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annotate libinterp/corefcn/quadcc.cc @ 29958:32c3a5805893

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move DEFUN and DEFMETHOD functions inside octave namespace * mk-opts.pl: Surround emitted function definitions with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. * mk-builtins.pl: Surround emitted function declarations with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags. Emit deprecated global inline functions. * __betainc__.cc, __contourc__.cc, __dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc, __ichol__.cc, __ilu__.cc, __lin_interpn__.cc, __magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, balance.cc, besselj.cc, bitfcns.cc, bsxfun.cc, call-stack.cc, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, display.cc, dlmread.cc, dmperm.cc, dot.cc, eig.cc, ellipj.cc, environment.cc, error.cc, event-manager.cc, fcn-info.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc, graphics.cc, gsvd.cc, hash.cc, help.cc, hess.cc, hex2num.cc, input.cc, interpreter.cc, inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, load-path.cc, load-save.cc, lookup.cc, ls-oct-text.cc, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mgorth.cc, nproc.cc, oct-hist.cc, ordqz.cc, ordschur.cc, pager.cc, pinv.cc, pr-flt-fmt.cc, pr-output.cc, psi.cc, qr.cc, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, sighandlers.cc, sparse.cc, spparms.cc, sqrtm.cc, stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symbfact.cc, symrcm.cc, symtab.cc, syscalls.cc, sysdep.cc, time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc, utils.cc, variables.cc, __delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc, audioread.cc, convhulln.cc, fftw.cc, gzip.cc, ov-base.cc, ov-bool-mat.cc, ov-cell.cc, ov-class.cc, ov-classdef.cc, ov-fcn-handle.cc, ov-java.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-struct.cc, ov-typeinfo.cc, ov-usr-fcn.cc, ov.cc, octave.cc, lex.ll, oct-parse.yy, profiler.cc, pt-eval.cc: Surround DEFUN and DEFMETHOD function defnitions with OCTAVE_NAMESPACE_BEGIN and OCTAVE_NAMESPACE_END tags.
author John W. Eaton <jwe@octave.org>
date Fri, 13 Aug 2021 21:53:51 -0400
parents 7854d5752dd2
children 7d6709900da7
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2010-2021 The Octave Project Developers
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4 //
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5 // See the file COPYRIGHT.md in the top-level directory of this
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6 // distribution or <https://octave.org/copyright/>.
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7 //
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8 // This file is part of Octave.
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9 //
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10 // Octave is free software: you can redistribute it and/or modify it
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11 // under the terms of the GNU General Public License as published by
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12 // the Free Software Foundation, either version 3 of the License, or
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13 // (at your option) any later version.
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14 //
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15 // Octave is distributed in the hope that it will be useful, but
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 // GNU General Public License for more details.
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19 //
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20 // You should have received a copy of the GNU General Public License
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21 // along with Octave; see the file COPYING. If not, see
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22 // <https://www.gnu.org/licenses/>.
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23 //
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24 ////////////////////////////////////////////////////////////////////////
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25
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26 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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29
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30 #include <cmath>
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31
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32 #include <algorithm>
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33
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34 #include "lo-ieee.h"
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35 #include "oct-locbuf.h"
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36
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37 #include "defun.h"
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38 #include "error.h"
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39 #include "interpreter-private.h"
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40 #include "ovl.h"
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41 #include "parse.h"
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42 #include "utils.h"
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43 #include "variables.h"
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44
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45 // Extended debugging.
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46 #define DEBUG_QUADCC 0
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47
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48 // Define the minimum size of the interval heap.
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49 static const int MIN_CQUAD_HEAPSIZE = 200;
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50
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51 // Data of a single interval.
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52 typedef struct
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53 {
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54 double a, b;
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55 double c[64];
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56 double fx[33];
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57 double igral, err;
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58 int depth, rdepth, ndiv;
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59 } cquad_ival;
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60
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61 // Define relative tolerance used when deciding to drop an interval.
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62 static const double DROP_RELTOL = std::numeric_limits<double>::epsilon () * 10;
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63
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64 // Some constants and matrices that we'll need.
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65
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66 static const double xi[33] =
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67 {
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68 -1., -0.99518472667219688624, -0.98078528040323044912,
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69 -0.95694033573220886493, -0.92387953251128675612,
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70 -0.88192126434835502970, -0.83146961230254523708,
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71 -0.77301045336273696082, -0.70710678118654752440,
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72 -0.63439328416364549822, -0.55557023301960222475,
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73 -0.47139673682599764857, -0.38268343236508977173,
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74 -0.29028467725446236764, -0.19509032201612826785,
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75 -0.098017140329560601995, 0., 0.098017140329560601995,
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76 0.19509032201612826785, 0.29028467725446236764, 0.38268343236508977173,
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77 0.47139673682599764857, 0.55557023301960222475, 0.63439328416364549822,
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78 0.70710678118654752440, 0.77301045336273696082, 0.83146961230254523708,
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79 0.88192126434835502970, 0.92387953251128675612, 0.95694033573220886493,
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80 0.98078528040323044912, 0.99518472667219688624, 1.
