octave: liboctave/numeric/CollocWt.cc annotate

annotate liboctave/numeric/CollocWt.cc @ 29680:e8a8ae9f512d

update coding style in CollocWt class * CollocWt.h, CollocWt.cc: Use m_ prefix for data members. Use default copy constructor and assignment operator definitions.

author	John W. Eaton <jwe@octave.org>
date	Sun, 16 May 2021 09:52:37 -0400
parents	7854d5752dd2
children	25246c1a1645

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ////////////////////////////////////////////////////////////////////////
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 //
29358 0a5b15007766 update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 27923 diff changeset	3 // Copyright (C) 1993-2021 The Octave Project Developers
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	4 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 // See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 // distribution or <https://octave.org/copyright/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	7 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	8 // This file is part of Octave.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	9 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	10 // Octave is free software: you can redistribute it and/or modify it
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	11 // under the terms of the GNU General Public License as published by
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	12 // the Free Software Foundation, either version 3 of the License, or
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	13 // (at your option) any later version.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	14 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	15 // Octave is distributed in the hope that it will be useful, but
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	16 // WITHOUT ANY WARRANTY; without even the implied warranty of
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	18 // GNU General Public License for more details.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	19 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	20 // You should have received a copy of the GNU General Public License
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	21 // along with Octave; see the file COPYING. If not, see
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	22 // <https://www.gnu.org/licenses/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ////////////////////////////////////////////////////////////////////////
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	25
21724 aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef" John W. Eaton <jwe@octave.org> parents: 21568 diff changeset	26 #if defined (HAVE_CONFIG_H)
21301 40de9f8f23a6 Use '#include "config.h"' rather than <config.h>. Rik <rik@octave.org> parents: 21202 diff changeset	27 # include "config.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	28 #endif
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	29
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	30 #include <cassert>
d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	31 #include <cmath>
d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	32
23443 3f1bf237908b maint: Eliminate <cfloat.h> header from liboctave files. Rik <rik@octave.org> parents: 23220 diff changeset	33 #include <limits>
25438 cb1606f78f6b prefer <istream>, <ostream>, or <iosfwd> to <iostream> where possible John W. Eaton <jwe@octave.org> parents: 25247 diff changeset	34 #include <ostream>
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	35
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	36 #include "Array.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	37 #include "CollocWt.h"
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	38 #include "lo-error.h"
23475 d691ed308237 maint: Clean up #includes in liboctave/numeric directory. Rik <rik@octave.org> parents: 23449 diff changeset	39 #include "lo-mappers.h"
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	40
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	41 // The following routines jcobi, dif, and dfopr are based on the code
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	42 // found in Villadsen, J. and M. L. Michelsen, Solution of Differential
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	43 // Equation Models by Polynomial Approximation, Prentice-Hall (1978)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	44 // pages 418-420.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	45 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	46 // Translated to C++ by jwe.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	47
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	48 // 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	49 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	50 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	51 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	52 // nt n
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 // 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	55 // 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	56 // nt = n + n0 + n1
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 // 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	59 // They may be computed using jcobi.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	60
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	61 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	62 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	63 double *dif3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	64 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	65 // Evaluate derivatives of node polynomial using recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	66
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	67 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	68 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	69 double x = root[i];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	70
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	71 dif1[i] = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	72 dif2[i] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	73 dif3[i] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	74
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	75 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	76 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	77 if (j != i)
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 double y = x - root[j];
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 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	82 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	83 dif1[i] = y * dif1[i];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	84 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	85 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	86 }
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
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	89 // Compute the zeros of the Jacobi 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 // (alpha,beta)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	92 // p (x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	93 // 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 // 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	96 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	97 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	98 // n0 (alpha,beta) n1
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	99 // p (x) = (x) * p (x) * (1 - x)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	100 // nt n
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	101 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	102 // at the interpolation points.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	103 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	104 // 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	105 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	106 // Input parameters:
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 // 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	109 //
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21724 diff changeset	110 // 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	111 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	112 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	113 // n0 : determines whether x = 0 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	114 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	115 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	116 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	117 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	118 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	119 // n1 : determines whether x = 1 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	120 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	121 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	122 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	123 // n1 = 1 ==> x = 1 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	124 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	125 // 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	126 // polynomial
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	127 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	128 // 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	129 // polynomial
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 // 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	132 // and Michelsen, pages 57 to 59.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	133 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	134 // Output parameters:
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 // root : one dimensional vector containing on exit the
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	137 // 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	138 // interpolation routine
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	139 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	140 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	141 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	142 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	143 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	144 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	145 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	146 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	147 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	148
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	149 static bool
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	150 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	151 double alpha, double beta, double dif1, double dif2,
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	152 double dif3, double root)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	153 {
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	154 assert (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	155 assert (n1 == 0 \|\| n1 == 1);
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 octave_idx_type nt = n + n0 + n1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	158
25247 db31e068f4db Rewrite incorrect assert statement in colloc calculation (bug #53653) Rik <rik@octave.org> parents: 25054 diff changeset	159 assert (nt >= 1);
10603 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 // -- first evaluation of coefficients in recursion formulas.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	162 // -- recursion coefficients are stored in dif1 and dif2.
