105 lines
3.0 KiB
JavaScript
105 lines
3.0 KiB
JavaScript
|
"use strict";
|
|||
|
|
|
|||
|
|
Object.defineProperty(exports, "__esModule", {
|
|||
|
|
value: true
|
|||
|
|
});
|
|||
|
|
exports.createSqrtm = void 0;
|
|||
|
|
var _is = require("../../utils/is.js");
|
|||
|
|
var _string = require("../../utils/string.js");
|
|||
|
|
var _array = require("../../utils/array.js");
|
|||
|
|
var _factory = require("../../utils/factory.js");
|
|||
|
|
const name = 'sqrtm';
|
|||
|
|
const dependencies = ['typed', 'abs', 'add', 'multiply', 'map', 'sqrt', 'subtract', 'inv', 'size', 'max', 'identity'];
|
|||
|
|
const createSqrtm = exports.createSqrtm = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
|
|||
|
|
let {
|
|||
|
|
typed,
|
|||
|
|
abs,
|
|||
|
|
add,
|
|||
|
|
multiply,
|
|||
|
|
map,
|
|||
|
|
sqrt,
|
|||
|
|
subtract,
|
|||
|
|
inv,
|
|||
|
|
size,
|
|||
|
|
max,
|
|||
|
|
identity
|
|||
|
|
} = _ref;
|
|||
|
|
const _maxIterations = 1e3;
|
|||
|
|
const _tolerance = 1e-6;
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* Calculate the principal square root matrix using the Denman–Beavers iterative method
|
|||
|
|
*
|
|||
|
|
* https://en.wikipedia.org/wiki/Square_root_of_a_matrix#By_Denman–Beavers_iteration
|
|||
|
|
*
|
|||
|
|
* @param {Array | Matrix} A The square matrix `A`
|
|||
|
|
* @return {Array | Matrix} The principal square root of matrix `A`
|
|||
|
|
* @private
|
|||
|
|
*/
|
|||
|
|
function _denmanBeavers(A) {
|
|||
|
|
let error;
|
|||
|
|
let iterations = 0;
|
|||
|
|
let Y = A;
|
|||
|
|
let Z = identity(size(A));
|
|||
|
|
do {
|
|||
|
|
const Yk = Y;
|
|||
|
|
Y = multiply(0.5, add(Yk, inv(Z)));
|
|||
|
|
Z = multiply(0.5, add(Z, inv(Yk)));
|
|||
|
|
error = max(abs(subtract(Y, Yk)));
|
|||
|
|
if (error > _tolerance && ++iterations > _maxIterations) {
|
|||
|
|
throw new Error('computing square root of matrix: iterative method could not converge');
|
|||
|
|
}
|
|||
|
|
} while (error > _tolerance);
|
|||
|
|
return Y;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* Calculate the principal square root of a square matrix.
|
|||
|
|
* The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.
|
|||
|
|
*
|
|||
|
|
* https://en.wikipedia.org/wiki/Square_root_of_a_matrix
|
|||
|
|
*
|
|||
|
|
* Syntax:
|
|||
|
|
*
|
|||
|
|
* math.sqrtm(A)
|
|||
|
|
*
|
|||
|
|
* Examples:
|
|||
|
|
*
|
|||
|
|
* math.sqrtm([[33, 24], [48, 57]]) // returns [[5, 2], [4, 7]]
|
|||
|
|
*
|
|||
|
|
* See also:
|
|||
|
|
*
|
|||
|
|
* sqrt, pow
|
|||
|
|
*
|
|||
|
|
* @param {Array | Matrix} A The square matrix `A`
|
|||
|
|
* @return {Array | Matrix} The principal square root of matrix `A`
|
|||
|
|
*/
|
|||
|
|
return typed(name, {
|
|||
|
|
'Array | Matrix': function (A) {
|
|||
|
|
const size = (0, _is.isMatrix)(A) ? A.size() : (0, _array.arraySize)(A);
|
|||
|
|
switch (size.length) {
|
|||
|
|
case 1:
|
|||
|
|
// Single element Array | Matrix
|
|||
|
|
if (size[0] === 1) {
|
|||
|
|
return map(A, sqrt);
|
|||
|
|
} else {
|
|||
|
|
throw new RangeError('Matrix must be square ' + '(size: ' + (0, _string.format)(size) + ')');
|
|||
|
|
}
|
|||
|
|
case 2:
|
|||
|
|
{
|
|||
|
|
// Two-dimensional Array | Matrix
|
|||
|
|
const rows = size[0];
|
|||
|
|
const cols = size[1];
|
|||
|
|
if (rows === cols) {
|
|||
|
|
return _denmanBeavers(A);
|
|||
|
|
} else {
|
|||
|
|
throw new RangeError('Matrix must be square ' + '(size: ' + (0, _string.format)(size) + ')');
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
default:
|
|||
|
|
// Multi dimensional array
|
|||
|
|
throw new RangeError('Matrix must be at most two dimensional ' + '(size: ' + (0, _string.format)(size) + ')');
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
});
|
|||
|
|
});
|