octave: liboctave/numeric/CollocWt.cc annotate

annotate 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

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ////////////////////////////////////////////////////////////////////////
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 //
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30394 diff changeset	3 // Copyright (C) 1993-2022 The Octave Project Developers
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	4 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 // See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 // distribution or <https://octave.org/copyright/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	7 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	8 // This file is part of Octave.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	9 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	10 // Octave is free software: you can redistribute it and/or modify it
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	11 // under the terms of the GNU General Public License as published by
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	12 // the Free Software Foundation, either version 3 of the License, or
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	13 // (at your option) any later version.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	14 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	15 // Octave is distributed in the hope that it will be useful, but
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	16 // WITHOUT ANY WARRANTY; without even the implied warranty of
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	18 // GNU General Public License for more details.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	19 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	20 // You should have received a copy of the GNU General Public License
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	21 // along with Octave; see the file COPYING. If not, see
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	22 // <https://www.gnu.org/licenses/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ////////////////////////////////////////////////////////////////////////
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	25
21724 aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef" John W. Eaton <jwe@octave.org> parents: 21568 diff changeset	26 #if defined (HAVE_CONFIG_H)
21301 40de9f8f23a6 Use '#include "config.h"' rather than <config.h>. Rik <rik@octave.org> parents: 21202 diff changeset	27 # include "config.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	28 #endif
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	29
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	30 #include <cassert>
d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	31 #include <cmath>
d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	32
23443 3f1bf237908b maint: Eliminate <cfloat.h> header from liboctave files. Rik <rik@octave.org> parents: 23220 diff changeset	33 #include <limits>
25438 cb1606f78f6b prefer <istream>, <ostream>, or <iosfwd> to <iostream> where possible John W. Eaton <jwe@octave.org> parents: 25247 diff changeset	34 #include <ostream>
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	35
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	36 #include "Array.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	37 #include "CollocWt.h"
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	38 #include "lo-error.h"
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	39 #include "lo-mappers.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	40
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	41 // The following routines jcobi, dif, and dfopr are based on the code
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	42 // found in Villadsen, J. and M. L. Michelsen, Solution of Differential
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	43 // Equation Models by Polynomial Approximation, Prentice-Hall (1978)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	44 // pages 418-420.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	45 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	46 // Translated to C++ by jwe.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	47
31605 e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 30564 diff changeset	48 OCTAVE_BEGIN_NAMESPACE(octave)
e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 30564 diff changeset	49
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	50 // Compute the first three derivatives of the node polynomial.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	51 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	52 // n0 (alpha,beta) n1
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	53 // p (x) = (x) * p (x) * (1 - x)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	54 // nt n
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	55 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	56 // at the interpolation points. Each of the parameters n0 and n1
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	57 // may be given the value 0 or 1. The total number of points
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	58 // nt = n + n0 + n1
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	59 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	60 // The values of root must be known before a call to dif is possible.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	61 // They may be computed using jcobi.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	62
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	63 static void dif (octave_idx_type nt, double root, double dif1,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	64 double dif2, double dif3)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	65 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	66 // Evaluate derivatives of node polynomial using recursion formulas.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	67
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	68 for (octave_idx_type i = 0; i < nt; i++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	69 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	70 double x = root[i];
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	71
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	72 dif1[i] = 1.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	73 dif2[i] = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	74 dif3[i] = 0.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	75
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	76 for (octave_idx_type j = 0; j < nt; j++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	77 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	78 if (j != i)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	79 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	80 double y = x - root[j];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	81
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	82 dif3[i] = y * dif3[i] + 3.0 * dif2[i];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	83 dif2[i] = y * dif2[i] + 2.0 * dif1[i];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	84 dif1[i] = y * dif1[i];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	85 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	86 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	87 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	88 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	89
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	90 // Compute the zeros of the Jacobi polynomial.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	91 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	92 // (alpha,beta)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	93 // p (x)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	94 // n
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	95 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	96 // Use dif to compute the derivatives of the node
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	97 // polynomial
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	98 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	99 // n0 (alpha,beta) n1
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	100 // p (x) = (x) * p (x) * (1 - x)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	101 // nt n
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	102 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	103 // at the interpolation points.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	104 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	105 // See Villadsen and Michelsen, pages 131-132 and 418.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	106 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	107 // Input parameters:
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	108 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	109 // nd : the dimension of the vectors dif1, dif2, dif3, and root
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	110 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	111 // n : the degree of the jacobi polynomial, (i.e., the number
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	112 // of interior interpolation points)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	113 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	114 // n0 : determines whether x = 0 is included as an
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	115 // interpolation point
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	116 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	117 // n0 = 0 ==> x = 0 is not included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	118 // n0 = 1 ==> x = 0 is included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	119 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	120 // n1 : determines whether x = 1 is included as an
