octave: liboctave/numeric/CollocWt.cc annotate

annotate liboctave/numeric/CollocWt.cc @ 25438:cb1606f78f6b

prefer <istream>, <ostream>, or <iosfwd> to <iostream> where possible Using <iostream> brings with it a static initializer for the std::cin, std::cout, and std::cerr streams. In most cases they are not needed and should be avoided if possible. Files affected: build-aux/mk-opts.pl libgui/qterminal/libqterminal/win32/QWinTerminalImpl.cpp libinterp/corefcn/__dsearchn__.cc libinterp/corefcn/c-file-ptr-stream.cc libinterp/corefcn/c-file-ptr-stream.h libinterp/corefcn/daspk.cc libinterp/corefcn/dasrt.cc libinterp/corefcn/dassl.cc libinterp/corefcn/defaults.cc libinterp/corefcn/defun.cc libinterp/corefcn/file-io.cc libinterp/corefcn/ft-text-renderer.cc libinterp/corefcn/gl-render.cc libinterp/corefcn/help.cc libinterp/corefcn/ls-ascii-helper.cc libinterp/corefcn/ls-hdf5.cc libinterp/corefcn/ls-hdf5.h libinterp/corefcn/ls-mat-ascii.cc libinterp/corefcn/ls-mat4.cc libinterp/corefcn/ls-mat5.cc libinterp/corefcn/ls-oct-binary.cc libinterp/corefcn/ls-oct-text.cc libinterp/corefcn/lsode.cc libinterp/corefcn/oct-iostrm.cc libinterp/corefcn/oct-procbuf.cc libinterp/corefcn/oct-stdstrm.h libinterp/corefcn/procstream.cc libinterp/corefcn/procstream.h libinterp/corefcn/quad.cc libinterp/corefcn/symscope.h libinterp/corefcn/symtab.h libinterp/corefcn/toplev.cc libinterp/corefcn/urlwrite.cc libinterp/corefcn/utils.cc libinterp/corefcn/zfstream.cc libinterp/dldfcn/__ode15__.cc libinterp/dldfcn/convhulln.cc libinterp/octave-value/ov-base-diag.cc libinterp/octave-value/ov-base-int.cc libinterp/octave-value/ov-base-mat.cc libinterp/octave-value/ov-base-scalar.cc libinterp/octave-value/ov-base-sparse.cc libinterp/octave-value/ov-base.cc libinterp/octave-value/ov-bool-mat.cc libinterp/octave-value/ov-bool-sparse.cc libinterp/octave-value/ov-bool.cc libinterp/octave-value/ov-cell.cc libinterp/octave-value/ov-ch-mat.cc libinterp/octave-value/ov-class.cc libinterp/octave-value/ov-colon.cc libinterp/octave-value/ov-complex.cc libinterp/octave-value/ov-cs-list.cc libinterp/octave-value/ov-cx-mat.cc libinterp/octave-value/ov-cx-sparse.cc libinterp/octave-value/ov-fcn-handle.cc libinterp/octave-value/ov-fcn-inline.cc libinterp/octave-value/ov-float.cc libinterp/octave-value/ov-flt-complex.cc libinterp/octave-value/ov-flt-cx-mat.cc libinterp/octave-value/ov-flt-re-mat.cc libinterp/octave-value/ov-int16.cc libinterp/octave-value/ov-int32.cc libinterp/octave-value/ov-int64.cc libinterp/octave-value/ov-int8.cc libinterp/octave-value/ov-java.cc libinterp/octave-value/ov-range.cc libinterp/octave-value/ov-re-mat.cc libinterp/octave-value/ov-re-sparse.cc libinterp/octave-value/ov-scalar.cc libinterp/octave-value/ov-str-mat.cc libinterp/octave-value/ov-struct.cc libinterp/octave-value/ov-typeinfo.cc libinterp/octave-value/ov-uint16.cc libinterp/octave-value/ov-uint32.cc libinterp/octave-value/ov-uint64.cc libinterp/octave-value/ov-uint8.cc libinterp/octave.cc libinterp/parse-tree/bp-table.cc libinterp/parse-tree/lex.h libinterp/parse-tree/profiler.cc libinterp/parse-tree/pt-arg-list.cc libinterp/parse-tree/pt-array-list.cc libinterp/parse-tree/pt-assign.cc libinterp/parse-tree/pt-cell.cc libinterp/parse-tree/pt-const.cc libinterp/parse-tree/pt-eval.cc libinterp/parse-tree/pt-exp.cc libinterp/parse-tree/pt-fcn-handle.cc libinterp/parse-tree/pt-jit.cc libinterp/parse-tree/pt-pr-code.cc libinterp/parse-tree/pt-tm-const.cc libinterp/parse-tree/pt.cc liboctave/array/Array.cc liboctave/array/CColVector.cc liboctave/array/CDiagMatrix.cc liboctave/array/CMatrix.cc liboctave/array/CNDArray.cc liboctave/array/CRowVector.cc liboctave/array/CSparse.cc liboctave/array/DiagArray2.cc liboctave/array/MArray.cc liboctave/array/Range.cc liboctave/array/Sparse.cc liboctave/array/boolMatrix.cc liboctave/array/boolSparse.cc liboctave/array/chMatrix.cc liboctave/array/dColVector.cc liboctave/array/dDiagMatrix.cc liboctave/array/dMatrix.cc liboctave/array/dNDArray.cc liboctave/array/dRowVector.cc liboctave/array/dSparse.cc liboctave/array/fCColVector.cc liboctave/array/fCDiagMatrix.cc liboctave/array/fCMatrix.cc liboctave/array/fCNDArray.cc liboctave/array/fCRowVector.cc liboctave/array/fColVector.cc liboctave/array/fDiagMatrix.cc liboctave/array/fMatrix.cc liboctave/array/fNDArray.cc liboctave/array/fRowVector.cc liboctave/array/idx-vector.cc liboctave/numeric/CollocWt.cc liboctave/numeric/eigs-base.cc liboctave/system/file-ops.cc liboctave/system/oct-time.cc liboctave/util/cmd-hist.cc liboctave/util/data-conv.cc liboctave/util/data-conv.h liboctave/util/file-info.cc liboctave/util/lo-utils.cc liboctave/util/lo-utils.h liboctave/util/quit.cc liboctave/util/str-vec.cc liboctave/util/url-transfer.cc liboctave/util/url-transfer.h

author	John W. Eaton <jwe@octave.org>
date	Thu, 07 Jun 2018 10:11:54 -0400
parents	db31e068f4db
children	00f796120a6d

rev	line source
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	1 /*
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	2
25054 6652d3823428 maint: Update copyright dates in all source files. John W. Eaton <jwe@octave.org> parents: 24534 diff changeset	3 Copyright (C) 1993-2018 John W. Eaton
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	4
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	5 This file is part of Octave.
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	6
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23807 diff changeset	7 Octave is free software: you can redistribute it and/or modify it
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	8 under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23807 diff changeset	9 the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	10 (at your option) any later version.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	11
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	12 Octave is distributed in the hope that it will be useful, but
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	13 WITHOUT ANY WARRANTY; without even the implied warranty of
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	15 GNU General Public License for more details.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	16
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	17 You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5307 diff changeset	18 along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23807 diff changeset	19 <https://www.gnu.org/licenses/>.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	20
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	21 */
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	22
21724 aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef" John W. Eaton <jwe@octave.org> parents: 21568 diff changeset	23 #if defined (HAVE_CONFIG_H)
21301 40de9f8f23a6 Use '#include "config.h"' rather than <config.h>. Rik <rik@octave.org> parents: 21202 diff changeset	24 # include "config.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	25 #endif
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	26
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	27 #include <cassert>
d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	28 #include <cmath>
d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	29
23443 3f1bf237908b maint: Eliminate <cfloat.h> header from liboctave files. Rik <rik@octave.org> parents: 23220 diff changeset	30 #include <limits>
25438 cb1606f78f6b prefer <istream>, <ostream>, or <iosfwd> to <iostream> where possible John W. Eaton <jwe@octave.org> parents: 25247 diff changeset	31 #include <ostream>
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	32
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	33 #include "Array.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	34 #include "CollocWt.h"
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	35 #include "lo-error.h"
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	36 #include "lo-mappers.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	37
