feat:node-modules

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

@@ -0,0 +1,222 @@
+import _extends from "@babel/runtime/helpers/extends";
+import { factory } from '../../../utils/factory.js';
+var name = 'qr';
+var dependencies = ['typed', 'matrix', 'zeros', 'identity', 'isZero', 'equal', 'sign', 'sqrt', 'conj', 'unaryMinus', 'addScalar', 'divideScalar', 'multiplyScalar', 'subtractScalar', 'complex'];
+export var createQr = /* #__PURE__ */factory(name, dependencies, _ref => {
+  var {
+    typed,
+    matrix,
+    zeros,
+    identity,
+    isZero,
+    equal,
+    sign,
+    sqrt,
+    conj,
+    unaryMinus,
+    addScalar,
+    divideScalar,
+    multiplyScalar,
+    subtractScalar,
+    complex
+  } = _ref;
+  /**
+   * Calculate the Matrix QR decomposition. Matrix `A` is decomposed in
+   * two matrices (`Q`, `R`) where `Q` is an
+   * orthogonal matrix and `R` is an upper triangular matrix.
+   *
+   * Syntax:
+   *
+   *    math.qr(A)
+   *
+   * Example:
+   *
+   *    const m = [
+   *      [1, -1,  4],
+   *      [1,  4, -2],
+   *      [1,  4,  2],
+   *      [1,  -1, 0]
+   *    ]
+   *    const result = math.qr(m)
+   *    // r = {
+   *    //   Q: [
+   *    //     [0.5, -0.5,   0.5],
+   *    //     [0.5,  0.5,  -0.5],
+   *    //     [0.5,  0.5,   0.5],
+   *    //     [0.5, -0.5,  -0.5],
+   *    //   ],
+   *    //   R: [
+   *    //     [2, 3,  2],
+   *    //     [0, 5, -2],
+   *    //     [0, 0,  4],
+   *    //     [0, 0,  0]
+   *    //   ]
+   *    // }
+   *
+   * See also:
+   *
+   *    lup, lusolve
+   *
+   * @param {Matrix | Array} A    A two dimensional matrix or array
+   * for which to get the QR decomposition.
+   *
+   * @return {{Q: Array | Matrix, R: Array | Matrix}} Q: the orthogonal
+   * matrix and R: the upper triangular matrix
+   */
+  return _extends(typed(name, {
+    DenseMatrix: function DenseMatrix(m) {
+      return _denseQR(m);
+    },
+    SparseMatrix: function SparseMatrix(m) {
+      return _sparseQR(m);
+    },
+    Array: function Array(a) {
+      // create dense matrix from array
+      var m = matrix(a);
+      // lup, use matrix implementation
+      var r = _denseQR(m);
+      // result
+      return {
+        Q: r.Q.valueOf(),
+        R: r.R.valueOf()
+      };
+    }
+  }), {
+    _denseQRimpl
+  });
+  function _denseQRimpl(m) {
+    // rows & columns (m x n)
+    var rows = m._size[0]; // m
+    var cols = m._size[1]; // n
+
+    var Q = identity([rows], 'dense');
+    var Qdata = Q._data;
+    var R = m.clone();
+    var Rdata = R._data;
+
+    // vars
+    var i, j, k;
+    var w = zeros([rows], '');
+    for (k = 0; k < Math.min(cols, rows); ++k) {
+      /*
+       * **k-th Household matrix**
+       *
+       * The matrix I - 2*v*transpose(v)
+       * x     = first column of A
+       * x1    = first element of x
+       * alpha = x1 / |x1| * |x|
+       * e1    = tranpose([1, 0, 0, ...])
+       * u     = x - alpha * e1
+       * v     = u / |u|
+       *
+       * Household matrix = I - 2 * v * tranpose(v)
+       *
+       *  * Initially Q = I and R = A.
+       *  * Household matrix is a reflection in a plane normal to v which
+       *    will zero out all but the top right element in R.
+       *  * Appplying reflection to both Q and R will not change product.
