// test multiply var assert = require('assert'), math = require('../../../index'), approx = require('../../../tools/approx'), market = require('../../../tools/matrixmarket'), multiply = math.multiply, divide = math.divide, matrix = math.matrix, complex = math.complex, bignumber = math.bignumber, i = math.i, unit = math.unit; describe('multiply', function() { describe('Scalar', function () { it('should multiply two numbers correctly', function() { approx.equal(multiply(2, 3), 6); approx.equal(multiply(-2, 3), -6); approx.equal(multiply(-2, -3), 6); approx.equal(multiply(5, 0), 0); approx.equal(multiply(0, 5), 0); approx.deepEqual(multiply(0, Infinity), NaN); approx.deepEqual(multiply(2, Infinity), Infinity); approx.deepEqual(multiply(-2, Infinity), -Infinity); }); it('should multiply booleans', function() { assert.equal(multiply(true, true), 1); assert.equal(multiply(true, false), 0); assert.equal(multiply(false, true), 0); assert.equal(multiply(false, false), 0); }); it('should multiply mixed numbers and booleans', function() { assert.equal(multiply(2, true), 2); assert.equal(multiply(2, false), 0); assert.equal(multiply(true, 2), 2); assert.equal(multiply(false, 2), 0); }); it('should multiply numbers and null', function () { assert.equal(multiply(1, null), 0); assert.equal(multiply(null, 1), 0); }); it('should multiply bignumbers', function() { assert.deepEqual(multiply(bignumber(1.5), bignumber(0.2)), bignumber(0.3)); assert.deepEqual(multiply(bignumber('1.3e5000'), bignumber('2')), bignumber('2.6e5000')); }); it('should multiply mixed numbers and bignumbers', function() { assert.deepEqual(multiply(bignumber(1.5), 0.2), bignumber(0.3)); assert.deepEqual(multiply(1.5, bignumber(0.2)), bignumber(0.3)); assert.deepEqual(multiply(bignumber('1.3e5000'), 2), bignumber('2.6e5000')); assert.throws(function () {multiply(1/3, bignumber(1).div(3));}, /Cannot implicitly convert a number with >15 significant digits to BigNumber/); assert.throws(function () {multiply(bignumber(1).div(3), 1/3);}, /Cannot implicitly convert a number with >15 significant digits to BigNumber/); }); it('should multiply mixed booleans and bignumbers', function() { assert.deepEqual(multiply(bignumber(0.3), true), bignumber(0.3)); assert.deepEqual(multiply(bignumber(0.3), false), bignumber(0)); assert.deepEqual(multiply(false, bignumber('2')), bignumber(0)); assert.deepEqual(multiply(true, bignumber('2')), bignumber(2)); }); it('should multiply two complex numbers correctly', function() { approx.deepEqual(multiply(complex(2, 3), 2), complex(4, 6)); approx.deepEqual(multiply(complex(2, -3), -2), complex(-4, 6)); approx.deepEqual(multiply(complex(2, -3), 2), complex(4, -6)); approx.deepEqual(multiply(complex(-2, 3), 2), complex(-4, 6)); approx.deepEqual(multiply(complex(-2, -3), 2), complex(-4, -6)); approx.deepEqual(multiply(2, complex(2, 3)), complex(4, 6)); approx.deepEqual(multiply(i, complex(2, 3)), complex(-3, 2)); approx.deepEqual(multiply(complex(0, 1), complex(2, 3)), complex(-3, 2)); approx.deepEqual(multiply(complex(1, 1), complex(2, 3)), complex(-1, 5)); approx.deepEqual(multiply(complex(2, 3), complex(1, 1)), complex(-1, 