/**
* @license
* Copyright The Closure Library Authors.
* SPDX-License-Identifier: Apache-2.0
*/
goog.module('goog.math.MatrixTest');
goog.setTestOnly();
const Matrix = goog.require('goog.math.Matrix');
const testSuite = goog.require('goog.testing.testSuite');
testSuite({
testConstuctorWithGoodArray() {
const a1 = [[1, 2], [2, 3], [4, 5]];
const m1 = new Matrix(a1);
assertArrayEquals('1. Internal array should be the same', m1.toArray(), a1);
assertEquals(3, m1.getSize().height);
assertEquals(2, m1.getSize().width);
const a2 = [[-61, 45, 123], [11112, 343, 1235]];
const m2 = new Matrix(a2);
assertArrayEquals('2. Internal array should be the same', m2.toArray(), a2);
assertEquals(2, m2.getSize().height);
assertEquals(3, m2.getSize().width);
const a3 = [[1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4]];
const m3 = new Matrix(a3);
assertArrayEquals('3. Internal array should be the same', m3.toArray(), a3);
assertEquals(4, m3.getSize().height);
assertEquals(4, m3.getSize().width);
},
testConstructorWithBadArray() {
assertThrows('1. All arrays should be of equal length', () => {
new Matrix([[1, 2, 3], [1, 2], [1]]);
});
assertThrows('2. All arrays should be of equal length', () => {
new Matrix([[1, 2], [1, 2], [1, 2, 3, 4]]);
});
assertThrows('3. Arrays should contain only numeric values', () => {
new Matrix([[1, 2], [1, 2], [1, 'a']]);
});
assertThrows('4. Arrays should contain only numeric values', () => {
new Matrix([[1, 2], [1, 2], [1, {a: 3}]]);
});
assertThrows('5. Arrays should contain only numeric values', () => {
new Matrix([[1, 2], [1, 2], [1, [1, 2, 3]]]);
});
},
testConstructorWithGoodNumbers() {
const m1 = new Matrix(2, 2);
assertEquals('Height should be 2', 2, m1.getSize().height);
assertEquals('Width should be 2', 2, m1.getSize().width);
const m2 = new Matrix(4, 2);
assertEquals('Height should be 4', 4, m2.getSize().height);
assertEquals('Width should be 2', 2, m2.getSize().width);
const m3 = new Matrix(4, 6);
assertEquals('Height should be 4', 4, m3.getSize().height);
assertEquals('Width should be 6', 6, m3.getSize().width);
},
testConstructorWithBadNumbers() {
assertThrows('1. Negative argument should have errored', () => {
new Matrix(-4, 6);
});
assertThrows('2. Negative argument should have errored', () => {
new Matrix(4, -6);
});
assertThrows('3. Zero argument should have errored', () => {
new Matrix(4, 0);
});
assertThrows('4. Zero argument should have errored', () => {
new Matrix(0, 1);
});
},
testConstructorWithMatrix() {
const a1 = [[1, 2], [2, 3], [4, 5]];
const m1 = new Matrix(a1);
const m2 = new Matrix(m1);
assertArrayEquals(
'Internal arrays should be the same', m1.toArray(), m2.toArray());
assertNotEquals(
'Should be different objects', goog.getUid(m1), goog.getUid(m2));
},
testCreateIdentityMatrix() {
const m1 = Matrix.createIdentityMatrix(3);
assertArrayEquals([[1, 0, 0], [0, 1, 0], [0, 0, 1]], m1.toArray());
const m2 = Matrix.createIdentityMatrix(4);
assertArrayEquals(
[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]], m2.toArray());
},