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 double ab = alpha + beta;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	165 double ad = beta - alpha;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	166 double ap = beta * alpha;
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 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	169 dif2[0] = 0.0;
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 if (n >= 2)
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 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	174 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	175 double z1 = i;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	176 double z = ab + 2 * z1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	177
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	178 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	179
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	180 if (i == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	181 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	182 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	183 {
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	184 z *= z;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	185 double y = z1 * (ab + z1);
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	186 y *= (ap + y);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	187 dif2[i] = y / z / (z - 1.0);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	188 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	189 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	190 }
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 // 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	193 // determined roots.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	194
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	195 double x = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	196
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	197 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	198 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	199 bool done = false;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	200
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	201 int k = 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 while (! done)
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 xd = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	206 double xn = 1.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	207 double xd1 = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	208 double xn1 = 0.0;
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 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	211 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	212 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	213 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	214
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	215 xd = xn;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	216 xd1 = xn1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	217 xn = xp;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	218 xn1 = xp1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	219 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	220
15018 3d8ace26c5b4 maint: Use Octave coding conventions for cuddled parentheses in liboctave/. Rik <rik@octave.org> parents: 14138 diff changeset	221 double zc = 1.0;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	222 double z = xn / xn1;
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 if (i != 0)
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 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	227 zc -= z / (x - root[j-1]);
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	228 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	229
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	230 z /= zc;
e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	231 x -= z;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	232
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	233 // 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	234 // enough in all cases.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	235
21782 2aef506f3fec use namespace for lo-mappers.h functions John W. Eaton <jwe@octave.org> parents: 21751 diff changeset	236 if (++k > 100 \|\| octave::math::isnan (z))
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	237 return false;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	238
15220 61822c866ba1 use std::numeric_limits<T>::epsilon in C++ code John W. Eaton <jwe@octave.org> parents: 15018 diff changeset	239 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	240 done = true;
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
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	243 root[i] = x;
23649 aabf6cd222ac Use sqrt from C++ std library in liboctave. Rik <rik@octave.org> parents: 23475 diff changeset	244 x += std::sqrt (std::numeric_limits<double>::epsilon ());
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	245 }
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 // 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	248
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	249 if (n0 != 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 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	252 root[i] = root[i-1];
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	253
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	254 root[0] = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	255 }
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 if (n1 != 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	258 root[nt-1] = 1.0;
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 dif (nt, root, dif1, dif2, dif3);
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 return true;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	263 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	264
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	265 // Compute derivative weights for orthogonal collocation.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	266 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	267 // See Villadsen and Michelsen, pages 133-134, 419.
