Mercurial > octave
view liboctave/numeric/CollocWt.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 796f54d4ddbf |
children | aac27ad79be6 |
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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. OCTAVE_BEGIN_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; } OCTAVE_END_NAMESPACE(octave)