {
+ return _dot(x, y.toArray());
+ }
+ else if (Array.isArray(y)) {
+ return _dot(x, y);
+ }
+ }
+
+ throw new math.error.UnsupportedTypeError('dot', math['typeof'](x), math['typeof'](y));
+ };
+
+ /**
+ * Calculate the dot product for two arrays
+ * @param {Array} x First vector
+ * @param {Array} y Second vector
+ * @returns {Number} Returns the dot product of x and y
+ * @private
+ */
+ // TODO: double code with math.multiply
+ function _dot(x, y) {
+ var xSize= array.size(x);
+ var ySize = array.size(y);
+ var len = xSize[0];
+
+ if (xSize.length !== 1 || ySize.length !== 1) throw new RangeError('Vector expected'); // TODO: better error message
+ if (xSize[0] != ySize[0]) throw new RangeError('Vectors must have equal length (' + xSize[0] + ' != ' + ySize[0] + ')');
+ if (len == 0) throw new RangeError('Cannot calculate the dot product of empty vectors');
+
+ var prod = 0;
+ for (var i = 0; i < len; i++) {
+ prod = math.add(prod, math.multiply(x[i], y[i]));
+ }
+
+ return prod;
+ }
+ };
+
+
+/***/ },
+/* 94 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger,
+ isArray = Array.isArray;
+
+ /**
+ * Create a 2-dimensional identity matrix with size m x n or n x n.
+ * The matrix has ones on the diagonal and zeros elsewhere.
+ *
+ * Syntax:
+ *
+ * math.eye(n)
+ * math.eye(m, n)
+ * math.eye([m, n])
+ *
+ * Examples:
+ *
+ * math.eye(3); // returns [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
+ * math.eye(3, 2); // returns [[1, 0], [0, 1], [0, 0]]
+ *
+ * var A = [[1, 2, 3], [4, 5, 6]];
+ * math.eye(math.size(b)); // returns [[1, 0, 0], [0, 1, 0]]
+ *
+ * See also:
+ *
+ * diag, ones, zeros, size, range
+ *
+ * @param {...Number | Matrix | Array} size The size for the matrix
+ * @return {Matrix | Array | Number} A matrix with ones on the diagonal.
+ */
+ math.eye = function eye (size) {
+ var args = collection.argsToArray(arguments),
+ asMatrix = (size instanceof Matrix) ? true :
+ (isArray(size) ? false : (config.matrix === 'matrix'));
+
+
+ if (args.length == 0) {
+ // return an empty array
+ return asMatrix ? new Matrix() : [];
+ }
+ else if (args.length == 1) {
+ // change to a 2-dimensional square
+ args[1] = args[0];
+ }
+ else if (args.length > 2) {
+ // error in case of an n-dimensional size
+ throw new math.error.ArgumentsError('eye', args.length, 0, 2);
+ }
+
+ var rows = args[0],
+ cols = args[1];
+
+ if (rows instanceof BigNumber) rows = rows.toNumber();
+ if (cols instanceof BigNumber) cols = cols.toNumber();
+
+ if (!isNumber(rows) || !isInteger(rows) || rows < 1) {
+ throw new Error('Parameters in function eye must be positive integers');
+ }
+ if (!isNumber(cols) || !isInteger(cols) || cols < 1) {
+ throw new Error('Parameters in function eye must be positive integers');
+ }
+
+ // convert arguments from bignumber to numbers if needed
+ var asBigNumber = false;
+ args = args.map(function (value) {
+ if (value instanceof BigNumber) {
+ asBigNumber = true;
+ return value.toNumber();
+ } else {
+ return value;
+ }
+ });
+
+ // create the matrix
+ var matrix = new Matrix();
+ var one = asBigNumber ? new BigNumber(1) : 1;
+ var defaultValue = asBigNumber ? new BigNumber(0) : 0;
+ matrix.resize(args, defaultValue);
+
+ // fill in ones on the diagonal
+ var minimum = math.min(args);
+ var data = matrix.valueOf();
+ for (var d = 0; d < minimum; d++) {
+ data[d][d] = one;
+ }
+
+ return asMatrix ? matrix : matrix.valueOf();
+ };
+ };
+
+
+/***/ },
+/* 95 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171);
+
+ var Matrix = __webpack_require__(10);
+
+ var object = util.object;
+ var array = util.array;
+ var isArray = Array.isArray;
+
+ /**
+ * Flatten a multi dimensional matrix into a single dimensional matrix.
+ *
+ * Syntax:
+ *
+ * math.flatten(x)
+ *
+ * Examples:
+ *
+ * math.flatten([[1,2], [3,4]]); // returns [1, 2, 3, 4]
+ *
+ * See also:
+ *
+ * concat, resize, size, squeeze
+ *
+ * @param {Matrix | Array} x Matrix to be flattened
+ * @return {Matrix | Array} Returns the flattened matrix
+ */
+ math.flatten = function flatten (x) {
+ if (arguments.length !== 1) {
+ throw new math.error.ArgumentsError('flatten', arguments.length, 1);
+ }
+
+ if (x instanceof Matrix) {
+ var clone = object.clone(x.toArray());
+ var flat = array.flatten(clone);
+ return new Matrix(flat);
+ }
+
+ if (isArray(x)) {
+ return array.flatten(object.clone(x));
+ }
+
+ throw new math.error.UnsupportedTypeError('flatten', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 96 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171);
+ var Matrix = __webpack_require__(10);
+
+ /**
+ * Calculate the inverse of a square matrix.
+ *
+ * Syntax:
+ *
+ * math.inv(x)
+ *
+ * Examples:
+ *
+ * math.inv([[1, 2], [3, 4]]); // returns [[-2, 1], [1.5, -0.5]]
+ * math.inv(4); // returns 0.25
+ * 1 / 4; // returns 0.25
+ *
+ * See also:
+ *
+ * det, transpose
+ *
+ * @param {Number | Complex | Array | Matrix} x Matrix to be inversed
+ * @return {Number | Complex | Array | Matrix} The inverse of `x`.
+ */
+ math.inv = function inv (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('inv', arguments.length, 1);
+ }
+ var size = math.size(x).valueOf();
+ switch (size.length) {
+ case 0:
+ // scalar
+ return math._divide(1, x);
+
+ case 1:
+ // vector
+ if (size[0] == 1) {
+ if (x instanceof Matrix) {
+ return new Matrix([
+ math._divide(1, x.valueOf()[0])
+ ]);
+ }
+ else {
+ return [
+ math._divide(1, x[0])
+ ];
+ }
+ }
+ else {
+ throw new RangeError('Matrix must be square ' +
+ '(size: ' + util.string.format(size) + ')');
+ }
+
+ case 2:
+ // two dimensional array
+ var rows = size[0];
+ var cols = size[1];
+ if (rows == cols) {
+ if (x instanceof Matrix) {
+ return new Matrix(
+ _inv(x.valueOf(), rows, cols)
+ );
+ }
+ else {
+ // return an Array
+ return _inv(x, rows, cols);
+ }
+ }
+ else {
+ throw new RangeError('Matrix must be square ' +
+ '(size: ' + util.string.format(size) + ')');
+ }
+
+ default:
+ // multi dimensional array
+ throw new RangeError('Matrix must be two dimensional ' +
+ '(size: ' + util.string.format(size) + ')');
+ }
+ };
+
+ /**
+ * Calculate the inverse of a square matrix
+ * @param {Array[]} matrix A square matrix
+ * @param {Number} rows Number of rows
+ * @param {Number} cols Number of columns, must equal rows
+ * @return {Array[]} inv Inverse matrix
+ * @private
+ */
+ function _inv (matrix, rows, cols){
+ var r, s, f, value, temp;
+
+ if (rows == 1) {
+ // this is a 1 x 1 matrix
+ value = matrix[0][0];
+ if (value == 0) {
+ throw Error('Cannot calculate inverse, determinant is zero');
+ }
+ return [[
+ math._divide(1, value)
+ ]];
+ }
+ else if (rows == 2) {
+ // this is a 2 x 2 matrix
+ var d = math.det(matrix);
+ if (d == 0) {
+ throw Error('Cannot calculate inverse, determinant is zero');
+ }
+ return [
+ [
+ math._divide(matrix[1][1], d),
+ math._divide(math.unaryMinus(matrix[0][1]), d)
+ ],
+ [
+ math._divide(math.unaryMinus(matrix[1][0]), d),
+ math._divide(matrix[0][0], d)
+ ]
+ ];
+ }
+ else {
+ // this is a matrix of 3 x 3 or larger
+ // calculate inverse using gauss-jordan elimination
+ // http://en.wikipedia.org/wiki/Gaussian_elimination
+ // http://mathworld.wolfram.com/MatrixInverse.html
+ // http://math.uww.edu/~mcfarlat/inverse.htm
+
+ // make a copy of the matrix (only the arrays, not of the elements)
+ var A = matrix.concat();
+ for (r = 0; r < rows; r++) {
+ A[r] = A[r].concat();
+ }
+
+ // create an identity matrix which in the end will contain the
+ // matrix inverse
+ var B = math.eye(rows).valueOf();
+
+ // loop over all columns, and perform row reductions
+ for (var c = 0; c < cols; c++) {
+ // element Acc should be non zero. if not, swap content
+ // with one of the lower rows
+ r = c;
+ while (r < rows && A[r][c] == 0) {
+ r++;
+ }
+ if (r == rows || A[r][c] == 0) {
+ // TODO: in case of zero det, just return a matrix wih Infinity values? (like octave)
+ throw Error('Cannot calculate inverse, determinant is zero');
+ }
+ if (r != c) {
+ temp = A[c]; A[c] = A[r]; A[r] = temp;
+ temp = B[c]; B[c] = B[r]; B[r] = temp;
+ }
+
+ // eliminate non-zero values on the other rows at column c
+ var Ac = A[c],
+ Bc = B[c];
+ for (r = 0; r < rows; r++) {
+ var Ar = A[r],
+ Br = B[r];
+ if(r != c) {
+ // eliminate value at column c and row r
+ if (Ar[c] != 0) {
+ f = math._divide(math.unaryMinus(Ar[c]), Ac[c]);
+
+ // add (f * row c) to row r to eliminate the value
+ // at column c
+ for (s = c; s < cols; s++) {
+ Ar[s] = math.add(Ar[s], math.multiply(f, Ac[s]));
+ }
+ for (s = 0; s < cols; s++) {
+ Br[s] = math.add(Br[s], math.multiply(f, Bc[s]));
+ }
+ }
+ }
+ else {
+ // normalize value at Acc to 1,
+ // divide each value on row r with the value at Acc
+ f = Ac[c];
+ for (s = c; s < cols; s++) {
+ Ar[s] = math._divide(Ar[s], f);
+ }
+ for (s = 0; s < cols; s++) {
+ Br[s] = math._divide(Br[s], f);
+ }
+ }
+ }
+ }
+ return B;
+ }
+ }
+ };
+
+
+/***/ },
+/* 97 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ array = util.array,
+
+ isArray = Array.isArray;
+
+ /**
+ * Create a matrix filled with ones. The created matrix can have one or
+ * multiple dimensions.
+ *
+ * Syntax:
+ *
+ * math.ones(m)
+ * math.ones(m, n)
+ * math.ones([m, n])
+ * math.ones([m, n, p, ...])
+ *
+ * Examples:
+ *
+ * math.ones(3); // returns [1, 1, 1]
+ * math.ones(3, 2); // returns [[1, 1], [1, 1], [1, 1]]
+ *
+ * var A = [[1, 2, 3], [4, 5, 6]];
+ * math.zeros(math.size(A)); // returns [[1, 1, 1], [1, 1, 1]]
+ *
+ * See also:
+ *
+ * zeros, eye, size, range
+ *
+ * @param {...Number | Array} size The size of each dimension of the matrix
+ * @return {Array | Matrix | Number} A matrix filled with ones
+ */
+ math.ones = function ones (size) {
+ var args = collection.argsToArray(arguments);
+ var asMatrix = (size instanceof Matrix) ? true :
+ (isArray(size) ? false : (config.matrix === 'matrix'));
+
+ if (args.length == 0) {
+ // output an empty matrix
+ return asMatrix ? new Matrix() : [];
+ }
+ else {
+ // output an array or matrix
+
+ // convert arguments from bignumber to numbers if needed
+ var asBigNumber = false;
+ args = args.map(function (value) {
+ if (value instanceof BigNumber) {
+ asBigNumber = true;
+ return value.toNumber();
+ } else {
+ return value;
+ }
+ });
+
+ // resize the matrix
+ var res = [];
+ var defaultValue = asBigNumber ? new BigNumber(1) : 1;
+ res = array.resize(res, args, defaultValue);
+
+ return asMatrix ? new Matrix(res) : res;
+ }
+ };
+ };
+
+
+/***/ },
+/* 98 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isNumber = util.number.isNumber;
+
+ /**
+ * Create an array from a range.