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	38 // 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	39 // 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	40 // Equation Models by Polynomial Approximation, Prentice-Hall (1978)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	41 // pages 418-420.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	42 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	43 // Translated to C++ by jwe.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	44
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	45 // Compute the first three derivatives of the node polynomial.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	46 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	47 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	48 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	49 // nt n
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	50 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	51 // at the interpolation points. Each of the parameters n0 and n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	52 // may be given the value 0 or 1. The total number of points
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	53 // nt = n + n0 + n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	54 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	55 // The values of root must be known before a call to dif is possible.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	56 // They may be computed using jcobi.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	57
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	58 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	59 dif (octave_idx_type nt, double root, double dif1, double *dif2,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	60 double *dif3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	61 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	62 // Evaluate derivatives of node polynomial using recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	63
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	64 for (octave_idx_type i = 0; i < nt; i++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	65 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	66 double x = root[i];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	67
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	68 dif1[i] = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	69 dif2[i] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	70 dif3[i] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	71
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	72 for (octave_idx_type j = 0; j < nt; j++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	73 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	74 if (j != i)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	75 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	76 double y = x - root[j];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	77
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	78 dif3[i] = y * dif3[i] + 3.0 * dif2[i];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	79 dif2[i] = y * dif2[i] + 2.0 * dif1[i];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	80 dif1[i] = y * dif1[i];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	81 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	82 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	83 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	84 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	85
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	86 // Compute the zeros of the Jacobi polynomial.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	87 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	88 // (alpha,beta)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	89 // p (x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	90 // n
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	91 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	92 // Use dif to compute the derivatives of the node
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	93 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	94 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	95 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	96 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	97 // nt n
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	98 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	99 // at the interpolation points.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	100 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	101 // See Villadsen and Michelsen, pages 131-132 and 418.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	102 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	103 // Input parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	104 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	105 // nd : the dimension of the vectors dif1, dif2, dif3, and root
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	106 //
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21724 diff changeset	107 // n : the degree of the jacobi polynomial, (i.e., the number
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	108 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	109 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	110 // n0 : determines whether x = 0 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	111 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	112 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	113 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	114 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	115 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	116 // n1 : determines whether x = 1 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	117 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	118 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	119 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	120 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	121 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	122 // alpha : the value of alpha in the description of the jacobi
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	123 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	124 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	125 // beta : the value of beta in the description of the jacobi
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	126 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	127 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	128 // For a more complete explanation of alpha an beta, see Villadsen
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	129 // and Michelsen, pages 57 to 59.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	130 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	131 // Output parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	132 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	133 // root : one dimensional vector containing on exit the
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	134 // n + n0 + n1 zeros of the node polynomial used in the
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	135 // interpolation routine
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	136 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	137 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	138 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	139 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	140 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	141 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	142 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	143 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	144 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	145
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	146 static bool
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	147 jcobi (octave_idx_type n, octave_idx_type n0, octave_idx_type n1,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	148 double alpha, double beta, double dif1, double dif2,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	149 double dif3, double root)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	150 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	151 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	152 assert (n1 == 0 \|\| n1 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	153
