mirror of
https://github.com/josdejong/mathjs.git
synced 2025-12-08 19:46:04 +00:00
849 lines
24 KiB
JavaScript
849 lines
24 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 addScalar = load(require('./addScalar'));
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var multiplyScalar = load(require('./multiplyScalar'));
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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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/**
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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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'any, any': multiplyScalar,
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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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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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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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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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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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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 (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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// 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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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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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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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 (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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// 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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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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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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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 (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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// 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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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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// result
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var cvalues = [];
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var cindex = [];
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var cptr = new Array(bcolumns + 1);
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// c matrix
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var c = 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, bcolumns],
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datatype: dt
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});
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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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// loop b columns
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for (var jb = 0; jb < bcolumns; jb++) {
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// update ptr
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cptr[jb] = cindex.length;
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// indeces in column jb
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var kb0 = bptr[jb];
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var kb1 = bptr[jb + 1];
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// do not process column jb if no data exists
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if (kb1 > kb0) {
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// last row mark processed
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var last = 0;
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// loop a rows
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for (var i = 0; i < arows; i++) {
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// column mark
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var mark = i + 1;
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// C[i, jb]
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var cij;
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// values in b column j
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for (var kb = kb0; kb < kb1; kb++) {
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// row
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var ib = bindex[kb];
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// check value has been initialized
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if (last !== mark) {
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// first value in column jb
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cij = mf(adata[i][ib], bvalues[kb]);
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// update mark
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last = mark;
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}
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else {
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// accumulate value
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cij = af(cij, mf(adata[i][ib], bvalues[kb]));
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}
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}
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// check column has been processed and value != 0
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if (last === mark && !equal(cij, 0)) {
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// push row & value
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cindex.push(i);
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cvalues.push(cij);
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}
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}
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}
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}
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// update ptr
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cptr[bcolumns] = cindex.length;
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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 cvalues.length === 1 ? cvalues[0] : 0;
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// return sparse matrix
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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 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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var adt = a._datatype;
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// validate a matrix
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if (!avalues)
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throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix');
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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 = 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 = new Array(2);
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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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// workspace
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var x = new Array(arows);
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// vector with marks indicating a value x[i] exists in a given column
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var w = new Array(arows);
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// update ptr
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cptr[0] = 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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// check value exists in current j
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if (!w[ia]) {
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// ia is new entry in j
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w[ia] = true;
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// add i to pattern of C
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cindex.push(ia);
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// x(ia) = A
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x[ia] = mf(vbi, avalues[ka]);
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}
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else {
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// i exists in C already
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x[ia] = af(x[ia], mf(vbi, avalues[ka]));
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}
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}
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}
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}
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// copy values from x to column jb of c
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for (var p1 = cindex.length, p = 0; p < p1; p++) {
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// row
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var ic = cindex[p];
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// copy value
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cvalues[p] = x[ic];
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}
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// update ptr
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cptr[1] = cindex.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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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 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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var adt = a._datatype;
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// validate a matrix
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if (!avalues)
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throw new Error('Cannot multiply Pattern only Matrix times Dense Matrix');
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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 = a._size[0];
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var brows = b._size[0];
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var bcolumns = b._size[1];
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|
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// process data types
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var dt = adt && bdt && adt === bdt ? adt : undefined;
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// multiply & add scalar implementations
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var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
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var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
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// result
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var cvalues = [];
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var cindex = [];
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var cptr = new Array(bcolumns + 1);
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// c matrix
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var c = 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, bcolumns],
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datatype: dt
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});
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// workspace
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|
var x = new Array(arows);
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// vector with marks indicating a value x[i] exists in a given column
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|
var w = new Array(arows);
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|
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// loop b columns
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for (var jb = 0; jb < bcolumns; jb++) {
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// update ptr
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cptr[jb] = cindex.length;
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// mark in workspace for current column
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|
var mark = jb + 1;
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// rows in jb
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for (var ib = 0; ib < brows; ib++) {
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// b[ib, jb]
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var vbij = bdata[ib][jb];
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// check b[ib, jb] != 0, avoid loops
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|
if (!equal(vbij, 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
|
|
var ia = aindex[ka];
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|
// check value exists in current j
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|
if (w[ia] !== mark) {
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|
// ia is new entry in j
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|
w[ia] = mark;
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|
// add i to pattern of C
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|
cindex.push(ia);
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|
// x(ia) = A
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|
x[ia] = mf(vbij, avalues[ka]);
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}
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else {
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|
// i exists in C already
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|
x[ia] = af(x[ia], mf(vbij, avalues[ka]));
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}
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|
}
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|
}
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}
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// copy values from x to column jb of c
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for (var p0 = cptr[jb], p1 = cindex.length, p = p0; p < p1; p++) {
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// row
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var ic = cindex[p];
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// copy value
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|
cvalues[p] = x[ic];
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|
}
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}
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|
// update ptr
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|
cptr[bcolumns] = cindex.length;
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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 cvalues.length === 1 ? cvalues[0] : 0;
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|
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|
// return sparse matrix
|
|
return c;
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|
};
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|
|
|
/**
|
|
* C = A * B
|
|
*
|
|
* @param {Matrix} a SparseMatrix (MxN)
|
|
* @param {Matrix} b SparseMatrix (NxC)
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|
*
|
|
* @return {Matrix} SparseMatrix (MxC)
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|
*/
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|
var _multiplySparseMatrixSparseMatrix = function (a, b) {
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// 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;
|
|
// process data types
|
|
var dt = adt && bdt && adt === bdt ? adt : undefined;
|
|
// multiply & add scalar implementations
|
|
var mf = dt ? multiplyScalar.signatures[dt + ',' + dt] || multiplyScalar : multiplyScalar;
|
|
var af = dt ? addScalar.signatures[dt + ',' + dt] || addScalar : addScalar;
|
|
// rows & columns
|
|
var arows = a._size[0];
|
|
var bcolumns = b._size[1];
|
|
// flag indicating both matrices (a & b) contain data
|
|
var values = avalues && bvalues;
|
|
// result
|
|
var cvalues = values ? [] : undefined;
|
|
var cindex = [];
|
|
var cptr = new Array(bcolumns + 1);
|
|
// c matrix
|
|
var c = new SparseMatrix({
|
|
values : cvalues,
|
|
index: cindex,
|
|
ptr: cptr,
|
|
size: [arows, bcolumns],
|
|
datatype: dt
|
|
});
|
|
// workspace
|
|
var x = values ? new Array(arows) : undefined;
|
|
// vector with marks indicating a value x[i] exists in a given column
|
|
var w = new Array(arows);
|
|
// 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;
|
|
|
|
// check we need to squeeze the result into a scalar
|
|
if (arows === 1 && bcolumns === 1 && values)
|
|
return cvalues.length === 1 ? cvalues[0] : 0;
|
|
|
|
// return sparse matrix
|
|
return c;
|
|
};
|
|
|
|
return multiply;
|
|
}
|
|
|
|
exports.name = 'multiply';
|
|
exports.factory = factory;
|