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81 };
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82
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83 static const double bee[68] =
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84 {
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85 0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
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86 -8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
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87 0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
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88 3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
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89 0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
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90 5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
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91 0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
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92 4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
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93 0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
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94 3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
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95 0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
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96 5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
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97 0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
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98 3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
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99 0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
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100 7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
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101 0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
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102 1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
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103 0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
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104 6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
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105 0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
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106 2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
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107 0.00000000000000e+00, 5.40679930965238e-01
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108 };
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109
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110 static const double Lalpha[33] =
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111 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
112 5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
113 5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
114 5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
115 5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
116 5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
117 5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
118 5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
119 5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
120 5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
121 5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
122 5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
123 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
124
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
125 static const double Lgamma[33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
126 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
127 0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
128 5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
129 5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
130 5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
131 5.00319182924304e-01, 5.00278009473803e-01, 5.00244319584578e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
132 5.00216403386025e-01, 5.00193012939056e-01, 5.00173220168024e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
133 5.00156323280355e-01, 5.00141783641018e-01, 5.00129182278347e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
134 5.00118189340972e-01, 5.00108542278496e-01, 5.00100030010003e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
135 5.00092481273333e-01, 5.00085755939229e-01, 5.00079738458365e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
136 5.00074332862969e-01, 5.00069458915387e-01, 5.00065049112355e-01,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
137 5.00061046334395e-01
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
138 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
139
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
140 static const double V1inv[5 * 5] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
141 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
142 .47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
143 .37712361663282534635, .47140452079103168293e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
144 -.81649658092772603273e-1, -.46188021535170061160, 0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
145 .46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
146 .12046772038736683169, -.54210474174315074262, .12046772038736683169,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
147 .15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
148 -.30237157840738178177, .21380899352993950775, .10774960475223581324,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
149 -.21549920950447162648, .21549920950447162648, -.21549920950447162648,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
150 .10774960475223581324
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
151 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
152
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
153 static const double V2inv[9 * 9] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
154 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
155 .11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
156 .25577315077753587922, .27835314560994251755, .25577315077753587922,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
157 .19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
158 -.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
159 -.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
160 .16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
161 .17766815796285469394, .11316664642449611462, -.16306601003711325980,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
162 -.30847037493128779631, -.16306601003711325980, .11316664642449611462,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
163 .17766815796285469394, .26466393115406349388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
164 -.32395302049990834508e-1, -.15521142532414866547,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
165 .88573492664788602740e-1, .29570405784974857322, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
166 -.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
167 .32395302049990834508e-1, .41442155673936851246e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
168 .98186757907405608245e-1, -.23056908429499411784,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
169 -.68047008326360625520e-1, .31797435808002456774,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
170 -.68047008326360625520e-1, -.23056908429499411784,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
171 .98186757907405608245e-1, .41442155673936851246e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
172 -.49981120317798783134e-1, -.24861810572835756217e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
173 .23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
174 -.23561326072010832539, .24861810572835756217e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
175 .49981120317798783134e-1, .79691635865674781228e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
176 -.95725617891693941833e-1, -.57957553356854386344e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
177 .21164072460540271452, -.27529837844505833514, .21164072460540271452,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
178 -.57957553356854386344e-1, -.95725617891693941833e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
179 .79691635865674781228e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
180 -.10894869830716590913, .20131094491947531782, -.15407672674888869038,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
181 .83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
182 .15407672674888869038, -.20131094491947531782, .10894869830716590913,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
183 .54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
184 -.10916211417928767644, .10916211417928767644, -.10916211417928767644,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
185 .10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
186 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
187
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
188 static const double V3inv[17 * 17] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
189 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
190 .27729677693590098996e-2, .26423663180333065153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
191 .53374068493933898312e-1, .77007854739523195947e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
192 .98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
193 .13612785914022865001, .13888293186236181317, .13612785914022865001,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
194 .12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
195 .77007854739523195947e-1, .53374068493933898312e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
196 .26423663180333065153e-1, .27729677693590098996e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
197 -.48029210642807413690e-2, -.44887724635478800254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
198 -.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
199 -.11102786862182788886, -.85054870109799336515e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
200 -.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
201 .85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
202 .11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
203 .48029210642807413690e-2, .62758546879582030087e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
204 .55561297093529155869e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
205 .93281491021051539742e-1, .92320151237493695139e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
206 .55077987469605684531e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
207 -.96998141716497488255e-2, -.80285961895427405567e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