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	154 octave_idx_type nt = n + n0 + n1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	155
25247 db31e068f4db Rewrite incorrect assert statement in colloc calculation (bug #53653) Rik <rik@octave.org> parents: 25054 diff changeset	156 assert (nt >= 1);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	157
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	158 // -- first evaluation of coefficients in recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	159 // -- recursion coefficients are stored in dif1 and dif2.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	160
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	161 double ab = alpha + beta;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	162 double ad = beta - alpha;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	163 double ap = beta * alpha;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	164
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	165 dif1[0] = (ad / (ab + 2.0) + 1.0) / 2.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	166 dif2[0] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	167
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	168 if (n >= 2)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	169 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	170 for (octave_idx_type i = 1; i < n; i++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	171 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	172 double z1 = i;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	173 double z = ab + 2 * z1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	174
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	175 dif1[i] = (ab * ad / z / (z + 2.0) + 1.0) / 2.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	176
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	177 if (i == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	178 dif2[i] = (ab + ap + z1) / z / z / (z + 1.0);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	179 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	180 {
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	181 z *= z;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	182 double y = z1 * (ab + z1);
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	183 y *= (ap + y);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	184 dif2[i] = y / z / (z - 1.0);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	185 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	186 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	187 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	188
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	189 // Root determination by Newton method with suppression of previously
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	190 // determined roots.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	191
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	192 double x = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	193
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	194 for (octave_idx_type i = 0; i < n; i++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	195 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	196 bool done = false;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	197
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	198 int k = 0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	199
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	200 while (! done)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	201 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	202 double xd = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	203 double xn = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	204 double xd1 = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	205 double xn1 = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	206
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	207 for (octave_idx_type j = 0; j < n; j++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	208 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	209 double xp = (dif1[j] - x) * xn - dif2[j] * xd;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	210 double xp1 = (dif1[j] - x) * xn1 - dif2[j] * xd1 - xn;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	211
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	212 xd = xn;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	213 xd1 = xn1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	214 xn = xp;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	215 xn1 = xp1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	216 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	217
15018 3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/. Rik <rik@octave.org> parents: 14138 diff changeset	218 double zc = 1.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	219 double z = xn / xn1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	220
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	221 if (i != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	222 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	223 for (octave_idx_type j = 1; j <= i; j++)
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	224 zc -= z / (x - root[j-1]);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	225 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	226
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	227 z /= zc;
e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	228 x -= z;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	229
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	230 // Famous last words: 100 iterations should be more than
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	231 // enough in all cases.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	232
21782 2aef506f3fec use namespace for lo-mappers.h functions John W. Eaton <jwe@octave.org> parents: 21751 diff changeset	233 if (++k > 100 \|\| octave::math::isnan (z))
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	234 return false;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	235
15220 61822c866ba1 use std::numeric_limits<T>::epsilon in C++ code John W. Eaton <jwe@octave.org> parents: 15018 diff changeset	236 if (std::abs (z) <= 100 * std::numeric_limits<double>::epsilon ())
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	237 done = true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	238 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	239
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	240 root[i] = x;
23649 aabf6cd222ac Use sqrt from C++ std library in liboctave. Rik <rik@octave.org> parents: 23475 diff changeset	241 x += std::sqrt (std::numeric_limits<double>::epsilon ());
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	242 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	243
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	244 // Add interpolation points at x = 0 and/or x = 1.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	245
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	246 if (n0 != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	247 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	248 for (octave_idx_type i = n; i > 0; i--)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	249 root[i] = root[i-1];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	250
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	251 root[0] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	252 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	253
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	254 if (n1 != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	255 root[nt-1] = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	256
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	257 dif (nt, root, dif1, dif2, dif3);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	258
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	259 return true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	260 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	261