+ * By default, the range end is excluded. This can be customized by providing
+ * an extra parameter `includeEnd`.
+ *
+ * Syntax:
+ *
+ * math.range(str [, includeEnd]) // Create a range from a string,
+ * // where the string contains the
+ * // start, optional step, and end,
+ * // separated by a colon.
+ * math.range(start, end [, includeEnd]) // Create a range with start and
+ * // end and a step size of 1.
+ * math.range(start, end, step [, includeEnd]) // Create a range with start, step,
+ * // and end.
+ *
+ * Where:
+ *
+ * - `str: String`
+ * A string 'start:end' or 'start:step:end'
+ * - `start: {Number | BigNumber}`
+ * Start of the range
+ * - `end: Number | BigNumber`
+ * End of the range, excluded by default, included when parameter includeEnd=true
+ * - `step: Number | BigNumber`
+ * Step size. Default value is 1.
+ * - `includeEnd: boolean`
+ * Option to specify whether to include the end or not. False by default.
+ *
+ * Examples:
+ *
+ * math.range(2, 6); // [2, 3, 4, 5]
+ * math.range(2, -3, -1); // [2, 1, 0, -1, -2]
+ * math.range('2:1:6'); // [2, 3, 4, 5]
+ * math.range(2, 6, true); // [2, 3, 4, 5, 6]
+ *
+ * See also:
+ *
+ * ones, zeros, size, subset
+ *
+ * @param {*} args Parameters describing the ranges `start`, `end`, and optional `step`.
+ * @return {Array | Matrix} range
+ */
+ math.range = function range(args) {
+ var params = Array.prototype.slice.call(arguments),
+ start,
+ end,
+ step,
+ includeEnd = false;
+
+ // read the includeEnd parameter
+ if (isBoolean(params[params.length - 1])) {
+ includeEnd = params.pop() ? true : false;
+ }
+
+ switch (params.length) {
+ case 1:
+ // range(str)
+ // parse string into a range
+ if (isString(params[0])) {
+ var r = _parse(params[0]);
+ if (!r){
+ throw new SyntaxError('String "' + params[0] + '" is no valid range');
+ }
+
+ start = r.start;
+ end = r.end;
+ step = r.step;
+ }
+ else {
+ throw new TypeError('Two or three numbers or a single string expected in function range');
+ }
+ break;
+
+ case 2:
+ // range(str, end)
+ // range(start, end)
+ start = params[0];
+ end = params[1];
+ step = 1;
+ break;
+
+ case 3:
+ // range(start, end, step)
+ start = params[0];
+ end = params[1];
+ step = params[2];
+ break;
+
+ case 4:
+ throw new TypeError('Parameter includeEnd must be a boolean');
+
+ default:
+ throw new math.error.ArgumentsError('range', arguments.length, 2, 4);
+ }
+
+ // verify type of parameters
+ if (!isNumber(start) && !(start instanceof BigNumber)) {
+ throw new TypeError('Parameter start must be a number');
+ }
+ if (!isNumber(end) && !(end instanceof BigNumber)) {
+ throw new TypeError('Parameter end must be a number');
+ }
+ if (!isNumber(step) && !(step instanceof BigNumber)) {
+ throw new TypeError('Parameter step must be a number');
+ }
+
+ // go big
+ if (start instanceof BigNumber || end instanceof BigNumber || step instanceof BigNumber) {
+ // create a range with big numbers
+ var asBigNumber = true;
+
+ // convert start, end, step to BigNumber
+ if (!(start instanceof BigNumber)) start = BigNumber.convert(start);
+ if (!(end instanceof BigNumber)) end = BigNumber.convert(end);
+ if (!(step instanceof BigNumber)) step = BigNumber.convert(step);
+
+ if (!(start instanceof BigNumber) || !(end instanceof BigNumber) || !(step instanceof BigNumber)) {
+ // not all values can be converted to big number :(
+ // fall back to numbers
+ asBigNumber = false;
+ if (start instanceof BigNumber) start = start.toNumber();
+ if (end instanceof BigNumber) end = end.toNumber();
+ if (step instanceof BigNumber) step = step.toNumber();
+ }
+ }
+
+ // generate the range
+ var fn = asBigNumber ?
+ (includeEnd ? _bigRangeInc : _bigRange) :
+ (includeEnd ? _rangeInc : _range);
+ var array = fn(start, end, step);
+
+ // return as array or matrix
+ return (config.matrix === 'array') ? array : new Matrix(array);
+ };
+
+ /**
+ * Create a range with numbers. End is excluded
+ * @param {Number} start
+ * @param {Number} end
+ * @param {Number} step
+ * @returns {Array} range
+ * @private
+ */
+ function _range (start, end, step) {
+ var array = [],
+ x = start;
+ if (step > 0) {
+ while (x < end) {
+ array.push(x);
+ x += step;
+ }
+ }
+ else if (step < 0) {
+ while (x > end) {
+ array.push(x);
+ x += step;
+ }
+ }
+
+ return array;
+ }
+
+ /**
+ * Create a range with numbers. End is included
+ * @param {Number} start
+ * @param {Number} end
+ * @param {Number} step
+ * @returns {Array} range
+ * @private
+ */
+ function _rangeInc (start, end, step) {
+ var array = [],
+ x = start;
+ if (step > 0) {
+ while (x <= end) {
+ array.push(x);
+ x += step;
+ }
+ }
+ else if (step < 0) {
+ while (x >= end) {
+ array.push(x);
+ x += step;
+ }
+ }
+
+ return array;
+ }
+
+ /**
+ * Create a range with big numbers. End is excluded
+ * @param {BigNumber} start
+ * @param {BigNumber} end
+ * @param {BigNumber} step
+ * @returns {Array} range
+ * @private
+ */
+ function _bigRange (start, end, step) {
+ var array = [],
+ x = start.clone(),
+ zero = new BigNumber(0);
+ if (step.gt(zero)) {
+ while (x.lt(end)) {
+ array.push(x);
+ x = x.plus(step);
+ }
+ }
+ else if (step.lt(zero)) {
+ while (x.gt(end)) {
+ array.push(x);
+ x = x.plus(step);
+ }
+ }
+
+ return array;
+ }
+
+ /**
+ * Create a range with big numbers. End is included
+ * @param {BigNumber} start
+ * @param {BigNumber} end
+ * @param {BigNumber} step
+ * @returns {Array} range
+ * @private
+ */
+ function _bigRangeInc (start, end, step) {
+ var array = [],
+ x = start.clone(),
+ zero = new BigNumber(0);
+ if (step.gt(zero)) {
+ while (x.lte(end)) {
+ array.push(x);
+ x = x.plus(step);
+ }
+ }
+ else if (step.lt(zero)) {
+ while (x.gte(end)) {
+ array.push(x);
+ x = x.plus(step);
+ }
+ }
+
+ return array;
+ }
+
+ /**
+ * Parse a string into a range,
+ * The string contains the start, optional step, and end, separated by a colon.
+ * If the string does not contain a valid range, null is returned.
+ * For example str='0:2:11'.
+ * @param {String} str
+ * @return {Object | null} range Object containing properties start, end, step
+ * @private
+ */
+ function _parse (str) {
+ var args = str.split(':'),
+ nums = null;
+
+ if (config.number === 'bignumber') {
+ // bignumber
+ try {
+ nums = args.map(function (arg) {
+ return new BigNumber(arg);
+ });
+ }
+ catch (err) {
+ return null;
+ }
+ }
+ else {
+ // number
+ nums = args.map(function (arg) {
+ // use Number and not parseFloat as Number returns NaN on invalid garbage in the string
+ return Number(arg);
+ });
+
+ var invalid = nums.some(function (num) {
+ return isNaN(num);
+ });
+ if(invalid) {
+ return null;
+ }
+ }
+
+ switch (nums.length) {
+ case 2:
+ return {
+ start: nums[0],
+ end: nums[1],
+ step: 1
+ };
+
+ case 3:
+ return {
+ start: nums[0],
+ end: nums[2],
+ step: nums[1]
+ };
+
+ default:
+ return null;
+ }
+ }
+
+ };
+
+
+/***/ },
+/* 99 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+
+ array = util.array,
+ clone = util.object.clone,
+ string = util.string,
+ isString = util.string.isString,
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger,
+ isArray = array.isArray;
+
+ /**
+ * Resize a matrix
+ *
+ * Syntax:
+ *
+ * math.resize(x, size)
+ * math.resize(x, size, defaultValue)
+ *
+ * Examples:
+ *
+ * math.resize([1, 2, 3, 4, 5], [3]); // returns Array [1, 2, 3]
+ * math.resize([1, 2, 3], [5], 0); // returns Array [1, 2, 3, 0, 0]
+ * math.resize(2, [2, 3], 0); // returns Matrix [[2, 0, 0], [0, 0, 0]]
+ * math.resize("hello", [8], "!"); // returns String 'hello!!!'
+ *
+ * See also:
+ *
+ * size, squeeze, subset
+ *
+ * @param {* | Array | Matrix} x Matrix to be resized
+ * @param {Array | Matrix} size One dimensional array with numbers
+ * @param {Number | String} [defaultValue=0] Zero by default, except in
+ * case of a string, in that case
+ * defaultValue = ' '
+ * @return {* | Array | Matrix} A resized clone of matrix `x`
+ */
+ math.resize = function resize (x, size, defaultValue) {
+ if (arguments.length != 2 && arguments.length != 3) {
+ throw new math.error.ArgumentsError('resize', arguments.length, 2, 3);
+ }
+
+ var asMatrix = (x instanceof Matrix) ? true : isArray(x) ? false : (config.matrix !== 'array');
+
+ if (x instanceof Matrix) {
+ x = x.valueOf(); // get Array
+ }
+ if (size instanceof Matrix) {
+ size = size.valueOf(); // get Array
+ }
+
+ if (size.length && size[0] instanceof BigNumber) {
+ // convert bignumbers to numbers
+ size = size.map(function (value) {
+ return (value instanceof BigNumber) ? value.toNumber() : value;
+ });
+ }
+
+ if (isString(x)) {
+ return _resizeString(x, size, defaultValue);
+ }
+ else {
+ if (size.length == 0) {
+ // output a scalar
+ while (isArray(x)) {
+ x = x[0];
+ }
+
+ return clone(x);
+ }
+ else {
+ // output an array/matrix
+ if (!isArray(x)) {
+ x = [x];
+ }
+ x = clone(x);
+
+ var res = array.resize(x, size, defaultValue);
+ return asMatrix ? new Matrix(res) : res;
+ }
+ }
+ };
+
+ /**
+ * Resize a string
+ * @param {String} str
+ * @param {Number[]} size
+ * @param {string} [defaultChar=' ']
+ * @private
+ */
+ function _resizeString(str, size, defaultChar) {
+ if (defaultChar !== undefined) {
+ if (!isString(defaultChar) || defaultChar.length !== 1) {
+ throw new TypeError('Single character expected as defaultValue');
+ }
+ }
+ else {
+ defaultChar = ' ';
+ }
+
+ if (size.length !== 1) {
+ throw new math.error.DimensionError(size.length, 1);
+ }
+ var len = size[0];
+ if (!isNumber(len) || !isInteger(len)) {
+ throw new TypeError('Invalid size, must contain positive integers ' +
+ '(size: ' + string.format(size) + ')');
+ }
+
+ if (str.length > len) {
+ return str.substring(0, len);
+ }
+ else if (str.length < len) {
+ var res = str;
+ for (var i = 0, ii = len - str.length; i < ii; i++) {
+ res += defaultChar;
+ }
+ return res;
+ }
+ else {
+ return str;
+ }
+ }
+ };
+
+
+/***/ },
+/* 100 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ Matrix = __webpack_require__(10),
+
+ array = util.array,
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit;
+
+ /**
+ * Calculate the size of a matrix or scalar.
+ *
+ * Syntax:
+ *
+ * math.size(x)
+ *
+ * Examples:
+ *
+ * math.size(2.3); // returns []
+ * math.size('hello world'); // returns [11]
+ *
+ * var A = [[1, 2, 3], [4, 5, 6]];
+ * math.size(A); // returns [2, 3]
+ * math.size(math.range(1,6)); // returns [5]
+ *
+ * See also:
+ *
+ * resize, squeeze, subset
+ *
+ * @param {Boolean | Number | Complex | Unit | String | Array | Matrix} x A matrix
+ * @return {Array | Matrix} A vector with size of `x`.