208 -.13496839655913850224,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
209 -.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
210 -.96998141716497488255e-2, .55077987469605684531e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
211 .92320151237493695139e-1, .93281491021051539742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
212 .55561297093529155869e-1, .62758546879582030087e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
213 -.74850969394858555939e-2, -.61751608943839234096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
214 -.82974150437304275958e-1, -.38437763431942633378e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
215 .45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
216 .98768034347019704401e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
217 -.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
218 -.45745502025779701366e-1, .38437763431942633378e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
219 .82974150437304275958e-1, .61751608943839234096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
220 .74850969394858555939e-2, .86710099994384056338e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
221 .64006230103659573344e-1, .58517426396091675690e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
222 -.29743410528985802680e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
223 -.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
224 .97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
225 -.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
226 -.29743410528985802680e-1, .58517426396091675690e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
227 .64006230103659573344e-1, .86710099994384056338e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
228 -.97486395666294840165e-2, -.62995604908060224672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
229 -.24373234450275529219e-1, .87760984413626872730e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
230 .12205204576993351394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
231 .16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
232 0.0, .13682714580929614678, .12422320942156845775,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
233 -.16216004196864002088e-1, -.12205204576993351394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
234 -.87760984413626872730e-1, .24373234450275529219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
235 .62995604908060224672e-1, .97486395666294840165e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
236 .10956271233750488468e-1, .58613204255294358939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
237 -.13306063940736618859e-1, -.11606666444978454399,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
238 -.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
239 -.44678658254872910434e-1, -.15617684362128533405,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
240 -.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
241 -.52059598001115805639e-1, -.11606666444978454399,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
242 -.13306063940736618859e-1, .58613204255294358939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
243 .10956271233750488468e-1, -.12098893000863087230e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
244 -.51626244709126208453e-1, .48919433304746979330e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
245 .10467644465949427090,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
246 -.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
247 .15434223333238741600, 0.0, -.15434223333238741600,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
248 -.28190838706814496438e-1, .13668732103524749234,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
249 .48729879523084673782e-1, -.10467644465949427090,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
250 -.48919433304746979330e-1, .51626244709126208453e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
251 .12098893000863087230e-1, .13542668300437944822e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
252 .41712033418258689308e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
253 -.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
254 .42121099930651007882e-1, -.14684425840766337756,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
255 -.16108203535058647043e-1, .15698075850757976092,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
256 -.16108203535058647043e-1, -.14684425840766337756,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
257 .42121099930651007882e-1, .12158068748245606853,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
258 -.58303943170068132010e-1, -.76190463272803434388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
259 .41712033418258689308e-1, .13542668300437944822e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
260 -.14939634995117694417e-1, -.30047246373341564039e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
261 .91624635082546425678e-1, -.79133374319110026377e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
262 -.12292558212072233355, .90013382617762643524e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
263 .84013717196539593395e-1, -.14813033309980695856, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
264 .14813033309980695856, -.84013717196539593395e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
265 -.90013382617762643524e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
266 .12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
267 .30047246373341564039e-1, .14939634995117694417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
268 .16986031342807474208e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
269 .15760203882617033601e-1, -.91494054040950941996e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
270 .70082459207876130806e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
271 .53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
272 .72456667788091316868e-1, -.15564535320096811360,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
273 .72456667788091316868e-1, .84048122493418898508e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
274 -.14340746778352039430, .53390713710144539104e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
275 .70082459207876130806e-1, -.91494054040950941996e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
276 .15760203882617033601e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
277 .16986031342807474208e-1, -.18994065631858742028e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
278 -.82901821370405592927e-3, .77239669773015192888e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
279 -.10850735431039424680, .47524484622086496464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
280 .69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
281 0.0, -.11992057742398672066, .14829314646228194928,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
282 -.69148184871588737021e-1, -.47524484622086496464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
283 .10850735431039424680, -.77239669773015192888e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
284 .82901821370405592927e-3, .18994065631858742028e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
285 .22761703826371535132e-1, -.17728848711449643358e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
286 -.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
287 .63073750910894244526e-1, .32928881123602721303e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
288 -.12280950532497593683, .15926189077282729505, -.12280950532497593683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
289 .32928881123602721303e-1, .63073750910894244526e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
290 -.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
291 -.17728848711449643358e-1, .22761703826371535132e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
292 -.26493215276042203434e-1, .35579780856128386192e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
293 .10447309718398935122e-1, -.68616154085314996709e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
294 .11775363082763954214, -.13918901977011837274, .12312819418827395690,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
295 -.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
296 -.12312819418827395690, .13918901977011837274, -.11775363082763954214,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
297 .68616154085314996709e-1, -.10447309718398935122e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
298 -.35579780856128386192e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
299 .26493215276042203434e-1, .40742523354399706918e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
300 -.73124912999529117195e-1, .49317266444153837821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
301 -.13686605413876015320e-1, -.28342624942191100464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
302 .70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
303 -.13817029659318161476, .12981016288391131812, -.10600251632853603875,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
304 .70371855298258216249e-1, -.28342624942191100464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
305 -.13686605413876015320e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
306 .49317266444153837821e-1, -.73124912999529117195e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
307 .40742523354399706918e-1, -.54944368958699908688e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
308 .10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
309 -.77703071757424700773e-1, .61050911730999815031e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
310 -.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
311 -.21438229266251454773e-1, .42052599404498348871e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
312 -.61050911730999815031e-1, .77703071757424700773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
313 -.91369146312596428468e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
314 .10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
315 .27485608464748840573e-1, -.54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
316 .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
317 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
318 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
319 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
320 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
321 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
322 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
323 -.54971216929497681146e-1, .27485608464748840573e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
324 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
325
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
326 static const double V4inv[33 * 33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
327 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
328 .69120897476690862600e-3, .66419939766331555194e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
329 .13600665164323186111e-1, .20122785860913684493e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
