mirror of
https://github.com/josdejong/mathjs.git
synced 2025-12-08 19:46:04 +00:00
971 lines
26 KiB
JavaScript
971 lines
26 KiB
JavaScript
'use strict';
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var extend = require('../../utils/object').extend;
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var array = require('../../utils/array');
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function factory (type, config, load, typed) {
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var latex = require('../../utils/latex');
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var matrix = load(require('../../type/matrix/function/matrix'));
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var addScalar = load(require('./addScalar'));
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var multiplyScalar = load(require('./multiplyScalar'));
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var equalScalar = load(require('../relational/equalScalar'));
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var algorithm11 = load(require('../../type/matrix/utils/algorithm11'));
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var algorithm14 = load(require('../../type/matrix/utils/algorithm14'));
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var DenseMatrix = type.DenseMatrix;
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var SparseMatrix = type.SparseMatrix;
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/**
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* Multiply two or more values, `x * y`.
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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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* math.multiply(x, y, z, ...)
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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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* math.multiply(2, 3, 4); // returns number 24
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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, prod, cross, dot
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*
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* @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} x First value to multiply
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* @param {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} y Second value to multiply
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* @return {number | BigNumber | Fraction | Complex | Unit | Array | Matrix} Multiplication of `x` and `y`
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*/
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var multiply = typed('multiply', extend({
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// we extend the signatures of multiplyScalar with signatures dealing with matrices
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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 type.isMatrix(m) ? 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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'Matrix, any': function (x, y) {
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// result
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var c;
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// process storage format
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switch (x.storage()) {
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case 'sparse':
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c = algorithm11(x, y, multiplyScalar, false);
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break;
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case 'dense':
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c = algorithm14(x, y, multiplyScalar, false);
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break;
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}
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return c;
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},
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'any, Matrix': function (x, y) {
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// result
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var c;
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// check storage format
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switch (y.storage()) {
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case 'sparse':
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c = algorithm11(y, x, multiplyScalar, true);
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break;
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case 'dense':
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c = algorithm14(y, x, multiplyScalar, true);
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break;
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}
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return c;
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},
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'Array, any': function (x, y) {
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// use matrix implementation
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return algorithm14(matrix(x), y, multiplyScalar, false).valueOf();
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},
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'any, Array': function (x, y) {
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// use matrix implementation
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return algorithm14(matrix(y), x, multiplyScalar, true).valueOf();
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},
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'any, any': multiplyScalar,
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'Array | Matrix | any, Array | Matrix | any, ...any': function (x, y, rest) {
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var result = multiply(x, y);
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for (var i = 0; i < rest.length; i++) {
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result = multiply(result, rest[i]);
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}
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return result;
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}
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}, multiplyScalar.signatures));
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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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var adt = a._datatype;
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// b dense
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var bdata = b._data;
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var bdt = b._datatype;
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// datatype
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var dt;
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// addScalar signature to use
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var af = addScalar;
