simple-squiggle

A restricted subset of Squiggle
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sqrtm.js (3264B)

      1 "use strict";
      2 
      3 Object.defineProperty(exports, "__esModule", {
      4   value: true
      5 });
      6 exports.createSqrtm = void 0;
      7 
      8 var _is = require("../../utils/is.js");
      9 
     10 var _string = require("../../utils/string.js");
     11 
     12 var _array = require("../../utils/array.js");
     13 
     14 var _factory = require("../../utils/factory.js");
     15 
     16 var name = 'sqrtm';
     17 var dependencies = ['typed', 'abs', 'add', 'multiply', 'sqrt', 'subtract', 'inv', 'size', 'max', 'identity'];
     18 var createSqrtm = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
     19   var typed = _ref.typed,
     20       abs = _ref.abs,
     21       add = _ref.add,
     22       multiply = _ref.multiply,
     23       sqrt = _ref.sqrt,
     24       subtract = _ref.subtract,
     25       inv = _ref.inv,
     26       size = _ref.size,
     27       max = _ref.max,
     28       identity = _ref.identity;
     29   var _maxIterations = 1e3;
     30   var _tolerance = 1e-6;
     31   /**
     32    * Calculate the principal square root matrix using the Denman–Beavers iterative method
     33    *
     34    * https://en.wikipedia.org/wiki/Square_root_of_a_matrix#By_Denman–Beavers_iteration
     35    *
     36    * @param  {Array | Matrix} A   The square matrix `A`
     37    * @return {Array | Matrix}     The principal square root of matrix `A`
     38    * @private
     39    */
     40 
     41   function _denmanBeavers(A) {
     42     var error;
     43     var iterations = 0;
     44     var Y = A;
     45     var Z = identity(size(A));
     46 
     47     do {
     48       var Yk = Y;
     49       Y = multiply(0.5, add(Yk, inv(Z)));
     50       Z = multiply(0.5, add(Z, inv(Yk)));
     51       error = max(abs(subtract(Y, Yk)));
     52 
     53       if (error > _tolerance && ++iterations > _maxIterations) {
     54         throw new Error('computing square root of matrix: iterative method could not converge');
     55       }
     56     } while (error > _tolerance);
     57 
     58     return Y;
     59   }
     60   /**
     61    * Calculate the principal square root of a square matrix.
     62    * The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.
     63    *
     64    * https://en.wikipedia.org/wiki/Square_root_of_a_matrix
     65    *
     66    * Syntax:
     67    *
     68    *     X = math.sqrtm(A)
     69    *
     70    * Examples:
     71    *
     72    *     math.sqrtm([[1, 2], [3, 4]]) // returns [[-2, 1], [1.5, -0.5]]
     73    *
     74    * See also:
     75    *
     76    *     sqrt, pow
     77    *
     78    * @param  {Array | Matrix} A   The square matrix `A`
     79    * @return {Array | Matrix}     The principal square root of matrix `A`
     80    */
     81 
     82 
     83   return typed(name, {
     84     'Array | Matrix': function ArrayMatrix(A) {
     85       var size = (0, _is.isMatrix)(A) ? A.size() : (0, _array.arraySize)(A);
     86 
     87       switch (size.length) {
     88         case 1:
     89           // Single element Array | Matrix
     90           if (size[0] === 1) {
     91             return sqrt(A);
     92           } else {
     93             throw new RangeError('Matrix must be square ' + '(size: ' + (0, _string.format)(size) + ')');
     94           }
     95 
     96         case 2:
     97           {
     98             // Two-dimensional Array | Matrix
     99             var rows = size[0];
    100             var cols = size[1];
    101 
    102             if (rows === cols) {
    103               return _denmanBeavers(A);
    104             } else {
    105               throw new RangeError('Matrix must be square ' + '(size: ' + (0, _string.format)(size) + ')');
    106             }
    107           }
    108 
    109         default:
    110           // Multi dimensional array
    111           throw new RangeError('Matrix must be at most two dimensional ' + '(size: ' + (0, _string.format)(size) + ')');
    112       }
    113     }
    114   });
    115 });
    116 exports.createSqrtm = createSqrtm;