330 .26583214101668429944e-1, .32712713318999268739e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
331 .38576221976287138036e-1, .44033030938268925133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
332 .49092709529622799673e-1, .53657949874312515646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
333 .57724533144734311859e-1, .61219564530655179096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
334 .64138907503837875026e-1, .66427905189318792009e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
335 .68088956652280022887e-1, .69083051391555695878e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
336 .69422738116739271449e-1, .69083051391555695878e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
337 .68088956652280022887e-1, .66427905189318792009e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
338 .64138907503837875026e-1, .61219564530655179096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
339 .57724533144734311859e-1, .53657949874312515646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
340 .49092709529622799673e-1, .44033030938268925133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
341 .38576221976287138036e-1, .32712713318999268739e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
342 .26583214101668429944e-1, .20122785860913684493e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
343 .13600665164323186111e-1, .66419939766331555194e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
344 .69120897476690862600e-3, -.11972090629438798134e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
345 -.11448874821643225573e-1, -.23104401104002905904e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
346 -.33352899418646530133e-1, -.42538626424075425908e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
347 -.49969730733911825941e-1, -.55555454015360728353e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
348 -.58955533624852604918e-1, -.60126044219122513907e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
349 -.58959430451175833624e-1, -.55546925396227130606e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
350 -.49984739749347973762e-1, -.42513009141170294365e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
351 -.33399140950669746346e-1, -.23007690803851790829e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
352 -.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
353 .23007690803851790829e-1, .33399140950669746346e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
354 .42513009141170294365e-1, .49984739749347973762e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
355 .55546925396227130606e-1, .58959430451175833624e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
356 .60126044219122513907e-1, .58955533624852604918e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
357 .55555454015360728353e-1, .49969730733911825941e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
358 .42538626424075425908e-1, .33352899418646530133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
359 .23104401104002905904e-1, .11448874821643225573e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
360 .11972090629438798134e-2, .15501585012936019146e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
361 .14628781502199620482e-1, .28684915921474815271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
362 .39299396074628048026e-1, .46393418975496284204e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
363 .48756902531094699526e-1, .46331333488337494692e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
364 .39012645376980228775e-1, .27452795421085791153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
365 .12430953621169863781e-1, -.47682978056024928800e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
366 -.22825828045428973853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
367 -.40195512090720278312e-1, -.55503004262826221955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
368 -.67424537752827046308e-1, -.75020199300113606452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
369 -.77607844312483656131e-1, -.75020199300113606452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
370 -.67424537752827046308e-1, -.55503004262826221955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
371 -.40195512090720278312e-1, -.22825828045428973853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
372 -.47682978056024928800e-2, .12430953621169863781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
373 .27452795421085791153e-1, .39012645376980228775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
374 .46331333488337494692e-1, .48756902531094699526e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
375 .46393418975496284204e-1, .39299396074628048026e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
376 .28684915921474815271e-1, .14628781502199620482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
377 .15501585012936019146e-2, -.18377757558949194214e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
378 -.17050470050949761565e-1, -.31952119564923250836e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
379 -.40197423449026348155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
380 -.41205649520281371624e-1, -.33909965817492272248e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
381 -.19393664422115332144e-1, .56661049630886784692e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
382 .22948272173686561721e-1, .44489719570904738207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
383 .61790363672287920596e-1, .72121014727028013894e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
384 .73627151185287858579e-1, .65784665375961398923e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
385 .49369676372333667559e-1, .26444326317059715065e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
386 -.26444326317059715065e-1, -.49369676372333667559e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
387 -.65784665375961398923e-1, -.73627151185287858579e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
388 -.72121014727028013894e-1, -.61790363672287920596e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
389 -.44489719570904738207e-1, -.22948272173686561721e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
390 -.56661049630886784692e-3, .19393664422115332144e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
391 .33909965817492272248e-1, .41205649520281371624e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
392 .40197423449026348155e-1, .31952119564923250836e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
393 .17050470050949761565e-1, .18377757558949194214e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
394 .20942714740729767769e-2, .18935902405146518232e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
395 .33335840852491735126e-1, .36770680999102286065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
396 .28873194534132768509e-1, .10267303017729535513e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
397 -.14607738306201572890e-1, -.40139568545572305818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
398 -.59808326733858291561e-1, -.68528358823372627506e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
399 -.63306535387619244879e-1, -.44508601817574921056e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
400 -.15449116105605395357e-1, .17941083795006546367e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
401 .48747356011657242123e-1, .70329553984201665523e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
402 .78106117292526169663e-1, .70329553984201665523e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
403 .48747356011657242123e-1, .17941083795006546367e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
404 -.15449116105605395357e-1, -.44508601817574921056e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
405 -.63306535387619244879e-1, -.68528358823372627506e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
406 -.59808326733858291561e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
407 -.40139568545572305818e-1, -.14607738306201572890e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
408 .10267303017729535513e-1, .28873194534132768509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
409 .36770680999102286065e-1, .33335840852491735126e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
410 .18935902405146518232e-1, .20942714740729767769e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
411 -.23245285491878278419e-2, -.20401404737639389919e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
412 -.33019548231022514097e-1, -.29709828426463720091e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
413 -.11760070922697422156e-1, .15987584743850393793e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
414 .43619012891472813485e-1, .61177322409671487721e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
415 .61144030218486655594e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
416 .41895377620089086167e-1, .80232011820644308033e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
417 -.30574701186675900915e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
418 -.62072243008844865848e-1, -.76336186183574765586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
419 -.68435466095345537115e-1, -.40237669208466966207e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
420 .40237669208466966207e-1, .68435466095345537115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
421 .76336186183574765586e-1, .62072243008844865848e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
422 .30574701186675900915e-1, -.80232011820644308033e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
423 -.41895377620089086167e-1, -.61144030218486655594e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
424 -.61177322409671487721e-1, -.43619012891472813485e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
425 -.15987584743850393793e-1, .11760070922697422156e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
426 .29709828426463720091e-1, .33019548231022514097e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
427 .20401404737639389919e-1, .23245285491878278419e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
428 .25451717261579269307e-2, .21480418595666878775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
429 .31177212469293007998e-1, .19816333607013379373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
430 -.72439496274458793681e-2, -.38404203906598342397e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
431 -.57633632255322221046e-1, -.54070547403585392952e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
432 -.26249823354368866005e-1, .15643058212336881516e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
433 .54539832735118677194e-1, .73283028002473989724e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
434 .62835303524135936213e-1, .26175977027801048141e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
435 -.22193636309998606610e-1, -.62597049956093311234e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
436 -.78206986173170212505e-1, -.62597049956093311234e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