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// multiplyScalar signature to use
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var mf = multiplyScalar;
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// process data types
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if (adt && bdt && adt === bdt && typeof adt === 'string') {
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// datatype
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dt = adt;
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// find signatures that matches (dt, dt)
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af = typed.find(addScalar, [dt, dt]);
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mf = typed.find(multiplyScalar, [dt, dt]);
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}
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// result (do not initialize it with zero)
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var c = mf(adata[0], bdata[0]);
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// loop data
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for (var i = 1; i < n; i++) {
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// multiply and accumulate
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c = af(c, mf(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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var adt = a._datatype;
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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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var bdt = b._datatype;
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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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// datatype
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var dt;
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// addScalar signature to use
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var af = addScalar;
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// multiplyScalar signature to use
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var mf = multiplyScalar;
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// process data types
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if (adt && bdt && adt === bdt && typeof adt === 'string') {
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// datatype
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dt = adt;
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// find signatures that matches (dt, dt)
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af = typed.find(addScalar, [dt, dt]);
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mf = typed.find(multiplyScalar, [dt, dt]);
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}
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// result
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var c = [];
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// loop matrix columns
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for (var j = 0; j < bcolumns; j++) {
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// sum (do not initialize it with zero)
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var sum = mf(adata[0], bdata[0][j]);
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// loop vector
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for (var i = 1; i < alength; i++) {
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// multiply & accumulate
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sum = af(sum, mf(adata[i], bdata[i][j]));
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}
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c[j] = sum;
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}
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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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datatype: dt
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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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var adt = a._datatype;
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// b dense
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var bdata = b._data;
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var bdt = b._datatype;
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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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// datatype
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var dt;
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// addScalar signature to use
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var af = addScalar;
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// multiplyScalar signature to use
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var mf = multiplyScalar;
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// process data types
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if (adt && bdt && adt === bdt && typeof adt === 'string') {
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// datatype
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dt = adt;
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// find signatures that matches (dt, dt)
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af = typed.find(addScalar, [dt, dt]);
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mf = typed.find(multiplyScalar, [dt, dt]);
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}
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// result
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var c = [];
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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 (do not initialize it with zero)
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var sum = mf(row[0], bdata[0]);
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// loop matrix a columns
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for (var j = 1; j < acolumns; j++) {
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// multiply & accumulate
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sum = af(sum, mf(row[j], bdata[j]));
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}
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c[i] = sum;
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}
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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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datatype: dt
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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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var adt = a._datatype;
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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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var bdt = b._datatype;
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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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// datatype
