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https://github.com/josdejong/mathjs.git
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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
111 lines
3.1 KiB
JavaScript
111 lines
3.1 KiB
JavaScript
'use strict';
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var array = require('../../utils/array');
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var latex = require('../../utils/latex');
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var string = require('../../utils/string');
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function factory(type, config, load, typed) {
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var matrix = load(require('../../type/matrix/function/matrix'));
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var abs = load(require('../arithmetic/abs'));
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var add = load(require('../arithmetic/add'));
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var divide = load(require('../arithmetic/divide'));
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var multiply = load(require('../arithmetic/multiply'));
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var sqrt = load(require('../arithmetic/sqrt'));
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var subtract = load(require('../arithmetic/subtract'));
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var inv = load(require('../matrix/inv'));
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var size = load(require('../matrix/size'));
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var max = load(require('../statistics/max'));
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var eye = load(require('./eye'));
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/**
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* Calculate the principal square root of a square matrix.
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* The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.
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*
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* https://en.wikipedia.org/wiki/Square_root_of_a_matrix
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*
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* Syntax:
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*
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* X = math.sqrtm(A)
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*
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* Examples:
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*
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* math.sqrtm([[1, 2], [3, 4]]); // returns [[-2, 1], [1.5, -0.5]]
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*
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* See also:
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*
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* sqrt, pow, abs, max
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*
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* @param {Array | Matrix} A The square matrix `A`
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* @return {Array | Matrix} The principal square root of matrix `A`
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*/
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var sqrtm = typed('sqrtm', {
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'Array | Matrix': function (A) {
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var size = type.isMatrix(A) ? A.size() : array.size(A);
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switch (size.length) {
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case 1:
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// Single element Array | Matrix
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if (size[0] == 1) {
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return sqrt(A);
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}
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else {
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throw new RangeError('Matrix must be square ' +
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'(size: ' + string.format(size) + ')');
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}
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case 2:
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// Two-dimensional Array | Matrix
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var rows = size[0];
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var cols = size[1];
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if (rows == cols) {
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return _denmanBeavers(A);
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}
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else {
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throw new RangeError('Matrix must be square ' +
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'(size: ' + string.format(size) + ')');
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}
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}
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}
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});
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var _maxIterations = 1e3;
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var _tolerance = 1e-6;
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/**
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* Calculate the principal square root matrix using the Denman–Beavers iterative method
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*
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* https://en.wikipedia.org/wiki/Square_root_of_a_matrix#By_Denman–Beavers_iteration
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*
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* @param {Array | Matrix} A The square matrix `A`
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* @return {Array | Matrix} The principal square root of matrix `A`
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* @private
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*/
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function _denmanBeavers(A) {
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var error;
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var iterations = 0;
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var Y = A;
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var Z = eye(size(A));
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do {
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var Y_k = Y;
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Y = multiply(0.5, add(Y_k, inv(Z)));
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Z = multiply(0.5, add(Z, inv(Y_k)));
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error = max(abs(subtract(Y, Y_k)));
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if (error > _tolerance && ++iterations > _maxIterations) {
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throw new Error('computing square root of matrix: iterative method could not converge');
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}
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} while (error > _tolerance);
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return Y;
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}
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sqrtm.toTex = {1: '{${args[0]}}' + latex.operators['pow'] + '{\\frac{1}{2}}'};
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return sqrtm;
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}
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exports.name = 'sqrtm';
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exports.factory = factory;
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