437 -.22193636309998606610e-1, .26175977027801048141e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
438 .62835303524135936213e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
439 .73283028002473989724e-1, .54539832735118677194e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
440 .15643058212336881516e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
441 -.26249823354368866005e-1, -.54070547403585392952e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
442 -.57633632255322221046e-1, -.38404203906598342397e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
443 -.72439496274458793681e-2, .19816333607013379373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
444 .31177212469293007998e-1, .21480418595666878775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
445 .25451717261579269307e-2, -.27506573922483820005e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
446 -.22224442095099251870e-1, -.27949927254215773020e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
447 -.80918481053370034987e-2, .25121859354449306916e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
448 .51563535009373061074e-1, .51936965107145960512e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
449 .22146626648171527753e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
450 -.24172689882103382748e-1, -.61731229104853568296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
451 -.68477262429344201201e-1, -.38311232728303704742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
452 .14160578713659552679e-1, .61248813427564184033e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
453 .77136328841293031805e-1, .52514801765183697988e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
454 -.52514801765183697988e-1, -.77136328841293031805e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
455 -.61248813427564184033e-1, -.14160578713659552679e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
456 .38311232728303704742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
457 .68477262429344201201e-1, .61731229104853568296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
458 .24172689882103382748e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
459 -.22146626648171527753e-1, -.51936965107145960512e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
460 -.51563535009373061074e-1, -.25121859354449306916e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
461 .80918481053370034987e-2, .27949927254215773020e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
462 .22224442095099251870e-1, .27506573922483820005e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
463 .29562461131654311467e-2, .22630271480554450613e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
464 .23547399831373800971e-1, -.43964593440902476642e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
465 -.39055315767504970597e-1, -.52369643937940066804e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
466 -.28506131614971613422e-1, .19906048093338832322e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
467 .60408880866392420279e-1, .62493397473656883090e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
468 .21391278377641297859e-1, -.37302864786623254746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
469 -.73665127933539496872e-1, -.61706142476854010202e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
470 -.78065168882546327888e-2, .52335307373945544428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
471 .78278746279419264777e-1, .52335307373945544428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
472 -.78065168882546327888e-2, -.61706142476854010202e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
473 -.73665127933539496872e-1, -.37302864786623254746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
474 .21391278377641297859e-1, .62493397473656883090e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
475 .60408880866392420279e-1, .19906048093338832322e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
476 -.28506131614971613422e-1, -.52369643937940066804e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
477 -.39055315767504970597e-1, -.43964593440902476642e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
478 .23547399831373800971e-1, .22630271480554450613e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
479 .29562461131654311467e-2, -.31515718415504761303e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
480 -.22739451096655080673e-1, -.18157123602272119779e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
481 .16496480897167303621e-1, .46921166788569301124e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
482 .40644395739978416354e-1, -.46275803430732216900e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
483 -.52883375891308909486e-1, -.61116483226324111734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
484 -.17411698764545629853e-1, .44773430013166822765e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
485 .73441577962383869198e-1, .42127368371995472815e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
486 -.25504645957196772465e-1, -.74126818045972742488e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
487 -.62780077864719287317e-1, 0.0, .62780077864719287317e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
488 .74126818045972742488e-1, .25504645957196772465e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
489 -.42127368371995472815e-1, -.73441577962383869198e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
490 -.44773430013166822765e-1, .17411698764545629853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
491 .61116483226324111734e-1, .52883375891308909486e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
492 .46275803430732216900e-2, -.40644395739978416354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
493 -.46921166788569301124e-1, -.16496480897167303621e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
494 .18157123602272119779e-1, .22739451096655080673e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
495 .31515718415504761303e-2, .33536559294882188208e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
496 .22535348942792006185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
497 .12048629300953560767e-1, -.27166076791299493403e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
498 -.47492745604230978367e-1, -.19246623430993153174e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
499 .36231297307556299322e-1, .61713617181636122004e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
500 .25928029734266134490e-1, -.40478700752883602818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
501 -.71053889866326412049e-1, -.31870824482961751482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
502 .41515251100219081281e-1, .76481960760098381651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
503 .36726509155999912440e-1, -.40090067032627055969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
504 -.78270742903374539397e-1, -.40090067032627055969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
505 .36726509155999912440e-1, .76481960760098381651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
506 .41515251100219081281e-1, -.31870824482961751482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
507 -.71053889866326412049e-1, -.40478700752883602818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
508 .25928029734266134490e-1, .61713617181636122004e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
509 .36231297307556299322e-1, -.19246623430993153174e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
510 -.47492745604230978367e-1, -.27166076791299493403e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
511 .12048629300953560767e-1, .22535348942792006185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
512 .33536559294882188208e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
513 -.35481220456925318865e-2, -.22062913693073191150e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
514 -.54487362861834144999e-2, .35438821865804087489e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
515 .40733077820527411302e-1, -.67403098138950720914e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
516 -.55559584405239171054e-1, -.42417050790865158745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
517 .24499901971884704925e-1, .68721232891705409302e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
518 .34086082787461126592e-1, -.43441000373118474002e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
519 -.73878085292669148950e-1, -.18846995664706657127e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
520 .59827776178286834498e-1, .70644634584085901794e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
521 -.70644634584085901794e-1, -.59827776178286834498e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
522 .18846995664706657127e-1, .73878085292669148950e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
523 .43441000373118474002e-1, -.34086082787461126592e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
524 -.68721232891705409302e-1, -.24499901971884704925e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
525 .42417050790865158745e-1, .55559584405239171054e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
526 .67403098138950720914e-2, -.40733077820527411302e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
527 -.35438821865804087489e-1, .54487362861834144999e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
528 .22062913693073191150e-1, .35481220456925318865e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
529 .37554176816665075631e-2, .21297045781589919482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
530 -.13327293083183431816e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
531 -.40635299172764596484e-1, -.27659860508374175359e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
532 .31089232744083445986e-1, .56113781541334176109e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
533 .37577840643257763400e-2, -.60511227350664590865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
534 -.46670556446129053853e-1, .33263195878575888247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
535 .72757324720645228775e-1, .15011712351692283635e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
536 -.65601212994924119078e-1, -.60016855838843789772e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
537 .26220858553188665966e-1, .78322776605833552980e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
538 .26220858553188665966e-1, -.60016855838843789772e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
539 -.65601212994924119078e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
540 .15011712351692283635e-1, .72757324720645228775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
541 .33263195878575888247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
542 -.46670556446129053853e-1, -.60511227350664590865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
543 .37577840643257763400e-2, .56113781541334176109e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
544 .31089232744083445986e-1, -.27659860508374175359e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
