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Added examples

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Ilya Shestakov
2015-11-11 21:53:29 +03:00
parent e5bb66c602
commit 25bb9f41e0
2 changed files with 283 additions and 21 deletions
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mathjs/mathjs-tests.ts
+251
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@@ -327,4 +327,255 @@ Expressions examples
// clear defined functions and variables
parser.clear();
}());
/*
Fractions examples
*/
(function(){
// configure the default type of numbers as Fractions
math.config({
number: 'fraction' // Default type of number:
// 'number' (default), 'bignumber', or 'fraction'
});
console.log('basic usage');
math.fraction(0.125); // Fraction, 1/8
math.fraction(0.32); // Fraction, 8/25
math.fraction('1/3'); // Fraction, 1/3
math.fraction('0.(3)'); // Fraction, 1/3
math.fraction(2, 3); // Fraction, 2/3
math.fraction('0.(285714)'); // Fraction, 2/7
console.log();
console.log('round-off errors with numbers');
math.add(0.1, 0.2); // number, 0.30000000000000004
math.divide(0.3, 0.2); // number, 1.4999999999999998
console.log();
console.log('no round-off errors with fractions :)');
math.add(math.fraction(0.1), math.fraction(0.2)); // Fraction, 3/10
math.divide(math.fraction(0.3), math.fraction(0.2)); // Fraction, 3/2
console.log();
console.log('represent an infinite number of repeating digits');
math.fraction('1/3'); // Fraction, 0.(3)
math.fraction('2/7'); // Fraction, 0.(285714)
math.fraction('23/11'); // Fraction, 2.(09)
console.log();
// one can work conveniently with fractions using the expression parser.
// note though that Fractions are only supported by basic arithmetic functions
console.log('use fractions in the expression parser');
math.eval('0.1 + 0.2'); // Fraction, 3/10
math.eval('0.3 / 0.2'); // Fraction, 3/2
math.eval('23 / 11'); // Fraction, 23/11
console.log();
// output formatting
console.log('output formatting of fractions');
var a = math.fraction('2/3');
console.log(math.format(a)); // Fraction, 2/3
console.log(math.format(a, {fraction: 'ratio'})); // Fraction, 2/3
console.log(math.format(a, {fraction: 'decimal'})); // Fraction, 0.(6)
console.log(a.toString()); // Fraction, 0.(6)
console.log();
}());
/*
Matrices examples
*/
(function() {
// create matrices and arrays. a matrix is just a wrapper around an Array,
// providing some handy utilities.
console.log('create a matrix');
var a = math.matrix([1, 4, 9, 16, 25]); // [1, 4, 9, 16, 25]
var b = math.matrix(math.ones([2, 3])); // [[1, 1, 1], [1, 1, 1]]
b.size(); // [2, 3]
// the Array data of a Matrix can be retrieved using valueOf()
var array = a.valueOf(); // [1, 4, 9, 16, 25]
// Matrices can be cloned
var clone = a.clone(); // [1, 4, 9, 16, 25]
console.log();
// perform operations with matrices
console.log('perform operations');
math.sqrt(a); // [1, 2, 3, 4, 5]
var c = [1, 2, 3, 4, 5];
math.factorial(c); // [1, 2, 6, 24, 120]
console.log();
// create and manipulate matrices. Arrays and Matrices can be used mixed.
console.log('manipulate matrices');
var d = [[1, 2], [3, 4]]; // [[1, 2], [3, 4]]
var e = math.matrix([[5, 6], [1, 1]]); // [[5, 6], [1, 1]]
// set a submatrix.