5)); approx.deepEqual(multiply(complex(2, 3), complex(2, 3)), complex(-5, 12)); approx.deepEqual(divide(complex(-5, 12), complex(2, 3)), complex(2, 3)); approx.deepEqual(multiply(complex(2, 3), 0), complex(0, 0)); approx.deepEqual(multiply(complex(0, 3), complex(0, -4)), complex(12, 0)); approx.deepEqual(multiply(multiply(3, i), multiply(-4, i)), complex(12, 0)); approx.deepEqual(multiply(math.i, Infinity), complex(NaN, Infinity)); approx.deepEqual(multiply(Infinity, math.i), complex(NaN, Infinity)); approx.deepEqual(multiply(complex(2,0), complex(0,2)), complex(0, 4)); approx.deepEqual(multiply(complex(0,2), complex(0,2)), -4); approx.deepEqual(multiply(complex(2,2), complex(0,2)), complex(-4, 4)); approx.deepEqual(multiply(complex(2,0), complex(2,2)), complex(4, 4)); approx.deepEqual(multiply(complex(0,2), complex(2,2)), complex(-4, 4)); approx.deepEqual(multiply(complex(2,2), complex(2,2)), complex(0, 8)); approx.deepEqual(multiply(complex(2,0), complex(2,0)), 4); approx.deepEqual(multiply(complex(0,2), complex(2,0)), complex(0, 4)); approx.deepEqual(multiply(complex(2,2), complex(2,0)), complex(4, 4)); approx.deepEqual(multiply(complex(2, 3), complex(4, 5)), complex(-7, 22)); approx.deepEqual(multiply(complex(2, 3), complex(4, -5)), complex(23, 2)); approx.deepEqual(multiply(complex(2, 3), complex(-4, 5)), complex(-23, -2)); approx.deepEqual(multiply(complex(2, 3), complex(-4, -5)), complex(7, -22)); approx.deepEqual(multiply(complex(2, -3), complex(4, 5)), complex(23, -2)); approx.deepEqual(multiply(complex(2, -3), complex(4, -5)), complex(-7, -22)); approx.deepEqual(multiply(complex(2, -3), complex(-4, 5)), complex(7, 22)); approx.deepEqual(multiply(complex(2, -3), complex(-4, -5)), complex(-23, 2)); approx.deepEqual(multiply(complex(-2, 3), complex(4, 5)), complex(-23, 2)); approx.deepEqual(multiply(complex(-2, 3), complex(4, -5)), complex(7, 22)); approx.deepEqual(multiply(complex(-2, 3), complex(-4, 5)), complex(-7, -22)); approx.deepEqual(multiply(complex(-2, 3), complex(-4, -5)), complex(23, -2)); approx.deepEqual(multiply(complex(-2, -3), complex(4, 5)), complex(7, -22)); approx.deepEqual(multiply(complex(-2, -3), complex(4, -5)), complex(-23, -2)); approx.deepEqual(multiply(complex(-2, -3), complex(-4, 5)), complex(23, 2)); approx.deepEqual(multiply(complex(-2, -3), complex(-4, -5)), complex(-7, 22)); }); it('should multiply mixed complex numbers and numbers', function() { assert.deepEqual(multiply(math.complex(6, -4), 2), math.complex(12, -8)); assert.deepEqual(multiply(2, math.complex(2, 4)), math.complex(4, 8)); }); it('should multiply mixed complex numbers and big numbers', function() { assert.deepEqual(multiply(math.complex(6, -4), math.bignumber(2)), math.complex(12, -8)); assert.deepEqual(multiply(math.bignumber(2), math.complex(2, 4)), math.complex(4, 8)); }); it('should multiply two fractions', function() { var a = math.fraction(1,4); assert.equal(multiply(a, math.fraction(1,2)).toString(), '0.125'); assert.equal(a.toString(), '0.25'); assert.equal(multiply(math.fraction(2), math.fraction(1,3)).toString(), '0.