545 -.40635299172764596484e-1, -.13327293083183431816e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
546 .21297045781589919482e-1, .37554176816665075631e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
547 -.39566995305720591229e-2, -.20291873414438919995e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
548 .80617453830770930551e-2, .42270189157016547906e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
549 .10332624526759093004e-1, -.48054759547616142024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
550 -.37678032941171643972e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
551 .36617192625732482394e-1, .61009425973424865714e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
552 -.95589113168026591466e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
553 -.71023202645076922361e-1, -.25097788086808784456e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
554 .62406621963267050244e-1, .56907293171100693511e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
555 -.36435383083882206257e-1, -.75790105119208756348e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
556 .75790105119208756348e-1, .36435383083882206257e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
557 -.56907293171100693511e-1, -.62406621963267050244e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
558 .25097788086808784456e-1, .71023202645076922361e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
559 .95589113168026591466e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
560 -.61009425973424865714e-1, -.36617192625732482394e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
561 .37678032941171643972e-1, .48054759547616142024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
562 -.10332624526759093004e-1, -.42270189157016547906e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
563 -.80617453830770930551e-2, .20291873414438919995e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
564 .39566995305720591229e-2, .41776092289182138591e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
565 .19013221163904414395e-1, -.14420609729849899876e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
566 -.40259160586844441220e-1, .86327811113710831649e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
567 .53564430703021034399e-1, .65469185402150431933e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
568 -.60383116311280629856e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
569 -.25657793784058876939e-1, .58745680576829226900e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
570 .45649937869034420296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
571 -.49167932056844167772e-1, -.62696614328552187977e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
572 .32540234556426699997e-1, .74280410383464269758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
573 -.11425672633410999870e-1, -.78280649404686404903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
574 -.11425672633410999870e-1, .74280410383464269758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
575 .32540234556426699997e-1, -.62696614328552187977e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
576 -.49167932056844167772e-1, .45649937869034420296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
577 .58745680576829226900e-1, -.25657793784058876939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
578 -.60383116311280629856e-1, .65469185402150431933e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
579 .53564430703021034399e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
580 .86327811113710831649e-2, -.40259160586844441220e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
581 -.14420609729849899876e-1, .19013221163904414395e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
582 .41776092289182138591e-2, -.43935502082478059199e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
583 -.17528761237509401631e-1, .20208915249153872535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
584 .34734743119040669109e-1, -.26275910172353637955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
585 -.46368003346018878786e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
586 .26800056330709381025e-1, .56681476464606609921e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
587 -.24749011438127255898e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
588 -.64934612189056658992e-1, .20333742247679279535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
589 .71429299070059318651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
590 -.14452513210428671266e-1, -.75793341281736586582e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
591 .74717094137184935270e-2, .78034921554757317374e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
592 -.78034921554757317374e-1, -.74717094137184935270e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
593 .75793341281736586582e-1, .14452513210428671266e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
594 -.71429299070059318651e-1, -.20333742247679279535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
595 .64934612189056658992e-1, .24749011438127255898e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
596 -.56681476464606609921e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
597 -.26800056330709381025e-1, .46368003346018878786e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
598 .26275910172353637955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
599 -.34734743119040669109e-1, -.20208915249153872535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
600 .17528761237509401631e-1, .43935502082478059199e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
601 .46379089482818671473e-2, .15791188144791287229e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
602 -.25134290048737455284e-1, -.26249795071946841205e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
603 .39960457575789924651e-1, .28111892450146525404e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
604 -.51026476400767918226e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
605 -.27266747278681831364e-1, .60708796647861610865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
606 .23532306960642115854e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
607 -.68169639871532441111e-1, -.18204924701958312032e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
608 .73822890510656128485e-1, .11373392486424717019e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
609 -.77133324017644609416e-1, -.39295877480342619961e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
610 .78351902829418987960e-1, -.39295877480342619961e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
611 -.77133324017644609416e-1, .11373392486424717019e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
612 .73822890510656128485e-1, -.18204924701958312032e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
613 -.68169639871532441111e-1, .23532306960642115854e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
614 .60708796647861610865e-1, -.27266747278681831364e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
615 -.51026476400767918226e-1, .28111892450146525404e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
616 .39960457575789924651e-1, -.26249795071946841205e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
617 -.25134290048737455284e-1, .15791188144791287229e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
618 .46379089482818671473e-2, -.48780095920069827068e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
619 -.13886961667516983541e-1, .29071311049368895844e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
620 .15480559452075811600e-1, -.47527977686242313065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
621 -.31929089844361042178e-2, .58015667638415922967e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
622 -.14547915466597622925e-1, -.61067668299848923244e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
623 .35093678009090186851e-1, .55378399159800654657e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
624 -.54277226474891610385e-1, -.42023830782434076509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
625 .69197384645944912066e-1, .22610783557709586445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
626 -.77269275900637030185e-1, 0.0, .77269275900637030185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
627 -.22610783557709586445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
628 -.69197384645944912066e-1, .42023830782434076509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
629 .54277226474891610385e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
630 -.55378399159800654657e-1, -.35093678009090186851e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
631 .61067668299848923244e-1, .14547915466597622925e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
632 -.58015667638415922967e-1, .31929089844361042178e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
633 .47527977686242313065e-1, -.15480559452075811600e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
634 -.29071311049368895844e-1, .13886961667516983541e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
635 .48780095920069827068e-2, .51591759101720291381e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
636 .11747497650231330965e-1, -.31777863364694653331e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
637 -.34555825499804605557e-2, .47914131921157015198e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
638 -.22573685920142225247e-1, -.45320344390022666738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
639 .49660630547172186418e-1, .25707858143963615736e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
640 -.68132707341917233933e-1, .67534860185243140399e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
641 .69268150370037450063e-1, -.41585011920451477177e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
642 -.51622397460510041271e-1, .68408139576363036148e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
643 .18981259024768933323e-1, -.78265472429342305554e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
644 .18981259024768933323e-1, .68408139576363036148e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
645 -.51622397460510041271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
646 -.41585011920451477177e-1, .69268150370037450063e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
647 .67534860185243140399e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
648 -.68132707341917233933e-1, .25707858143963615736e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
649 .49660630547172186418e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
650 -.45320344390022666738e-1, -.22573685920142225247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
651 .47914131921157015198e-1, -.34555825499804605557e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
652 -.31777863364694653331e-1, .11747497650231330965e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
653 .51591759101720291381e-2, -.54365757412741340377e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
654 -.94862516619529080191e-2, .33240472093448190877e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
