octave-nkf: liboctave/CollocWt.cc annotate

annotate liboctave/CollocWt.cc @ 10843:229675bb7647 ss-3-3-52

version is now 3.3.52

author	John W. Eaton <jwe@octave.org>
date	Sun, 01 Aug 2010 11:49:45 -0400
parents	d909c4c14b63
children	fd0a3ac60b0e

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
7017 a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	3 Copyright (C) 1993, 1994, 1995, 1996, 1997, 2000, 2002, 2003, 2004,
a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	4 2005, 2007 John W. Eaton
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	5
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	6 This file is part of Octave.
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	7
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	8 Octave is free software; you can redistribute it and/or modify it
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	9 under the terms of the GNU General Public License as published by the
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5307 diff changeset	10 Free Software Foundation; either version 3 of the License, or (at your
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 5307 diff changeset	11 option) any later version.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	12
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	13 Octave is distributed in the hope that it will be useful, but WITHOUT
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	16 for more details.
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	17
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	18 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	19 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	20 <http://www.gnu.org/licenses/>.
3 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 */
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	23
238 780cbbc57b7c [project @ 1993-11-30 20:23:04 by jwe] jwe parents: 227 diff changeset	24 #ifdef HAVE_CONFIG_H
1192 b6360f2d4fa6 [project @ 1995-03-30 21:38:35 by jwe] jwe parents: 1011 diff changeset	25 #include <config.h>
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	26 #endif
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	27
3503 d14c483b3c12 [project @ 2000-02-01 04:06:07 by jwe] jwe parents: 2847 diff changeset	28 #include <iostream>
238 780cbbc57b7c [project @ 1993-11-30 20:23:04 by jwe] jwe parents: 227 diff changeset	29
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	30 #include <cfloat>
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	31
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	32 #include "CollocWt.h"
1847 2ffe49eb95a5 [project @ 1996-02-03 12:47:55 by jwe] jwe parents: 1528 diff changeset	33 #include "f77-fcn.h"
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	34 #include "lo-error.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	35
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	36 // 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	37 // 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	38 // Equation Models by Polynomial Approximation, Prentice-Hall (1978)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	39 // pages 418-420.
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 // Translated to C++ by jwe.
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 // 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	44 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	45 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	46 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	47 // nt n
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	48 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	49 // 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	50 // 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	51 // nt = n + n0 + n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	52 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	53 // 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	54 // They may be computed using jcobi.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	55
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	56 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	57 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	58 double *dif3)
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 // Evaluate derivatives of node polynomial using recursion formulas.
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 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	63 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	64 double x = root[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 dif1[i] = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	67 dif2[i] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	68 dif3[i] = 0.0;
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 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	71 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	72 if (j != i)
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 double y = x - root[j];
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 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	77 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	78 dif1[i] = y * dif1[i];
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 }
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 // Compute the zeros of the Jacobi polynomial.
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 // (alpha,beta)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	87 // p (x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	88 // n
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	89 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	90 // 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	91 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	92 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	93 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	94 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	95 // nt n
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 // at the interpolation points.
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 // 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	100 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	101 // Input parameters:
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 // 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	104 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	105 // n : the degree of the jacobi polynomial, (i.e. the number
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	106 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	107 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	108 // 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	109 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	110 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	111 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	112 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	113 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	114 // 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	115 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	116 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	117 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	118 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	119 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	120 // 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	121 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	122 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	123 // 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	124 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	125 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	126 // 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	127 // and Michelsen, pages 57 to 59.
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 // Output parameters:
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 // root : one dimensional vector containing on exit the
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	132 // 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	133 // interpolation routine
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	134 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	135 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	136 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	137 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	138 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	139 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	140 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	141 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	142 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	143
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	144 static bool
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	145 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	146 double alpha, double beta, double dif1, double dif2,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	147 double dif3, double root)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	148 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	149 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	150 assert (n1 == 0 \|\| n1 == 1);
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 octave_idx_type nt = n + n0 + n1;
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 assert (nt > 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	155
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	156 // -- first evaluation of coefficients in recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	157 // -- recursion coefficients are stored in dif1 and dif2.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	158
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	159 double ab = alpha + beta;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	160 double ad = beta - alpha;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	161 double ap = beta * alpha;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	162
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	163 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	164 dif2[0] = 0.0;
