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308d55dac4
* Adds Matrix function math.sqrtm(A) The current implementation is based on the Babylonian iterative method * Removing default parameter as they are only supported from ES6/ES2015 onwards * Increases the robustness of the `math.sqrtm()` Babylonian iterative method * Adds Denman–Beavers iteration method to compute `X*X = A` The Babylonian method is numerically unstable and more likely to fail to converge. For that reason, the Denman–Beavers iteration method is the one being used in the current version. * Adds LaTeX for math.sqrtm(A) * Updates `math.sqrtm(A)` suggestions list * Forgot to require latex... * Adds unit tests for `math.pow(math.sqrtm(A), 2) == A` * Switches from SyntaxError to Error Edits error message * Adds unit tests for non-square matrices and LaTeX conversion * Changes according to feedback - Removes Babylonian method implementation; - Adds unit tests for BigNumber matrices - sqrtm.test.js refactoring - Edits LaTeX conversion * Ensures input/output type persistence * Changes math.deepEqual to assert.deepEqual (or to approx.deepEqual where appropriate) * Fixes BigNumber unit test
73 lines
3.0 KiB
JavaScript
73 lines
3.0 KiB
JavaScript
// test sqrtm
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var assert = require('assert'),
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approx = require('../../../tools/approx'),
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math = require('../../../index');
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describe('sqrtm', function () {
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var A = [[ 5, 2], [ 4, 7]];
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var AA = [[33, 24], [48, 57]];
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var B = [[1.5667, 1.7408], [2.6112, 4.1779]];
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var BB = [[ 7, 10], [15, 22]];
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it('should return the principal square root of a matrix', function() {
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approx.deepEqual(math.sqrtm(AA), A);
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approx.deepEqual(math.sqrtm(BB), B);
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approx.deepEqual(
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math.sqrtm(
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[[ 5, -4, 1, 0, 0],
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[-4, 6, -4, 1, 0],
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[ 1, -4, 6, -4, 1],
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[ 0, 1, -4, 6, -4],
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[ 0, 0, 1, -4, 6]]),
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[[ 2.001450032980806, -0.997069854672086, 0.004226841220338, 0.004648098208404, 0.003162179891248],
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[-0.997069854672086, 2.006191486385745, -0.990363307725271, 0.011838782789231, 0.009369460553432],
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[ 0.004226841220338, -0.990363307725271, 2.017072849046023, -0.974622709753106, 0.026274470491696],
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[ 0.004648098208404, 0.011838782789231, -0.974622709753106, 2.050268428894304, -0.919971837350421],
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[ 0.003162179891248, 0.009369460553432, 0.026274470491696, -0.919971837350421, 2.269992000979243]]);
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});
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it('should return the principal square root of a matrix with just one value', function() {
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assert.deepEqual(math.sqrtm([ 4]), [2]);
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assert.deepEqual(math.sqrtm([16]), [4]);
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assert.deepEqual(math.sqrtm([20.25]), [4.5]);
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});
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it('should return the principal square root of a matrix of big numbers', function() {
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assert.deepEqual(math.round(math.sqrtm(math.bignumber(AA)), 20), math.bignumber(A));
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});
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it('math.pow(math.sqrtm(A), 2) should equal A', function() {
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approx.deepEqual(math.pow(math.sqrtm(A), 2), A);
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approx.deepEqual(math.pow(math.sqrtm(B), 2), B);
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approx.deepEqual(math.pow(math.sqrtm(AA), 2), AA);
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approx.deepEqual(math.pow(math.sqrtm(BB), 2), BB);
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});
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it('should throw an error in case of non-square matrices', function() {
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assert.throws(function () { math.sqrtm([1, 2, 3]) }, /Matrix must be square/);
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assert.throws(function () { math.sqrtm([[1, 2, 3]]) }, /Matrix must be square/);
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assert.throws(function () { math.sqrtm([[1, 2, 3], [4, 5, 6]]) }, /Matrix must be square/);
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});
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it('should LaTeX sqrtm', function () {
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var expression = math.parse('sqrtm([[33, 24], [48, 57]])');
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assert.equal(expression.toTex(), '{\\begin{bmatrix}33&24\\\\48&57\\\\\\end{bmatrix}}^{\\frac{1}{2}}');
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});
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it('should return the result in the same format as the input', function() {
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assert.equal(math.typeof(math.sqrtm(A)), 'Array');
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assert.equal(math.typeof(math.sqrtm(B)), 'Array');
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assert.equal(math.typeof(math.sqrtm(AA)), 'Array');
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assert.equal(math.typeof(math.sqrtm(BB)), 'Array');
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assert.equal(math.typeof(math.sqrtm(math.matrix(A))), 'Matrix');
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assert.equal(math.typeof(math.sqrtm(math.matrix(B))), 'Matrix');
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assert.equal(math.typeof(math.sqrtm(math.matrix(AA))), 'Matrix');
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assert.equal(math.typeof(math.sqrtm(math.matrix(BB))), 'Matrix');
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});
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});
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