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var dt;
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// addScalar signature to use
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var af = addScalar;
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// multiplyScalar signature to use
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var mf = multiplyScalar;
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// process data types
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if (adt && bdt && adt === bdt && typeof adt === 'string') {
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// datatype
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dt = adt;
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// find signatures that matches (dt, dt)
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af = typed.find(addScalar, [dt, dt]);
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mf = typed.find(multiplyScalar, [dt, dt]);
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}
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// result
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var c = [];
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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] = [];
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// loop matrix b columns
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for (var j = 0; j < bcolumns; j++) {
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// sum (avoid initializing sum to zero)
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var sum = mf(row[0], bdata[0][j]);
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// loop matrix a columns
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for (var x = 1; x < acolumns; x++) {
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// multiply & accumulate
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sum = af(sum, mf(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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// 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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datatype: dt
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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} SparseMatrix (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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var adt = a._datatype;
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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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var bdt = b._datatype;
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// validate b matrix
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if (!bvalues)
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throw new Error('Cannot multiply Dense Matrix times Pattern only Matrix');
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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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// datatype
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var dt;
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// addScalar signature to use
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var af = addScalar;
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// multiplyScalar signature to use
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var mf = multiplyScalar;
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// equalScalar signature to use
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var eq = equalScalar;
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// zero value
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var zero = 0;
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// process data types
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if (adt && bdt && adt === bdt && typeof adt === 'string') {
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// datatype
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dt = adt;
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// find signatures that matches (dt, dt)
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af = typed.find(addScalar, [dt, dt]);
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mf = typed.find(multiplyScalar, [dt, dt]);
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eq = typed.find(equalScalar, [dt, dt]);
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// convert 0 to the same datatype
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zero = typed.convert(0, dt);
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}
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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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|
// c matrix
|
|
var c = new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, bcolumns],
|
|
datatype: dt
|
|
});
|
|
|
|
// loop b columns
|
|
for (var jb = 0; jb < bcolumns; jb++) {
|
|
// update ptr
|
|
cptr[jb] = cindex.length;
|
|
// indeces in column jb
|
|
var kb0 = bptr[jb];
|
|
var kb1 = bptr[jb + 1];
|
|
// do not process column jb if no data exists
|
|
if (kb1 > kb0) {
|
|
// last row mark processed
|
|
var last = 0;
|
|
// loop a rows
|
|
for (var i = 0; i < arows; i++) {
|
|
// column mark
|
|
var mark = i + 1;
|
|
// C[i, jb]
|
|
var cij;
|
|
// values in b column j
|
|
for (var kb = kb0; kb < kb1; kb++) {
|
|
// row
|
|
var ib = bindex[kb];
|
|
// check value has been initialized
|
|
if (last !== mark) {
|
|
// first value in column jb
|
|
cij = mf(adata[i][ib], bvalues[kb]);
|
|
// update mark
|
|
last = mark;
|
|
}
|
|
else {
|
|
// accumulate value
|
|
cij = af(cij, mf(adata[i][ib], bvalues[kb]));
|
|
}
|
|
}
|
|
// check column has been processed and value != 0
|
|
if (last === mark && !eq(cij, zero)) {
|
|
// push row & value
|
|
cindex.push(i);
|
|
cvalues.push(cij);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// update ptr
|
|
cptr[bcolumns] = cindex.length;
|
|
|
|
// return sparse matrix
|
|
return c;
|
|
};
|
|
|
|
/**
|
|
* C = A * B
|
|
*
|
|
* @param {Matrix} a SparseMatrix (MxN)
|
|
* @param {Matrix} b Dense Vector (N)
|
|
*
|
|
* @return {Matrix} SparseMatrix (M, 1)
|
|
*/
|
|
var _multiplySparseMatrixVector = function (a, b) {
|
|
// a sparse
|
|
var avalues = a._values;
|
|
var aindex = a._index;
|
|
var aptr = a._ptr;
|
|
var adt = a._datatype;
|
|
// validate a matrix
|
|
if (!avalues)
|
|
throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix');
|
|
// b dense
|
|
var bdata = b._data;
|
|
var bdt = b._datatype;
|
|
// rows & columns
|
|
var arows = a._size[0];
|
|
var brows = b._size[0];
|
|
// result
|
|
var cvalues = [];
|
|
var cindex = [];
|
|
var cptr = [];
|
|
|
|
// datatype
|
|
var dt;
|
|
// addScalar signature to use
|
|
var af = addScalar;
|
|
// multiplyScalar signature to use
|
|
var mf = multiplyScalar;
|
|
// equalScalar signature to use
|
|
var eq = equalScalar;
|
|
// zero value
|
|
var zero = 0;
|
|
|
|
// process data types
|
|