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	121 // interpolation point
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	122 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	123 // n1 = 0 ==> x = 1 is not included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	124 // n1 = 1 ==> x = 1 is included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	125 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	126 // alpha : the value of alpha in the description of the jacobi
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	127 // polynomial
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	128 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	129 // beta : the value of beta in the description of the jacobi
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	130 // polynomial
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	131 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	132 // For a more complete explanation of alpha an beta, see Villadsen
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	133 // and Michelsen, pages 57 to 59.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	134 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	135 // Output parameters:
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	136 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	137 // root : one dimensional vector containing on exit the
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	138 // n + n0 + n1 zeros of the node polynomial used in the
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	139 // interpolation routine
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	140 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	141 // dif1 : one dimensional vector containing the first derivative
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	142 // of the node polynomial at the zeros
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	143 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	144 // dif2 : one dimensional vector containing the second derivative
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	145 // of the node polynomial at the zeros
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	146 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	147 // dif3 : one dimensional vector containing the third derivative
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	148 // of the node polynomial at the zeros
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	149
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	150 static bool jcobi (octave_idx_type n, octave_idx_type n0, octave_idx_type n1,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	151 double alpha, double beta, double dif1, double dif2,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	152 double dif3, double root)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	153 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	154 assert (n0 == 0 \|\| n0 == 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	155 assert (n1 == 0 \|\| n1 == 1);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	156
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	157 octave_idx_type nt = n + n0 + n1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	158
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	159 assert (nt >= 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	160
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	161 // -- first evaluation of coefficients in recursion formulas.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	162 // -- recursion coefficients are stored in dif1 and dif2.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	163
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	164 double ab = alpha + beta;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	165 double ad = beta - alpha;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	166 double ap = beta * alpha;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	167
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	168 dif1[0] = (ad / (ab + 2.0) + 1.0) / 2.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	169 dif2[0] = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	170
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	171 if (n >= 2)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	172 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	173 for (octave_idx_type i = 1; i < n; i++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	174 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	175 double z1 = i;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	176 double z = ab + 2 * z1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	177
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	178 dif1[i] = (ab * ad / z / (z + 2.0) + 1.0) / 2.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	179
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	180 if (i == 1)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	181 dif2[i] = (ab + ap + z1) / z / z / (z + 1.0);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	182 else
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	183 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	184 z *= z;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	185 double y = z1 * (ab + z1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	186 y *= (ap + y);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	187 dif2[i] = y / z / (z - 1.0);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	188 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	189 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	190 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	191
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	192 // Root determination by Newton method with suppression of previously
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	193 // determined roots.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	194
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	195 double x = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	196
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	197 for (octave_idx_type i = 0; i < n; i++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	198 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	199 bool done = false;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	200
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	201 int k = 0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	202
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	203 while (! done)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	204 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	205 double xd = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	206 double xn = 1.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	207 double xd1 = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	208 double xn1 = 0.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	209
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	210 for (octave_idx_type j = 0; j < n; j++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	211 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	212 double xp = (dif1[j] - x) * xn - dif2[j] * xd;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	213 double xp1 = (dif1[j] - x) * xn1 - dif2[j] * xd1 - xn;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	214
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	215 xd = xn;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	216 xd1 = xn1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	217 xn = xp;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	218 xn1 = xp1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	219 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	220
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	221 double zc = 1.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	222 double z = xn / xn1;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	223
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	224 if (i != 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	225 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	226 for (octave_idx_type j = 1; j <= i; j++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	227 zc -= z / (x - root[j-1]);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	228 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	229
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	230 z /= zc;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	231 x -= z;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	232
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	233 // Famous last words: 100 iterations should be more than
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	234 // enough in all cases.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	235
29950 6549fa7558ba eliminate some unnecessary octave:: namespace tags John W. Eaton <jwe@octave.org> parents: 29681 diff changeset	236 if (++k > 100 \|\| math::isnan (z))
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	237 return false;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	238
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	239 if (std::abs (z) <= 100 * std::numeric_limits<double>::epsilon ())
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	240 done = true;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	241 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	242
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	243 root[i] = x;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	244 x += std::sqrt (std::numeric_limits<double>::epsilon ());
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	245 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	246
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	247 // Add interpolation points at x = 0 and/or x = 1.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	248
