feat:node-modules

node_modules/mathjs/lib/cjs/function/algebra/decomposition/schur.js

@@ -0,0 +1,76 @@
+"use strict";
+
+Object.defineProperty(exports, "__esModule", {
+  value: true
+});
+exports.createSchur = void 0;
+var _factory = require("../../../utils/factory.js");
+const name = 'schur';
+const dependencies = ['typed', 'matrix', 'identity', 'multiply', 'qr', 'norm', 'subtract'];
+const createSchur = exports.createSchur = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
+  let {
+    typed,
+    matrix,
+    identity,
+    multiply,
+    qr,
+    norm,
+    subtract
+  } = _ref;
+  /**
+   *
+   * Performs a real Schur decomposition of the real matrix A = UTU' where U is orthogonal
+   * and T is upper quasi-triangular.
+   * https://en.wikipedia.org/wiki/Schur_decomposition
+   *
+   * Syntax:
+   *
+   *     math.schur(A)
+   *
+   * Examples:
+   *
+   *     const A = [[1, 0], [-4, 3]]
+   *     math.schur(A) // returns {T: [[3, 4], [0, 1]], R: [[0, 1], [-1, 0]]}
+   *
+   * See also:
+   *
+   *     sylvester, lyap, qr
+   *
+   * @param {Array | Matrix} A  Matrix A
+   * @return {{U: Array | Matrix, T: Array | Matrix}} Object containing both matrix U and T of the Schur Decomposition A=UTU'
+   */
+  return typed(name, {
+    Array: function (X) {
+      const r = _schur(matrix(X));
+      return {
+        U: r.U.valueOf(),
+        T: r.T.valueOf()
+      };
+    },
+    Matrix: function (X) {
+      return _schur(X);
+    }
+  });
+  function _schur(X) {
+    const n = X.size()[0];
+    let A = X;
+    let U = identity(n);
+    let k = 0;
+    let A0;
+    do {
+      A0 = A;
+      const QR = qr(A);
+      const Q = QR.Q;
+      const R = QR.R;
+      A = multiply(R, Q);
+      U = multiply(U, Q);
+      if (k++ > 100) {
+        break;
+      }
+    } while (norm(subtract(A, A0)) > 1e-4);
+    return {
+      U,
+      T: A
+    };
+  }
+});