(6)'); }); it('should multiply mixed fractions and numbers', function() { assert.deepEqual(multiply(2, math.fraction(1,3)), math.fraction(2,3)); assert.deepEqual(multiply(math.fraction(1,3), 2), math.fraction(2,3)); }); it('should multiply a number and a unit correctly', function() { assert.equal(multiply(2, unit('5 mm')).toString(), '10 mm'); assert.equal(multiply(2, unit('5 mm')).toString(), '10 mm'); assert.equal(multiply(10, unit('celsius')).toString(), '10 celsius'); assert.equal(multiply(unit('5 mm'), 2).toString(), '10 mm'); assert.equal(multiply(unit('5 mm'), 0).toString(), '0 mm'); assert.equal(multiply(unit('celsius'), 10).toString(), '10 celsius'); assert.equal(multiply(unit(math.fraction(1,4), 'm'), 3).toString(), '3/4 m'); assert.equal(multiply(3, unit(math.fraction(1,4), 'm')).toString(), '3/4 m'); assert.equal(multiply(math.fraction(1,4), unit(3, 'm')).toString(), '3/4 m'); assert.equal(multiply(unit(3, 'm'), math.fraction(1,4)).toString(), '3/4 m'); assert.equal(multiply(unit(math.complex(9, 8), 'm'), 2).toString(), '(18 + 16i) m'); assert.equal(math.format(multiply(unit(math.complex(2, 3), 'g'), math.complex(4, 5)), 14), '(-7 + 22i) g'); }); it('should multiply a number and a unit without value correctly', function() { assert.equal(multiply(2, unit('mm')).toString(), '2 mm'); assert.equal(multiply(2, unit('km')).toString(), '2 km'); assert.equal(multiply(2, unit('inch')).toString(), '2 inch'); assert.equal(multiply(unit('mm'), 2).toString(), '2 mm'); assert.equal(multiply(unit('km'), 2).toString(), '2 km'); assert.equal(multiply(unit('inch'), 2).toString(), '2 inch'); }); it('should multiply two units correctly', function() { assert.equal(multiply(unit('2 m'), unit('4 m')).toString(), '8 m^2'); assert.equal(multiply(unit('2 ft'), unit('4 ft')).toString(), '8 ft^2'); assert.equal(multiply(unit('65 mi/h'), unit('2 h')).to('mi').toString(), '130 mi'); assert.equal(multiply(unit('2 L'), unit('1 s^-1')).toString(), '2 L / s'); assert.equal(multiply(unit('2 m/s'), unit('0.5 s/m')).toString(), '1'); assert.equal(multiply(unit(math.complex(3,-4), 'N'), unit(math.complex(7,-2), 'm')).toString(), '(13 - 34i) J'); }); it('should multiply valueless units correctly', function() { assert.equal(multiply(unit('m'), unit('4 m')).toString(), '4 m^2'); assert.equal(multiply(unit('ft'), unit('4 ft')).format(5), '4 ft^2'); assert.equal(multiply(unit('65 mi/h'), unit('h')).to('mi').toString(), '65 mi'); assert.equal(multiply(unit('2 L'), unit('s^-1')).toString(), '2 L / s'); assert.equal(multiply(unit('m/s'), unit('h/m')).toString(), '(m h) / (s m)'); }); // TODO: cleanup once decided to not downgrade BigNumber to number it.skip('should multiply a bignumber and a unit correctly', function() { assert.equal(multiply(bignumber(2), unit('5 mm')).toString(), '10 mm'); assert.equal(multiply(bignumber(2), unit('5 mm')).toString(), '10 mm'); assert.equal(multiply(unit('5 mm'), bignumber(2)).toString(), '10 mm'); assert.equal(multiply(unit('5 mm'), bignumber(0)).toString(), '0 m'); }); // TODO: cleanup once decided to not downgrade BigNumber to number it.skip('should multiply a bignumber and a unit without value