+ */
+ math.size = function size (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('size', arguments.length, 1);
+ }
+
+ var asArray = (config.matrix === 'array');
+
+ if (isNumber(x) || isComplex(x) || isUnit(x) || isBoolean(x) ||
+ x == null || x instanceof BigNumber) {
+ return asArray ? [] : new Matrix([]);
+ }
+
+ if (isString(x)) {
+ return asArray ? [x.length] : new Matrix([x.length]);
+ }
+
+ if (Array.isArray(x)) {
+ return array.size(x);
+ }
+
+ if (x instanceof Matrix) {
+ return new Matrix(x.size());
+ }
+
+ throw new math.error.UnsupportedTypeError('size', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 101 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+
+ object = util.object,
+ array = util.array,
+ isArray = Array.isArray;
+
+ /**
+ * Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.
+ *
+ * Syntax:
+ *
+ * math.squeeze(x)
+ *
+ * Examples:
+ *
+ * math.squeeze([3]); // returns 3
+ * math.squeeze([[3]]); // returns 3
+ *
+ * var A = math.zeros(3, 1); // returns [[0], [0], [0]] (size 3x1)
+ * math.squeeze(A); // returns [0, 0, 0] (size 3)
+ *
+ * var B = math.zeros(1, 3); // returns [[0, 0, 0]] (size 1x3)
+ * math.squeeze(B); // returns [0, 0, 0] (size 3)
+ *
+ * // only inner and outer dimensions are removed
+ * var C = math.zeros(2, 1, 3); // returns [[[0, 0, 0]], [[0, 0, 0]]] (size 2x1x3)
+ * math.squeeze(C); // returns [[[0, 0, 0]], [[0, 0, 0]]] (size 2x1x3)
+ *
+ * See also:
+ *
+ * subset
+ *
+ * @param {Matrix | Array} x Matrix to be squeezed
+ * @return {Matrix | Array} Squeezed matrix
+ */
+ math.squeeze = function squeeze (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('squeeze', arguments.length, 1);
+ }
+
+ if (isArray(x)) {
+ return array.squeeze(object.clone(x));
+ }
+ else if (x instanceof Matrix) {
+ var res = array.squeeze(x.toArray());
+ return isArray(res) ? new Matrix(res) : res;
+ }
+ else {
+ // scalar
+ return object.clone(x);
+ }
+ };
+ };
+
+
+/***/ },
+/* 102 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+ Index = __webpack_require__(9),
+
+ array = util.array,
+ isString = util.string.isString,
+ isArray = Array.isArray;
+
+ /**
+ * Get or set a subset of a matrix or string.
+ *
+ * Syntax:
+ * math.subset(value, index) // retrieve a subset
+ * math.subset(value, index, replacement [, defaultValue]) // replace a subset
+ *
+ * Examples:
+ *
+ * // get a subset
+ * var d = [[1, 2], [3, 4]];
+ * math.subset(d, math.index(1, 0)); // returns 3
+ * math.subset(d, math.index([0, 2], 1)); // returns [[2], [4]]
+ *
+ * // replace a subset
+ * var e = [];
+ * var f = math.subset(e, math.index(0, [0, 2]), [5, 6]); // f = [[5, 6]]
+ * var g = math.subset(f, math.index(1, 1), 7, 0); // g = [[5, 6], [0, 7]]
+ *
+ * See also:
+ *
+ * size, resize, squeeze, index
+ *
+ * @param {Array | Matrix | String} matrix An array, matrix, or string
+ * @param {Index} index An index containing ranges for each
+ * dimension
+ * @param {*} [replacement] An array, matrix, or scalar.
+ * If provided, the subset is replaced with replacement.
+ * If not provided, the subset is returned
+ * @param {*} [defaultValue=undefined] Default value, filled in on new entries when
+ * the matrix is resized. If not provided,
+ * new matrix elements will be left undefined.
+ * @return {Array | Matrix | String} Either the retrieved subset or the updated matrix.
+ */
+ math.subset = function subset (matrix, index, replacement, defaultValue) {
+ switch (arguments.length) {
+ case 2: // get subset
+ return _getSubset(arguments[0], arguments[1]);
+
+ // intentional fall through
+ case 3: // set subset
+ case 4: // set subset with default value
+ return _setSubset(arguments[0], arguments[1], arguments[2], arguments[3]);
+
+ default: // wrong number of arguments
+ throw new math.error.ArgumentsError('subset', arguments.length, 2, 4);
+ }
+ };
+
+ /**
+ * Retrieve a subset of an value such as an Array, Matrix, or String
+ * @param {Array | Matrix | String} value Object from which to get a subset
+ * @param {Index} index An index containing ranges for each
+ * dimension
+ * @returns {Array | Matrix | *} subset
+ * @private
+ */
+ function _getSubset(value, index) {
+ var m, subset;
+
+ if (isArray(value)) {
+ m = new Matrix(value);
+ subset = m.subset(index); // returns a Matrix
+ return subset && subset.valueOf(); // return an Array (like the input)
+ }
+ else if (value instanceof Matrix) {
+ return value.subset(index);
+ }
+ else if (isString(value)) {
+ return _getSubstring(value, index);
+ }
+ else {
+ throw new math.error.UnsupportedTypeError('subset', math['typeof'](value));
+ }
+ }
+
+ /**
+ * Retrieve a subset of a string
+ * @param {String} str String from which to get a substring
+ * @param {Index} index An index containing ranges for each dimension
+ * @returns {string} substring
+ * @private
+ */
+ function _getSubstring(str, index) {
+ if (!(index instanceof Index)) {
+ // TODO: better error message
+ throw new TypeError('Index expected');
+ }
+ if (index.size().length != 1) {
+ throw new math.error.DimensionError(index.size().length, 1);
+ }
+
+ // validate whether the range is out of range
+ var strLen = str.length;
+ array.validateIndex(index.min()[0], strLen);
+ array.validateIndex(index.max()[0], strLen);
+
+ var range = index.range(0);
+
+ var substr = '';
+ range.forEach(function (v) {
+ substr += str.charAt(v);
+ });
+
+ return substr;
+ }
+
+ /**
+ * Replace a subset in an value such as an Array, Matrix, or String
+ * @param {Array | Matrix | String} value Object to be replaced
+ * @param {Index} index An index containing ranges for each
+ * dimension
+ * @param {Array | Matrix | *} replacement
+ * @param {*} [defaultValue=0] Default value, filled in on new entries when
+ * the matrix is resized. If not provided,
+ * new matrix elements will be filled with zeros.
+ * @returns {*} result
+ * @private
+ */
+ function _setSubset(value, index, replacement, defaultValue) {
+ var m;
+
+ if (isArray(value)) {
+ m = new Matrix(math.clone(value));
+ m.subset(index, replacement, defaultValue);
+ return m.valueOf();
+ }
+ else if (value instanceof Matrix) {
+ return value.clone().subset(index, replacement, defaultValue);
+ }
+ else if (isString(value)) {
+ return _setSubstring(value, index, replacement, defaultValue);
+ }
+ else {
+ throw new math.error.UnsupportedTypeError('subset', math['typeof'](value));
+ }
+ }
+
+ /**
+ * Replace a substring in a string
+ * @param {String} str String to be replaced
+ * @param {Index} index An index containing ranges for each dimension
+ * @param {String} replacement Replacement string
+ * @param {String} [defaultValue] Default value to be uses when resizing
+ * the string. is ' ' by default
+ * @returns {string} result
+ * @private
+ */
+ function _setSubstring(str, index, replacement, defaultValue) {
+ if (!(index instanceof Index)) {
+ // TODO: better error message
+ throw new TypeError('Index expected');
+ }
+ if (index.size().length != 1) {
+ throw new math.error.DimensionError(index.size().length, 1);
+ }
+ if (defaultValue !== undefined) {
+ if (!isString(defaultValue) || defaultValue.length !== 1) {
+ throw new TypeError('Single character expected as defaultValue');
+ }
+ }
+ else {
+ defaultValue = ' ';
+ }
+
+ var range = index.range(0);
+ var len = range.size()[0];
+
+ if (len != replacement.length) {
+ throw new math.error.DimensionError(range.size()[0], replacement.length);
+ }
+
+ // validate whether the range is out of range
+ var strLen = str.length;
+ array.validateIndex(index.min()[0]);
+ array.validateIndex(index.max()[0]);
+
+ // copy the string into an array with characters
+ var chars = [];
+ for (var i = 0; i < strLen; i++) {
+ chars[i] = str.charAt(i);
+ }
+
+ range.forEach(function (v, i) {
+ chars[v] = replacement.charAt(i);
+ });
+
+ // initialize undefined characters with a space
+ if (chars.length > strLen) {
+ for (i = strLen - 1, len = chars.length; i < len; i++) {
+ if (!chars[i]) {
+ chars[i] = defaultValue;
+ }
+ }
+ }
+
+ return chars.join('');
+ }
+ };
+
+
+/***/ },
+/* 103 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+
+ object = util.object,
+ string = util.string;
+
+ /**
+ * Calculate the trace of a matrix: the sum of the elements on the main
+ * diagonal of a square matrix.
+ *
+ * Syntax:
+ *
+ * math.trace(x)
+ *
+ * Examples:
+ *
+ * math.trace([[1, 2], [3, 4]]); // returns 5
+ *
+ * var A = [
+ * [1, 2, 3],
+ * [-1, 2, 3],
+ * [2, 0, 3]
+ * ]
+ * math.trace(A); // returns 6
+ *
+ * See also:
+ *
+ * diag
+ *
+ * @param {Array | Matrix} x A matrix
+ * @return {Number} The trace of `x`
+ */
+ math.trace = function trace (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('trace', arguments.length, 1);
+ }
+
+ var size;
+ if (x instanceof Matrix) {
+ size = x.size();
+ }
+ else if (x instanceof Array) {
+ x = new Matrix(x);
+ size = x.size();
+ }
+ else {
+ // a scalar
+ size = [];
+ }
+
+ switch (size.length) {
+ case 0:
+ // scalar
+ return object.clone(x);
+
+ case 1:
+ // vector
+ if (size[0] == 1) {
+ return object.clone(x.valueOf()[0]);
+ }
+ else {
+ throw new RangeError('Matrix must be square ' +
+ '(size: ' + string.format(size) + ')');
+ }
+
+ case 2:
+ // two dimensional array
+ var rows = size[0];
+ var cols = size[1];
+ if (rows == cols) {
+ return _trace(x.clone().valueOf());
+ }
+ else {
+ throw new RangeError('Matrix must be square ' +
+ '(size: ' + string.format(size) + ')');
+ }
+
+ default:
+ // multi dimensional array
+ throw new RangeError('Matrix must be two dimensional ' +
+ '(size: ' + string.format(size) + ')');
+ }
+ };
+
+ /**
+ * Calculate the trace of a matrix
+ * @param {Array[]} matrix A square, two dimensional matrix
+ * @returns {Number} trace
+ * @private
+ */
+ function _trace (matrix) {
+ var sum = 0;
+ for (var i = 0; i < matrix.length; i++) {
+ sum = math.add(sum, matrix[i][i]);
+ }
+ return sum;
+ }
+ };
+
+
+/***/ },
+/* 104 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ Matrix = __webpack_require__(10),
+
+ object = util.object,
+ string = util.string;
+
+ /**
+ * Transpose a matrix. All values of the matrix are reflected over its
+ * main diagonal. Only two dimensional matrices are supported.
+ *
+ * Syntax:
+ *
+ * math.transpose(x)
+ *
+ * Examples:
+ *
+ * var A = [[1, 2, 3], [4, 5, 6]];
+ * math.transpose(A); // returns [[1, 4], [2, 5], [3, 6]]
+ *
+ * See also:
+ *
+ * diag, inv, subset, squeeze
+ *
+ * @param {Array | Matrix} x Matrix to be transposed
+ * @return {Array | Matrix} The transposed matrix
+ */
+ math.transpose = function transpose (x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('transpose', arguments.length, 1);
+ }
+
+ var size = math.size(x).valueOf();
+ switch (size.length) {
+ case 0:
+ // scalar
+ return object.clone(x);
+
+ case 1:
+ // vector
+ return object.clone(x);
+
+ case 2:
+ // two dimensional array
+ var rows = size[1],
+ cols = size[0],
+ asMatrix = (x instanceof Matrix),
+ data = x.valueOf(),
+ transposed = [],
+ transposedRow,
+ clone = object.clone;
+
+ if (rows === 0) {
+ // whoops
+ throw new RangeError('Cannot transpose a 2D matrix with no rows' +
+ '(size: ' + string.format(size) + ')');
+ }
+
+ for (var r = 0; r < rows; r++) {
+ transposedRow = transposed[r] = [];
+ for (var c = 0; c < cols; c++) {
+ transposedRow[c] = clone(data[c][r]);
+ }
+ }
+
+ return asMatrix ? new Matrix(transposed) : transposed;
+
+ default:
+ // multi dimensional array
+ throw new RangeError('Matrix must be two dimensional ' +
+ '(size: ' + string.format(size) + ')');
+ }
+ };
+ };
+
+
+/***/ },
+/* 105 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ array = util.array,
+ isArray = Array.isArray;
+
+ /**
+ * Create a matrix filled with zeros. The created matrix can have one or
+ * multiple dimensions.