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	249 if (n0 != 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	250 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	251 for (octave_idx_type i = n; i > 0; i--)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	252 root[i] = root[i-1];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	253
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	254 root[0] = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	255 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	256
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	257 if (n1 != 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	258 root[nt-1] = 1.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	259
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	260 dif (nt, root, dif1, dif2, dif3);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	261
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	262 return true;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	263 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	264
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	265 // Compute derivative weights for orthogonal collocation.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	266 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	267 // See Villadsen and Michelsen, pages 133-134, 419.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	268 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	269 // Input parameters:
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	270 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	271 // nd : the dimension of the vectors dif1, dif2, dif3, and root
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	272 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	273 // n : the degree of the jacobi polynomial, (i.e., the number
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	274 // of interior interpolation points)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	275 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	276 // n0 : determines whether x = 0 is included as an
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	277 // interpolation point
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	278 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	279 // n0 = 0 ==> x = 0 is not included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	280 // n0 = 1 ==> x = 0 is included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	281 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	282 // n1 : determines whether x = 1 is included as an
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	283 // interpolation point
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	284 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	285 // n1 = 0 ==> x = 1 is not included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	286 // n1 = 1 ==> x = 1 is included
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	287 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	288 // i : the index of the node for which the weights are to be
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	289 // calculated
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	290 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	291 // id : indicator
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	292 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	293 // id = 1 ==> first derivative weights are computed
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	294 // id = 2 ==> second derivative weights are computed
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	295 // id = 3 ==> gaussian weights are computed (in this
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	296 // case, the value of i is irrelevant)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	297 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	298 // Output parameters:
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	299 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	300 // dif1 : one dimensional vector containing the first derivative
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	301 // of the node polynomial at the zeros
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	302 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	303 // dif2 : one dimensional vector containing the second derivative
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	304 // of the node polynomial at the zeros
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	305 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	306 // dif3 : one dimensional vector containing the third derivative
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	307 // of the node polynomial at the zeros
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	308 //
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	309 // vect : one dimensional vector of computed weights
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	310
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	311 static void dfopr (octave_idx_type n, octave_idx_type n0, octave_idx_type n1,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	312 octave_idx_type i, octave_idx_type id, double *dif1,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	313 double dif2, double dif3, double root, double vect)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	314 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	315 assert (n0 == 0 \|\| n0 == 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	316 assert (n1 == 0 \|\| n1 == 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	317
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	318 octave_idx_type nt = n + n0 + n1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	319
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	320 assert (nt >= 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	321
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	322 assert (id == 1 \|\| id == 2 \|\| id == 3);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	323
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	324 if (id != 3)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	325 assert (i >= 0 && i < nt);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	326
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	327 // Evaluate discretization matrices and Gaussian quadrature weights.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	328 // Quadrature weights are normalized to sum to one.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	329
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	330 if (id != 3)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	331 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	332 for (octave_idx_type j = 0; j < nt; j++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	333 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	334 if (j == i)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	335 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	336 if (id == 1)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	337 vect[i] = dif2[i] / dif1[i] / 2.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	338 else
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	339 vect[i] = dif3[i] / dif1[i] / 3.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	340 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	341 else
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	342 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	343 double y = root[i] - root[j];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	344
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	345 vect[j] = dif1[i] / dif1[j] / y;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	346
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	347 if (id == 2)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	348 vect[j] = vect[j] * (dif2[i] / dif1[i] - 2.0 / y);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	349 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	350 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	351 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	352 else
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	353 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	354 double y = 0.0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	355
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	356 for (octave_idx_type j = 0; j < nt; j++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	357 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	358 double x = root[j];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	359
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	360 double ax = x * (1.0 - x);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	361
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	362 if (n0 == 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	363 ax = ax / x / x;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	364
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	365 if (n1 == 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	366 ax = ax / (1.0 - x) / (1.0 - x);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	367
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	368 vect[j] = ax / (dif1[j] * dif1[j]);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	369
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	370 y += vect[j];
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	371 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	372
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	373 for (octave_idx_type j = 0; j < nt; j++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	374 vect[j] = vect[j] / y;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	375 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	376 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	377
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	378 // Error handling.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	379
