mirror of
https://github.com/josdejong/mathjs.git
synced 2025-12-08 19:46:04 +00:00
695 lines
18 KiB
JavaScript
695 lines
18 KiB
JavaScript
'use strict';
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var util = require('../../util/index');
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var array = util.array;
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function factory (type, config, load, typed) {
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var matrix = load(require('../construction/matrix'));
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var add = load(require('./add'));
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var equal = load(require('../relational/equal'));
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var collection = load(require('../../type/collection'));
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var DenseMatrix = type.DenseMatrix;
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var SparseMatrix = type.SparseMatrix;
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var Spa = type.Spa;
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/**
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* Multiply two values, `x * y`. The result is squeezed.
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* For matrices, the matrix product is calculated.
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*
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* Syntax:
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*
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* math.multiply(x, y)
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*
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* Examples:
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*
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* math.multiply(4, 5.2); // returns Number 20.8
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*
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* var a = math.complex(2, 3);
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* var b = math.complex(4, 1);
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* math.multiply(a, b); // returns Complex 5 + 14i
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*
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* var c = [[1, 2], [4, 3]];
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* var d = [[1, 2, 3], [3, -4, 7]];
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* math.multiply(c, d); // returns Array [[7, -6, 17], [13, -4, 33]]
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*
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* var e = math.unit('2.1 km');
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* math.multiply(3, e); // returns Unit 6.3 km
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*
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* See also:
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*
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* divide
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*
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* @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x First value to multiply
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* @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} y Second value to multiply
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* @return {Number | BigNumber | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`
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*/
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var multiply = typed('multiply', {
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'number, number': function (x, y) {
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return x * y;
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},
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'BigNumber, BigNumber': function (x, y) {
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return x.times(y);
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},
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'Complex, Complex': function (x, y) {
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return new type.Complex(
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x.re * y.re - x.im * y.im,
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x.re * y.im + x.im * y.re
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);
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},
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'number, Unit': function (x, y) {
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var res = y.clone();
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res.value = (res.value === null) ? res._normalize(x) : (res.value * x);
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return res;
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},
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'Unit, number': function (x, y) {
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var res = x.clone();
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res.value = (res.value === null) ? res._normalize(y) : (res.value * y);
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return res;
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},
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'Array, Array': function (x, y) {
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// check dimensions
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_validateMatrixDimensions(array.size(x), array.size(y));
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// use dense matrix implementation
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var m = multiply(matrix(x), matrix(y));
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// return array or scalar
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return m instanceof type.Matrix ? m.valueOf() : m;
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},
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'Matrix, Matrix': function (x, y) {
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// dimensions
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var xsize = x.size();
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var ysize = y.size();
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// check dimensions
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_validateMatrixDimensions(xsize, ysize);
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// process dimensions
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if (xsize.length === 1) {
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// process y dimensions
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if (ysize.length === 1) {
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// Vector * Vector
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return _multiplyVectorVector(x, y, xsize[0]);
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}
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// Vector * Matrix
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return _multiplyVectorMatrix(x, y);
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}
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// process y dimensions
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if (ysize.length === 1) {
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// Matrix * Vector
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return _multiplyMatrixVector(x, y);
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}
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// Matrix * Matrix
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return _multiplyMatrixMatrix(x, y);
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},
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'Matrix, Array': function (x, y) {
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// use Matrix * Matrix implementation
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return multiply(x, matrix(y));
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},
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'Array, Matrix': function (x, y) {
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// use Matrix * Matrix implementation
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return multiply(matrix(x, y.storage()), y);
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},
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'Array, any': function (x, y) {
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return collection.deepMap2(x, y, multiply);
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},
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'Matrix, any': function (x, y) {
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// use matrix map, skip zeros since 0 * X = 0
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return x.map(function (v) {
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return multiply(v, y);
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}, true);
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},
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'any, Array | Matrix': function (x, y) {
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// use matrix map, skip zeros since 0 * X = 0
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return y.map(function (v) {
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return multiply(v, x);
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}, true);
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}
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});
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var _validateMatrixDimensions = function (size1, size2) {
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// check left operand dimensions