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 // Input parameters:
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 // 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	272 //
21751 b571fc85953f maint: Use two spaces after period to indicate sentence break. Rik <rik@octave.org> parents: 21724 diff changeset	273 // 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	274 // of interior interpolation points)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	275 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	276 // n0 : determines whether x = 0 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	277 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	278 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	279 // n0 = 0 ==> x = 0 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	280 // n0 = 1 ==> x = 0 is included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	281 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	282 // n1 : determines whether x = 1 is included as an
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	283 // interpolation point
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	284 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	285 // n1 = 0 ==> x = 1 is not included
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	286 // n1 = 1 ==> x = 1 is included
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 // 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	289 // calculated
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 // id : indicator
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 // id = 1 ==> first derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	294 // id = 2 ==> second derivative weights are computed
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	295 // id = 3 ==> gaussian weights are computed (in this
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	296 // case, the value of i is irrelevant)
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 // Output parameters:
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	299 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	300 // dif1 : one dimensional vector containing the first derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	301 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	302 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	303 // dif2 : one dimensional vector containing the second derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	304 // of the node polynomial at the zeros
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	305 //
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	306 // dif3 : one dimensional vector containing the third derivative
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	307 // of the node polynomial at the zeros
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 // vect : one dimensional vector of computed weights
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 static void
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	312 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	313 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	314 double dif2, double dif3, double root, double vect)
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 (n0 == 0 \|\| n0 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	317 assert (n1 == 0 \|\| n1 == 1);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	318
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	319 octave_idx_type nt = n + n0 + n1;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	320
25247 db31e068f4db Rewrite incorrect assert statement in colloc calculation (bug #53653) Rik <rik@octave.org> parents: 25054 diff changeset	321 assert (nt >= 1);
10603 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 assert (id == 1 \|\| id == 2 \|\| id == 3);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	324
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	325 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	326 assert (i >= 0 && i < nt);
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 // Evaluate discretization matrices and Gaussian quadrature weights.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	329 // Quadrature weights are normalized to sum to one.
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	330
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	331 if (id != 3)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	332 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	333 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	334 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	335 if (j == i)
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 if (id == 1)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	338 vect[i] = dif2[i] / dif1[i] / 2.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	339 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	340 vect[i] = dif3[i] / dif1[i] / 3.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	341 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	342 else
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 double y = root[i] - root[j];
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 vect[j] = dif1[i] / dif1[j] / y;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	347
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	348 if (id == 2)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	349 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	350 }
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 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	353 else
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	354 {
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	355 double y = 0.0;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	356
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	357 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	358 {
21568 3d60ed163b70 maint: Eliminate bad spacing around '='. Rik <rik@octave.org> parents: 21301 diff changeset	359 double x = root[j];
10603 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 double ax = x * (1.0 - x);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	362
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	363 if (n0 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	364 ax = ax / x / x;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	365
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	366 if (n1 == 0)
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	367 ax = ax / (1.0 - x) / (1.0 - x);
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 vect[j] = ax / (dif1[j] * dif1[j]);
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	370
20230 e914b5399c67 Use in-place operators in C++ code where possible. Rik <rik@octave.org> parents: 19697 diff changeset	371 y += vect[j];
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	372 }
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	373
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	374 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	375 vect[j] = vect[j] / y;
d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	376 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	377 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	378
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	379 // Error handling.
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 void
23449 c763214a8260 maint: Use convention 'int x' for naming pointers. Rik <rik@octave.org>* parents: 23443 diff changeset	382 CollocWt::error (const char *msg)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	383 {
20726 25d676f9619c Preface error() messages with name of function when possible. Rik <rik@octave.org> parents: 20230 diff changeset	384 (*current_liboctave_error_handler) ("CollocWt: fatal error '%s'", msg);
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
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	387 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	388 CollocWt::set_left (double val)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	389 {
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	390 if (val >= m_rb)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	391 error ("CollocWt: left bound greater than right bound");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	392
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	393 m_lb = val;