correctly', function() { assert.equal(multiply(bignumber(2), unit('mm')).toString(), '2 mm'); assert.equal(multiply(bignumber(2), unit('km')).toString(), '2 km'); assert.equal(multiply(bignumber(2), unit('inch')).toString(), '2 inch'); assert.equal(multiply(unit('mm'), bignumber(2)).toString(), '2 mm'); assert.equal(multiply(unit('km'), bignumber(2)).toString(), '2 km'); assert.equal(multiply(unit('inch'), bignumber(2)).toString(), '2 inch'); }); it('should throw an error in case of unit non-numeric argument', function() { // Multiplying two units is supported now //assert.throws(function () {multiply(math.unit('5cm'), math.unit('4cm'));}, /TypeError: Unexpected type/); // Complex units are supported now //assert.throws(function () {multiply(math.unit('5cm'), math.complex('2+3i'));}, /TypeError: Unexpected type/); //assert.throws(function () {multiply(math.complex('2+3i'), math.unit('5cm'));}, /TypeError: Unexpected type/); }); it('should throw an error if used with strings', function() { assert.throws(function () {multiply("hello", "world");}); assert.throws(function () {multiply("hello", 2);}); }); }); it('should multiply mixed array and matrix', function () { var a = [[1, 2], [3, 4]]; var b = [[2, 0], [0, 2]]; approx.deepEqual(multiply(a, matrix(b)), matrix([[2, 4], [6, 8]])); approx.deepEqual(multiply(matrix(a), b), matrix([[2, 4], [6, 8]])); // test with vectors, returning a scalar var c = [1, 2, 3]; var d = [4, 5, 6]; assert.strictEqual(multiply(c, matrix(d)), 32); assert.strictEqual(multiply(matrix(c), d), 32); }); describe('squeeze', function () { it ('should squeeze scalar results of matrix * matrix', function () { var a = [[1, 2, 3]]; var b = [[4], [5], [6]]; assert.strictEqual(multiply(a, b), 32); }); it ('should squeeze scalar results of vector * matrix', function () { var a = [1, 2, 3]; var b = [[4], [5], [6]]; assert.strictEqual(multiply(a, b), 32); }); it ('should squeeze scalar results of matrix * vector', function () { var a = [[1, 2, 3]]; var b = [4, 5, 6]; assert.strictEqual(multiply(a, b), 32); }); }); it('should throw an error when multiplying matrices with incompatible sizes', function() { // vector * vector assert.throws(function () {multiply([1,1], [1,1, 1]);}); // matrix * matrix assert.throws(function () {multiply([[1,1]], [[1,1]]);}); assert.throws(function () {multiply([[1,1]], [[1,1], [1,1], [1,1]]);}); // matrix * vector assert.throws(function () {multiply([[1,1], [1,1]], [1,1,1]);}); // vector * matrix assert.throws(function () {multiply([1,1,1], [[1,1], [1,1]]);}); }); it('should throw an error when multiplying multi dimensional matrices', function() { assert.throws(function () {multiply([[[1]]], [1]);}); assert.throws(function () {multiply([[[1]]], [[1]]);}); assert.throws(function () {multiply([1], [[[1]]]);}); assert.throws(function () {multiply([[1]], [[[1]]]);}); }); it('should throw an error in case of invalid number of arguments', function() { assert.throws(function () {multiply(1);}, /TypeError: Too few arguments/); assert.throws(function () {multiply(1, 2, 3);}, /TypeError: Too many arguments/); }); describe('Vector', function () { it('should multiply vectors correctly (dot product)', function () { var a = [1, 2, 3]; var b = [4, 5, 6]; approx.deepEqual(multiply(a, b), 32); approx.deepEqual(multiply(matrix(a), matrix(b)), 32); }); it('should multiply row vector x column vector', function () { var v = [[1, 2, 3, 0, 0, 5, 6]]; var r = multiply(v, [[3], [4], [6], [0], [1], [2], [0]]); assert.equal(r, 39); r = multiply(v, math.matrix([[3], [4], [6], [0], [1], [2], [0]], 'dense')); assert.equal(r, 39); r = multiply(v, math.matrix([[3], [4], [6], [0], [1], [2], [0]], 'sparse')); assert.equal(r, 39); }); it('should multiply dense row vector x column vector', function () { var v = math.matrix([[1, 2, 3, 0, 0, 5, 6]], 'dense'); var r = multiply(v, [[3], [4], [6], [0], [1], [2], [0]]); assert.equal(r, 39); r = multiply(v, math.matrix([[3], [4], [6], [0], [1], [2], [0]], 'dense')); assert.equal(r, 39); r = multiply(v, math.matrix([[3], [4], [6], [0], [1], [2], [0]], 'sparse')); assert.equal(r, 39); }); it('should throw an error when multiplying empty vectors', function () { assert.throws(function () {multiply([], []);}, /Cannot multiply two empty vectors/); }); it('should multiply a vector with a matrix correctly', function () { var a = [1, 2, 3]; var b = [ [8, 1, 6], [3, 5, 7], [4, 9, 2] ]; approx.deepEqual(multiply(a, b), [26, 38, 26]); approx.deepEqual(multiply(b, a), [28, 34, 28]); approx.deepEqual(multiply(matrix(a), matrix(b)), matrix([26, 38, 26])); approx.deepEqual(multiply(matrix(b), matrix(a)), matrix([28, 34, 28])); }); }); describe('Dense Matrix', function () { it('should multiply matrix x scalar', function() { var m = math.matrix([ [2, 0], [4, 0] ]); var r = multiply(m, 3); assert.deepEqual(r._size, m._size); assert.deepEqual(r._data, [[6, 0], [12, 0]]); r = multiply(m, math.complex(3, 3)); assert.deepEqual(r._size, m._size); assert.deepEqual(r._data, [[math.complex(6, 6), math.complex(0, 0)], [math.complex(12, 12), math.complex(0, 0)]]); r = multiply(m, math.bignumber(3)); assert.deepEqual(r._size, m._size); assert.deepEqual(r._data, [[math.bignumber(6), math.bignumber(0)], [math.bignumber(12), math.bignumber(0)]]); r = multiply(m, true); assert.deepEqual(r._size, m._size); assert.deepEqual(r._data, [[2, 0], [4, 0]]); r = multiply(m, false); assert.deepEqual(r._size, m._size); assert.deepEqual(r._data, [[0, 0], [0, 0]]); }); it('should multiply matrix x matrix with zeros', function() { var m = math.matrix([ [2, 0], [4, 0] ]); var r = multiply(m, math.matrix([ [2, 0], [4, 0] ])); assert.deepEqual( r.valueOf(), [ [4, 0], [8, 0] ]); r = multiply(m, math.matrix([ [2, 0], [4, 0] ], 'sparse')); assert.deepEqual( r.valueOf(), [ [4, 0], [8, 0] ]); }); it('should multiply matrix x matrix', function() { var m = math.matrix([[1, 2], [3, 4]], 'dense'); var r = multiply(m, math.matrix([[5, 6], [7, 8]], 'sparse')); assert.deepEqual( r.valueOf(), [ [19, 22], [43, 50] ]); r = multiply(m, math.matrix([[5, 6], [7, 8]], 'dense')); assert.deepEqual( r.valueOf(), [ [19, 22], [43, 50] ]); }); it('should multiply matrix x matrix, number datatype', function() { var m1 = math.matrix([[1, 2], [3, 4]], 'dense', 'number'); var m2 = math.matrix([[5, 6], [7, 8]], 'dense', 'number'); var r = multiply(m1, m2); assert(r.datatype() === 'number'); assert.deepEqual( r.valueOf(), [ [19, 22], [43, 50] ]); }); it('should multiply matrix x array', function() { var m = math.matrix([ [2, 0], [4, 0] ]); var r = multiply( m, [ [2, 0], [4, 0] ]); assert.deepEqual( r.valueOf(), [ [4, 0], [8, 0] ]); r = multiply( m, [ [2, 0, 1], [4, 0, 1] ]); assert.deepEqual( r.valueOf(), [ [4, 0, 2], [8, 0, 4] ]); }); it('should multiply matrix x vector array', function() { var m = math.matrix([ [2, 0], [4, 0] ]); var r = multiply( m, [ [2], [4] ]); assert.deepEqual( r.valueOf(), [ [4], [8] ]); }); it ('should squeeze scalar results of matrix * matrix', function () { var a = math.matrix( [ [1, 2, 3] ]); var b = math.matrix( [ [4], [5], [6] ]); assert.strictEqual(multiply(a, b), 32); }); it ('should squeeze scalar results of matrix * vector', function () { var a = math.matrix( [ [1, 2, 3] ]); var b = [4, 5, 6]; assert.strictEqual(multiply(a, b), 32); }); it('should throw an error when multiplying matrices with incompatible sizes', function() { // vector * vector assert.throws(function () {multiply(math.matrix([1,1], 'dense'), [1, 1, 1]);}); // matrix * matrix assert.throws(function () {multiply(math.matrix([[1,1]], 'dense'), [[1,1]]);}); assert.throws(function () {multiply(math.matrix([[1,1]], 'dense'), [[1,1], [1,1], [1,1]]);}); // matrix * vector assert.throws(function () {multiply(math.matrix([[1,1], [1,1]], 'dense'), [1,1,1]);}); // vector * matrix assert.throws(function () {multiply(math.matrix([1,1,1], 'dense'), [[1,1], [1,1]]);}); }); it('should multiply triangular matrices', function () { var l = [ [1, 0, 0, 0], [-0.5, 1, 0, 0], [0, -0.7, 1, 0], [0.0666667, -0.4, -0.5714286, 1] ]; var u = [ [240, -2700, 6480, -4200], [0, -150, 540, -420], [0, 0, -42, 56], [0, 0, 0, 4] ]; var r = multiply(l, u); approx.deepEqual( r.valueOf(), [ [240, -2700, 6480, -4200], [-120, 1200, -2700, 1680], [0, 105, -420, 350], [16, -120, 240, -140] ]); }); var a = matrix([[1,2],[3,4]]); var b = matrix([[5,6],[7,8]]); var c = matrix([[5],[6]]); var d = matrix([[5,6]]); it('should perform element-wise multiplication if multiplying a matrix and a number', function() { approx.deepEqual(multiply(a, 3), matrix([[3,6],[9,12]])); approx.deepEqual(multiply(3, a), matrix([[3,6],[9,12]])); }); it('should perform matrix multiplication', function () { approx.deepEqual(multiply(a, b), matrix([[19,22],[43,50]])); approx.deepEqual(multiply(a, c), matrix([[17],[39]])); approx.deepEqual(multiply(d, a), matrix([[23,34]])); approx.deepEqual(multiply(d, b), matrix([[67,78]])); approx.deepEqual(multiply(d, c), 61); approx.deepEqual(multiply([[1,2],[3,4]], [[5,6],[7,8]]), [[19,22],[43,50]]); approx.deepEqual(multiply([1,2,3,4], 2), [2, 4, 6, 8]); approx.deepEqual(multiply(matrix([1,2,3,4]), 2), matrix([2, 4, 6, 8])); }); }); describe('Sparse Matrix', function () { it('should multiply matrix x scalar', function() { var m = math.matrix([[2, 0], [4, 0]], 'sparse'); var r = multiply(m, 3); assert.deepEqual(r._size, m._size); assert.deepEqual(r._values, [6, 12]); assert.deepEqual(r._index, m._index); assert.deepEqual(r._ptr, m._ptr); r = multiply(m, math.complex(3, 