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switch (size1.length) {
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case 1:
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// check size2
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switch (size2.length) {
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case 1:
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// Vector x Vector
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if (size1[0] !== size2[0]) {
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// throw error
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throw new RangeError('Dimension mismatch in multiplication. Vectors must have the same length');
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}
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break;
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case 2:
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// Vector x Matrix
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if (size1[0] !== size2[0]) {
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// throw error
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throw new RangeError('Dimension mismatch in multiplication. Vector length (' + size1[0] + ') must match Matrix rows (' + size2[0] + ')');
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}
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break;
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default:
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throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)');
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}
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break;
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case 2:
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// check size2
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switch (size2.length) {
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case 1:
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// Matrix x Vector
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if (size1[1] !== size2[0]) {
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// throw error
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throw new RangeError('Dimension mismatch in multiplication. Matrix columns (' + size1[1] + ') must match Vector length (' + size2[0] + ')');
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}
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break;
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case 2:
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// Matrix x Matrix
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if (size1[1] !== size2[0]) {
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// throw error
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throw new RangeError('Dimension mismatch in multiplication. Matrix A columns (' + size1[1] + ') must match Matrix B rows (' + size2[0] + ')');
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}
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break;
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default:
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throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix B has ' + size2.length + ' dimensions)');
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}
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break;
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default:
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throw new Error('Can only multiply a 1 or 2 dimensional matrix (Matrix A has ' + size1.length + ' dimensions)');
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}
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a Dense Vector (N)
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* @param {Matrix} b Dense Vector (N)
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*
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* @return {Number} Scalar value
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*/
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var _multiplyVectorVector = function (a, b, n) {
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// check empty vector
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if (n === 0)
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throw new Error('Cannot multiply two empty vectors');
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// a dense
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var adata = a._data;
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// b dense
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var bdata = b._data;
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// result
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var c = 0;
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// loop data
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for (var i = 0; i < n; i++) {
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// multiply and accumulate
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c = add(c, multiply(adata[i], bdata[i]));
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}
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return c;
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a Dense Vector (M)
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* @param {Matrix} b Matrix (MxN)
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*
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* @return {Matrix} Dense Vector (N)
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*/
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var _multiplyVectorMatrix = function (a, b) {
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// process storage
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switch (b.storage()) {
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case 'dense':
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return _multiplyVectorDenseMatrix(a, b);
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}
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throw new Error('Not implemented');
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a Dense Vector (M)
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* @param {Matrix} b Dense Matrix (MxN)
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*
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* @return {Matrix} Dense Vector (N)
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*/
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var _multiplyVectorDenseMatrix = function (a, b) {
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// a dense
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var adata = a._data;
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var asize = a._size;
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// b dense
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var bdata = b._data;
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var bsize = b._size;
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// rows & columns
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var alength = asize[0];
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var bcolumns = bsize[1];
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// result
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var c = new Array(bcolumns);
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// loop matrix columns
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for (var j = 0; j < bcolumns; j++) {
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// sum
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var sum = 0;
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// loop vector
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for (var i = 0; i < alength; i++) {
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// multiply & accumulate
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sum = add(sum, multiply(adata[i], bdata[i][j]));
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}
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c[j] = sum;
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}
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// check we need to squeeze the result into a scalar
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if (bcolumns === 1)
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return c[0];
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// return matrix
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return new DenseMatrix({
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data: c,
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size: [bcolumns]
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});
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a Matrix (MxN)
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* @param {Matrix} b Dense Vector (N)
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*
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* @return {Matrix} Dense Vector (M)
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*/
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var _multiplyMatrixVector = function (a, b) {
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// process storage
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switch (a.storage()) {
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case 'dense':
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return _multiplyDenseMatrixVector(a, b);
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case 'sparse':
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return _multiplySparseMatrixVector(a, b);
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}
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a Matrix (MxN)