+ *
+ * Syntax:
+ *
+ * math.zeros(m)
+ * math.zeros(m, n)
+ * math.zeros([m, n])
+ * math.zeros([m, n, p, ...])
+ *
+ * Examples:
+ *
+ * math.zeros(3); // returns [0, 0, 0]
+ * math.zeros(3, 2); // returns [[0, 0], [0, 0], [0, 0]]
+ *
+ * var A = [[1, 2, 3], [4, 5, 6]];
+ * math.zeros(math.size(A)); // returns [[0, 0, 0], [0, 0, 0]]
+ *
+ * See also:
+ *
+ * ones, eye, size, range
+ *
+ * @param {...Number | Array} size The size of each dimension of the matrix
+ * @return {Array | Matrix | Number} A matrix filled with zeros
+ */
+ math.zeros = function zeros (size) {
+ var args = collection.argsToArray(arguments);
+ var asMatrix = (size instanceof Matrix) ? true :
+ (isArray(size) ? false : (config.matrix === 'matrix'));
+
+ if (args.length == 0) {
+ // output an empty matrix
+ return asMatrix ? new Matrix() : [];
+ }
+ else {
+ // output an array or matrix
+
+ // convert arguments from bignumber to numbers if needed
+ var asBigNumber = false;
+ args = args.map(function (value) {
+ if (value instanceof BigNumber) {
+ asBigNumber = true;
+ return value.toNumber();
+ } else {
+ return value;
+ }
+ });
+
+ // resize the matrix
+ var res = [];
+ var defaultValue = asBigNumber ? new BigNumber(0) : 0;
+ res = array.resize(res, args, defaultValue);
+
+ return asMatrix ? new Matrix(res) : res;
+ }
+ };
+ };
+
+
+/***/ },
+/* 106 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isInteger = util.number.isInteger,
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the factorial of a value
+ *
+ * Factorial only supports an integer value as argument.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.factorial(n)
+ *
+ * Examples:
+ *
+ * math.factorial(5); // returns 120
+ * math.factorial(3); // returns 6
+ *
+ * See also:
+ *
+ * combinations, gamma, permutations
+ *
+ * @param {Number | BigNumber | Array | Matrix | Boolean | null} n An integer number
+ * @return {Number | BigNumber | Array | Matrix} The factorial of `n`
+ */
+ math.factorial = function factorial (n) {
+ var value, res, preciseFacs;
+
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('factorial', arguments.length, 1);
+ }
+
+ if (isNumber(n)) {
+ return n !== Number.POSITIVE_INFINITY
+ ? math.gamma(n + 1)
+ : Math.sqrt(2*Math.PI);
+ }
+
+ if (n instanceof BigNumber) {
+ if (!(isNonNegativeInteger(n))) {
+ return n.isNegative() || n.isFinite()
+ ? math.gamma(n.plus(1))
+ : util.bignumber.tau(config.precision).sqrt();
+ }
+
+ n = n.toNumber(); // should definitely be below Number.MAX_VALUE
+ if (n < smallBigFacs.length) {
+ return BigNumber.convert(smallBigFacs[n]).toSD(config.precision);
+ }
+
+ // be wary of round-off errors
+ var precision = config.precision + (Math.log(n) | 0);
+ var Big = BigNumber.constructor({precision: precision});
+
+ // adjust n do align with the precision specific tables
+ n -= smallBigFacs.length;
+ if (preciseFacs = bigBigFacs[precision]) {
+ if (preciseFacs[n]) {
+ return new BigNumber(preciseFacs[n].toPrecision(config.precision));
+ }
+ res = preciseFacs[preciseFacs.length-1];
+ } else {
+ preciseFacs = bigBigFacs[precision] = [];
+ res = new Big(smallBigFacs[smallBigFacs.length-1])
+ .toSD(precision);
+ }
+
+ var one = new Big(1);
+ value = new Big(preciseFacs.length + smallBigFacs.length);
+ for (var i = preciseFacs.length; i < n; ++i) {
+ preciseFacs[i] = res = res.times(value);
+ value = value.plus(one);
+ }
+
+ preciseFacs[n] = res.times(value);
+ return new BigNumber(preciseFacs[n].toPrecision(config.precision));
+ }
+
+ if (isBoolean(n) || n === null) {
+ return 1; // factorial(1) = 1, factorial(0) = 1
+ }
+
+ if (isCollection(n)) {
+ return collection.deepMap(n, factorial);
+ }
+
+ throw new math.error.UnsupportedTypeError('factorial', math['typeof'](n));
+ };
+
+ /**
+ * Test whether BigNumber n is a non-negative integer
+ * @param {BigNumber} n
+ * @returns {boolean} isNonNegativeInteger
+ */
+ var isNonNegativeInteger = function(n) {
+ return n.isInteger() && (!n.isNegative() || n.isZero());
+ };
+
+ // 21! >= values for each precision
+ var bigBigFacs = [];
+
+ // 0-20! values
+ var smallBigFacs = [
+ 1,
+ 1,
+ 2,
+ 6,
+ 24,
+ 120,
+ 720,
+ 5040,
+ 40320,
+ 362880,
+ 3628800,
+ 39916800,
+ 479001600,
+ 6227020800,
+ 87178291200,
+ 1307674368000,
+ 20922789888000,
+ 355687428096000,
+ 6402373705728000,
+ 121645100408832000,
+ 2432902008176640000
+ ]
+ };
+
+
+/***/ },
+/* 107 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger,
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the gamma function of a value using Lanczos approximation for
+ * small values, and an extended Stirling approximation for large values.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.gamma(n)
+ *
+ * Examples:
+ *
+ * math.gamma(5); // returns 24
+ * math.gamma(-0.5); // returns -3.5449077018110335
+ * math.gamma(math.i); // returns -0.15494982830180973 - 0.49801566811835596i
+ *
+ * See also:
+ *
+ * combinations, factorial, permutations
+ *
+ * @param {Number | Array | Matrix | Boolean | null} n An integer number
+ * @return {Number | Array | Matrix} The gamma of `n`
+ */
+ math.gamma = function gamma (n) {
+ var t, x;
+ var g = 4.7421875;
+
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('gamma', arguments.length, 1);
+ }
+
+ if (isNumber(n)) {
+ if (isInteger(n)) {
+ if (n <= 0) {
+ return isFinite(n)
+ ? Infinity
+ : NaN;
+ }
+
+ if (n > 171) {
+ return Infinity; // Will overflow
+ }
+
+ var value = n - 2;
+ var res = n - 1;
+ while (value > 1) {
+ res *= value;
+ value--;
+ }
+
+ if (res == 0) {
+ res = 1; // 0! is per definition 1
+ }
+
+ return res;
+ }
+
+ if (n < 0.5) {
+ return Math.PI / (Math.sin(Math.PI*n) * gamma(1-n));
+ }
+
+ if (n >= 171.35) {
+ return Infinity; // will overflow
+ }
+
+ if (n > 85.0) { // Extended Stirling Approx
+ var twoN = n*n;
+ var threeN = twoN*n;
+ var fourN = threeN*n;
+ var fiveN = fourN*n;
+ return Math.sqrt(2*Math.PI/n) * Math.pow((n/Math.E), n) *
+ (1 + 1/(12*n) + 1/(288*twoN) - 139/(51840*threeN) -
+ 571/(2488320*fourN) + 163879/(209018880*fiveN) +
+ 5246819/(75246796800*fiveN*n));
+ }
+
+ --n;
+ x = p[0];
+ for (var i = 1; i < p.length; ++i) {
+ x += p[i] / (n+i);
+ }
+
+ t = n + g + 0.5;
+ return Math.sqrt(2*Math.PI) * Math.pow(t, n+0.5) * Math.exp(-t) * x;
+ }
+
+ if (isComplex(n)) {
+ if (n.im == 0) {
+ return gamma(n.re);
+ }
+
+ n = new Complex(n.re - 1, n.im);
+ x = new Complex(p[0], 0);
+ for (var i = 1; i < p.length; ++i) {
+ var real = n.re + i; // x += p[i]/(n+i)
+ var den = real*real + n.im*n.im;
+ if (den != 0) {
+ x.re += p[i] * real / den;
+ x.im += -(p[i] * n.im) / den;
+ } else {
+ x.re = p[i] < 0
+ ? -Infinity
+ : Infinity;
+ }
+ }
+
+ t = new Complex(n.re + g + 0.5, n.im);
+ var twoPiSqrt = Math.sqrt(2*Math.PI);
+
+ n.re += 0.5;
+ var result = math.pow(t, n);
+ if (result.im == 0) { // sqrt(2*PI)*result
+ result.re *= twoPiSqrt;
+ } else if (result.re == 0) {
+ result.im *= twoPiSqrt;
+ } else {
+ result.re *= twoPiSqrt;
+ result.im *= twoPiSqrt;
+ }
+
+ var r = Math.exp(-t.re); // exp(-t)
+ t.re = r * Math.cos(-t.im);
+ t.im = r * Math.sin(-t.im);
+
+ return math.multiply(math.multiply(result, t), x);
+ }
+
+ if (n instanceof BigNumber) {
+ if (n.isInteger()) {
+ return n.isNegative() || n.isZero()
+ ? new BigNumber(Infinity)
+ : math.factorial(n.minus(1));
+ }
+
+ if (!n.isFinite()) {
+ return new BigNumber(n.isNegative()
+ ? NaN
+ : Infinity);
+ }
+ }
+
+ if (isBoolean(n) || n === null) {
+ return n
+ ? 1
+ : Infinity;
+ }
+
+ if (isCollection(n)) {
+ return collection.deepMap(n, gamma);
+ }
+
+ throw new math.error.UnsupportedTypeError('gamma', math['typeof'](n));
+ };
+
+ var p = [
+ 0.99999999999999709182,
+ 57.156235665862923517,
+ -59.597960355475491248,
+ 14.136097974741747174,
+ -0.49191381609762019978,
+ 0.33994649984811888699e-4,
+ 0.46523628927048575665e-4,
+ -0.98374475304879564677e-4,
+ 0.15808870322491248884e-3,
+ -0.21026444172410488319e-3,
+ 0.21743961811521264320e-3,
+ -0.16431810653676389022e-3,
+ 0.84418223983852743293e-4,
+ -0.26190838401581408670e-4,
+ 0.36899182659531622704e-5
+ ];
+
+ };
+
+
+/***/ },
+/* 108 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var distribution = __webpack_require__(333)(math);
+
+ /**
+ * Return a random number larger or equal to `min` and smaller than `max`
+ * using a uniform distribution.
+ *
+ * Syntax:
+ *
+ * math.random() // generate a random number between 0 and 1
+ * math.random(max) // generate a random number between 0 and max
+ * math.random(min, max) // generate a random number between min and max
+ * math.random(size) // generate a matrix with random numbers between 0 and 1
+ * math.random(size, max) // generate a matrix with random numbers between 0 and max
+ * math.random(size, min, max) // generate a matrix with random numbers between min and max
+ *
+ * Examples:
+ *
+ * math.random(); // returns a random number between 0 and 1
+ * math.random(100); // returns a random number between 0 and 100
+ * math.random(30, 40); // returns a random number between 30 and 40
+ * math.random([2, 3]); // returns a 2x3 matrix with random numbers between 0 and 1
+ *
+ * See also:
+ *
+ * randomInt, pickRandom
+ *
+ * @param {Array | Matrix} [size] If provided, an array or matrix with given
+ * size and filled with random values is returned
+ * @param {Number} [min] Minimum boundary for the random value, included
+ * @param {Number} [max] Maximum boundary for the random value, excluded
+ * @return {Number | Array | Matrix} A random number
+ */
+ math.random = distribution('uniform').random;
+ };
+
+
+/***/ },
+/* 109 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var distribution = __webpack_require__(333)(math);
+
+ /**
+ * Return a random integer number larger or equal to `min` and smaller than `max`
+ * using a uniform distribution.