// Matrix indexes are zero-based.
e.subset(math.index(1, [0, 1]), [[7, 8]]); // [[5, 6], [7, 8]]
var f = math.multiply(d, e); // [[19, 22], [43, 50]]
var g = f.subset(math.index(1, 0)); // 43
console.log();
// get a sub matrix
// Matrix indexes are zero-based.
console.log('get a sub matrix');
var h = math.diag(math.range(1,4)); // [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
h.subset( math.index([1, 2], [1, 2])); // [[2, 0], [0, 3]]
var i = math.range(1,6); // [1, 2, 3, 4, 5]
i.subset(math.index(math.range(1,4))); // [2, 3, 4]
console.log();
// resize a multi dimensional matrix
console.log('resizing a matrix');
var j = math.matrix();
var defaultValue = 0;
j.resize([2, 2, 2], defaultValue); // [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
j.size(); // [2, 2, 2]
j.resize([2, 2]); // [[0, 0], [0, 0]]
j.size(); // [2, 2]
console.log();
// setting a value outside the matrices range will resize the matrix.
// new elements will be initialized with zero.
console.log('set a value outside a matrices range');
var k = math.matrix();
k.subset(math.index(2), 6); // [0, 0, 6]
console.log();
console.log('set a value outside a matrices range, leaving new entries uninitialized');
var m = math.matrix();
defaultValue = math.uninitialized;
m.subset(math.index(2), 6, defaultValue); // [undefined, undefined, 6]
console.log();
// create ranges
console.log('create ranges');
math.range(1, 6); // [1, 2, 3, 4, 5]
math.range(0, 18, 3); // [0, 3, 6, 9, 12, 15]
math.range('2:-1:-3'); // [2, 1, 0, -1, -2]
math.factorial(math.range('1:6')); // [1, 2, 6, 24, 120]
console.log();
}());
/*
Sparse matrices examples
*/
(function() {
// create a sparse matrix
console.log('creating a 1000x1000 sparse matrix...');
var a = math.eye(1000, 1000, 'sparse');
// do operations with a sparse matrix
console.log('doing some operations on the sparse matrix...');
var b = math.multiply(a, a);
var c = math.multiply(b, math.complex(2, 2));
var d = math.transpose(c);
var e = math.multiply(d, a);
// we will not print the output, but doing the same operations
// with a dense matrix are very slow, try it for yourself.
console.log('already done');
console.log('now try this with a dense matrix :)');
}());
/*
Units examples
*/
(function() {
// units can be created by providing a value and unit name, or by providing
// a string with a valued unit.
console.log('create units');
var a = math.unit(45, 'cm'); // 450 mm
var b = math.unit('0.1m'); // 100 mm
console.log();
// units can be added, subtracted, and multiplied or divided by numbers and by other units
console.log('perform operations');
math.add(a, b); // 0.55 m
math.multiply(b, 2); // 200 mm
math.divide(math.unit('1 m'), math.unit('1 s')); // 1 m / s
math.pow(math.unit('12 in'), 3); // 1728 in^3
console.log();
// units can be converted to a specific type, or to a number
console.log('convert to another type or to a number');
b.to('cm'); // 10 cm Alternatively: math.to(b, 'cm')
math.to(b, 'inch'); // 3.9370... inch
b.toNumber('cm'); // 10
math.number(b, 'cm'); // 10
console.log();
// the expression parser supports units too
console.log('parse expressions');
math.eval('2 inch to cm'); // 5.08 cm
math.eval('cos(45 deg)'); // 0.70711...
