octave: liboctave/numeric/CollocWt.cc annotate

annotate liboctave/numeric/CollocWt.cc @ 23443:3f1bf237908b

maint: Eliminate <cfloat.h> header from liboctave files. * build-aux/mk-opts.pl: Remove "#include <cfloat>" from script which creates *-opts.h * Array-util.cc, Array-util.h, Array.cc, Array.h, CColVector.h, CDiagMatrix.h, CMatrix.cc, CMatrix.h, CNDArray.cc, CNDArray.h, CRowVector.h, CSparse.cc, CSparse.h, MSparse.h, Matrix.h, Range.cc, Sparse.h, boolMatrix.h, boolNDArray.h, boolSparse.h, chMatrix.h, chNDArray.h, dColVector.h, dDiagMatrix.h, dMatrix.cc, dMatrix.h, dNDArray.cc, dNDArray.h, dRowVector.h, dSparse.cc, dSparse.h, dim-vector.cc, dim-vector.h, fCColVector.h, fCDiagMatrix.h, fCMatrix.cc, fCMatrix.h, fCNDArray.cc, fCNDArray.h, fCRowVector.h, fColVector.h, fDiagMatrix.h, fMatrix.cc, fMatrix.h, fNDArray.cc, fNDArray.h, fRowVector.h, int16NDArray.h, int32NDArray.h, int64NDArray.h, int8NDArray.h, intNDArray.h, uint16NDArray.h, uint32NDArray.h, uint64NDArray.h, uint8NDArray.h, CollocWt.cc, DASPK.cc, DASPK.h, DASRT.cc, DASRT.h, DASSL.cc, DASSL.h, LSODE.cc, LSODE.h, Quad.h, eigs-base.cc, eigs-base.h, lo-mappers.cc, lo-mappers.h, oct-norm.cc, lo-ieee.cc, lo-utils.cc, lo-utils.h, oct-refcount.h: Remove "#include <cfloat>". Add "#include <limits>" if necessary. Remove redundant #includes. Alphabetize #includes.

author	Rik <rik@octave.org>
date	Wed, 26 Apr 2017 09:57:28 -0700
parents	092078913d54
children	c763214a8260