+ *
+ * Syntax:
+ *
+ * math.randomInt() // generate a random integer between 0 and 1
+ * math.randomInt(max) // generate a random integer between 0 and max
+ * math.randomInt(min, max) // generate a random integer between min and max
+ * math.randomInt(size) // generate a matrix with random integer between 0 and 1
+ * math.randomInt(size, max) // generate a matrix with random integer between 0 and max
+ * math.randomInt(size, min, max) // generate a matrix with random integer between min and max
+ *
+ * Examples:
+ *
+ * math.randomInt(); // returns a random integer between 0 and 1
+ * math.randomInt(100); // returns a random integer between 0 and 100
+ * math.randomInt(30, 40); // returns a random integer between 30 and 40
+ * math.randomInt([2, 3]); // returns a 2x3 matrix with random integers between 0 and 1
+ *
+ * See also:
+ *
+ * random, pickRandom
+ *
+ * @param {Array | Matrix} [size] If provided, an array or matrix with given
+ * size and filled with random values is returned
+ * @param {Number} [min] Minimum boundary for the random value, included
+ * @param {Number} [max] Maximum boundary for the random value, excluded
+ * @return {Number | Array | Matrix} A random integer value
+ */
+ math.randomInt = distribution('uniform').randomInt;
+ };
+
+
+/***/ },
+/* 110 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var distribution = __webpack_require__(333)(math);
+
+ /**
+ * Random pick a value from a one dimensional array.
+ * Array element is picked using a random function with uniform distribution.
+ *
+ * Syntax:
+ *
+ * math.pickRandom(array)
+ *
+ * Examples:
+ *
+ * math.pickRandom([3, 6, 12, 2]); // returns one of the values in the array
+ *
+ * See also:
+ *
+ * random, randomInt
+ *
+ * @param {Array} array A one dimensional array
+ * @return {Number} One of the elements of the provided input array
+ */
+ math.pickRandom = distribution('uniform').pickRandom;
+ };
+
+
+/***/ },
+/* 111 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger;
+
+ /**
+ * Compute the number of ways of obtaining an ordered subset of `k` elements
+ * from a set of `n` elements.
+ *
+ * Permutations only takes integer arguments.
+ * The following condition must be enforced: k <= n.
+ *
+ * Syntax:
+ *
+ * math.permutations(n)
+ * math.permutations(n, k)
+ *
+ * Examples:
+ *
+ * math.permutations(5); // 120
+ * math.permutations(5, 3); // 60
+ *
+ * See also:
+ *
+ * combinations, factorial
+ *
+ * @param {Number | BigNumber} n The number of objects in total
+ * @param {Number | BigNumber} k The number of objects in the subset
+ * @return {Number | BigNumber} The number of permutations
+ */
+ math.permutations = function permutations (n, k) {
+ var result, i;
+
+ var arity = arguments.length;
+ if (arity > 2) {
+ throw new math.error.ArgumentsError('permutations', arguments.length, 2);
+ }
+
+ if (isNumber(n)) {
+ if (!isInteger(n) || n < 0) {
+ throw new TypeError('Positive integer value expected in function permutations');
+ }
+
+ // Permute n objects
+ if (arity == 1) {
+ return math.factorial(n);
+ }
+
+ // Permute n objects, k at a time
+ if (arity == 2) {
+ if (isNumber(k)) {
+ if (!isInteger(k) || k < 0) {
+ throw new TypeError('Positive integer value expected in function permutations');
+ }
+ if (k > n) {
+ throw new TypeError('second argument k must be less than or equal to first argument n');
+ }
+
+ result = 1;
+ for (i = n - k + 1; i <= n; i++) {
+ result = result * i;
+ }
+ return result;
+ }
+ }
+ }
+
+ if (n instanceof BigNumber) {
+ if (k === undefined && isPositiveInteger(n)) {
+ return math.factorial(n);
+ }
+
+ // make sure k is a BigNumber as well
+ // not all numbers can be converted to BigNumber
+ k = BigNumber.convert(k);
+
+ if (!(k instanceof BigNumber) || !isPositiveInteger(n) || !isPositiveInteger(k)) {
+ throw new TypeError('Positive integer value expected in function permutations');
+ }
+ if (k.gt(n)) {
+ throw new TypeError('second argument k must be less than or equal to first argument n');
+ }
+
+ result = new BigNumber(1);
+ for (i = n.minus(k).plus(1); i.lte(n); i = i.plus(1)) {
+ result = result.times(i);
+ }
+ return result;
+ }
+
+ throw new math.error.UnsupportedTypeError('permutations', math['typeof'](n));
+ };
+
+ /**
+ * Test whether BigNumber n is a positive integer
+ * @param {BigNumber} n
+ * @returns {boolean} isPositiveInteger
+ */
+ var isPositiveInteger = function(n) {
+ return n.isInteger() && n.gte(0);
+ };
+ };
+
+
+/***/ },
+/* 112 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isInteger = util.number.isInteger;
+
+ /**
+ * Compute the number of ways of picking `k` unordered outcomes from `n`
+ * possibilities.
+ *
+ * Combinations only takes integer arguments.
+ * The following condition must be enforced: k <= n.
+ *
+ * Syntax:
+ *
+ * math.combinations(n, k)
+ *
+ * Examples:
+ *
+ * math.combinations(7, 5); // returns 21
+ *
+ * See also:
+ *
+ * permutations, factorial
+ *
+ * @param {Number | BigNumber} n Total number of objects in the set
+ * @param {Number | BigNumber} k Number of objects in the subset
+ * @return {Number | BigNumber} Number of possible combinations.
+ */
+ math.combinations = function combinations (n, k) {
+ var max, result, i,ii;
+
+ var arity = arguments.length;
+ if (arity != 2) {
+ throw new math.error.ArgumentsError('combinations', arguments.length, 2);
+ }
+
+ if (isNumber(n)) {
+ if (!isInteger(n) || n < 0) {
+ throw new TypeError('Positive integer value enpected in function combinations');
+ }
+ if (k > n) {
+ throw new TypeError('k must be less than or equal to n');
+ }
+
+ max = Math.max(k, n - k);
+ result = 1;
+ for (i = 1; i <= n - max; i++) {
+ result = result * (max + i) / i;
+ }
+ return result;
+ }
+
+ if (n instanceof BigNumber) {
+ // make sure k is a BigNumber as well
+ // not all numbers can be converted to BigNumber
+ k = BigNumber.convert(k);
+
+ if (!(k instanceof BigNumber) || !isPositiveInteger(n) || !isPositiveInteger(k)) {
+ throw new TypeError('Positive integer value expected in function combinations');
+ }
+ if (k.gt(n)) {
+ throw new TypeError('k must be less than n in function combinations');
+ }
+
+ max = n.minus(k);
+ if (k.lt(max)) max = k;
+ result = new BigNumber(1);
+ for (i = new BigNumber(1), ii = n.minus(max); i.lte(ii); i = i.plus(1)) {
+ result = result.times(max.plus(i)).dividedBy(i);
+ }
+ return result;
+ }
+
+ throw new math.error.UnsupportedTypeError('combinations', math['typeof'](n));
+ };
+
+ /**
+ * Test whether BigNumber n is a positive integer
+ * @param {BigNumber} n
+ * @returns {boolean} isPositiveInteger
+ */
+ var isPositiveInteger = function(n) {
+ return n.isInteger() && n.gte(0);
+ };
+ };
+
+
+/***/ },
+/* 113 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.
+ *
+ * x and y are considered equal when the relative difference between x and y
+ * is smaller than the configured epsilon. The function cannot be used to
+ * compare values smaller than approximately 2.22e-16.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.compare(x, y)
+ *
+ * Examples:
+ *
+ * math.compare(6, 1); // returns 1
+ * math.compare(2, 3); // returns -1
+ * math.compare(7, 7); // returns 0
+ *
+ * var a = math.unit('5 cm');
+ * var b = math.unit('40 mm');
+ * math.compare(a, b); // returns 1
+ *
+ * math.compare(2, [1, 2, 3]); // returns [1, 0, -1]
+ *
+ * See also:
+ *
+ * equal, unequal, smaller, smallerEq, larger, largerEq
+ *
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} x First value to compare
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} y Second value to compare
+ * @return {Number | BigNumber | Array | Matrix} Returns the result of the comparison: 1, 0 or -1.
+ */
+ math.compare = function compare(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('compare', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ return nearlyEqual(x, y, config.epsilon) ? 0 : (x > y ? 1 : -1);
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return new BigNumber(x.cmp(y));
+ }
+
+ // downgrade to Number
+ return compare(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return new BigNumber(x.cmp(y));
+ }
+
+ // downgrade to Number
+ return compare(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return (x.value > y.value) ? 1 : ((x.value < y.value) ? -1 : 0);
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, compare);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can't compare a string with a matrix
+ if (isString(x) || isString(y)) {
+ return (x > y) ? 1 : ((x < y) ? -1 : 0);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return compare(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return compare(x, +y);
+ }
+
+ if (isComplex(x) || isComplex(y)) {
+ throw new TypeError('No ordering relation is defined for complex numbers');
+ }
+
+ throw new math.error.UnsupportedTypeError('compare', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 114 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+ isArray = Array.isArray;
+
+ /**
+ * Test element wise whether two matrices are equal.
+ * The function accepts both matrices and scalar values.
+ *
+ * Syntax:
+ *
+ * math.deepEqual(x, y)
+ *
+ * Examples:
+ *
+ * math.deepEqual(2, 4); // returns false
+ *
+ * a = [2, 5, 1];
+ * b = [2, 7, 1];
+ *
+ * math.deepEqual(a, b); // returns false
+ * math.equal(a, b); // returns [true, false, true]
+ *
+ * See also:
+ *
+ * equal, unequal
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First matrix to compare
+ * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Second matrix to compare
+ * @return {Number | BigNumber | Complex | Unit | Array | Matrix}
+ * Returns true when the input matrices have the same size and each of their elements is equal.
+ */
+ math.deepEqual = function deepEqual(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('deepEqual', arguments.length, 2);
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return _deepEqual(x.valueOf(), y.valueOf());
+ }
+
+ return math.equal(x, y);
+ };
+
+ /**
+ * Test whether two arrays have the same size and all elements are equal
+ * @param {Array | *} x
+ * @param {Array | *} y
+ * @return {boolean} Returns true if both arrays are deep equal
+ */
+ function _deepEqual(x, y) {
+ if (isArray(x)) {
+ if (isArray(y)) {
+ var len = x.length;
+ if (len !== y.length) return false;
+
+ for (var i = 0; i < len; i++) {
+ if (!_deepEqual(x[i], y[i])) return false;
+ }
+
+ return true;
+ }
+ else {
+ return false;
+ }
+ }
+ else {
+ if (isArray(y)) {
+ return false;
+ }
+ else {
+ return math.equal(x, y);
+ }
+ }
+ }
+ };
+
+
+/***/ },
+/* 115 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Test whether two values are equal.
+ *
+ * The function tests whether the relative difference between x and y is
+ * smaller than the configured epsilon. The function cannot be used to
+ * compare values smaller than approximately 2.22e-16.
+ *
+ * For matrices, the function is evaluated element wise.
+ * In case of complex numbers, x.re must equal y.re, and x.im must equal y.im.
+ *
+ * Values `null` and `undefined` are compared strictly, thus `null` is only
+ * equal to `null` and nothing else, and `undefined` is only equal to
+ * `undefined` and nothing else.
+ *
+ * Syntax:
+ *
+ * math.equal(x, y)
+ *
+ * Examples:
+ *
+ * math.equal(2 + 2, 3); // returns false
+ * math.equal(2 + 2, 4); // returns true
+ *
+ * var a = math.unit('50 cm');
+ * var b = math.unit('5 m');
+ * math.equal(a, b); // returns true
+ *
+ * var c = [2, 5, 1];
+ * var d = [2, 7, 1];
+ *
+ * math.equal(c, d); // returns [true, false, true]
+ * math.deepEqual(c, d); // returns false
+ *
+ * math.equal(0, null); // returns false
+ *
+ * See also:
+ *
+ * unequal, smaller, smallerEq, larger, largerEq, compare, deepEqual
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | String | Array | Matrix | null | undefined} x First value to compare
+ * @param {Number | BigNumber | Boolean | Complex | Unit | String | Array | Matrix | null | undefined} y Second value to compare
+ * @return {Boolean | Array | Matrix} Returns true when the compared values are equal, else returns false
+ */
+ math.equal = function equal(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('equal', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ return nearlyEqual(x, y, config.epsilon);
+ }
+ else if (isComplex(y)) {
+ return nearlyEqual(x, y.re, config.epsilon) && nearlyEqual(y.im, 0, config.epsilon);
+ }
+ }
+
+ if (isComplex(x)) {
+ if (isNumber(y)) {
+ return nearlyEqual(x.re, y, config.epsilon) && nearlyEqual(x.im, 0, config.epsilon);
+ }
+ else if (isComplex(y)) {
+ return nearlyEqual(x.re, y.re, config.epsilon) && nearlyEqual(x.im, y.im, config.epsilon);
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y)) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.eq(y);
+ }
+
+ // downgrade to Number
+ return equal(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x)) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.eq(y);
+ }
+
+ // downgrade to Number
+ return equal(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return x.value == y.value;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, equal);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can accidentally compare a stringified array with a string
+ if (isString(x) || isString(y)) {
+ return x == y;
+ }
+
+ if (isBoolean(x)) {
+ return equal(+x, y);
+ }
+ if (isBoolean(y)) {
+ return equal(x, +y);
+ }
+
+ if (x === null) {
+ return y === null;
+ }
+ if (y === null) {
+ return x === null;
+ }
+
+ if (x === undefined) {
+ return y === undefined;
+ }
+ if (y === undefined) {
+ return x === undefined;
+ }
+
+ throw new math.error.UnsupportedTypeError('equal', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 116 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Test whether value x is larger than y.