655 -.88698898099681552229e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
656 -.40973252097216337576e-1, .42995673349795657065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
657 .17320914507876958783e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
658 -.62201292691914856803e-1, .24726274174637346693e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
659 .51320859246515407288e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
660 -.62882063373810501763e-1, -.11003569131725622672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
661 .73842261324108943465e-1, -.39240120294802923208e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
662 -.49293966443941122807e-1, .73552644778818223475e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
663 -.73552644778818223475e-1, .49293966443941122807e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
664 .39240120294802923208e-1, -.73842261324108943465e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
665 .11003569131725622672e-1, .62882063373810501763e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
666 -.51320859246515407288e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
667 -.24726274174637346693e-1, .62201292691914856803e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
668 -.17320914507876958783e-1, -.42995673349795657065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
669 .40973252097216337576e-1, .88698898099681552229e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
670 -.33240472093448190877e-1, .94862516619529080191e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
671 .54365757412741340377e-2, .57750194549356126240e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
672 .69981166020044116791e-2, -.33274982140403110792e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
673 .20297071020698356116e-1, .27898517839646066582e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
674 -.53368678853282030262e-1, .16656482990394548343e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
675 .46342901447260614255e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
676 -.60536796508149003365e-1, .29109107483842596340e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
677 .63224486124385124504e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
678 -.59028872851312033411e-1, -.14783105962696191734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
679 .74269399241069253865e-1, -.49053677339382384625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
680 -.33525466624811186739e-1, .78397349622515386647e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
681 -.33525466624811186739e-1, -.49053677339382384625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
682 .74269399241069253865e-1, -.14783105962696191734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
683 -.59028872851312033411e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
684 .63224486124385124504e-1, .29109107483842596340e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
685 -.60536796508149003365e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
686 .46342901447260614255e-1, .16656482990394548343e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
687 -.53368678853282030262e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
688 .27898517839646066582e-1, .20297071020698356116e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
689 -.33274982140403110792e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
690 .69981166020044116791e-2, .57750194549356126240e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
691 -.61100308370519200637e-2, -.44383614355738148616e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
692 .32011283412619094811e-1, -.29965011866372897633e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
693 -.10560682331349193348e-1, .51110336443392506342e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
694 -.45012284729681775492e-1, -.94236825555873320102e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
695 .60860695783141264746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
696 -.55014628647083368926e-1, -.73474782382499482121e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
697 .66640148475243034781e-1, -.62533116045749887988e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
698 -.38650525912400102585e-2, .68429769005837003777e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
699 -.66984505412544901945e-1, 0.0, .66984505412544901945e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
700 -.68429769005837003777e-1, .38650525912400102585e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
701 .62533116045749887988e-1, -.66640148475243034781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
702 .73474782382499482121e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
703 .55014628647083368926e-1, -.60860695783141264746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
704 .94236825555873320102e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
705 .45012284729681775492e-1, -.51110336443392506342e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
706 .10560682331349193348e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
707 .29965011866372897633e-1, -.32011283412619094811e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
708 .44383614355738148616e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
709 .61100308370519200637e-2, .65409373892036191538e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
710 .16350101107071157065e-2, -.29301957285983144319e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
711 .36838667173388832579e-1, -.81922703976491586393e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
712 -.36955670021050133434e-1, .58374851095540469865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
713 -.31977016246946181856e-1, -.25311073698658094646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
714 .66674413950106952577e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
715 -.54865713324521039571e-1, -.39797027891537985440e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
716 .62830285264808449064e-1, -.72226313251296100676e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
717 .22560232697133353980e-1, .46455784709904033738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
718 -.78200930751070349956e-1, .46455784709904033738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
719 .22560232697133353980e-1, -.72226313251296100676e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
720 .62830285264808449064e-1, -.39797027891537985440e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
721 -.54865713324521039571e-1, .66674413950106952577e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
722 -.25311073698658094646e-1, -.31977016246946181856e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
723 .58374851095540469865e-1, -.36955670021050133434e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
724 -.81922703976491586393e-2, .36838667173388832579e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
725 -.29301957285983144319e-1, .16350101107071157065e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
726 .65409373892036191538e-2, -.69686180931868703196e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
727 .11849538727632789870e-2, .25452286414610537766e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
728 -.40522480651713943230e-1, .25694679053362813183e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
729 .14057118113748390637e-1, -.52037614725803488893e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
730 .58849342223684035589e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
731 -.25075229077361409271e-1, -.29559771094034181083e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
732 .68296746944165720199e-1, -.62890462146423984955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
733 .14457636466274596445e-1, .45787612031322361496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
734 -.77231759014655809742e-1, .57881203613910543657e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
735 -.57881203613910543657e-1, .77231759014655809742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
736 -.45787612031322361496e-1, -.14457636466274596445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
737 .62890462146423984955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
738 -.68296746944165720199e-1, .29559771094034181083e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
739 .25075229077361409271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
740 -.58849342223684035589e-1, .52037614725803488893e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
741 -.14057118113748390637e-1, -.25694679053362813183e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
742 .40522480651713943230e-1, -.25452286414610537766e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
743 -.11849538727632789870e-2, .69686180931868703196e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
744 .75611653617520254845e-2, -.43290610418608409141e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
745 -.20277062025115566914e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
746 .40362947027704828926e-1, -.38938808024132120254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
747 .11831186195916702262e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
748 .28476667401744525357e-1, -.59320969056617684621e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
749 .61101629747436200186e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
750 -.29514834848355389223e-1, -.20668001885001084821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
751 .62923592802445122793e-1, -.73558456263588833115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
752 .45314556330160999776e-1, .79031645918426015574e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
753 -.58136953576334689357e-1, .78538474524006405758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
754 -.58136953576334689357e-1, .79031645918426015574e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
755 .45314556330160999776e-1, -.73558456263588833115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
756 .62923592802445122793e-1, -.20668001885001084821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
757 -.29514834848355389223e-1, .61101629747436200186e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
758 -.59320969056617684621e-1, .28476667401744525357e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
759 .11831186195916702262e-1, -.38938808024132120254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
760 .40362947027704828926e-1, -.20277062025115566914e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
761 -.43290610418608409141e-2, .75611653617520254845e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
762 -.81505692478987769484e-2, .74297333588288568430e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
763 .14314212513540223314e-1, -.36711242251332751607e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
764 .46240027755503814626e-1, -.34921532671769023773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
765 .46930051972353714773e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
766 .32842770336385381562e-1, -.61317813706529588466e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