math.eval('90 km/h to m/s'); // 25 m / s
console.log();
// convert a unit to a number
// A second parameter with the unit for the exported number must be provided
math.eval('number(5 cm, mm)'); // number, 50
console.log();
// simplify units
console.log('simplify units');
math.eval('100000 N / m^2'); // 100 kPa
math.eval('9.81 m/s^2 * 100 kg * 40 m'); // 39.24 kJ
console.log();
// example engineering calculations
console.log('compute molar volume of ideal gas at 65 Fahrenheit, 14.7 psi in L/mol');
var Rg = math.unit('8.314 N m / (mol K)');
var T = math.unit('65 degF');
var P = math.unit('14.7 psi');
var v = math.divide(math.multiply(Rg, T), P);
console.log('gas constant (Rg) = ', format(Rg));
console.log('P = ' + format(P));
console.log('T = ' + format(T));
console.log('v = Rg * T / P = ' + format(math.to(v, 'L/mol'))); // 23.910... L / mol
console.log();
console.log('compute speed of fluid flowing out of hole in a container');
var g = math.unit('9.81 m / s^2');
var h = math.unit('1 m');
var v2 = math.pow(math.multiply(2, math.multiply(g, h)), 0.5); // Can also use math.sqrt
console.log('g = ' + format(g));
console.log('h = ' + format(h));
console.log('v = (2 g h) ^ 0.5 = ' + format(v2)); // 4.429... m / s
console.log();
console.log('electrical power consumption:');
var expr = '460 V * 20 A * 30 days to kWh';
console.log(expr + ' = ' + math.eval(expr)); // 6624 kWh
console.log();
console.log('circuit design:');
var expr = '24 V / (6 mA)';
console.log(expr + ' = ' + math.eval(expr)); // 4 kohm
console.log();
console.log('operations on arrays:');
var B = math.eval('[1, 0, 0] T');
var v3 = math.eval('[0, 1, 0] m/s');
var q = math.eval('1 C');
var F = math.multiply(q, math.cross(v3, B));
console.log('B (magnetic field strength) = ' + format(B)); // [1 T, 0 T, 0 T]
console.log('v (particle velocity) = ' + format(v3)); // [0 m / s, 1 m / s, 0 m / s]
console.log('q (particle charge) = ' + format(q)); // 1 C
console.log('F (force) = q (v cross B) = ' + format(F)); // [0 N, 0 N, -1 N]
/**
* Helper function to format an output a value.
* @param {*} value
* @return {string} Returns the formatted value
*/
function format (value: any): string {
var precision = 14;
return math.format(value, precision);
}
}());
mathjs/mathjs.d.ts
Vendored
+32 -21
View File
@@ -7,7 +7,7 @@ declare var math: mathjs.IMathJsStatic;
declare module mathjs {
type MathArray = Array<Number>;
type MathArray = number[]|number[][];
type MathType = number|BigNumber|Fraction|Complex|Unit|MathArray|Matrix;
type MathExpression = string|string[]|MathArray|Matrix;
@@ -15,6 +15,7 @@ declare module mathjs {
e: number;
pi: number;
uninitialized: any;
config(options: any): void;
@@ -132,6 +133,8 @@ declare module mathjs {
* @param y Denominator
* @returns Quotient, x / y
*/
divide(x: Unit, y: Unit): Unit;
divide(x: number, y: number): number;
divide(x:MathType, y:MathType): MathType;
/**
@@ -250,6 +253,10 @@ declare module mathjs {
/**
* Multiply two values, x * y. The result is squeezed. For matrices, the matrix product is calculated.
*/
multiply(x: MathArray|Matrix, y: MathArray|Matrix): Matrix;
multiply(x: MathArray|Matrix, y: MathType): Matrix;
multiply(x: Unit, y: Unit): Unit;
multiply(x: number, y: number): number;
multiply(x: MathType, y: MathType): MathType;
/**
@@ -491,7 +498,7 @@ declare module mathjs {
/**
* Create a fraction convert a value to a fraction.
*/
fraction(numerator: number|string|MathArray|Matrix, denominator: number|string|MathArray|Matrix): Fraction|MathArray|Matrix;
fraction(numerator: number|string|MathArray|Matrix, denominator?: number|string|MathArray|Matrix): Fraction|MathArray|Matrix;
/**
* 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.
@@ -529,8 +536,8 @@ declare module mathjs {
* 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.
*/
unit(unit: string): Unit|MathArray|Matrix;
unit(value: number, unit: string): Unit|MathArray|Matrix;
unit(unit: string): Unit;
unit(value: number, unit: string): Unit;
/**
* Parse and compile an expression. Returns a an object with a function eval([scope]) to evaluate the compiled expression.