+ *
+ * The function returns true when x is larger than y and the relative
+ * difference between x and y is larger than the configured epsilon. The
+ * function cannot be used to compare values smaller than approximately 2.22e-16.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.larger(x, y)
+ *
+ * Examples:
+ *
+ * math.larger(2, 3); // returns false
+ * math.larger(5, 2 + 2); // returns true
+ *
+ * var a = math.unit('5 cm');
+ * var b = math.unit('2 inch');
+ * math.larger(a, b); // returns false
+ *
+ * See also:
+ *
+ * equal, unequal, smaller, smallerEq, largerEq, compare
+ *
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} x First value to compare
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} y Second value to compare
+ * @return {Boolean | Array | Matrix} Returns true when the x is larger than y, else returns false
+ */
+ math.larger = function larger(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('larger', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ return !nearlyEqual(x, y, config.epsilon) && x > y;
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.gt(y);
+ }
+
+ // downgrade to Number
+ return larger(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.gt(y)
+ }
+
+ // downgrade to Number
+ return larger(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return x.value > y.value;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, larger);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can't compare a string with a matrix
+ if (isString(x) || isString(y)) {
+ return x > y;
+ }
+
+ if (isBoolean(x) || x === null) {
+ return larger(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return larger(x, +y);
+ }
+
+ if (isComplex(x) || isComplex(y)) {
+ throw new TypeError('No ordering relation is defined for complex numbers');
+ }
+
+ throw new math.error.UnsupportedTypeError('larger', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 117 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Test whether value x is larger or equal to y.
+ *
+ * The function returns true when x is larger than y or the relative
+ * difference between x and y is smaller than the configured epsilon. The
+ * function cannot be used to compare values smaller than approximately 2.22e-16.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.largerEq(x, y)
+ *
+ * Examples:
+ *
+ * math.larger(2, 1 + 1); // returns false
+ * math.largerEq(2, 1 + 1); // returns true
+ *
+ * See also:
+ *
+ * equal, unequal, smaller, smallerEq, larger, compare
+ *
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} x First value to compare
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} y Second value to compare
+ * @return {Boolean | Array | Matrix} Returns true when the x is larger or equal to y, else returns false
+ */
+ math.largerEq = function largerEq(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('largerEq', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ return nearlyEqual(x, y, config.epsilon) || x > y;
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.gte(y);
+ }
+
+ // downgrade to Number
+ return largerEq(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.gte(y)
+ }
+
+ // downgrade to Number
+ return largerEq(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return x.value >= y.value;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, largerEq);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can't compare a string with a matrix
+ if (isString(x) || isString(y)) {
+ return x >= y;
+ }
+
+ if (isBoolean(x) || x === null) {
+ return largerEq(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return largerEq(x, +y);
+ }
+
+ if (isComplex(x) || isComplex(y)) {
+ throw new TypeError('No ordering relation is defined for complex numbers');
+ }
+
+ throw new math.error.UnsupportedTypeError('largerEq', math['typeof'](x), math['typeof'](y));
+ };
+
+ // TODO: deprecated since version 0.23.0, cleanup some day
+ math.largereq = function () {
+ throw new Error('Function largereq is renamed to largerEq');
+ }
+ };
+
+
+/***/ },
+/* 118 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Test whether value x is smaller than y.
+ *
+ * The function returns true when x is smaller than y and the relative
+ * difference between x and y is larger than the configured epsilon. The
+ * function cannot be used to compare values smaller than approximately 2.22e-16.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.smaller(x, y)
+ *
+ * Examples:
+ *
+ * math.smaller(2, 3); // returns true
+ * math.smaller(5, 2 * 2); // returns false
+ *
+ * var a = math.unit('5 cm');
+ * var b = math.unit('2 inch');
+ * math.smaller(a, b); // returns true
+ *
+ * See also:
+ *
+ * equal, unequal, smallerEq, larger, largerEq, compare
+ *
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} x First value to compare
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} y Second value to compare
+ * @return {Boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false
+ */
+ math.smaller = function smaller(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('smaller', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ return !nearlyEqual(x, y, config.epsilon) && x < y;
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.lt(y);
+ }
+
+ // downgrade to Number
+ return smaller(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.lt(y)
+ }
+
+ // downgrade to Number
+ return smaller(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return x.value < y.value;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, smaller);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can't compare a string with a matrix
+ if (isString(x) || isString(y)) {
+ return x < y;
+ }
+
+ if (isBoolean(x) || x === null) {
+ return smaller(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return smaller(x, +y);
+ }
+
+ if (isComplex(x) || isComplex(y)) {
+ throw new TypeError('No ordering relation is defined for complex numbers');
+ }
+
+ throw new math.error.UnsupportedTypeError('smaller', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 119 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Test whether value x is smaller or equal to y.
+ *
+ * The function returns true when x is smaller than y or the relative
+ * difference between x and y is smaller than the configured epsilon. The
+ * function cannot be used to compare values smaller than approximately 2.22e-16.
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.smallerEq(x, y)
+ *
+ * Examples:
+ *
+ * math.smaller(1 + 2, 3); // returns false
+ * math.smallerEq(1 + 2, 3); // returns true
+ *
+ * See also:
+ *
+ * equal, unequal, smaller, larger, largerEq, compare
+ *
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} x First value to compare
+ * @param {Number | BigNumber | Boolean | Unit | String | Array | Matrix | null} y Second value to compare
+ * @return {Boolean | Array | Matrix} Returns true when the x is smaller than y, else returns false
+ */
+ math.smallerEq = function smallerEq(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('smallerEq', arguments.length, 2);
+ }
+
+ if (isNumber(x) && isNumber(y)) {
+ return nearlyEqual(x, y, config.epsilon) || x < y;
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y) || y === null) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return x.lte(y);
+ }
+
+ // downgrade to Number
+ return smallerEq(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x) || x === null) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return x.lte(y)
+ }
+
+ // downgrade to Number
+ return smallerEq(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return x.value <= y.value;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, smallerEq);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can't compare a string with a matrix
+ if (isString(x) || isString(y)) {
+ return x <= y;
+ }
+
+ if (isBoolean(x) || x === null) {
+ return smallerEq(+x, y);
+ }
+ if (isBoolean(y) || y === null) {
+ return smallerEq(x, +y);
+ }
+
+ if (isComplex(x) || isComplex(y)) {
+ throw new TypeError('No ordering relation is defined for complex numbers');
+ }
+
+ throw new math.error.UnsupportedTypeError('smallerEq', math['typeof'](x), math['typeof'](y));
+ };
+
+ // TODO: deprecated since version 0.23.0, cleanup some day
+ math.smallereq = function () {
+ throw new Error('Function smallereq is renamed to smallerEq');
+ }
+ };
+
+
+/***/ },
+/* 120 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math, config) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ nearlyEqual = util.number.nearlyEqual,
+ isBoolean = util['boolean'].isBoolean,
+ isString = util.string.isString,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection;
+
+ /**
+ * Test whether two values are unequal.
+ *
+ * The function tests whether the relative difference between x and y is
+ * larger than the configured epsilon. The function cannot be used to compare
+ * values smaller than approximately 2.22e-16.
+ *
+ * For matrices, the function is evaluated element wise.
+ * In case of complex numbers, x.re must unequal y.re, or x.im must unequal y.im.
+ *
+ * Values `null` and `undefined` are compared strictly, thus `null` is unequal
+ * with everything except `null`, and `undefined` is unequal with everying
+ * except. `undefined`.
+ *
+ * Syntax:
+ *
+ * math.unequal(x, y)
+ *
+ * Examples:
+ *
+ * math.unequal(2 + 2, 3); // returns true
+ * math.unequal(2 + 2, 4); // returns false
+ *
+ * var a = math.unit('50 cm');
+ * var b = math.unit('5 m');
+ * math.unequal(a, b); // returns false
+ *
+ * var c = [2, 5, 1];
+ * var d = [2, 7, 1];
+ *
+ * math.unequal(c, d); // returns [false, true, false]
+ * math.deepEqual(c, d); // returns false
+ *
+ * math.unequal(0, null); // returns true
+ * See also:
+ *
+ * equal, deepEqual, smaller, smallerEq, larger, largerEq, compare
+ *
+ * @param {Number | BigNumber | Boolean | Complex | Unit | String | Array | Matrix | null | undefined} x First value to compare
+ * @param {Number | BigNumber | Boolean | Complex | Unit | String | Array | Matrix | null | undefined} y Second value to compare
+ * @return {Boolean | Array | Matrix} Returns true when the compared values are unequal, else returns false
+ */
+ math.unequal = function unequal(x, y) {
+ if (arguments.length != 2) {
+ throw new math.error.ArgumentsError('unequal', arguments.length, 2);
+ }
+
+ if (isNumber(x)) {
+ if (isNumber(y)) {
+ return !nearlyEqual(x, y, config.epsilon);
+ }
+ else if (isComplex(y)) {
+ return !nearlyEqual(x, y.re, config.epsilon) || !nearlyEqual(y.im, 0, config.epsilon);
+ }
+ }
+
+ if (isComplex(x)) {
+ if (isNumber(y)) {
+ return !nearlyEqual(x.re, y, config.epsilon) || !nearlyEqual(x.im, 0, config.epsilon);
+ }
+ else if (isComplex(y)) {
+ return !nearlyEqual(x.re, y.re, config.epsilon) || !nearlyEqual(x.im, y.im, config.epsilon);
+ }
+ }
+
+ if (x instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(y)) {
+ y = BigNumber.convert(y);
+ }
+ else if (isBoolean(y)) {
+ y = new BigNumber(y ? 1 : 0);
+ }
+
+ if (y instanceof BigNumber) {
+ return !x.eq(y);
+ }
+
+ // downgrade to Number
+ return unequal(x.toNumber(), y);
+ }
+ if (y instanceof BigNumber) {
+ // try to convert to big number
+ if (isNumber(x)) {
+ x = BigNumber.convert(x);
+ }
+ else if (isBoolean(x)) {
+ x = new BigNumber(x ? 1 : 0);
+ }
+
+ if (x instanceof BigNumber) {
+ return !x.eq(y)
+ }
+
+ // downgrade to Number
+ return unequal(x, y.toNumber());
+ }
+
+ if ((isUnit(x)) && (isUnit(y))) {
+ if (!x.equalBase(y)) {
+ throw new Error('Cannot compare units with different base');
+ }
+ return x.value != y.value;
+ }
+
+ if (isCollection(x) || isCollection(y)) {
+ return collection.deepMap2(x, y, unequal);
+ }
+
+ // Note: test strings after testing collections,
+ // else we can accidentally compare a stringified array with a string
+ if (isString(x) || isString(y)) {
+ return x != y;
+ }
+
+ if (isBoolean(x)) {
+ return unequal(+x, y);
+ }
+ if (isBoolean(y)) {
+ return unequal(x, +y);
+ }
+
+ if (x === null) {
+ return y !== null;
+ }
+ if (y === null) {
+ return x !== null;
+ }
+
+ if (x === undefined) {
+ return y !== undefined;
+ }
+ if (y === undefined) {
+ return x !== undefined;
+ }
+
+ throw new math.error.UnsupportedTypeError('unequal', math['typeof'](x), math['typeof'](y));
+ };
+ };
+
+
+/***/ },
+/* 121 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the maximum value of a matrix or a list of values.
+ * In case of a multi dimensional array, the maximum of the flattened array
+ * will be calculated. When `dim` is provided, the maximum over the selected
+ * dimension will be calculated. Parameter `dim` is zero-based.
+ *
+ * Syntax:
+ *
+ * math.min(a, b, c, ...)
+ * math.min(A)
+ * math.min(A, dim)
+ *
+ * Examples:
+ *
+ * math.min(2, 1, 4, 3); // returns 1
+ * math.min([2, 1, 4, 3]); // returns 1
+ *
+ * // maximum over a specified dimension (zero-based)
+ * math.min([[2, 5], [4, 3], [1, 7]], 0); // returns [1, 3]
+ * math.min([[2, 5], [4, 3], [1, 7]], 1); // returns [2, 3, 1]
+ *
+ * math.max(2.7, 7.1, -4.5, 2.0, 4.1); // returns 7.1
+ * math.min(2.7, 7.1, -4.5, 2.0, 4.1); // returns -4.5
+ *
+ * See also:
+ *
+ * mean, median, max, prod, std, sum, var
+ *
+ * @param {... *} args A single matrix or or multiple scalar values
+ * @return {*} The minimum value
+ */
+ math.min = function min(args) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function min requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(args)) {
+ if (arguments.length == 1) {
+ // min([a, b, c, d, ...])