if (adt && bdt && adt === bdt && typeof adt === 'string') {
|
|
// datatype
|
|
dt = adt;
|
|
// find signatures that matches (dt, dt)
|
|
af = typed.find(addScalar, [dt, dt]);
|
|
mf = typed.find(multiplyScalar, [dt, dt]);
|
|
eq = typed.find(equalScalar, [dt, dt]);
|
|
// convert 0 to the same datatype
|
|
zero = typed.convert(0, dt);
|
|
}
|
|
|
|
// workspace
|
|
var x = [];
|
|
// vector with marks indicating a value x[i] exists in a given column
|
|
var w = [];
|
|
|
|
// update ptr
|
|
cptr[0] = 0;
|
|
// rows in b
|
|
for (var ib = 0; ib < brows; ib++) {
|
|
// b[ib]
|
|
var vbi = bdata[ib];
|
|
// check b[ib] != 0, avoid loops
|
|
if (!eq(vbi, zero)) {
|
|
// 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];
|
|
// check value exists in current j
|
|
if (!w[ia]) {
|
|
// ia is new entry in j
|
|
w[ia] = true;
|
|
// add i to pattern of C
|
|
cindex.push(ia);
|
|
// x(ia) = A
|
|
x[ia] = mf(vbi, avalues[ka]);
|
|
}
|
|
else {
|
|
// i exists in C already
|
|
x[ia] = af(x[ia], mf(vbi, avalues[ka]));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// copy values from x to column jb of c
|
|
for (var p1 = cindex.length, p = 0; p < p1; p++) {
|
|
// row
|
|
var ic = cindex[p];
|
|
// copy value
|
|
cvalues[p] = x[ic];
|
|
}
|
|
// update ptr
|
|
cptr[1] = cindex.length;
|
|
|
|
// return sparse matrix
|
|
return new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, 1],
|
|
datatype: dt
|
|
});
|
|
};
|
|
|
|
/**
|
|
* C = A * B
|
|
*
|
|
* @param {Matrix} a SparseMatrix (MxN)
|
|
* @param {Matrix} b DenseMatrix (NxC)
|
|
*
|
|
* @return {Matrix} SparseMatrix (MxC)
|
|
*/
|
|
var _multiplySparseMatrixDenseMatrix = function (a, b) {
|
|
// a sparse
|
|
var avalues = a._values;
|
|
var aindex = a._index;
|
|
var aptr = a._ptr;
|
|
var adt = a._datatype;
|
|
// validate a matrix
|
|
if (!avalues)
|
|
throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix');
|
|
// b dense
|
|
var bdata = b._data;
|
|
var bdt = b._datatype;
|
|
// rows & columns
|
|
var arows = a._size[0];
|
|
var brows = b._size[0];
|
|
var bcolumns = b._size[1];
|
|
|
|
// datatype
|
|
var dt;
|
|
// addScalar signature to use
|
|
var af = addScalar;
|
|
// multiplyScalar signature to use
|
|
var mf = multiplyScalar;
|
|
// equalScalar signature to use
|
|
var eq = equalScalar;
|
|
// zero value
|
|
var zero = 0;
|
|
|
|
// process data types
|
|
if (adt && bdt && adt === bdt && typeof adt === 'string') {
|
|
// datatype
|
|
dt = adt;
|
|
// find signatures that matches (dt, dt)
|
|
af = typed.find(addScalar, [dt, dt]);
|
|
mf = typed.find(multiplyScalar, [dt, dt]);
|
|
eq = typed.find(equalScalar, [dt, dt]);
|
|
// convert 0 to the same datatype
|
|
zero = typed.convert(0, dt);
|
|
}
|
|
|
|
// result
|
|
var cvalues = [];
|
|
var cindex = [];
|
|
var cptr = [];
|
|
// c matrix
|
|
var c = new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, bcolumns],
|
|
datatype: dt
|
|
});
|
|
|
|
// workspace
|
|
var x = [];
|
|
// vector with marks indicating a value x[i] exists in a given column
|
|
var w = [];
|
|
|
|
// loop b columns
|
|
for (var jb = 0; jb < bcolumns; jb++) {
|
|
// update ptr
|
|
cptr[jb] = cindex.length;
|
|
// mark in workspace for current column
|
|
var mark = jb + 1;
|
|
// 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 (!eq(vbij, zero)) {
|
|
// 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];
|
|
// check value exists in current j
|
|
if (w[ia] !== mark) {
|
|
// ia is new entry in j
|
|
w[ia] = mark;
|
|
// add i to pattern of C
|
|
cindex.push(ia);
|
|
// x(ia) = A
|
|
x[ia] = mf(vbij, avalues[ka]);
|
|
}
|
|
else {
|
|
// i exists in C already
|
|
x[ia] = af(x[ia], mf(vbij, avalues[ka]));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// copy values from x to column jb of c
|
|
for (var p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {
|
|
// row
|
|
var ic = cindex[p];
|
|
// copy value
|
|
cvalues[p] = x[ic];
|
|
}
|
|
}
|
|
// update ptr
|
|
cptr[bcolumns] = cindex.length;
|
|
|
|
// return sparse matrix
|
|
return c;
|
|
};
|
|
|
|
/**
|
|
* 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;
|
|
var adt = a._datatype;
|
|
// b sparse
|
|
var bvalues = b._values;
|
|
var bindex = b._index;
|
|
var bptr = b._ptr;
|
|
var bdt = b._datatype;
|
|
|
|
// rows & columns
|
|
var arows = a._size[0];
|
|
var bcolumns = b._size[1];
|
|
// flag indicating both matrices (a & b) contain data
|
|
var values = avalues && bvalues;
|
|
|
|
// datatype
|
|
var dt;
|
|
// addScalar signature to use
|
|
var af = addScalar;
|
|
// multiplyScalar signature to use
|
|
var mf = multiplyScalar;
|
|
|
|
// process data types
|
|
if (adt && bdt && adt === bdt && typeof adt === 'string') {
|
|
// datatype
|
|
dt = adt;
|
|
// find signatures that matches (dt, dt)
|
|
af = typed.find(addScalar, [dt, dt]);
|
|
mf = typed.find(multiplyScalar, [dt, dt]);
|
|
}
|
|
|
|
// result
|
|
var cvalues = values ? [] : undefined;
|
|
var cindex = [];
|
|
var cptr = [];
|
|
// c matrix
|
|
var c = new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, bcolumns],
|
|
datatype: dt
|
|
});
|
|
|
|
// workspace
|
|
var x = values ? [] : undefined;
|
|
// vector with marks indicating a value x[i] exists in a given column
|
|
var w = [];
|
|
// variables
|
|
var ka, ka0, ka1, kb, kb0, kb1, ia, ib;
|
|
// loop b columns
|
|
for (var jb = 0; jb < bcolumns; jb++) {
|
|
// update ptr
|
|
cptr[jb] = cindex.length;
|
|
// mark in workspace for current column
|
|
var mark = jb + 1;
|
|
// B values & index in j
|
|
for (kb0 = bptr[jb], kb1 = bptr[jb + 1], kb = kb0; kb < kb1; kb++) {
|
|
// b row
|
|
ib = bindex[kb];
|
|
// check we need to process values
|
|
if (values) {
|
|
// loop values in a[:,ib]
|
|
for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
|
|
// row
|
|
ia = aindex[ka];
|
|
// check value exists in current j
|
|
if (w[ia] !== mark) {
|
|
// ia is new entry in j
|
|
w[ia] = mark;
|
|
// add i to pattern of C
|
|
cindex.push(ia);
|
|
// x(ia) = A
|
|
x[ia] = mf(bvalues[kb], avalues[ka]);
|
|
}
|
|
else {
|
|
// i exists in C already
|
|
x[ia] = af(x[ia], mf(bvalues[kb], avalues[ka]));
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
// loop values in a[:,ib]
|
|
for (ka0 = aptr[ib], ka1 = aptr[ib + 1], ka = ka0; ka < ka1; ka++) {
|
|
// row
|
|
ia = aindex[ka];
|
|
// check value exists in current j
|
|
if (w[ia] !== mark) {
|
|
// ia is new entry in j
|
|
w[ia] = mark;
|
|
// add i to pattern of C
|
|
cindex.push(ia);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// check we need to process matrix values (pattern matrix)
|
|
if (values) {
|
|
// copy values from x to column jb of c
|
|
for (var p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {
|
|
// row
|
|
var ic = cindex[p];
|
|
// copy value
|
|
cvalues[p] = x[ic];
|
|
}
|
|
}
|
|
}
|
|
// update ptr
|
|
cptr[bcolumns] = cindex.length;
|
|
|
|
// return sparse matrix
|
|
return c;
|
|
};
|
|
|
|
multiply.toTex = {
|
|
2: '\\left(${args[0]}' + latex.operators['multiply'] + '${args[1]}\\right)'
|
|
};
|
|
|
|
return multiply;
|
|
}
|
|
|
|
exports.name = 'multiply';
|
|
exports.factory = factory;
|