+       *  * Repeat this process on the (1,1) minor to get R as an upper
+       *    triangular matrix.
+       *  * Reflections leave the magnitude of the columns of Q unchanged
+       *    so Q remains othoganal.
+       *
+       */
+
+      var pivot = Rdata[k][k];
+      var sgn = unaryMinus(equal(pivot, 0) ? 1 : sign(pivot));
+      var conjSgn = conj(sgn);
+      var alphaSquared = 0;
+      for (i = k; i < rows; i++) {
+        alphaSquared = addScalar(alphaSquared, multiplyScalar(Rdata[i][k], conj(Rdata[i][k])));
+      }
+      var alpha = multiplyScalar(sgn, sqrt(alphaSquared));
+      if (!isZero(alpha)) {
+        // first element in vector u
+        var u1 = subtractScalar(pivot, alpha);
+
+        // w = v * u1 / |u|    (only elements k to (rows-1) are used)
+        w[k] = 1;
+        for (i = k + 1; i < rows; i++) {
+          w[i] = divideScalar(Rdata[i][k], u1);
+        }
+
+        // tau = - conj(u1 / alpha)
+        var tau = unaryMinus(conj(divideScalar(u1, alpha)));
+        var s = void 0;
+
+        /*
+         * tau and w have been choosen so that
+         *
+         * 2 * v * tranpose(v) = tau * w * tranpose(w)
+         */
+
+        /*
+         * -- calculate R = R - tau * w * tranpose(w) * R --
+         * Only do calculation with rows k to (rows-1)
+         * Additionally columns 0 to (k-1) will not be changed by this
+         *   multiplication so do not bother recalculating them
+         */
+        for (j = k; j < cols; j++) {
+          s = 0.0;
+
+          // calculate jth element of [tranpose(w) * R]
+          for (i = k; i < rows; i++) {
+            s = addScalar(s, multiplyScalar(conj(w[i]), Rdata[i][j]));
+          }
+
+          // calculate the jth element of [tau * transpose(w) * R]
+          s = multiplyScalar(s, tau);
+          for (i = k; i < rows; i++) {
+            Rdata[i][j] = multiplyScalar(subtractScalar(Rdata[i][j], multiplyScalar(w[i], s)), conjSgn);
+          }
+        }
+        /*
+         * -- calculate Q = Q - tau * Q * w * transpose(w) --
+         * Q is a square matrix (rows x rows)
+         * Only do calculation with columns k to (rows-1)
+         * Additionally rows 0 to (k-1) will not be changed by this
+         *   multiplication so do not bother recalculating them
+         */
+        for (i = 0; i < rows; i++) {
+          s = 0.0;
+
+          // calculate ith element of [Q * w]
+          for (j = k; j < rows; j++) {
+            s = addScalar(s, multiplyScalar(Qdata[i][j], w[j]));
+          }
+
+          // calculate the ith element of [tau * Q * w]
+          s = multiplyScalar(s, tau);
+          for (j = k; j < rows; ++j) {
+            Qdata[i][j] = divideScalar(subtractScalar(Qdata[i][j], multiplyScalar(s, conj(w[j]))), conjSgn);
+          }
+        }
+      }
+    }
+
+    // return matrices
+    return {
+      Q,
+      R,
+      toString: function toString() {
+        return 'Q: ' + this.Q.toString() + '\nR: ' + this.R.toString();
+      }
+    };
+  }
+  function _denseQR(m) {
+    var ret = _denseQRimpl(m);
+    var Rdata = ret.R._data;
+    if (m._data.length > 0) {
+      var zero = Rdata[0][0].type === 'Complex' ? complex(0) : 0;
+      for (var i = 0; i < Rdata.length; ++i) {
+        for (var j = 0; j < i && j < (Rdata[0] || []).length; ++j) {
+          Rdata[i][j] = zero;
+        }
+      }
+    }
+    return ret;
+  }
+  function _sparseQR(m) {
+    throw new Error('qr not implemented for sparse matrices yet');
+  }
+});