feat:node-modules

node_modules/mathjs/lib/esm/function/matrix/sqrtm.js

@@ -0,0 +1,99 @@
+import { isMatrix } from '../../utils/is.js';
+import { format } from '../../utils/string.js';
+import { arraySize } from '../../utils/array.js';
+import { factory } from '../../utils/factory.js';
+var name = 'sqrtm';
+var dependencies = ['typed', 'abs', 'add', 'multiply', 'map', 'sqrt', 'subtract', 'inv', 'size', 'max', 'identity'];
+export var createSqrtm = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    typed,
+    abs,
+    add,
+    multiply,
+    map,
+    sqrt,
+    subtract,
+    inv,
+    size,
+    max,
+    identity
+  } = _ref;
+  var _maxIterations = 1e3;
+  var _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) {
+    var error;
+    var iterations = 0;
+    var Y = A;
+    var Z = identity(size(A));
+    do {
+      var 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 Array__Matrix(A) {
+      var size = isMatrix(A) ? A.size() : 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: ' + format(size) + ')');
+          }
+        case 2:
+          {
+            // Two-dimensional Array | Matrix
+            var rows = size[0];
+            var cols = size[1];
+            if (rows === cols) {
+              return _denmanBeavers(A);
+            } else {
+              throw new RangeError('Matrix must be square ' + '(size: ' + format(size) + ')');
+            }
+          }
+        default:
+          // Multi dimensional array
+          throw new RangeError('Matrix must be at most two dimensional ' + '(size: ' + format(size) + ')');
+      }
+    }
+  });
+});