3)); assert.deepEqual(r._size, m._size); assert.deepEqual(r._values, [math.complex(6, 6), math.complex(12, 12)]); assert.deepEqual(r._index, m._index); assert.deepEqual(r._ptr, m._ptr); r = multiply(m, math.bignumber(3)); assert.deepEqual(r._size, m._size); assert.deepEqual(r._values, [math.bignumber(6), math.bignumber(12)]); assert.deepEqual(r._index, m._index); assert.deepEqual(r._ptr, m._ptr); r = multiply(m, true); assert.deepEqual(r._size, m._size); assert.deepEqual(r._values, [2, 4]); assert.deepEqual(r._index, m._index); assert.deepEqual(r._ptr, m._ptr); r = multiply(m, false); assert.deepEqual(r._size, m._size); assert.deepEqual(r._values, []); assert.deepEqual(r._index, []); assert.deepEqual(r._ptr, [0, 0, 0]); }); it('should multiply matrix x matrix with zeros', function() { var m = math.matrix([[2, 0], [4, 0]], 'sparse'); var r = multiply(m, math.matrix([[2, 0], [4, 0]], 'sparse')); assert.deepEqual( r.valueOf(), [ [4, 0], [8, 0] ]); r = multiply(m, math.matrix([[2, 0], [4, 0]], 'dense')); assert.deepEqual( r.valueOf(), [ [4, 0], [8, 0] ]); }); it('should multiply matrix x matrix', function() { var m = math.matrix([[1, 2], [3, 4]], 'sparse'); var r = multiply(m, math.matrix([[5, 6], [7, 8]], 'sparse')); assert.deepEqual( r.valueOf(), [ [19, 22], [43, 50] ]); r = multiply(m, math.matrix([[5, 6], [7, 8]], 'dense')); assert.deepEqual( r.valueOf(), [ [19, 22], [43, 50] ]); }); it('should multiply matrix x matrix, number datatype', function() { var m1 = math.matrix([[1, 2], [3, 4]], 'sparse', 'number'); var m2 = math.matrix([[5, 6], [7, 8]], 'sparse', 'number'); var r = multiply(m1, m2); assert(r.datatype() === 'number'); assert.deepEqual( r.valueOf(), [ [19, 22], [43, 50] ]); }); it('should multiply matrix x array', function() { var m = math.matrix([[2, 0], [4, 0]], 'sparse'); var r = multiply(m, [ [2, 0], [4, 0] ]); assert.deepEqual( r.valueOf(), [ [4, 0], [8, 0] ]); r = multiply(m, [ [2, 0, 1], [4, 0, 1] ]); assert.deepEqual( r.valueOf(), [ [4, 0, 2], [8, 0, 4] ]); }); it('should multiply matrix x vector array', function() { var m = math.matrix([[2, 0], [4, 0]], 'sparse'); var r = multiply(m, [ [2], [4] ]); assert.deepEqual( r.valueOf(), [ [4], [8] ]); }); it ('should squeeze scalar results of matrix * matrix', function () { var a = math.matrix([[1, 2, 3]], 'sparse'); var b = math.matrix([[4], [5], [6]], 'sparse'); assert.strictEqual(multiply(a, b), 32); }); it ('should squeeze scalar results of matrix * vector', function () { var a = math.matrix([[1, 2, 3]], 'sparse'); var b = [4, 5, 6]; assert.strictEqual(multiply(a, b), 32); }); it('should throw an error when multiplying matrices with incompatible sizes', function() { // vector * vector assert.throws(function () {math.matrix([1,1], 'sparse').multiply([1, 1, 1]);}); // matrix * matrix assert.throws(function () {math.matrix([[1,1]], 'sparse').multiply([[1,1]]);}); assert.throws(function () {math.matrix([[1,1]], 'sparse').multiply([[1,1], [1,1], [1,1]]);}); // matrix * vector assert.throws(function () {math.matrix([[1,1], [1,1]], 'sparse').multiply([1,1,1]);}); // vector * matrix assert.throws(function () {math.matrix([1,1,1], 