testIsValidArrayWithGoodArrays() {
const fn = Matrix.isValidArray;
assertTrue('2x2 array should be fine', fn([[1, 2], [3, 5]]));
assertTrue('3x2 array should be fine', fn([[1, 2, 3], [3, 5, 6]]));
assertTrue(
'3x3 array should be fine', fn([[1, 2, 3], [3, 5, 6], [10, 10, 10]]));
assertTrue('[[1]] should be fine', fn([[1]]));
assertTrue('1D array should work', fn([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]));
assertTrue(
'Negs and decimals should be ok',
fn([[0], [-4], [-10], [1.2345], [123.53]]));
assertTrue(
'Hex, Es and decimals are ok', fn([[0x100, 10E-2], [1.213, 213]]));
},
testIsValidArrayWithBadArrays() {
const fn = Matrix.isValidArray;
assertFalse('Arrays should have same size', fn([[1, 2], [3]]));
assertFalse('Arrays should have same size 2', fn([[1, 2], [3, 4, 5]]));
assertFalse('2D arrays are ok', fn([[1, 2], [3, 4], []]));
assertFalse('Values should be numeric', fn([[1, 2], [3, 'a']]));
assertFalse('Values can not be strings', fn([['bah'], ['foo']]));
assertFalse('Flat array not supported', fn([1, 2, 3, 4, 5]));
},
testForEach() {
const m = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
let count = 0;
let sum = 0;
let xs = '';
let ys = '';
Matrix.forEach(m, (val, x, y) => {
count++;
sum += val;
xs += x;
ys += y;
});
assertEquals('forEach should have visited every item', 9, count);
assertEquals('forEach should have summed all values', 45, sum);
assertEquals('Xs should have been visited in order', '000111222', xs);
assertEquals('Ys should have been visited sequentially', '012012012', ys);
},
testMap() {
const m1 = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
const m2 = Matrix.map(m1, (val, x, y) => val + 1);
assertArrayEquals([[2, 3, 4], [5, 6, 7], [8, 9, 10]], m2.toArray());
},
testSetValueAt() {
const m = new Matrix(3, 3);
for (let x = 0; x < 3; x++) {
for (let y = 0; y < 3; y++) {
m.setValueAt(x, y, 3 * x - y);
}
}
assertArrayEquals([[0, -1, -2], [3, 2, 1], [6, 5, 4]], m.toArray());
},
testGetValueAt() {
const m = new Matrix([[0, -1, -2], [3, 2, 1], [6, 5, 4]]);
for (let x = 0; x < 3; x++) {
for (let y = 0; y < 3; y++) {
assertEquals(
'Value at (x, y) should equal 3x - y', 3 * x - y,
m.getValueAt(x, y));
}
}
assertNull('Out of bounds value should be null', m.getValueAt(-1, 2));
assertNull('Out of bounds value should be null', m.getValueAt(-1, 0));
assertNull('Out of bounds value should be null', m.getValueAt(0, 4));
},
testSum1() {
const m1 = new Matrix([[1, 1, 1], [2, 2, 2], [3, 3, 3]]);
const m2 = new Matrix([[3, 3, 3], [2, 2, 2], [1, 1, 1]]);
assertArrayEquals(
'Sum should be all the 4s', [[4, 4, 4], [4, 4, 4], [4, 4, 4]],
m1.add(m2).toArray());
assertArrayEquals(
'Addition should be commutative', m1.add(m2).toArray(),
m2.add(m1).toArray());
},
testSum2() {
const m1 = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
const m2 = new Matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]);
assertArrayEquals(
'Sum should be all 0s', [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
m1.add(m2).toArray());
assertArrayEquals(