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 if (n >= 2)
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 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	169 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	170 double z1 = i;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	171 double z = ab + 2 * z1;
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 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	174
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	175 if (i == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	176 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	177 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	178 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	179 z = z * z;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	180 double y = z1 * (ab + z1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	181 y = y * (ap + y);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	182 dif2[i] = y / z / (z - 1.0);
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 }
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 // 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	188 // determined roots.
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 double x = 0.0;
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 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	193 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	194 bool done = false;
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 int k = 0;
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 while (! done)
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 double xd = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	201 double xn = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	202 double xd1 = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	203 double xn1 = 0.0;
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 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	206 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	207 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	208 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	209
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	210 xd = xn;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	211 xd1 = xn1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	212 xn = xp;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	213 xn1 = xp1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	214 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	215
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	216 double zc = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	217 double z = xn / xn1;
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 if (i != 0)
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 for (octave_idx_type j = 1; j <= i; j++)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	222 zc = zc - z / (x - root[j-1]);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	223 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	224
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	225 z = z / zc;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	226 x = x - z;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	227
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	228 // 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	229 // enough in all cases.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	230
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	231 if (++k > 100 \|\| xisnan (z))
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	232 return false;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	233
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	234 if (std::abs (z) <= 100 * DBL_EPSILON)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	235 done = true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	236 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	237
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	238 root[i] = x;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	239 x = x + sqrt (DBL_EPSILON);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	240 }
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 // 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	243
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	244 if (n0 != 0)
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 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	247 root[i] = root[i-1];
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 root[0] = 0.0;
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
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	252 if (n1 != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	253 root[nt-1] = 1.0;
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 dif (nt, root, dif1, dif2, dif3);
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 return true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	258 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	259
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	260 // Compute derivative weights for orthogonal collocation.
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 // See Villadsen and Michelsen, pages 133-134, 419.
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 // Input parameters:
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 // 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	267 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	268 // n : the degree of the jacobi polynomial, (i.e. the number
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	269 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	270 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	271 // 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	272 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	273 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	274 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	275 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	276 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	277 // 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	278 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	279 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	280 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	281 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	282 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	283 // 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	284 // calculated
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 : indicator
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 = 1 ==> first derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	289 // id = 2 ==> second derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	290 // id = 3 ==> gaussian weights are computed (in this
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	291 // case, the value of i is irrelevant)
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 // Output parameters:
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 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	296 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	297 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	298 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	299 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	300 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	301 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	302 // of the node polynomial at the zeros
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 // vect : one dimensional vector of computed weights
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 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	307 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	308 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	309 double dif2, double dif3, double root, double vect)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	310 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	311 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	312 assert (n1 == 0 \|\| n1 == 1);
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 octave_idx_type nt = n + n0 + n1;
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 (nt > 1);
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 assert (id == 1 \|\| id == 2 \|\| id == 3);
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 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	321 assert (i >= 0 && i < nt);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	322
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	323 // Evaluate discretization matrices and Gaussian quadrature weights.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	324 // Quadrature weights are normalized to sum to one.
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 if (id != 3)
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 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	329 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	330 if (j == i)
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 (id == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	333 vect[i] = dif2[i] / dif1[i] / 2.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	334 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	335 vect[i] = dif3[i] / dif1[i] / 3.0;
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 else
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 double y = root[i] - root[j];
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 vect[j] = dif1[i] / dif1[j] / y;
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 if (id == 2)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	344 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	345 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	346 }
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 else
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 double y = 0.0;
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 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	353 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	354 double x = root[j];
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 double ax = x * (1.0 - x);