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
23219 3ac9f9ecfae5 maint: Update copyright dates. John W. Eaton <jwe@octave.org> parents: 23083 diff changeset	3 Copyright (C) 1993-2017 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
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: 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
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22402 diff changeset	9 the Free Software Foundation; either version 3 of the License, or
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
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5307 diff changeset	19 <http://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
3503 d14c483b3c12 [project @ 2000-02-01 04:06:07 by jwe] jwe parents: 2847 diff changeset	27 #include <iostream>
23443 3f1bf237908b maint: Eliminate <cfloat.h> header from liboctave files. Rik <rik@octave.org> parents: 23220 diff changeset	28 #include <limits>
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	29
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	30 #include "CollocWt.h"
1847 2ffe49eb95a5 [project @ 1996-02-03 12:47:55 by jwe] jwe parents: 1528 diff changeset	31 #include "f77-fcn.h"
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	32 #include "lo-error.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	33
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	34 // 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	35 // 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	36 // Equation Models by Polynomial Approximation, Prentice-Hall (1978)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	37 // pages 418-420.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	38 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	39 // Translated to C++ by jwe.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	40
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	41 // 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	42 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	43 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	44 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	45 // nt n
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 // 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	48 // 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	49 // nt = n + n0 + n1
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 // 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	52 // They may be computed using jcobi.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	53
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	54 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	55 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	56 double *dif3)
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 // Evaluate derivatives of node polynomial using recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	59
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	60 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	61 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	62 double x = root[i];
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 dif1[i] = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	65 dif2[i] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	66 dif3[i] = 0.0;
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 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	69 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	70 if (j != i)
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 double y = x - root[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 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	75 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	76 dif1[i] = y * dif1[i];
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 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	79 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	80 }
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 // Compute the zeros of the Jacobi polynomial.
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 // (alpha,beta)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	85 // p (x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	86 // n
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 // 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	89 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	90 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	91 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	92 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	93 // nt n
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 // at the interpolation points.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	96 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	97 // 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	98 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	99 // Input parameters:
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 // 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	102 //
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21724 diff changeset	103 // 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	104 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	105 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	106 // 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	107 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	108 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	109 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	110 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	111 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	112 // 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	113 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	114 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	115 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	116 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	117 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	118 // 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	119 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	120 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	121 // 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	122 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	123 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	124 // 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	125 // and Michelsen, pages 57 to 59.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	126 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	127 // Output parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	128 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	129 // root : one dimensional vector containing on exit the
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	130 // 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	131 // interpolation routine
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 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	134 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	135 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	136 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	137 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	138 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	139 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	140 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	141
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	142 static bool
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	143 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	144 double alpha, double beta, double dif1, double dif2,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	145 double dif3, double root)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	146 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	147 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	148 assert (n1 == 0 \|\| n1 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	149
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	150 octave_idx_type nt = n + n0 + n1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	151
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	152 assert (nt > 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 // -- first evaluation of coefficients in recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	155 // -- recursion coefficients are stored in dif1 and dif2.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	156
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	157 double ab = alpha + beta;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	158 double ad = beta - alpha;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	159 double ap = beta * alpha;
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 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	162 dif2[0] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	163
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	164 if (n >= 2)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	165 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	166 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	167 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	168 double z1 = i;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	169 double z = ab + 2 * z1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	170
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	171 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	172
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	173 if (i == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	174 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	175 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	176 {
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	177 z *= z;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	178 double y = z1 * (ab + z1);
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	179 y *= (ap + y);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	180 dif2[i] = y / z / (z - 1.0);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	181 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	182 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	183 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	184
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	185 // 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	186 // determined roots.
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 double x = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	189
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	190 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	191 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	192 bool done = false;
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 int k = 0;
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 while (! done)
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 double xd = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	199 double xn = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	200 double xd1 = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	201 double xn1 = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	202
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	203 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	204 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	205 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	206 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	207
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	208 xd = xn;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	209 xd1 = xn1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	210 xn = xp;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	211 xn1 = xp1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	212 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	213
15018 3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/. Rik <rik@octave.org> parents: 14138 diff changeset	214 double zc = 1.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	215 double z = xn / xn1;
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 if (i != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	218 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	219 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	220 zc -= z / (x - root[j-1]);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	221 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	222
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	223 z /= zc;
e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	224 x -= z;
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 // 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	227 // enough in all cases.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	228
21782 2aef506f3fec use namespace for lo-mappers.h functions John W. Eaton <jwe@octave.org> parents: 21751 diff changeset	229 if (++k > 100 \|\| octave::math::isnan (z))
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	230 return false;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	231
15220 61822c866ba1 use std::numeric_limits<T>::epsilon in C++ code John W. Eaton <jwe@octave.org> parents: 15018 diff changeset	232 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	233 done = true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	234 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	235
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	236 root[i] = x;
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	237 x += sqrt (std::numeric_limits<double>::epsilon ());
10603 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 // 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	241
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	242 if (n0 != 0)
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 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	245 root[i] = root[i-1];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	246
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	247 root[0] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	248 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	249
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	250 if (n1 != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	251 root[nt-1] = 1.0;
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 dif (nt, root, dif1, dif2, dif3);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	254
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	255 return true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	256 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	257
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	258 // Compute derivative weights for orthogonal collocation.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	259 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	260 // See Villadsen and Michelsen, pages 133-134, 419.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	261 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	262 // Input parameters:
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 // 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	265 //
