feat:node-modules

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

@@ -0,0 +1,70 @@
+import { factory } from '../../../utils/factory.js';
+var name = 'schur';
+var dependencies = ['typed', 'matrix', 'identity', 'multiply', 'qr', 'norm', 'subtract'];
+export var createSchur = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    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 Array(X) {
+      var r = _schur(matrix(X));
+      return {
+        U: r.U.valueOf(),
+        T: r.T.valueOf()
+      };
+    },
+    Matrix: function Matrix(X) {
+      return _schur(X);
+    }
+  });
+  function _schur(X) {
+    var n = X.size()[0];
+    var A = X;
+    var U = identity(n);
+    var k = 0;
+    var A0;
+    do {
+      A0 = A;
+      var QR = qr(A);
+      var Q = QR.Q;
+      var 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/esm/function/algebra/leafCount.js

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+import { factory } from '../../utils/factory.js';
+var name = 'leafCount';
+var dependencies = ['parse', 'typed'];
+export var createLeafCount = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    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) {
+    var 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 Node(expr) {
+      return countLeaves(expr);
+    }
+  });
+});

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

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+import { factory } from '../../utils/factory.js';
+var name = 'lyap';
+var dependencies = ['typed', 'matrix', 'sylvester', 'multiply', 'transpose'];
+export var createLyap = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    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 Matrix_Matrix(A, Q) {
+      return sylvester(A, transpose(A), multiply(-1, Q));
+    },
+    'Array, Matrix': function Array_Matrix(A, Q) {
+      return sylvester(matrix(A), transpose(matrix(A)), multiply(-1, Q));
+    },
+    'Matrix, Array': function Matrix_Array(A, Q) {
+      return sylvester(A, transpose(matrix(A)), matrix(multiply(-1, Q)));
+    },
+    'Array, Array': function Array_Array(A, Q) {
+      return sylvester(matrix(A), transpose(matrix(A)), matrix(multiply(-1, Q))).toArray();
+    }
+  });
+});

node_modules/mathjs/lib/esm/function/algebra/resolve.js

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+import { createMap } from '../../utils/map.js';
+import { isFunctionNode, isNode, isOperatorNode, isParenthesisNode, isSymbolNode } from '../../utils/is.js';
+import { factory } from '../../utils/factory.js';
+var name = 'resolve';
+var dependencies = ['typed', 'parse', 'ConstantNode', 'FunctionNode', 'OperatorNode', 'ParenthesisNode'];
+export var createResolve = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    typed,
+    parse,
+    ConstantNode,
+    FunctionNode,
+    OperatorNode,
+    ParenthesisNode
+  } = _ref;
+  /**
+   * resolve(expr, scope) replaces variable nodes with their scoped values
+   *
+   * Syntax:
+   *
+   *     math.resolve(expr, scope)
+   *
+   * Examples:
+   *
+   *     math.resolve('x + y', {x:1, y:2})           // Node '1 + 2'
+   *     math.resolve(math.parse('x+y'), {x:1, y:2}) // Node '1 + 2'
+   *     math.simplify('x+y', {x:2, y: math.parse('x+x')}).toString() // "6"
+   *
+   * See also:
+   *
+   *     simplify, evaluate
+   *
+   * @param {Node | Node[]} node
+   *     The expression tree (or trees) to be simplified
+   * @param {Object} scope
+   *     Scope specifying variables to be resolved
+   * @return {Node | Node[]} Returns `node` with variables recursively substituted.
+   * @throws {ReferenceError}
+   *     If there is a cyclic dependency among the variables in `scope`,
+   *     resolution is impossible and a ReferenceError is thrown.
+   */
+  function _resolve(node, scope) {
+    var within = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : new Set();
+    // note `within`:
+    // `within` is not documented, since it is for internal cycle
+    // detection only
+    if (!scope) {
+      return node;
+    }
+    if (isSymbolNode(node)) {
+      if (within.has(node.name)) {
+        var variables = Array.from(within).join(', ');
+        throw new ReferenceError("recursive loop of variable definitions among {".concat(variables, "}"));
+      }
+      var value = scope.get(node.name);
+      if (isNode(value)) {
+        var nextWithin = new Set(within);
+        nextWithin.add(node.name);
+        return _resolve(value, scope, nextWithin);
+      } else if (typeof value === 'number') {
+        return parse(String(value));
+      } else if (value !== undefined) {
+        return new ConstantNode(value);
+      } else {
+        return node;
+      }
+    } else if (isOperatorNode(node)) {
+      var args = node.args.map(function (arg) {
+        return _resolve(arg, scope, within);
+      });
+      return new OperatorNode(node.op, node.fn, args, node.implicit);
+    } else if (isParenthesisNode(node)) {
+      return new ParenthesisNode(_resolve(node.content, scope, within));
+    } else if (isFunctionNode(node)) {
+      var _args = node.args.map(function (arg) {
+        return _resolve(arg, scope, within);
+      });
+      return new FunctionNode(node.name, _args);
+    }
+
+    // Otherwise just recursively resolve any children (might also work
+    // for some of the above special cases)
+    return node.map(child => _resolve(child, scope, within));
+  }
+  return typed('resolve', {
+    Node: _resolve,
+    'Node, Map | null | undefined': _resolve,
+    'Node, Object': (n, scope) => _resolve(n, createMap(scope)),
+    // For arrays and matrices, we map `self` rather than `_resolve`
+    // because resolve is fairly expensive anyway, and this way
+    // we get nice error messages if one entry in the array has wrong type.
+    'Array | Matrix': typed.referToSelf(self => A => A.map(n => self(n))),
+    'Array | Matrix, null | undefined': typed.referToSelf(self => A => A.map(n => self(n))),
+    'Array, Object': typed.referTo('Array,Map', selfAM => (A, scope) => selfAM(A, createMap(scope))),
+    'Matrix, Object': typed.referTo('Matrix,Map', selfMM => (A, scope) => selfMM(A, createMap(scope))),
+    'Array | Matrix, Map': typed.referToSelf(self => (A, scope) => A.map(n => self(n, scope)))
+  });
+});