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 if (n0 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	359 ax = ax / x / x;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	360
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	361 if (n1 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	362 ax = ax / (1.0 - x) / (1.0 - x);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	363
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	364 vect[j] = ax / (dif1[j] * dif1[j]);
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 y = y + vect[j];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	367 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	368
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	369 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	370 vect[j] = vect[j] / y;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	371 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	372 }
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 // Error handling.
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 void
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	377 CollocWt::error (const char* msg)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	378 {
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	379 (*current_liboctave_error_handler) ("fatal CollocWt error: %s", msg);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	380 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	381
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	382 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	383 CollocWt::set_left (double val)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	384 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	385 if (val >= rb)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	386 {
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	387 error ("left bound greater than right bound");
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	388 return *this;
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	389 }
3 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 lb = val;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	392 initialized = 0;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	393 return *this;
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
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	396 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	397 CollocWt::set_right (double val)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	398 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	399 if (val <= lb)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	400 {
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	401 error ("right bound less than left bound");
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	402 return *this;
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	403 }
3 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 rb = val;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	406 initialized = 0;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	407 return *this;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	408 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	409
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	410 void
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	411 CollocWt::init (void)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	412 {
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	413 // Check for possible errors.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	414
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	415 double wid = rb - lb;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	416 if (wid <= 0.0)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	417 {
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	418 error ("width less than or equal to zero");
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	419 return;
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	420 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	421
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	422 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	423
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	424 if (nt < 0)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	425 {
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	426 error ("total number of collocation points less than zero");
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	427 return;
1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	428 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	429 else if (nt == 0)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	430 return;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	431
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	432 Array<double> dif1 (nt, 1);
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	433 double *pdif1 = dif1.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	434
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	435 Array<double> dif2 (nt, 1);
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	436 double *pdif2 = dif2.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	437
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	438 Array<double> dif3 (nt, 1);
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	439 double *pdif3 = dif3.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	440
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	441 Array<double> vect (nt, 1);
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	442 double *pvect = vect.fortran_vec ();
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	443
10350 12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	444 r.resize (nt, 1);
12884915a8e4 merge MArray classes & improve Array interface Jaroslav Hajek <highegg@gmail.com> parents: 10314 diff changeset	445 q.resize (nt, 1);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	446 A.resize (nt, nt);
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	447 B.resize (nt, nt);
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 double *pr = r.fortran_vec ();
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 // Compute roots.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	452
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	453 if (! jcobi (n, inc_left, inc_right, Alpha, Beta, pdif1, pdif2, pdif3, pr))
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	454 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	455 error ("jcobi: newton iteration failed");
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	456 return;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	457 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	458
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	459 octave_idx_type id;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	460
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	461 // First derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	462
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	463 id = 1;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	464 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	465 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	466 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	467
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	468 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	469 A(i,j) = vect(j);
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
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	472 // Second derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	473
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	474 id = 2;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	475 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	476 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	477 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	478
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	479 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	480 B(i,j) = vect(j);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	481 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	482
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	483 // Gaussian quadrature weights.
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 id = 3;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	486 double *pq = q.fortran_vec ();
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	487 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	488
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	489 initialized = 1;
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
3504 5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	492 std::ostream&
5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	493 operator << (std::ostream& os, const CollocWt& a)
3 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 if (a.left_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	496 os << "left boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	497 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	498 os << "left boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	499
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	500 if (a.right_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	501 os << "right boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	502 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	503 os << "right boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	504
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	505 os << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	506
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	507 os << a.Alpha << " " << a.Beta << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	508 << a.r << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	509 << a.q << "\n\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	510 << a.A << "\n"
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	511 << a.B << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	512
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	513 return os;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	514 }

Mercurial > octave-nkf

annotate liboctave/CollocWt.cc @ 10843:229675bb7647 ss-3-3-52