+ return _min(args);
+ }
+ else if (arguments.length == 2) {
+ // min([a, b, c, d, ...], dim)
+ return collection.reduce(arguments[0], arguments[1], _getSmaller);
+ }
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // min(a, b, c, d, ...)
+ return _min(arguments);
+ }
+ };
+
+ function _getSmaller(x, y){
+ return math.smaller(x, y) ? x : y;
+ }
+
+ /**
+ * Recursively calculate the minimum value in an n-dimensional array
+ * @param {Array} array
+ * @return {Number} min
+ * @private
+ */
+ function _min(array) {
+ var min = undefined;
+
+ collection.deepForEach(array, function (value) {
+ if (min === undefined || math.smaller(value, min)) {
+ min = value;
+ }
+ });
+
+ if (min === undefined) {
+ throw new Error('Cannot calculate min of an empty array');
+ }
+
+ return min;
+ }
+ };
+
+
+/***/ },
+/* 122 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the maximum value of a matrix or a list with values.
+ * In case of a multi dimensional array, the maximum of the flattened array
+ * will be calculated. When `dim` is provided, the maximum over the selected
+ * dimension will be calculated. Parameter `dim` is zero-based.
+ *
+ * Syntax:
+ *
+ * math.max(a, b, c, ...)
+ * math.max(A)
+ * math.max(A, dim)
+ *
+ * Examples:
+ *
+ * math.max(2, 1, 4, 3); // returns 4
+ * math.max([2, 1, 4, 3]); // returns 4
+ *
+ * // maximum over a specified dimension (zero-based)
+ * math.max([[2, 5], [4, 3], [1, 7]], 0); // returns [4, 7]
+ * math.max([[2, 5], [4, 3]], [1, 7], 1); // returns [5, 4, 7]
+ *
+ * math.max(2.7, 7.1, -4.5, 2.0, 4.1); // returns 7.1
+ * math.min(2.7, 7.1, -4.5, 2.0, 4.1); // returns -4.5
+ *
+ * See also:
+ *
+ * mean, median, min, prod, std, sum, var
+ *
+ * @param {... *} args A single matrix or or multiple scalar values
+ * @return {*} The maximum value
+ */
+ math.max = function max(args) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function max requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(args)) {
+ if (arguments.length == 1) {
+ // max([a, b, c, d, ...])
+ return _max(args);
+ }
+ else if (arguments.length == 2) {
+ // max([a, b, c, d, ...], dim)
+ return collection.reduce(arguments[0], arguments[1], _getLarger);
+ }
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // max(a, b, c, d, ...)
+ return _max(arguments);
+ }
+ };
+
+ function _getLarger(x, y){
+ return math.larger(x, y) ? x : y;
+ }
+
+ /**
+ * Recursively calculate the maximum value in an n-dimensional array
+ * @param {Array} array
+ * @return {Number} max
+ * @private
+ */
+ function _max(array) {
+ var max = undefined;
+
+ collection.deepForEach(array, function (value) {
+ if (max === undefined || math.larger(value, max)) {
+ max = value;
+ }
+ });
+
+ if (max === undefined) {
+ throw new Error('Cannot calculate max of an empty array');
+ }
+
+ return max;
+ }
+ };
+
+
+/***/ },
+/* 123 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+
+ size = __webpack_require__(165).size,
+ isArray = Array.isArray;
+
+ /**
+ * Compute the mean value of matrix or a list with values.
+ * In case of a multi dimensional array, the mean of the flattened array
+ * will be calculated. When `dim` is provided, the maximum over the selected
+ * dimension will be calculated. Parameter `dim` is zero-based.
+ *
+ * Syntax:
+ *
+ * mean.mean(a, b, c, ...)
+ * mean.mean(A)
+ * mean.mean(A, dim)
+ *
+ * Examples:
+ *
+ * math.mean(2, 1, 4, 3); // returns 2.5
+ * math.mean([1, 2.7, 3.2, 4]); // returns 2.725
+ *
+ * math.mean([[2, 5], [6, 3], [1, 7]], 0); // returns [3, 5]
+ * math.mean([[2, 5], [6, 3], [1, 7]], 1); // returns [3.5, 4.5, 4]
+ *
+ * See also:
+ *
+ * median, min, max, sum, prod, std, var
+ *
+ * @param {... *} args A single matrix or or multiple scalar values
+ * @return {*} The mean of all values
+ */
+ math.mean = function mean(args) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function mean requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(args)) {
+ if (arguments.length == 1) {
+ // mean([a, b, c, d, ...])
+ return _mean(args);
+ }
+ else if (arguments.length == 2) {
+ // mean([a, b, c, d, ...], dim)
+ return _nmean(arguments[0], arguments[1]);
+ }
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // mean(a, b, c, d, ...)
+ return _mean(arguments);
+ }
+ };
+
+ /**
+ * Calculate the mean value in an n-dimensional array, returning a
+ * n-1 dimensional array
+ * @param {Array} array
+ * @param {Number} dim
+ * @return {Number} mean
+ * @private
+ */
+ function _nmean(array, dim){
+ var sum = collection.reduce(array, dim, math.add);
+ var s = isArray(array) ? size(array) : array.size();
+ return math.divide(sum, s[dim]);
+ }
+
+ /**
+ * Recursively calculate the mean value in an n-dimensional array
+ * @param {Array} array
+ * @return {Number} mean
+ * @private
+ */
+ function _mean(array) {
+ var sum = 0;
+ var num = 0;
+
+ collection.deepForEach(array, function (value) {
+ sum = math.add(sum, value);
+ num++;
+ });
+
+ if (num === 0) {
+ throw new Error('Cannot calculate mean of an empty array');
+ }
+
+ return math.divide(sum, num);
+ }
+ };
+
+
+/***/ },
+/* 124 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ Unit = __webpack_require__(11),
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isNumber = __webpack_require__(3).isNumber,
+ isCollection = collection.isCollection,
+
+ flatten = __webpack_require__(165).flatten;
+
+ /**
+ * Compute the median of a matrix or a list with values. The values are
+ * sorted and the middle value is returned. In case of an even number of
+ * values, the average of the two middle values is returned.
+ * Supported types of values are: Number, BigNumber, Unit
+ *
+ * In case of a (multi dimensional) array or matrix, the median of all
+ * elements will be calculated.
+ *
+ * Syntax:
+ *
+ * mean.median(a, b, c, ...)
+ * mean.median(A)
+ *
+ * Examples:
+ *
+ * math.median(5, 2, 7); // returns 5
+ * math.median([3, -1, 5, 7]); // returns 4
+ *
+ * See also:
+ *
+ * mean, min, max, sum, prod, std, var
+ *
+ * @param {... *} args A single matrix or or multiple scalar values
+ * @return {*} The median
+ */
+ math.median = function median(args) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function median requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(args)) {
+ if (arguments.length == 1) {
+ // median([a, b, c, d, ...])
+ return _median(args.valueOf());
+ }
+ else if (arguments.length == 2) {
+ // median([a, b, c, d, ...], dim)
+ // TODO: implement median(A, dim)
+ throw new Error('median(A, dim) is not yet supported');
+ //return collection.reduce(arguments[0], arguments[1], ...);
+ }
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // median(a, b, c, d, ...)
+ return _median(Array.prototype.slice.call(arguments));
+ }
+ };
+
+ /**
+ * Recursively calculate the median of an n-dimensional array
+ * @param {Array} array
+ * @return {Number} median
+ * @private
+ */
+ function _median(array) {
+ var flat = flatten(array);
+
+ flat.sort(math.compare);
+
+ var num = flat.length;
+
+ if (num == 0) {
+ throw new Error('Cannot calculate median of an empty array');
+ }
+
+ if (num % 2 == 0) {
+ // even: return the average of the two middle values
+ var left = flat[num / 2 - 1];
+ var right = flat[num / 2];
+
+ if (!isNumber(left) && !(left instanceof BigNumber) && !(left instanceof Unit)) {
+ throw new math.error.UnsupportedTypeError('median', math['typeof'](left));
+ }
+ if (!isNumber(right) && !(right instanceof BigNumber) && !(right instanceof Unit)) {
+ throw new math.error.UnsupportedTypeError('median', math['typeof'](right));
+ }
+
+ return math.divide(math.add(left, right), 2);
+ }
+ else {
+ // odd: return the middle value
+ var middle = flat[(num - 1) / 2];
+
+ if (!isNumber(middle) && !(middle instanceof BigNumber) && !(middle instanceof Unit)) {
+ throw new math.error.UnsupportedTypeError('median', math['typeof'](middle));
+ }
+
+ return middle;
+ }
+ }
+ };
+
+
+/***/ },
+/* 125 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the product of a matrix or a list with values.
+ * In case of a (multi dimensional) array or matrix, the sum of all
+ * elements will be calculated.
+ *
+ * Syntax:
+ *
+ * math.prod(a, b, c, ...)
+ * math.prod(A)
+ *
+ * Examples:
+ *
+ * math.multiply(2, 3); // returns 6
+ * math.prod(2, 3); // returns 6
+ * math.prod(2, 3, 4); // returns 24
+ * math.prod([2, 3, 4]); // returns 24
+ * math.prod([[2, 5], [4, 3]]); // returns 120
+ *
+ * See also:
+ *
+ * mean, median, min, max, sum, std, var
+ *
+ * @param {... *} args A single matrix or or multiple scalar values
+ * @return {*} The product of all values
+ */
+ math.prod = function prod(args) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function prod requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(args)) {
+ if (arguments.length == 1) {
+ // prod([a, b, c, d, ...])
+ return _prod(args);
+ }
+ else if (arguments.length == 2) {
+ // prod([a, b, c, d, ...], dim)
+ // TODO: implement prod(A, dim)
+ throw new Error('prod(A, dim) is not yet supported');
+ //return collection.reduce(arguments[0], arguments[1], math.prod);
+ }
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // prod(a, b, c, d, ...)
+ return _prod(arguments);
+ }
+ };
+
+ /**
+ * Recursively calculate the product of an n-dimensional array
+ * @param {Array} array
+ * @return {Number} prod
+ * @private
+ */
+ function _prod(array) {
+ var prod = undefined;
+
+ collection.deepForEach(array, function (value) {
+ prod = (prod === undefined) ? value : math.multiply(prod, value);
+ });
+
+ if (prod === undefined) {
+ throw new Error('Cannot calculate prod of an empty array');
+ }
+
+ return prod;
+ }
+ };
+
+
+/***/ },
+/* 126 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+
+
+ /**
+ * Compute the standard deviation of a matrix or a list with values.
+ * The standard deviations is defined as the square root of the variance:
+ * `std(A) = sqrt(var(A))`.
+ * In case of a (multi dimensional) array or matrix, the standard deviation
+ * over all elements will be calculated.
+ *
+ * Optionally, the type of normalization can be specified as second
+ * parameter. The parameter `normalization` can be one of the following values:
+ *
+ * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)
+ * - 'uncorrected' The sum of squared errors is divided by n
+ * - 'biased' The sum of squared errors is divided by (n + 1)
+ *
+ * Syntax:
+ *
+ * math.std(a, b, c, ...)
+ * math.std(A)
+ * math.std(A, normalization)
+ *
+ * Examples:
+ *
+ * math.std(2, 4, 6); // returns 2
+ * math.std([2, 4, 6, 8]); // returns 2.581988897471611
+ * math.std([2, 4, 6, 8], 'uncorrected'); // returns 2.23606797749979
+ * math.std([2, 4, 6, 8], 'biased'); // returns 2
+ *
+ * math.std([[1, 2, 3], [4, 5, 6]]); // returns 1.8708286933869707
+ *
+ * See also:
+ *
+ * mean, median, max, min, prod, sum, var
+ *
+ * @param {Array | Matrix} array
+ * A single matrix or or multiple scalar values
+ * @param {String} [normalization='unbiased']
+ * Determines how to normalize the variance.
+ * Choose 'unbiased' (default), 'uncorrected', or 'biased'.
+ * @return {*} The standard deviation
+ */
+ math.std = function std(array, normalization) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function std requires one or more parameters (0 provided)');
+ }
+
+ var variance = math['var'].apply(null, arguments);
+ return math.sqrt(variance);
+ };
+ };
+
+
+/***/ },
+/* 127 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection;
+
+ /**
+ * Compute the sum of a matrix or a list with values.
+ * In case of a (multi dimensional) array or matrix, the sum of all
+ * elements will be calculated.
+ *
+ * Syntax:
+ *
+ * math.sum(a, b, c, ...)