@@ -612,7 +619,7 @@ declare module mathjs {
* and B =[b1, b2, b3] is defined as:
* cross(A, B) = [ a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1 * b2 - a2 * b1 ]
*/
cross(x: MathArray|Matrix, y: MathArray|Matrix): MathArray|Matrix;
cross(x: MathArray|Matrix, y: MathArray|Matrix): Matrix;
/**
* Calculate the determinant of a matrix.
@@ -629,8 +636,8 @@ declare module mathjs {
* @param k The diagonal where the vector will be filled in or retrieved. Default value: 0.
* @param format The matrix storage format. Default value: 'dense'.
*/
diag(X: MathArray|Matrix, format?: string): MathArray|Matrix;
diag(X: MathArray|Matrix, k: number|BigNumber, format?: string): MathArray|Matrix;
diag(X: MathArray|Matrix, format?: string): Matrix;
diag(X: MathArray|Matrix, k: number|BigNumber, format?: string): Matrix;
/**
* Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn]
@@ -642,9 +649,9 @@ declare module mathjs {
/**
* 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.
*/
eye(n: number, format?: string): MathArray|Matrix|number;
eye(m: number, n: number, format?: string): MathArray|Matrix|number;
eye(size: number[], format?: string): MathArray|Matrix|number;
eye(n: number, format?: string): Matrix;
eye(m: number, n: number, format?: string): Matrix;
eye(size: number[], format?: string): Matrix;
/**
* Flatten a multi dimensional matrix into a single dimensional matrix.
@@ -659,9 +666,9 @@ declare module mathjs {
/**
* Create a matrix filled with ones. The created matrix can have one or multiple dimensions.
*/
ones(n: number, format?: string): MathArray|Matrix|number;
ones(m: number, n: number, format?: string): MathArray|Matrix|number;
ones(size: number[], format?: string): MathArray|Matrix|number;
ones(n: number, format?: string): MathArray|Matrix;
ones(m: number, n: number, format?: string): MathArray|Matrix;
ones(size: number[], format?: string): MathArray|Matrix;
/**
* Create an array from a range. By default, the range end is excluded. This can be customized by providing an extra parameter includeEnd.
@@ -671,9 +678,9 @@ declare module mathjs {
* @param step Step size. Default value is 1.
* @returns Parameters describing the ranges start, end, and optional step.
*/
range(str: string, includeEnd?: boolean): MathArray|Matrix;
range(start: number|BigNumber, end:number|BigNumber, includeEnd?:boolean): MathArray|Matrix;
range(start: number|BigNumber, end: number|BigNumber, step: number|BigNumber, includeEnd?:boolean): MathArray|Matrix;
range(str: string, includeEnd?: boolean): Matrix;
range(start: number|BigNumber, end:number|BigNumber, includeEnd?:boolean): Matrix;
range(start: number|BigNumber, end: number|BigNumber, step: number|BigNumber, includeEnd?:boolean): Matrix;
/**
* Resize a matrix
@@ -715,9 +722,9 @@ declare module mathjs {
/**
* Create a matrix filled with zeros. The created matrix can have one or multiple dimensions.
*/
zeros(n: number, format?: string): MathArray|Matrix|number;
zeros(m: number, n: number, format?: string): MathArray|Matrix|number;
zeros(size: number[], format?: string): MathArray|Matrix|number;
zeros(n: number, format?: string): MathArray|Matrix;
zeros(m: number, n: number, format?: string): MathArray|Matrix;
zeros(size: number[], format?: string): MathArray|Matrix;
/**
* Compute the number of ways of picking k unordered outcomes from n possibilities.
@@ -1269,7 +1276,10 @@ declare module mathjs {
}
export interface Matrix {
size(): number[];
subset(index: Index, replacement?: any, defaultValue?: any): Matrix;
resize(size: MathArray|Matrix, defaultValue?: number|string): Matrix;
clone(): Matrix;
}
export interface BigNumber {
@@ -1293,7 +1303,8 @@ declare module mathjs {
}
export interface Unit {
to(unit: string): Unit;
toNumber(unit: string): number;
}
export interface Index {