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	380 void CollocWt::error (const char *msg)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	381 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	382 (*current_liboctave_error_handler) ("CollocWt: fatal error '%s'", msg);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	383 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	384
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	385 CollocWt& CollocWt::set_left (double val)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	386 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	387 if (val >= m_rb)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	388 error ("CollocWt: left bound greater than right bound");
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	389
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	390 m_lb = val;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	391 m_initialized = 0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	392 return *this;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	393 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	394
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	395 CollocWt& CollocWt::set_right (double val)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	396 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	397 if (val <= m_lb)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	398 error ("CollocWt: right bound less than left bound");
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	399
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	400 m_rb = val;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	401 m_initialized = 0;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	402 return *this;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	403 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	404
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	405 void CollocWt::init (void)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	406 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	407 // Check for possible errors.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	408
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	409 double wid = m_rb - m_lb;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	410 if (wid <= 0.0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	411 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	412 error ("CollocWt: width less than or equal to zero");
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	413 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	414
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	415 octave_idx_type nt = m_n + m_inc_left + m_inc_right;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	416
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	417 if (nt < 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	418 error ("CollocWt: total number of collocation points less than zero");
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	419 else if (nt == 0)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	420 return;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	421
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	422 Array<double> dif1 (dim_vector (nt, 1));
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	423 double *pdif1 = dif1.fortran_vec ();
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	424
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	425 Array<double> dif2 (dim_vector (nt, 1));
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	426 double *pdif2 = dif2.fortran_vec ();
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	427
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	428 Array<double> dif3 (dim_vector (nt, 1));
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	429 double *pdif3 = dif3.fortran_vec ();
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	430
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	431 Array<double> vect (dim_vector (nt, 1));
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	432 double *pvect = vect.fortran_vec ();
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	433
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	434 m_r.resize (nt, 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	435 m_q.resize (nt, 1);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	436 m_A.resize (nt, nt);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	437 m_B.resize (nt, nt);
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	438
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	439 double *pr = m_r.fortran_vec ();
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	440
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	441 // Compute roots.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	442
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	443 if (! jcobi (m_n, m_inc_left, m_inc_right, m_alpha, m_beta, pdif1,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	444 pdif2, pdif3, pr))
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	445 error ("jcobi: newton iteration failed");
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	446
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	447 octave_idx_type id;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	448
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	449 // First derivative weights.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	450
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	451 id = 1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	452 for (octave_idx_type i = 0; i < nt; i++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	453 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	454 dfopr (m_n, m_inc_left, m_inc_right, i, id, pdif1, pdif2, pdif3,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	455 pr, pvect);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	456
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	457 for (octave_idx_type j = 0; j < nt; j++)
30394 f3f3e3793fb5 maint: style check C++ files in liboctave/ ahead of 7.1 release. Rik <rik@octave.org> parents: 29950 diff changeset	458 m_A(i, j) = vect(j);
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	459 }
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	460
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	461 // Second derivative weights.
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	462
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	463 id = 2;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	464 for (octave_idx_type i = 0; i < nt; i++)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	465 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	466 dfopr (m_n, m_inc_left, m_inc_right, i, id, pdif1, pdif2, pdif3,
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	467 pr, pvect);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	468
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	469 for (octave_idx_type j = 0; j < nt; j++)
30394 f3f3e3793fb5 maint: style check C++ files in liboctave/ ahead of 7.1 release. Rik <rik@octave.org> parents: 29950 diff changeset	470 m_B(i, j) = vect(j);
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	471 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	472
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	473 // Gaussian quadrature weights.
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	474
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	475 id = 3;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	476 double *pq = m_q.fortran_vec ();
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	477 dfopr (m_n, m_inc_left, m_inc_right, id, id, pdif1, pdif2, pdif3, pr, pq);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	478
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	479 m_initialized = 1;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	480 }
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	481
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	482 std::ostream& operator << (std::ostream& os, const CollocWt& a)
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	483 {
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	484 if (a.left_included ())
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	485 os << "left boundary is included\n";
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	486 else
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	487 os << "left boundary is not included\n";
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	488
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	489 if (a.right_included ())
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	490 os << "right boundary is included\n";
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	491 else
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	492 os << "right boundary is not included\n";
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	493
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	494 os << "\n";
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	495
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	496 os << a.m_alpha << ' ' << a.m_beta << "\n\n"
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	497 << a.m_r << "\n\n"
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	498 << a.m_q << "\n\n"
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	499 << a.m_A << "\n"
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	500 << a.m_B << "\n";
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	501
29681 25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	502 return os;
25246c1a1645 move CollocWt class inside octave namespace John W. Eaton <jwe@octave.org> parents: 29680 diff changeset	503 }
31605 e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 30564 diff changeset	504
e88a07dec498 maint: Use macros to begin/end C++ namespaces. Rik <rik@octave.org> parents: 30564 diff changeset	505 OCTAVE_END_NAMESPACE(octave)

Mercurial > octave

annotate liboctave/numeric/CollocWt.cc @ 31605:e88a07dec498 stable