feat:node-modules

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

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+"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
+    };
+  }
+});

node_modules/mathjs/lib/cjs/function/algebra/leafCount.js

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+"use strict";
+
+Object.defineProperty(exports, "__esModule", {
+  value: true
+});
+exports.createLeafCount = void 0;
+var _factory = require("../../utils/factory.js");
+const name = 'leafCount';
+const dependencies = ['parse', 'typed'];
+const createLeafCount = exports.createLeafCount = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
+  let {
+    parse,
+    typed
+  } = _ref;
+  // This does the real work, but we don't have to recurse through
+  // a typed call if we separate it out
+  function countLeaves(node) {
+    let count = 0;
+    node.forEach(n => {
+      count += countLeaves(n);
+    });
+    return count || 1;
+  }
+
+  /**
+   * Gives the number of "leaf nodes" in the parse tree of the given expression
+   * A leaf node is one that has no subexpressions, essentially either a
+   * symbol or a constant. Note that `5!` has just one leaf, the '5'; the
+   * unary factorial operator does not add a leaf. On the other hand,
+   * function symbols do add leaves, so `sin(x)/cos(x)` has four leaves.
+   *
+   * The `simplify()` function should generally not increase the `leafCount()`
+   * of an expression, although currently there is no guarantee that it never
+   * does so. In many cases, `simplify()` reduces the leaf count.
+   *
+   * Syntax:
+   *
+   *     math.leafCount(expr)
+   *
+   * Examples:
+   *
+   *     math.leafCount('x') // 1
+   *     math.leafCount(math.parse('a*d-b*c')) // 4
+   *     math.leafCount('[a,b;c,d][0,1]') // 6
+   *
+   * See also:
+   *
+   *     simplify
+   *
+   * @param {Node|string} expr    The expression to count the leaves of
+   *
+   * @return {number}  The number of leaves of `expr`
+   *
+   */
+  return typed(name, {
+    Node: function (expr) {
+      return countLeaves(expr);
+    }
+  });
+});

node_modules/mathjs/lib/cjs/function/algebra/lyap.js

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+"use strict";
+
+Object.defineProperty(exports, "__esModule", {
+  value: true
+});
+exports.createLyap = void 0;
+var _factory = require("../../utils/factory.js");
+const name = 'lyap';
+const dependencies = ['typed', 'matrix', 'sylvester', 'multiply', 'transpose'];
+const createLyap = exports.createLyap = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
+  let {
+    typed,
+    matrix,
+    sylvester,
+    multiply,
+    transpose
+  } = _ref;
+  /**
+   *
+   * Solves the Continuous-time Lyapunov equation AP+PA'+Q=0 for P, where
+   * Q is an input matrix. When Q is symmetric, P is also symmetric. Notice
+   * that different equivalent definitions exist for the Continuous-time
+   * Lyapunov equation.
+   * https://en.wikipedia.org/wiki/Lyapunov_equation
+   *
+   * Syntax:
+   *
+   *     math.lyap(A, Q)
+   *
+   * Examples:
+   *
+   *     const A = [[-2, 0], [1, -4]]
+   *     const Q = [[3, 1], [1, 3]]
+   *     const P = math.lyap(A, Q)
+   *
+   * See also:
+   *
+   *     sylvester, schur
+   *
+   * @param {Matrix | Array} A  Matrix A
+   * @param {Matrix | Array} Q  Matrix Q
+   * @return {Matrix | Array} Matrix P solution to the Continuous-time Lyapunov equation AP+PA'=Q
+   */
+  return typed(name, {
+    'Matrix, Matrix': function (A, Q) {
+      return sylvester(A, transpose(A), multiply(-1, Q));
+    },
+    'Array, Matrix': function (A, Q) {
+      return sylvester(matrix(A), transpose(matrix(A)), multiply(-1, Q));
+    },
+    'Matrix, Array': function (A, Q) {
+      return sylvester(A, transpose(matrix(A)), matrix(multiply(-1, Q)));
+    },
+    'Array, Array': function (A, Q) {
+      return sylvester(matrix(A), transpose(matrix(A)), matrix(multiply(-1, Q))).toArray();
+    }
+  });
+});