106 lines
2.9 KiB
JavaScript
106 lines
2.9 KiB
JavaScript
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import { isMatrix } from '../../utils/is.js';
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import { format } from '../../utils/string.js';
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import { arraySize } from '../../utils/array.js';
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import { factory } from '../../utils/factory.js';
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var name = 'sqrtm';
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var dependencies = ['typed', 'abs', 'add', 'multiply', 'sqrt', 'subtract', 'inv', 'size', 'max', 'identity'];
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export var createSqrtm = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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abs,
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add,
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multiply,
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sqrt,
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subtract,
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inv,
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size,
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max,
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identity
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} = _ref;
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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 = identity(size(A));
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do {
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var Yk = Y;
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Y = multiply(0.5, add(Yk, inv(Z)));
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Z = multiply(0.5, add(Z, inv(Yk)));
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error = max(abs(subtract(Y, Yk)));
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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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/**
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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
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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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return typed(name, {
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'Array | Matrix': function ArrayMatrix(A) {
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var size = isMatrix(A) ? A.size() : arraySize(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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} else {
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throw new RangeError('Matrix must be square ' + '(size: ' + format(size) + ')');
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}
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case 2:
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{
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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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} else {
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throw new RangeError('Matrix must be square ' + '(size: ' + format(size) + ')');
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}
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}
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default:
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// Multi dimensional array
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throw new RangeError('Matrix must be at most two dimensional ' + '(size: ' + format(size) + ')');
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}
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}
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});
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});
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