Mercurial > octave
view liboctave/numeric/CollocWt.cc @ 31202:434b5a1b9498
isequal.m: Add ability to compare Java objects (bug #62930)
* isequal.m: Add elseif clause to detect Java objects and use built-in Java
"equals" method for comparison. Add BIST test for Java object comparison.
author | Rik <rik@octave.org> |
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date | Thu, 25 Aug 2022 15:35:25 -0700 |
parents | 796f54d4ddbf |
children | e88a07dec498 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1993-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cassert> #include <cmath> #include <limits> #include <ostream> #include "Array.h" #include "CollocWt.h" #include "lo-error.h" #include "lo-mappers.h" // The following routines jcobi, dif, and dfopr are based on the code // found in Villadsen, J. and M. L. Michelsen, Solution of Differential // Equation Models by Polynomial Approximation, Prentice-Hall (1978) // pages 418-420. // // Translated to C++ by jwe. namespace octave { // Compute the first three derivatives of the node polynomial. // // n0 (alpha,beta) n1 // p (x) = (x) * p (x) * (1 - x) // nt n // // at the interpolation points. Each of the parameters n0 and n1 // may be given the value 0 or 1. The total number of points // nt = n + n0 + n1 // // The values of root must be known before a call to dif is possible. // They may be computed using jcobi. static void dif (octave_idx_type nt, double *root, double *dif1, double *dif2, double *dif3) { // Evaluate derivatives of node polynomial using recursion formulas. for (octave_idx_type i = 0; i < nt; i++) { double x = root[i]; dif1[i] = 1.0; dif2[i] = 0.0; dif3[i] = 0.0; for (octave_idx_type j = 0; j < nt; j++) { if (j != i) { double y = x - root[j]; dif3[i] = y * dif3[i] + 3.0 * dif2[i]; dif2[i] = y * dif2[i] + 2.0 * dif1[i]; dif1[i] = y * dif1[i]; } } } } // Compute the zeros of the Jacobi polynomial. // // (alpha,beta) // p (x) // n // // Use dif to compute the derivatives of the node // polynomial // // n0 (alpha,beta) n1 // p (x) = (x) * p (x) * (1 - x) // nt n // // at the interpolation points. // // See Villadsen and Michelsen, pages 131-132 and 418. // // Input parameters: // // nd : the dimension of the vectors dif1, dif2, dif3, and root // // n : the degree of the jacobi polynomial, (i.e., the number // of interior interpolation points) // // n0 : determines whether x = 0 is included as an // interpolation point // // n0 = 0 ==> x = 0 is not included // n0 = 1 ==> x = 0 is included // // n1 : determines whether x = 1 is included as an // interpolation point // // n1 = 0 ==> x = 1 is not included // n1 = 1 ==> x = 1 is included // // alpha : the value of alpha in the description of the jacobi // polynomial // // beta : the value of beta in the description of the jacobi // polynomial // // For a more complete explanation of alpha an beta, see Villadsen // and Michelsen, pages 57 to 59. // // Output parameters: // // root : one dimensional vector containing on exit the // n + n0 + n1 zeros of the node polynomial used in the // interpolation routine // // dif1 : one dimensional vector containing the first derivative // of the node polynomial at the zeros // // dif2 : one dimensional vector containing the second derivative // of the node polynomial at the zeros // // dif3 : one dimensional vector containing the third derivative // of the node polynomial at the zeros static bool jcobi (octave_idx_type n, octave_idx_type n0, octave_idx_type n1, double alpha, double beta, double *dif1, double *dif2, double *dif3, double *root) { assert (n0 == 0 || n0 == 1); assert (n1 == 0 || n1 == 1); octave_idx_type nt = n + n0 + n1; assert (nt >= 1); // -- first evaluation of coefficients in recursion formulas. // -- recursion coefficients are stored in dif1 and dif2. double ab = alpha + beta; double ad = beta - alpha; double ap = beta * alpha; dif1[0] = (ad / (ab + 2.0) + 1.0) / 2.0; dif2[0] = 0.0; if (n >= 2) { for (octave_idx_type i = 1; i < n; i++) { double z1 = i; double z = ab + 2 * z1; dif1[i] = (ab * ad / z / (z + 2.0) + 1.0) / 2.0; if (i == 1) dif2[i] = (ab + ap + z1) / z / z / (z + 1.0); else { z *= z; double y = z1 * (ab + z1); y *= (ap + y); dif2[i] = y / z / (z - 1.0); } } } // Root determination by Newton method with suppression of previously // determined roots. double x = 0.0; for (octave_idx_type i = 0; i < n; i++) { bool done = false; int k = 0; while (! done) { double xd = 0.0; double xn = 1.0; double xd1 = 0.0; double xn1 = 0.0; for (octave_idx_type j = 0; j < n; j++) { double xp = (dif1[j] - x) * xn - dif2[j] * xd; double xp1 = (dif1[j] - x) * xn1 - dif2[j] * xd1 - xn; xd = xn; xd1 = xn1; xn = xp; xn1 = xp1; } double zc = 1.0; double z = xn / xn1; if (i != 0) { for (octave_idx_type j = 1; j <= i; j++) zc -= z / (x - root[j-1]); } z /= zc; x -= z; // Famous last words: 100 iterations should be more than // enough in all cases. if (++k > 100 || math::isnan (z)) return false; if (std::abs (z) <= 100 * std::numeric_limits<double>::epsilon ()) done = true; } root[i] = x; x += std::sqrt (std::numeric_limits<double>::epsilon ()); } // Add interpolation points at x = 0 and/or x = 1. if (n0 != 0) { for (octave_idx_type i = n; i > 0; i--) root[i] = root[i-1]; root[0] = 0.0; } if (n1 != 0) root[nt-1] = 1.0; dif (nt, root, dif1, dif2, dif3); return true; } // Compute derivative weights for orthogonal collocation. // // See Villadsen and Michelsen, pages 133-134, 419. // // Input parameters: // // nd : the dimension of the vectors dif1, dif2, dif3, and root // // n : the degree of the jacobi polynomial, (i.e., the number // of interior interpolation points) // // n0 : determines whether x = 0 is included as an // interpolation point // // n0 = 0 ==> x = 0 is not included // n0 = 1 ==> x = 0 is included // // n1 : determines whether x = 1 is included as an // interpolation point // // n1 = 0 ==> x = 1 is not included // n1 = 1 ==> x = 1 is included // // i : the index of the node for which the weights are to be // calculated // // id : indicator // // id = 1 ==> first derivative weights are computed // id = 2 ==> second derivative weights are computed // id = 3 ==> gaussian weights are computed (in this // case, the value of i is irrelevant) // // Output parameters: // // dif1 : one dimensional vector containing the first derivative // of the node polynomial at the zeros // // dif2 : one dimensional vector containing the second derivative // of the node polynomial at the zeros // // dif3 : one dimensional vector containing the third derivative // of the node polynomial at the zeros // // vect : one dimensional vector of computed weights static void dfopr (octave_idx_type n, octave_idx_type n0, octave_idx_type n1, octave_idx_type i, octave_idx_type id, double *dif1, double *dif2, double *dif3, double *root, double *vect) { assert (n0 == 0 || n0 == 1); assert (n1 == 0 || n1 == 1); octave_idx_type nt = n + n0 + n1; assert (nt >= 1); assert (id == 1 || id == 2 || id == 3); if (id != 3) assert (i >= 0 && i < nt); // Evaluate discretization matrices and Gaussian quadrature weights. // Quadrature weights are normalized to sum to one. if (id != 3) { for (octave_idx_type j = 0; j < nt; j++) { if (j == i) { if (id == 1) vect[i] = dif2[i] / dif1[i] / 2.0; else vect[i] = dif3[i] / dif1[i] / 3.0; } else { double y = root[i] - root[j]; vect[j] = dif1[i] / dif1[j] / y; if (id == 2) vect[j] = vect[j] * (dif2[i] / dif1[i] - 2.0 / y); } } } else { double y = 0.0; for (octave_idx_type j = 0; j < nt; j++) { double x = root[j]; double ax = x * (1.0 - x); if (n0 == 0) ax = ax / x / x; if (n1 == 0) ax = ax / (1.0 - x) / (1.0 - x); vect[j] = ax / (dif1[j] * dif1[j]); y += vect[j]; } for (octave_idx_type j = 0; j < nt; j++) vect[j] = vect[j] / y; } } // Error handling. void CollocWt::error (const char *msg) { (*current_liboctave_error_handler) ("CollocWt: fatal error '%s'", msg); } CollocWt& CollocWt::set_left (double val) { if (val >= m_rb) error ("CollocWt: left bound greater than right bound"); m_lb = val; m_initialized = 0; return *this; } CollocWt& CollocWt::set_right (double val) { if (val <= m_lb) error ("CollocWt: right bound less than left bound"); m_rb = val; m_initialized = 0; return *this; } void CollocWt::init (void) { // Check for possible errors. double wid = m_rb - m_lb; if (wid <= 0.0) { error ("CollocWt: width less than or equal to zero"); } octave_idx_type nt = m_n + m_inc_left + m_inc_right; if (nt < 0) error ("CollocWt: total number of collocation points less than zero"); else if (nt == 0) return; Array<double> dif1 (dim_vector (nt, 1)); double *pdif1 = dif1.fortran_vec (); Array<double> dif2 (dim_vector (nt, 1)); double *pdif2 = dif2.fortran_vec (); Array<double> dif3 (dim_vector (nt, 1)); double *pdif3 = dif3.fortran_vec (); Array<double> vect (dim_vector (nt, 1)); double *pvect = vect.fortran_vec (); m_r.resize (nt, 1); m_q.resize (nt, 1); m_A.resize (nt, nt); m_B.resize (nt, nt); double *pr = m_r.fortran_vec (); // Compute roots. if (! jcobi (m_n, m_inc_left, m_inc_right, m_alpha, m_beta, pdif1, pdif2, pdif3, pr)) error ("jcobi: newton iteration failed"); octave_idx_type id; // First derivative weights. id = 1; for (octave_idx_type i = 0; i < nt; i++) { dfopr (m_n, m_inc_left, m_inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect); for (octave_idx_type j = 0; j < nt; j++) m_A(i, j) = vect(j); } // Second derivative weights. id = 2; for (octave_idx_type i = 0; i < nt; i++) { dfopr (m_n, m_inc_left, m_inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect); for (octave_idx_type j = 0; j < nt; j++) m_B(i, j) = vect(j); } // Gaussian quadrature weights. id = 3; double *pq = m_q.fortran_vec (); dfopr (m_n, m_inc_left, m_inc_right, id, id, pdif1, pdif2, pdif3, pr, pq); m_initialized = 1; } std::ostream& operator << (std::ostream& os, const CollocWt& a) { if (a.left_included ()) os << "left boundary is included\n"; else os << "left boundary is not included\n"; if (a.right_included ()) os << "right boundary is included\n"; else os << "right boundary is not included\n"; os << "\n"; os << a.m_alpha << ' ' << a.m_beta << "\n\n" << a.m_r << "\n\n" << a.m_q << "\n\n" << a.m_A << "\n" << a.m_B << "\n"; return os; } }