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* @param {Matrix} b Matrix (NxC)
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*
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* @return {Matrix} Matrix (MxC)
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*/
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var _multiplyMatrixMatrix = function (a, b) {
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// process storage
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switch (a.storage()) {
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case 'dense':
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// process storage
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switch (b.storage()) {
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case 'dense':
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return _multiplyDenseMatrixDenseMatrix(a, b);
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case 'sparse':
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return _multiplyDenseMatrixSparseMatrix(a, b);
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}
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break;
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case 'sparse':
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// process storage
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switch (b.storage()) {
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case 'dense':
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return _multiplySparseMatrixDenseMatrix(a, b);
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case 'sparse':
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return _multiplySparseMatrixSparseMatrix(a, b);
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}
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break;
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}
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a DenseMatrix (MxN)
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* @param {Matrix} b Dense Vector (N)
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*
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* @return {Matrix} Dense Vector (M)
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*/
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var _multiplyDenseMatrixVector = function (a, b) {
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// a dense
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var adata = a._data;
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var asize = a._size;
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// b dense
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var bdata = b._data;
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// rows & columns
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var arows = asize[0];
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var acolumns = asize[1];
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// result
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var c = new Array(arows);
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// loop matrix a rows
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for (var i = 0; i < arows; i++) {
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// current row
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var row = adata[i];
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// sum
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var sum = 0;
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// loop matrix a columns
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for (var j = 0; j < acolumns; j++) {
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// multiply & accumulate
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sum = add(sum, multiply(row[j], bdata[j]));
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}
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c[i] = sum;
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}
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// check we need to squeeze the result into a scalar
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if (arows === 1)
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return c[0];
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// return matrix
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return new DenseMatrix({
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data: c,
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size: [arows]
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});
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a DenseMatrix (MxN)
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* @param {Matrix} b DenseMatrix (NxC)
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*
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* @return {Matrix} DenseMatrix (MxC)
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*/
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var _multiplyDenseMatrixDenseMatrix = function (a, b) {
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// a dense
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var adata = a._data;
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var asize = a._size;
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// b dense
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var bdata = b._data;
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var bsize = b._size;
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// rows & columns
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var arows = asize[0];
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var acolumns = asize[1];
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var bcolumns = bsize[1];
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// result
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var c = new Array(arows);
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// loop matrix a rows
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for (var i = 0; i < arows; i++) {
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// current row
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var row = adata[i];
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// initialize row array
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c[i] = new Array(bcolumns);
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// loop matrix b columns
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for (var j = 0; j < bcolumns; j++) {
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// sum
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var sum = 0;
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// loop matrix a columns
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for (var x = 0; x < acolumns; x++) {
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// multiply & accumulate
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sum = add(sum, multiply(row[x], bdata[x][j]));
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}
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c[i][j] = sum;
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}
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}
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// check we need to squeeze the result into a scalar
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if (arows === 1 && bcolumns === 1)
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return c[0][0];
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// return matrix
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return new DenseMatrix({
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data: c,
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size: [arows, bcolumns]
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});
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a DenseMatrix (MxN)
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* @param {Matrix} b SparseMatrix (NxC)
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*
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* @return {Matrix} DenseMatrix (MxC)
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*/
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var _multiplyDenseMatrixSparseMatrix = function (a, b) {
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// a dense
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var adata = a._data;
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var asize = a._size;
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// b sparse
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var bvalues = b._values;
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var bindex = b._index;
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var bptr = b._ptr;
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var bsize = b._size;
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// rows & columns
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var arows = asize[0];
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var bcolumns = bsize[1];
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// result
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var c = new Array(arows);
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// loop a rows
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for (var i = 0; i < arows; i++) {
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// initialize row
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c[i] = new Array(bcolumns);
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// current row
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var row = adata[i];
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// loop b columns
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for (var j = 0; j < bcolumns; j++) {