'Addition should be commutative', m1.add(m2).toArray(),
m2.add(m1).toArray());
},
testSubtract1() {
const m1 = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
const m2 = new Matrix([[5, 5, 5], [5, 5, 5], [5, 5, 5]]);
assertArrayEquals(
[[-4, -3, -2], [-1, 0, 1], [2, 3, 4]], m1.subtract(m2).toArray());
assertArrayEquals(
[[4, 3, 2], [1, 0, -1], [-2, -3, -4]], m2.subtract(m1).toArray());
},
testSubtract2() {
const m1 = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
const m2 = new Matrix([[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]]);
assertArrayEquals(
[[2, 4, 6], [8, 10, 12], [14, 16, 18]], m1.subtract(m2).toArray());
assertArrayEquals(
[[-2, -4, -6], [-8, -10, -12], [-14, -16, -18]],
m2.subtract(m1).toArray());
},
testScalarMultiplication() {
const m1 = new Matrix([[1, 1, 1], [2, 2, 2], [3, 3, 3]]);
assertArrayEquals(
[[2, 2, 2], [4, 4, 4], [6, 6, 6]], m1.multiply(2).toArray());
assertArrayEquals(
[[3, 3, 3], [6, 6, 6], [9, 9, 9]], m1.multiply(3).toArray());
assertArrayEquals(
[[4, 4, 4], [8, 8, 8], [12, 12, 12]], m1.multiply(4).toArray());
const m2 = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assertArrayEquals(
[[2, 4, 6], [8, 10, 12], [14, 16, 18]], m2.multiply(2).toArray());
},
testMatrixMultiplication() {
const m1 = new Matrix([[1, 2], [3, 4]]);
const m2 = new Matrix([[3, 4], [5, 6]]);
// m1 * m2
assertArrayEquals(
[[1 * 3 + 2 * 5, 1 * 4 + 2 * 6], [3 * 3 + 4 * 5, 3 * 4 + 4 * 6]],
m1.multiply(m2).toArray());
// m2 * m1 != m1 * m2
assertArrayEquals(
[[3 * 1 + 4 * 3, 3 * 2 + 4 * 4], [5 * 1 + 6 * 3, 5 * 2 + 6 * 4]],
m2.multiply(m1).toArray());
const m3 = new Matrix([[1, 2, 3, 4], [5, 6, 7, 8]]);
const m4 = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]);
// m3 * m4
assertArrayEquals(
[
[
1 * 1 + 2 * 4 + 3 * 7 + 4 * 10,
1 * 2 + 2 * 5 + 3 * 8 + 4 * 11,
1 * 3 + 2 * 6 + 3 * 9 + 4 * 12,
],
[
5 * 1 + 6 * 4 + 7 * 7 + 8 * 10,
5 * 2 + 6 * 5 + 7 * 8 + 8 * 11,
5 * 3 + 6 * 6 + 7 * 9 + 8 * 12,
],
],
m3.multiply(m4).toArray());
assertThrows('Matrix dimensions should not line up.', () => {
m4.multiply(m3);
});
},
testMatrixMultiplicationIsAssociative() {
const A = new Matrix([[1, 2], [3, 4]]);
const B = new Matrix([[3, 4], [5, 6]]);
const C = new Matrix([[2, 7], [9, 1]]);
assertArrayEquals(
'A(BC) == (AB)C', A.multiply(B.multiply(C)).toArray(),
A.multiply(B).multiply(C).toArray());
},
testMatrixMultiplicationIsDistributive() {
const A = new Matrix([[1, 2], [3, 4]]);
const B = new Matrix([[3, 4], [5, 6]]);
const C = new Matrix([[2, 7], [9, 1]]);
assertArrayEquals(
'A(B + C) = AB + AC', A.multiply(B.add(C)).toArray(),
A.multiply(B).add(A.multiply(C)).toArray());
assertArrayEquals(
'(A + B)C = AC + BC', A.add(B).multiply(C).toArray(),
A.multiply(C).add(B.multiply(C)).toArray());
},
testTranspose() {
const m = new Matrix([[1, 3, 1], [0, -6, 0]]);
const t = [[1, 0], [3, -6], [1, 0]];
assertArrayEquals(t, m.getTranspose().toArray());
},
testAppendColumns() {
const m = new Matrix([[1, 3, 2], [2, 0, 1], [5, 2, 2]]);
const b = new Matrix([[4], [3], [1]]);
const result = [[1, 3, 2, 4], [2, 0, 1, 3], [5, 2, 2, 1]];