'sparse').multiply([[1,1], [1,1]]);}); }); it('should multiply triangular matrices', function () { var l = math.matrix([ [1, 0, 0, 0], [-0.5, 1, 0, 0], [0, -0.7, 1, 0], [0.0666667, -0.4, -0.5714286, 1] ], 'sparse'); var u = math.matrix([ [240, -2700, 6480, -4200], [0, -150, 540, -420], [0, 0, -42, 56], [0, 0, 0, 4] ], 'sparse'); var r = multiply(l, u); assert(r.storage(), 'sparse'); approx.deepEqual( r.valueOf(), [ [240, -2700, 6480, -4200], [-120, 1200, -2700, 1680], [0, 105, -420, 350], [16, -120, 240, -140] ]); }); var a = matrix([[1,2],[3,4]], 'sparse'); var b = matrix([[5,6],[7,8]], 'sparse'); var c = matrix([[5],[6]], 'sparse'); var d = matrix([[5,6]], 'sparse'); it('should perform element-wise multiplication if multiplying a matrix and a number', function() { approx.deepEqual(multiply(a, 3), matrix([[3,6],[9,12]], 'sparse')); approx.deepEqual(multiply(3, a), matrix([[3,6],[9,12]], 'sparse')); }); it('should perform matrix multiplication', function () { approx.deepEqual(multiply(a, b), matrix([[19,22],[43,50]], 'sparse')); approx.deepEqual(multiply(a, c), matrix([[17],[39]], 'sparse')); approx.deepEqual(multiply(d, a), matrix([[23,34]], 'sparse')); approx.deepEqual(multiply(d, b), matrix([[67,78]], 'sparse')); approx.deepEqual(multiply(d, c), 61); }); it('should multiply two pattern matrices correctly', function() { var a = new math.type.SparseMatrix({ values: undefined, index: [0, 1, 2, 0], ptr: [0, 2, 3, 4], size: [3, 3] }); var b = new math.type.SparseMatrix({ values: undefined, index: [0, 1, 2, 1], ptr: [0, 3, 3, 4], size: [3, 3] }); var c = multiply(a, b); assert.deepEqual( c.valueOf(), [ [1, 0, 0], [1, 0, 0], [1, 0, 1] ]); }); it('should multiply pattern and value matrices correctly', function() { var a = new math.type.SparseMatrix({ values: undefined, index: [0, 1, 2, 0], ptr: [0, 2, 3, 4], size: [3, 3] }); var b = new math.type.SparseMatrix({ values: [1, 2, 3, 4], index: [0, 1, 2, 1], ptr: [0, 3, 3, 4], size: [3, 3] }); var c = multiply(a, b); assert.deepEqual( c.valueOf(), [ [1, 0, 0], [1, 0, 0], [1, 0, 1] ]); }); it('should multiply value and pattern matrices correctly', function() { var a = new math.type.SparseMatrix({ values: [1, 2, 3, 4], index: [0, 1, 2, 0], ptr: [0, 2, 3, 4], size: [3, 3] }); var b = new math.type.SparseMatrix({ values: undefined, index: [0, 1, 2, 1], ptr: [0, 3, 3, 4], size: [3, 3] }); var c = multiply(a, b); assert.deepEqual( c.valueOf(), [ [1, 0, 0], [1, 0, 0], [1, 0, 1] ]); }); }); describe('Matrix Market', function () { it('should multiply matrix x matrix 1220 x 1220, Matrix Market, sparse x sparse', function (done) { // import matrix market.import('tools/matrices/fpga_dcop_01.tar.gz', ['fpga_dcop_01/fpga_dcop_01.mtx']) .then(function (matrices) { // matrix var m = matrices[0]; // multiply matrices, used to compare performance in different implementations math.multiply(m, m); // indicate test has completed done(); }) .fail(function (error) { // indicate test has completed done(error); }); }); }); it('should LaTeX mutliply', function () { var expression = math.parse('multiply(2,3)'); assert.equal(expression.toTex(), '\\left(2\\cdot3\\right)'); }); });