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	262 // Compute derivative weights for orthogonal collocation.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	263 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	264 // See Villadsen and Michelsen, pages 133-134, 419.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	265 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	266 // Input parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	267 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	268 // nd : the dimension of the vectors dif1, dif2, dif3, and root
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	269 //
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21724 diff changeset	270 // n : the degree of the jacobi polynomial, (i.e., the number
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	271 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	272 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	273 // n0 : determines whether x = 0 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	274 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	275 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	276 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	277 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	278 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	279 // n1 : determines whether x = 1 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	280 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	281 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	282 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	283 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	284 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	285 // i : the index of the node for which the weights are to be
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	286 // calculated
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	287 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	288 // id : indicator
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	289 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	290 // id = 1 ==> first derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	291 // id = 2 ==> second derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	292 // id = 3 ==> gaussian weights are computed (in this
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	293 // case, the value of i is irrelevant)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	294 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	295 // Output parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	296 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	297 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	298 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	299 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	300 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	301 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	302 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	303 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	304 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	305 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	306 // vect : one dimensional vector of computed weights
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	307
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	308 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	309 dfopr (octave_idx_type n, octave_idx_type n0, octave_idx_type n1,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	310 octave_idx_type i, octave_idx_type id, double *dif1,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	311 double dif2, double dif3, double root, double vect)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	312 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	313 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	314 assert (n1 == 0 \|\| n1 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	315
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	316 octave_idx_type nt = n + n0 + n1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	317
25247 db31e068f4db Rewrite incorrect assert statement in colloc calculation (bug #53653) Rik <rik@octave.org> parents: 25054 diff changeset	318 assert (nt >= 1);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	319
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	320 assert (id == 1 \|\| id == 2 \|\| id == 3);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	321
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	322 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	323 assert (i >= 0 && i < nt);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	324
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	325 // Evaluate discretization matrices and Gaussian quadrature weights.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	326 // Quadrature weights are normalized to sum to one.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	327
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	328 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	329 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	330 for (octave_idx_type j = 0; j < nt; j++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	331 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	332 if (j == i)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	333 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	334 if (id == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	335 vect[i] = dif2[i] / dif1[i] / 2.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	336 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	337 vect[i] = dif3[i] / dif1[i] / 3.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	338 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	339 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	340 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	341 double y = root[i] - root[j];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	342
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	343 vect[j] = dif1[i] / dif1[j] / y;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	344
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	345 if (id == 2)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	346 vect[j] = vect[j] * (dif2[i] / dif1[i] - 2.0 / y);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	347 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	348 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	349 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	350 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	351 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	352 double y = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	353
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	354 for (octave_idx_type j = 0; j < nt; j++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	355 {
21568 3d60ed163b70 maint: Eliminate bad spacing around '='. Rik <rik@octave.org> parents: 21301 diff changeset	356 double x = root[j];
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	357
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	358 double ax = x * (1.0 - x);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	359
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	360 if (n0 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	361 ax = ax / x / x;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	362
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	363 if (n1 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	364 ax = ax / (1.0 - x) / (1.0 - x);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	365
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	366 vect[j] = ax / (dif1[j] * dif1[j]);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	367
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	368 y += vect[j];
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	369 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	370
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	371 for (octave_idx_type j = 0; j < nt; j++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	372 vect[j] = vect[j] / y;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	373 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	374 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	375
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	376 // Error handling.