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	394 m_initialized = 0;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	395 return *this;
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
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	398 CollocWt&
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	399 CollocWt::set_right (double val)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	400 {
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	401 if (val <= m_lb)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	402 error ("CollocWt: right bound less than left bound");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	403
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	404 m_rb = val;
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	405 m_initialized = 0;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	406 return *this;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	407 }
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 void
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	410 CollocWt::init (void)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	411 {
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	412 // Check for possible errors.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	413
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	414 double wid = m_rb - m_lb;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	415 if (wid <= 0.0)
227 1a48a1b91489 [project @ 1993-11-15 10:10:35 by jwe] jwe parents: 3 diff changeset	416 {
20726 25d676f9619c Preface error() messages with name of function when possible. Rik <rik@octave.org> parents: 20230 diff changeset	417 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	418 }
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	419
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	420 octave_idx_type nt = m_n + m_inc_left + m_inc_right;
1870 34c0a016c6f0 [project @ 1996-02-04 11:55:23 by jwe] jwe parents: 1847 diff changeset	421
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	422 if (nt < 0)
21055 5e00ed38a58b maint: Replace if/error/else paradigm with just if/error. Rik <rik@octave.org> parents: 20726 diff changeset	423 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	424 else if (nt == 0)
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	425 return;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: 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> dif1 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	428 double *pdif1 = dif1.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> dif2 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	431 double *pdif2 = dif2.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	432
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	433 Array<double> dif3 (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	434 double *pdif3 = dif3.fortran_vec ();
126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	435
11570 57632dea2446 attempt better backward compatibility for Array constructors John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	436 Array<double> vect (dim_vector (nt, 1));
1938 126ebfbf3f99 [project @ 1996-02-12 04:46:09 by jwe] jwe parents: 1882 diff changeset	437 double *pvect = vect.fortran_vec ();
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	438
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	439 m_r.resize (nt, 1);
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	440 m_q.resize (nt, 1);
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	441 m_A.resize (nt, nt);
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	442 m_B.resize (nt, nt);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	443
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	444 double *pr = m_r.fortran_vec ();
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	445
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	446 // Compute roots.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	447
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	448 if (! jcobi (m_n, m_inc_left, m_inc_right, m_alpha, m_beta, pdif1, pdif2, pdif3, pr))
21056 d48fdf3a8c0c maint: one more addition to cset 5e00ed38a58b. Rik <rik@octave.org> parents: 21055 diff changeset	449 error ("jcobi: newton iteration failed");
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	450
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	451 octave_idx_type id;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	452
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	453 // First derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	454
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	455 id = 1;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	456 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	457 {
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	458 dfopr (m_n, m_inc_left, m_inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	459
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	460 for (octave_idx_type j = 0; j < nt; j++)
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	461 m_A(i,j) = vect(j);
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
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	464 // Second derivative weights.
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	465
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	466 id = 2;
10603 d909c4c14b63 convert villad functions to C++ John W. Eaton <jwe@octave.org> parents: 10350 diff changeset	467 for (octave_idx_type i = 0; i < nt; i++)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	468 {
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	469 dfopr (m_n, m_inc_left, m_inc_right, i, id, pdif1, pdif2, pdif3, pr, pvect);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	470
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5105 diff changeset	471 for (octave_idx_type j = 0; j < nt; j++)
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	472 m_B(i,j) = vect(j);
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
1360 7eb93d12654c [project @ 1995-09-05 21:51:54 by jwe] jwe parents: 1321 diff changeset	475 // Gaussian quadrature weights.
3 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 id = 3;
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	478 double *pq = m_q.fortran_vec ();
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	479 dfopr (m_n, m_inc_left, m_inc_right, id, id, pdif1, pdif2, pdif3, pr, pq);
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	480
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	481 m_initialized = 1;
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	482 }
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	483
3504 5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	484 std::ostream&
5eef8a2294bd [project @ 2000-02-01 10:06:51 by jwe] jwe parents: 3503 diff changeset	485 operator << (std::ostream& os, const CollocWt& a)
3 9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	486 {
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	487 if (a.left_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	488 os << "left boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	489 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	490 os << "left boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	491
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	492 if (a.right_included ())
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	493 os << "right boundary is included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	494 else
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	495 os << "right boundary is not included\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	496
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	497 os << "\n";
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	498
29680 e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	499 os << a.m_alpha << ' ' << a.m_beta << "\n\n"
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	500 << a.m_r << "\n\n"
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	501 << a.m_q << "\n\n"
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	502 << a.m_A << "\n"
e8a8ae9f512d update coding style in CollocWt class John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	503 << a.m_B << "\n";
3 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 return os;
9a4c07481e61 [project @ 1993-08-08 01:20:23 by jwe] jwe parents: diff changeset	506 }

Mercurial > octave

annotate liboctave/numeric/CollocWt.cc @ 29680:e8a8ae9f512d