+ * math.sum(A)
+ *
+ * Examples:
+ *
+ * math.sum(2, 1, 4, 3); // returns 10
+ * math.sum([2, 1, 4, 3]); // returns 10
+ * math.sum([[2, 5], [4, 3], [1, 7]]); // returns 22
+ *
+ * See also:
+ *
+ * mean, median, min, max, prod, std, var
+ *
+ * @param {... *} args A single matrix or or multiple scalar values
+ * @return {*} The sum of all values
+ */
+ math.sum = function sum(args) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function sum requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(args)) {
+ if (arguments.length == 1) {
+ // sum([a, b, c, d, ...])
+ return _sum(args);
+ }
+ else if (arguments.length == 2) {
+ // sum([a, b, c, d, ...], dim)
+ // TODO: implement sum(A, dim)
+ throw new Error('sum(A, dim) is not yet supported');
+ //return collection.reduce(arguments[0], arguments[1], math.add);
+ }
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // sum(a, b, c, d, ...)
+ return _sum(arguments);
+ }
+ };
+
+ /**
+ * Recursively calculate the sum of an n-dimensional array
+ * @param {Array} array
+ * @return {Number} sum
+ * @private
+ */
+ function _sum(array) {
+ var sum = undefined;
+
+ collection.deepForEach(array, function (value) {
+ sum = (sum === undefined) ? value : math.add(sum, value);
+ });
+
+ if (sum === undefined) {
+ throw new Error('Cannot calculate sum of an empty array');
+ }
+
+ return sum;
+ }
+ };
+
+
+/***/ },
+/* 128 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var Matrix = __webpack_require__(10),
+ BigNumber = math.type.BigNumber,
+ collection = __webpack_require__(14),
+
+ isCollection = collection.isCollection,
+ isString = __webpack_require__(205).isString,
+
+ DEFAULT_NORMALIZATION = 'unbiased';
+
+ /**
+ * Compute the variance of a matrix or a list with values.
+ * In case of a (multi dimensional) array or matrix, the variance over all
+ * elements will be calculated.
+ *
+ * Optionally, the type of normalization can be specified as second
+ * parameter. The parameter `normalization` can be one of the following values:
+ *
+ * - 'unbiased' (default) The sum of squared errors is divided by (n - 1)
+ * - 'uncorrected' The sum of squared errors is divided by n
+ * - 'biased' The sum of squared errors is divided by (n + 1)
+
+ * Note that older browser may not like the variable name `var`. In that
+ * case, the function can be called as `math['var'](...)` instead of
+ * `math.var(...)`.
+ *
+ * Syntax:
+ *
+ * math.var(a, b, c, ...)
+ * math.var(A)
+ * math.var(A, normalization)
+ *
+ * Examples:
+ *
+ * math.var(2, 4, 6); // returns 4
+ * math.var([2, 4, 6, 8]); // returns 6.666666666666667
+ * math.var([2, 4, 6, 8], 'uncorrected'); // returns 5
+ * math.var([2, 4, 6, 8], 'biased'); // returns 4
+ *
+ * math.var([[1, 2, 3], [4, 5, 6]]); // returns 3.5
+ *
+ * See also:
+ *
+ * mean, median, max, min, prod, std, sum
+ *
+ * @param {Array | Matrix} array
+ * A single matrix or or multiple scalar values
+ * @param {String} [normalization='unbiased']
+ * Determines how to normalize the variance.
+ * Choose 'unbiased' (default), 'uncorrected', or 'biased'.
+ * @return {*} The variance
+ */
+ math['var'] = function variance(array, normalization) {
+ if (arguments.length == 0) {
+ throw new SyntaxError('Function var requires one or more parameters (0 provided)');
+ }
+
+ if (isCollection(array)) {
+ if (arguments.length == 1) {
+ // var([a, b, c, d, ...])
+ return _var(array, DEFAULT_NORMALIZATION);
+ }
+ else if (arguments.length == 2) {
+ // var([a, b, c, d, ...], normalization)
+
+ if (!isString(normalization)) {
+ throw new Error('String expected for parameter normalization');
+ }
+
+ return _var(array, normalization);
+ }
+ /* TODO: implement var(A [, normalization], dim)
+ else if (arguments.length == 3) {
+ // var([a, b, c, d, ...], dim)
+ // var([a, b, c, d, ...], normalization, dim)
+ //return collection.reduce(arguments[0], arguments[1], ...);
+ }
+ */
+ else {
+ throw new SyntaxError('Wrong number of parameters');
+ }
+ }
+ else {
+ // var(a, b, c, d, ...)
+ return _var(arguments, DEFAULT_NORMALIZATION);
+ }
+ };
+
+ /**
+ * Recursively calculate the variance of an n-dimensional array
+ * @param {Array} array
+ * @param {String} normalization
+ * Determines how to normalize the variance:
+ * - 'unbiased' The sum of squared errors is divided by (n - 1)
+ * - 'uncorrected' The sum of squared errors is divided by n
+ * - 'biased' The sum of squared errors is divided by (n + 1)
+ * @return {Number | BigNumber} variance
+ * @private
+ */
+ function _var(array, normalization) {
+ var sum = 0;
+ var num = 0;
+
+ // calculate the mean and number of elements
+ collection.deepForEach(array, function (value) {
+ sum = math.add(sum, value);
+ num++;
+ });
+ if (num === 0) throw new Error('Cannot calculate var of an empty array');
+
+ var mean = math.divide(sum, num);
+
+ // calculate the variance
+ sum = 0;
+ collection.deepForEach(array, function (value) {
+ var diff = math.subtract(value, mean);
+ sum = math.add(sum, math.multiply(diff, diff));
+ });
+
+ switch (normalization) {
+ case 'uncorrected':
+ return math.divide(sum, num);
+
+ case 'biased':
+ return math.divide(sum, num + 1);
+
+ case 'unbiased':
+ var zero = (sum instanceof BigNumber) ? new BigNumber(0) : 0;
+ return (num == 1) ? zero : math.divide(sum, num - 1);
+
+ default:
+ throw new Error('Unknown normalization "' + normalization + '". ' +
+ 'Choose "unbiased" (default), "uncorrected", or "biased".');
+ }
+ }
+ };
+
+
+/***/ },
+/* 129 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection,
+
+ bigArcCos = util.bignumber.arccos_arcsec;
+
+ /**
+ * Calculate the inverse cosine of a value.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.acos(x)
+ *
+ * Examples:
+ *
+ * math.acos(0.5); // returns Number 1.0471975511965979
+ * math.acos(math.cos(1.5)); // returns Number 1.5
+ *
+ * math.acos(2); // returns Complex 0 + 1.3169578969248166 i
+ *
+ * See also:
+ *
+ * cos, atan, asin
+ *
+ * @param {Number | BigNumber Boolean | Complex | Array | Matrix | null} x Function input
+ * @return {Number | BigNumber | Complex | Array | Matrix} The arc cosine of x
+ */
+ math.acos = function acos(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('acos', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ if (x >= -1 && x <= 1) {
+ return Math.acos(x);
+ }
+ else {
+ return acos(new Complex(x, 0));
+ }
+ }
+
+ if (isComplex(x)) {
+ // acos(z) = 0.5*pi + i*log(iz + sqrt(1-z^2))
+ var temp1 = new Complex(
+ x.im * x.im - x.re * x.re + 1.0,
+ -2.0 * x.re * x.im
+ );
+ var temp2 = math.sqrt(temp1);
+ var temp3 = new Complex(
+ temp2.re - x.im,
+ temp2.im + x.re
+ );
+ var temp4 = math.log(temp3);
+
+ // 0.5*pi = 1.5707963267948966192313216916398
+ return new Complex(
+ 1.57079632679489661923 - temp4.im,
+ temp4.re
+ );
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, acos);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return Math.acos(x);
+ }
+
+ if (x instanceof BigNumber) {
+ return bigArcCos(x, BigNumber, false);
+ }
+
+ throw new math.error.UnsupportedTypeError('acos', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 130 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection,
+
+ bigAcosh = util.bignumber.acosh_asinh_asech_acsch;
+
+ /**
+ * Calculate the hyperbolic arccos of a value,
+ * defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.acosh(x)
+ *
+ * Examples:
+ *
+ * math.acosh(1.5); // returns 0.9624236501192069
+ *
+ * See also:
+ *
+ * cosh, asinh, atanh
+ *
+ * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x Function input
+ * @return {Number | Complex | Array | Matrix} Hyperbolic arccosine of x
+ */
+ math.acosh = function acosh(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('acosh', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ if (x >= 1) {
+ return Math.log(Math.sqrt(x*x - 1) + x);
+ }
+ if (x <= -1) {
+ return new Complex(Math.log(Math.sqrt(x*x - 1) - x), Math.PI);
+ }
+ return acosh(new Complex(x, 0));
+ }
+
+ if (isComplex(x)) {
+ // acosh(z) = (-acos(z).im, acos(z).re) for acos(z).im <= 0
+ // ( acos(z).im, -acos(z).re) otherwise
+ var temp;
+ var acos = math.acos(x);
+ if (acos.im <= 0) {
+ temp = acos.re;
+ acos.re = -acos.im;
+ acos.im = temp;
+ } else {
+ temp = acos.im;
+ acos.im = -acos.re;
+ acos.re = temp;
+ }
+
+ return acos;
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, acosh);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return (x) ? 0 : new Complex(0, 1.5707963267948966);
+ }
+
+ if (x instanceof BigNumber) {
+ return bigAcosh(x, BigNumber, false, false);
+ }
+
+ throw new math.error.UnsupportedTypeError('acosh', math['typeof'](x));
+ };
+ };
+
+
+/***/ },
+/* 131 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isCollection = collection.isCollection,
+
+ bigArcCot = util.bignumber.arctan_arccot;
+
+ /**
+ * Calculate the inverse cotangent of a value.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.acot(x)
+ *
+ * Examples:
+ *
+ * math.acot(0.5); // returns Number 0.4636476090008061
+ * math.acot(math.cot(1.5)); // returns Number 1.5
+ *
+ * math.acot(2); // returns Complex 1.5707963267948966 -1.3169578969248166 i
+ *
+ * See also:
+ *
+ * cot, atan
+ *
+ * @param {Number | Boolean | Complex | Array | Matrix | null} x Function input
+ * @return {Number | Complex | Array | Matrix} The arc cotangent of x
+ */
+ math.acot = function acot(x) {
+ if (arguments.length != 1) {
+ throw new math.error.ArgumentsError('acot', arguments.length, 1);
+ }
+
+ if (isNumber(x)) {
+ return (x) ? Math.atan(1 / x) : halfPi;
+ }
+
+ if (isComplex(x)) {
+ if (x.im == 0) {
+ return new Complex(x.re ? Math.atan(1 / x.re) : halfPi, 0);
+ }
+
+ var den = x.re*x.re + x.im*x.im;
+ x = (den != 0)
+ ? new Complex(
+ x.re = x.re / den,
+ x.im = -x.im / den)
+ : new Complex(
+ (x.re != 0) ? (x.re / 0) : 0,
+ (x.im != 0) ? -(x.im / 0) : 0);
+
+ return math.atan(x);
+ }
+
+ if (isCollection(x)) {
+ return collection.deepMap(x, acot);
+ }
+
+ if (isBoolean(x) || x === null) {
+ return (x) ? 0.7853981633974483 : halfPi;
+ }
+
+ if (x instanceof BigNumber) {
+ return bigArcCot(x, BigNumber, true);
+ }
+
+ throw new math.error.UnsupportedTypeError('acot', math['typeof'](x));
+ };
+
+ var halfPi = 1.5707963267948966;
+ };
+
+
+/***/ },
+/* 132 */
+/***/ function(module, exports, __webpack_require__) {
+
+ 'use strict';
+
+ module.exports = function (math) {
+ var util = __webpack_require__(171),
+
+ BigNumber = math.type.BigNumber,
+ Complex = __webpack_require__(7),
+ Unit = __webpack_require__(11),
+ collection = __webpack_require__(14),
+
+ isNumber = util.number.isNumber,
+ isBoolean = util['boolean'].isBoolean,
+ isComplex = Complex.isComplex,
+ isUnit = Unit.isUnit,
+ isCollection = collection.isCollection,
+
+ bigAcoth = util.bignumber.atanh_acoth;
+
+ /**
+ * Calculate the hyperbolic arccotangent of a value,
+ * defined as `acoth(x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.
+ *
+ * For matrices, the function is evaluated element wise.
+ *
+ * Syntax:
+ *
+ * math.acoth(x)
+ *
+ * Examples:
+ *
+ * math.acoth(0.5); // returns 0.8047189562170503
+ *
+ * See also:
+ *
+ * acsch, asech
+ *
+ * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x Function
Follow ups