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	377
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	378 void
23449 c763214a8260 maint: Use convention 'int x' for naming pointers. Rik <rik@octave.org>* parents: 23443 diff changeset	379 CollocWt::error (const char *msg)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	380 {
20726 25d676f9619c Preface error() messages with name of function when possible. Rik <rik@octave.org> parents: 20230 diff changeset	381 (*current_liboctave_error_handler) ("CollocWt: fatal error '%s'", msg);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	382 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	383
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	384 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	385 CollocWt::set_left (double val)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	386 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	387 if (val >= rb)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	388 error ("CollocWt: left bound greater than right bound");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	389
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	390 lb = val;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	391 initialized = 0;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	392 return *this;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	393 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	394
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	395 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	396 CollocWt::set_right (double val)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	397 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	398 if (val <= lb)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	399 error ("CollocWt: right bound less than left bound");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	400
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	401 rb = val;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	402 initialized = 0;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	403 return *this;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	404 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	405
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	406 void
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	407 CollocWt::init (void)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	408 {
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	409 // Check for possible errors.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	410
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	411 double wid = rb - lb;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	412 if (wid <= 0.0)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	413 {
20726 25d676f9619c Preface error() messages with name of function when possible. Rik <rik@octave.org> parents: 20230 diff changeset	414 error ("CollocWt: width less than or equal to zero");
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	415 return;
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	416 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	417
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	418 octave_idx_type nt = n + inc_left + inc_right;
1870 34c0a016c6f0 [project @ 1996-02-04 11:55:23 by jwe] jwe parents: 1847 diff changeset	419
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	420 if (nt < 0)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	421 error ("CollocWt: total number of collocation points less than zero");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	422 else if (nt == 0)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	423 return;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	424
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	425 Array<double> dif1 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	426 double *pdif1 = dif1.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	427
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	428 Array<double> dif2 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	429 double *pdif2 = dif2.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	430
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	431 Array<double> dif3 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	432 double *pdif3 = dif3.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	433
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	434 Array<double> vect (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	435 double *pvect = vect.fortran_vec ();
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	436
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	437 r.resize (nt, 1);
12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	438 q.resize (nt, 1);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	439 A.resize (nt, nt);
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	440 B.resize (nt, nt);
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	441
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	442 double *pr = r.fortran_vec ();
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	443
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	444 // Compute roots.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	445
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	446 if (! jcobi (n, inc_left, inc_right, Alpha, Beta, pdif1, pdif2, pdif3, pr))
21056 d48fdf3a8c0c maint: one more addition to cset 5e00ed38a58b. Rik <rik@octave.org> parents: 21055 diff changeset	447 error ("jcobi: newton iteration failed");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	448
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	449 octave_idx_type id;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	450
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	451 // First derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	452
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	453 id = 1;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	454 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	455 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	456 dfopr (n, inc_left, inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	457
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	458 for (octave_idx_type j = 0; j < nt; j++)
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	459 A(i,j) = vect(j);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	460 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	461
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	462 // Second derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	463
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	464 id = 2;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	465 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	466 {
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11570 diff changeset	467 dfopr (n, inc_left, inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	468
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	469 for (octave_idx_type j = 0; j < nt; j++)
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	470 B(i,j) = vect(j);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	471 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	472
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	473 // Gaussian quadrature weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	474
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	475 id = 3;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	476 double *pq = q.fortran_vec ();
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	477 dfopr (n, inc_left, inc_right, id, id, pdif1, pdif2, pdif3, pr, pq);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	478
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	479 initialized = 1;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	480 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	481
3504 5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	482 std::ostream&
5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	483 operator << (std::ostream& os, const CollocWt& a)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	484 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	485 if (a.left_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	486 os << "left boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	487 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	488 os << "left boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	489
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	490 if (a.right_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	491 os << "right boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	492 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	493 os << "right boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	494
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	495 os << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	496
23807 336f89b6208b Use character literals 'c' rather than string literals "c" when possible. Rik <rik@octave.org> parents: 23649 diff changeset	497 os << a.Alpha << ' ' << a.Beta << "\n\n"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	498 << a.r << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	499 << a.q << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	500 << a.A << "\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	501 << a.B << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	502
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	503 return os;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	504 }

Mercurial > octave

annotate liboctave/numeric/CollocWt.cc @ 25438:cb1606f78f6b