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21724 diff changeset	266 // 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	267 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	268 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	269 // 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	270 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	271 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	272 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	273 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	274 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	275 // 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	276 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	277 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	278 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	279 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	280 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	281 // 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	282 // calculated
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	283 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	284 // id : indicator
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	285 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	286 // id = 1 ==> first derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	287 // id = 2 ==> second derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	288 // id = 3 ==> gaussian weights are computed (in this
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	289 // case, the value of i is irrelevant)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	290 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	291 // Output parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	292 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	293 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	294 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	295 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	296 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	297 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	298 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	299 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	300 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	301 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	302 // vect : one dimensional vector of computed weights
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	303
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	304 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	305 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	306 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	307 double dif2, double dif3, double root, double vect)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	308 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	309 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	310 assert (n1 == 0 \|\| n1 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	311
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	312 octave_idx_type nt = n + n0 + n1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	313
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	314 assert (nt > 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 assert (id == 1 \|\| id == 2 \|\| id == 3);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	317
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	318 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	319 assert (i >= 0 && i < nt);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	320
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	321 // Evaluate discretization matrices and Gaussian quadrature weights.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	322 // Quadrature weights are normalized to sum to one.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	323
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	324 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	325 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	326 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	327 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	328 if (j == i)
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 if (id == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	331 vect[i] = dif2[i] / dif1[i] / 2.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	332 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	333 vect[i] = dif3[i] / dif1[i] / 3.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	334 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	335 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	336 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	337 double y = root[i] - root[j];
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 vect[j] = dif1[i] / dif1[j] / y;
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 if (id == 2)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	342 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	343 }
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 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	346 else
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 double y = 0.0;
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 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	351 {
21568 3d60ed163b70 maint: Eliminate bad spacing around '='. Rik <rik@octave.org> parents: 21301 diff changeset	352 double x = root[j];
10603 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 double ax = x * (1.0 - x);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	355
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	356 if (n0 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	357 ax = ax / x / x;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	358
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	359 if (n1 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	360 ax = ax / (1.0 - x) / (1.0 - x);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	361
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	362 vect[j] = ax / (dif1[j] * dif1[j]);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	363
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	364 y += vect[j];
10603 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
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	367 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	368 vect[j] = vect[j] / y;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	369 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	370 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	371
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	372 // Error handling.
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	373
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	374 void
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	375 CollocWt::error (const char* msg)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	376 {
20726 25d676f9619c Preface error() messages with name of function when possible. Rik <rik@octave.org> parents: 20230 diff changeset	377 (*current_liboctave_error_handler) ("CollocWt: fatal error '%s'", msg);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	378 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	379
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	380 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	381 CollocWt::set_left (double val)
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 if (val >= rb)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	384 error ("CollocWt: left bound greater than right bound");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	385
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	386 lb = val;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	387 initialized = 0;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	388 return *this;
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
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	391 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	392 CollocWt::set_right (double val)
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 if (val <= lb)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	395 error ("CollocWt: right bound less than left bound");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	396
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	397 rb = val;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	398 initialized = 0;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	399 return *this;
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
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	402 void
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	403 CollocWt::init (void)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	404 {
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	405 // Check for possible errors.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	406
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	407 double wid = rb - lb;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	408 if (wid <= 0.0)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	409 {
20726 25d676f9619c Preface error() messages with name of function when possible. Rik <rik@octave.org> parents: 20230 diff changeset	410 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	411 return;
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	412 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	413
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	414 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	415
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	416 if (nt < 0)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	417 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	418 else if (nt == 0)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	419 return;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	420
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	421 Array<double> dif1 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	422 double *pdif1 = dif1.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	423
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	424 Array<double> dif2 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	425 double *pdif2 = dif2.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	426
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	427 Array<double> dif3 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	428 double *pdif3 = dif3.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	429
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	430 Array<double> vect (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	431 double *pvect = vect.fortran_vec ();
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	432
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	433 r.resize (nt, 1);
12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	434 q.resize (nt, 1);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	435 A.resize (nt, nt);
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	436 B.resize (nt, nt);
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	437
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	438 double *pr = r.fortran_vec ();
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	439
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	440 // Compute roots.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	441
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	442 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	443 error ("jcobi: newton iteration failed");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	444
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	445 octave_idx_type id;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	446
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	447 // First derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	448
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	449 id = 1;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	450 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	451 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	452 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	453
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	454 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	455 A(i,j) = vect(j);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	456 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	457
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	458 // Second derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	459
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	460 id = 2;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	461 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	462 {
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11570 diff changeset	463 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	464
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	465 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	466 B(i,j) = vect(j);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	467 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	468
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	469 // Gaussian quadrature weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	470
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	471 id = 3;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	472 double *pq = q.fortran_vec ();
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	473 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	474
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	475 initialized = 1;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	476 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	477
3504 5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	478 std::ostream&
5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	479 operator << (std::ostream& os, const CollocWt& a)
3 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 if (a.left_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	482 os << "left boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	483 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	484 os << "left boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	485
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	486 if (a.right_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	487 os << "right boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	488 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	489 os << "right boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	490
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	491 os << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	492
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	493 os << a.Alpha << " " << a.Beta << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	494 << a.r << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	495 << a.q << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	496 << a.A << "\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	497 << a.B << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	498
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	499 return os;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	500 }

Mercurial > octave

annotate liboctave/numeric/CollocWt.cc @ 23443:3f1bf237908b