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// sum
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var sum = 0;
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// values & index in column j
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for (var k0 = bptr[j], k1 = bptr[j + 1], k = k0; k < k1; k++) {
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// row
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var x = bindex[k];
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// multiply & accumulate
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sum = add(sum, multiply(row[x], bvalues[k]));
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}
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c[i][j] = sum;
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}
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}
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// check we need to squeeze the result into a scalar
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if (arows === 1 && bcolumns === 1)
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return c[0][0];
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// return matrix
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return new DenseMatrix({
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data: c,
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size: [arows, bcolumns]
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});
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a SparseMatrix (MxN)
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* @param {Matrix} b Dense Vector (N)
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*
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* @return {Matrix} SparseMatrix (M, 1)
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*/
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var _multiplySparseMatrixVector = function (a, b) {
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// a sparse
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var avalues = a._values;
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var aindex = a._index;
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var aptr = a._ptr;
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// b dense
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var bdata = b._data;
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// rows & columns
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var arows = a._size[0];
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var brows = b._size[0];
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// result
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var cvalues = [];
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var cindex = [];
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var cptr = [];
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// create sparse accumulator
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var spa = new Spa(arows);
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// update ptr
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cptr.push(0);
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// rows in b
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for (var ib = 0; ib < brows; ib++) {
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// b[ib]
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var vbi = bdata[ib];
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// check b[ib] != 0, avoid loops
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if (!equal(vbi, 0)) {
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// A values & index in ib column
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for (var ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
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// a row
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var ia = aindex[ka];
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// accumulate
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spa.accumulate(ia, multiply(vbi, avalues[ka]));
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}
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}
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}
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// process spa
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spa.forEach(0, arows - 1, function (x, v) {
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cindex.push(x);
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cvalues.push(v);
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});
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// update ptr
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cptr.push(cvalues.length);
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// check we need to squeeze the result into a scalar
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if (arows === 1)
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return cvalues.length === 1 ? cvalues[0] : 0;
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// return sparse matrix
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return new SparseMatrix({
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values : cvalues,
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index: cindex,
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ptr: cptr,
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size: [arows, 1]
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});
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};
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/**
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* C = A * B
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*
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* @param {Matrix} a SparseMatrix (MxN)
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* @param {Matrix} b DenseMatrix (NxC)
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*
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* @return {Matrix} SparseMatrix (MxC)
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*/
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var _multiplySparseMatrixDenseMatrix = function (a, b) {
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// a sparse
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var avalues = a._values;
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var aindex = a._index;
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var aptr = a._ptr;
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// b dense
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var bdata = b._data;
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// rows & columns
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|
var arows = a._size[0];
|
|
var brows = b._size[0];
|
|
var bcolumns = b._size[1];
|
|
// result
|
|
var cvalues = [];
|
|
var cindex = [];
|
|
var cptr = [];
|
|
|
|
// process column
|
|
var processColumn = function (j, v) {
|
|
cindex.push(j);
|
|
cvalues.push(v);
|
|
};
|
|
|
|
// loop b columns
|
|
for (var jb = 0; jb < bcolumns; jb++) {
|
|
// update ptr
|
|
cptr.push(cvalues.length);
|
|
// create sparse accumulator
|
|
var spa = new Spa(arows);
|
|
// rows in jb
|
|
for (var ib = 0; ib < brows; ib++) {
|
|
// b[ib, jb]
|
|
var vbij = bdata[ib][jb];
|
|
// check b[ib, jb] != 0, avoid loops
|
|
if (!equal(vbij, 0)) {
|
|
// A values & index in ib column
|
|
for (var ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
|
|
// a row
|
|
var ia = aindex[ka];
|
|
// accumulate
|
|
spa.accumulate(ia, multiply(vbij, avalues[ka]));
|
|
}
|
|
}
|
|
}
|
|
// process sparse accumulator
|
|
spa.forEach(0, arows - 1, processColumn);
|
|
}
|
|
// update ptr
|
|
cptr.push(cvalues.length);
|
|
|
|
// check we need to squeeze the result into a scalar
|
|
if (arows === 1 && bcolumns === 1)
|
|
return cvalues.length === 1 ? cvalues[0] : 0;
|
|
|
|
// return sparse matrix
|
|
return new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, bcolumns]
|
|
});
|
|
};
|
|
|
|
/**
|
|
* C = A * B
|
|
*
|
|
* @param {Matrix} a SparseMatrix (MxN)
|
|
* @param {Matrix} b SparseMatrix (NxC)
|
|
*
|
|
* @return {Matrix} SparseMatrix (MxC)
|
|
*/
|
|
var _multiplySparseMatrixSparseMatrix = function (a, b) {
|
|
// a sparse
|
|
var avalues = a._values;
|
|
var aindex = a._index;
|
|
var aptr = a._ptr;
|
|
// b sparse
|
|
var bvalues = b._values;
|
|
var bindex = b._index;
|
|
var bptr = b._ptr;
|
|
// rows & columns
|
|
var arows = a._size[0];
|
|
var bcolumns = b._size[1];
|
|
// result
|
|
var cvalues = [];
|
|
var cindex = [];
|
|
var cptr = [];
|
|
|
|
// process column in C
|
|
var processColumn = function (i, v) {
|
|
cindex.push(i);
|
|
cvalues.push(v);
|
|
};
|
|
|
|
// loop b columns
|
|
for (var jb = 0; jb < bcolumns; jb++) {
|
|
// update ptr
|
|
cptr.push(cvalues.length);
|
|
// create sparse accumulator
|
|
var spa = new Spa(arows);
|
|
// B values & index in j
|
|
for (var kb0 = bptr[jb], kb1 = bptr[jb + 1], kb = kb0; kb < kb1; kb++) {
|
|
// b row
|
|
var ib = bindex[kb];
|
|
// A values & index in ib column
|
|
for (var ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
|
|
// a row
|
|
var ia = aindex[ka];
|
|
// accumulate
|
|
spa.accumulate(ia, multiply(bvalues[kb], avalues[ka]));
|
|
}
|
|
}
|
|
// process sparse accumulator
|
|
spa.forEach(0, arows - 1, processColumn);
|
|
}
|
|
// update ptr
|
|
cptr.push(cvalues.length);
|
|
|
|
// check we need to squeeze the result into a scalar
|
|
if (arows === 1 && bcolumns === 1)
|
|
return cvalues.length === 1 ? cvalues[0] : 0;
|
|
|
|
// return sparse matrix
|
|
return new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, bcolumns]
|
|
});
|
|
};
|
|
|
|
return multiply;
|
|
}
|
|
|
|
exports.name = 'multiply';
|
|
exports.factory = factory;
|