assertArrayEquals(result, m.appendColumns(b).toArray());
},
testAppendRows() {
const m = new Matrix([[1, 3, 2], [2, 0, 1], [5, 2, 2]]);
const b = new Matrix([[4, 3, 1]]);
const result = [[1, 3, 2], [2, 0, 1], [5, 2, 2], [4, 3, 1]];
assertArrayEquals(result, m.appendRows(b).toArray());
},
/** @suppress {visibility} suppression added to enable type checking */
testSubmatrixByDeletion() {
const m = new Matrix(
[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]);
const arr = [[1, 2, 3], [5, 6, 7], [13, 14, 15]];
assertArrayEquals(arr, m.getSubmatrixByDeletion_(2, 3).toArray());
},
/** @suppress {visibility} suppression added to enable type checking */
testMinor() {
const m = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assertEquals(-3, m.getMinor_(0, 0));
},
/** @suppress {visibility} suppression added to enable type checking */
testCofactor() {
const m = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assertEquals(6, m.getCofactor_(0, 1));
},
testDeterminantForOneByOneMatrix() {
const m = new Matrix([[3]]);
assertEquals(3, m.getDeterminant());
},
testDeterminant() {
const m = new Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assertEquals(0, m.getDeterminant());
},
/** @suppress {visibility} suppression added to enable type checking */
testGetSubmatrix() {
const m = new Matrix(
[[2, -1, 0, 1, 0, 0], [-1, 2, -1, 0, 1, 0], [0, -1, 2, 0, 0, 1]]);
const sub1 = [[2, -1, 0], [-1, 2, -1], [0, -1, 2]];
assertArrayEquals(sub1, m.getSubmatrixByCoordinates_(0, 0, 2, 2).toArray());
const sub2 = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];
assertArrayEquals(sub2, m.getSubmatrixByCoordinates_(0, 3).toArray());
},
testGetReducedRowEchelonForm() {
const m = new Matrix(
[[2, -1, 0, 1, 0, 0], [-1, 2, -1, 0, 1, 0], [0, -1, 2, 0, 0, 1]]);
const expected = new Matrix([
[1, 0, 0, .75, .5, .25], [0, 1, 0, .5, 1, .5], [0, 0, 1, .25, .5, .75]
]);
assertTrue(expected.equals(m.getReducedRowEchelonForm()));
},
testInverse() {
const m1 = new Matrix([[2, -1, 0], [-1, 2, -1], [0, -1, 2]]);
const expected1 = new Matrix([[.75, .5, .25], [.5, 1, .5], [.25, .5, .75]]);
assertTrue(expected1.equals(m1.getInverse()));
const m2 = new Matrix([[4, 8], [7, -2]]);
const expected2 = new Matrix([[.03125, .125], [.10936, -.0625]]);
assertTrue(expected2.equals(m2.getInverse(), .0001));
const m3 = new Matrix([[0, 0], [0, 0]]);
assertNull(m3.getInverse());
const m4 = new Matrix([[2]]);
const expected4 = new Matrix([[.5]]);
assertTrue(expected4.equals(m4.getInverse(), .0001));
const m5 = new Matrix([[0]]);
assertNull(m5.getInverse());
},
testEquals() {
const a1 = new Matrix([
[1, 0, 0, .75, .5, .25], [0, 1, 0, .5, 1, .5], [0, 0, 1, .25, .5, .75]
]);
const a2 = new Matrix([
[1, 0, 0, .75, .5, .25], [0, 1, 0, .5, 1, .5], [0, 0, 1, .25, .5, .75]
]);
const a3 = new Matrix([
[1, 0, 0, .749, .5, .25],
[0, 1, 0, .5, 1, .5],
[0, 0, 1, .25, .5, .75],
]);
assertTrue(a1.equals(a2));
assertTrue(a1.equals(a3, .01));
assertFalse(a1.equals(a3, .001));
},
});
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