767 .67000809902468893103e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
768 -.45337449655535622885e-1, .35794459576271920867e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
769 .41830061526027213385e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
770 -.72091371931944711708e-1, .74150028530317793195e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
771 -.46487632538609942002e-1, 0.0, .46487632538609942002e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
772 -.74150028530317793195e-1, .72091371931944711708e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
773 -.41830061526027213385e-1, -.35794459576271920867e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
774 .45337449655535622885e-1, -.67000809902468893103e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
775 .61317813706529588466e-1, -.32842770336385381562e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
776 -.46930051972353714773e-2, .34921532671769023773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
777 -.46240027755503814626e-1, .36711242251332751607e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
778 -.14314212513540223314e-1, -.74297333588288568430e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
779 .81505692478987769484e-2, .90693182942442189743e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
780 -.11121000903959576737e-1, -.71308296141317458546e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
781 .29219439765986671645e-1, -.45820286629778129593e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
782 .49088381175879124421e-1, -.35614888785023038938e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
783 .78906970900092777895e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
784 .26262843038404929480e-1, -.56143674270125757857e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
785 .71700220472378350694e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
786 -.66963544500697307945e-1, .42215091779892228883e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
787 -.41338867413966866997e-2, -.36164891772995367321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
788 .66584367783847858225e-1, -.77874712365070098328e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
789 .66584367783847858225e-1, -.36164891772995367321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
790 -.41338867413966866997e-2, .42215091779892228883e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
791 -.66963544500697307945e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
792 .71700220472378350694e-1, -.56143674270125757857e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
793 .26262843038404929480e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
794 .78906970900092777895e-2, -.35614888785023038938e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
795 .49088381175879124421e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
796 -.45820286629778129593e-1, .29219439765986671645e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
797 -.71308296141317458546e-2, -.11121000903959576737e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
798 .90693182942442189743e-2, -.99848472706332791043e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
799 .14701271465939718856e-1, -.32917820356048383366e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
800 -.19201195309873585230e-1, .38409681836626963278e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
801 -.51647324405878909521e-1, .54522171113149311354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
802 -.45040302741689006270e-1, .24183738595685990149e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
803 .42204134165479735097e-2, -.34317295181348742251e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
804 .59542472465494579941e-1, -.74135115907618101263e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
805 .74491937840566532596e-1, -.60042604725161994304e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
806 .33437677409000083169e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
807 -.33437677409000083169e-1, .60042604725161994304e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
808 -.74491937840566532596e-1, .74135115907618101263e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
809 -.59542472465494579941e-1, .34317295181348742251e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
810 -.42204134165479735097e-2, -.24183738595685990149e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
811 .45040302741689006270e-1, -.54522171113149311354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
812 .51647324405878909521e-1, -.38409681836626963278e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
813 .19201195309873585230e-1, .32917820356048383366e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
814 -.14701271465939718856e-1, .99848472706332791043e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
815 .11775579274769383373e-1, -.19892153937316935880e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
816 .95335114477449041055e-2, .57661528440359081617e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
817 -.23382690532380910781e-1, .40237257037170725321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
818 -.53280289903551636474e-1, .59974361806023689068e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
819 -.58701684061992853224e-1, .49033407111597129616e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
820 -.31818835267847249219e-1, .90800541261162098886e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
821 .16272906819312603838e-1, -.40863896581186229487e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
822 .61346046297517367703e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
823 -.74896047554167268919e-1, .79632642148310325817e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
824 -.74896047554167268919e-1, .61346046297517367703e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
825 -.40863896581186229487e-1, .16272906819312603838e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
826 .90800541261162098886e-2, -.31818835267847249219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
827 .49033407111597129616e-1, -.58701684061992853224e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
828 .59974361806023689068e-1, -.53280289903551636474e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
829 .40237257037170725321e-1, -.23382690532380910781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
830 .57661528440359081617e-2, .95335114477449041055e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
831 -.19892153937316935880e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
832 .11775579274769383373e-1, -.13562702617218467450e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
833 .24885419969649845849e-1, -.18368693901908875583e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
834 .81673147806084084638e-2, .47890591326129587131e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
835 -.19313752945227974024e-1, .34065953398362954708e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
836 -.47667045133463415672e-1, .58820377816690514309e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
837 -.66424139824618415970e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
838 .69667606260856092515e-1, -.68102459384364543253e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
839 .61683024923302547971e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
840 -.50771943476441639136e-1, .36110771847327189215e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
841 -.18758028464284563358e-1, 0.0, .18758028464284563358e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
842 -.36110771847327189215e-1, .50771943476441639136e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
843 -.61683024923302547971e-1, .68102459384364543253e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
844 -.69667606260856092515e-1, .66424139824618415970e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
845 -.58820377816690514309e-1, .47667045133463415672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
846 -.34065953398362954708e-1, .19313752945227974024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
847 -.47890591326129587131e-2, -.81673147806084084638e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
848 .18368693901908875583e-1, -.24885419969649845849e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
849 .13562702617218467450e-1, .20576545037980523979e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
850 -.40093155172981004337e-1, .36954083167944054826e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
851 -.31856506837591907746e-1, .24996323181546255126e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
852 -.16637165210473614136e-1, .71002706773325085237e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
853 .32478629093205201133e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
854 -.14009562579050569518e-1, .24771262248780618922e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
855 -.35119395835433647559e-1, .44656290368574753171e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
856 -.53015448339647394161e-1, .59875631995693046782e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
857 -.64973208326045193862e-1, .68112280331082143373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
858 -.69172215234062186994e-1, .68112280331082143373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
859 -.64973208326045193862e-1, .59875631995693046782e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
860 -.53015448339647394161e-1, .44656290368574753171e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
861 -.35119395835433647559e-1, .24771262248780618922e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
862 -.14009562579050569518e-1, .32478629093205201133e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
863 .71002706773325085237e-2, -.16637165210473614136e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
864 .24996323181546255126e-1, -.31856506837591907746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
865 .36954083167944054826e-1, -.40093155172981004337e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
866 .20576545037980523979e-1, -.27584914609096156163e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
867 .54904171411058497973e-1, -.54109756419563083153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
868 .52794234894345577483e-1, -.50970276026831042415e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
869 .48655445537990983379e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
870 -.45872036510847994332e-1, .42646854695899611372e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
871 -.39010960357087507670e-1, .34999369144476467749e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
872 -.30650714874402762189e-1, .26006877464703437057e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
873 -.21112579608213651273e-1, .16014956068786763273e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
874 -.10763099747751940252e-1, .54075888924374485533e-2, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
875 -.54075888924374485533e-2, .10763099747751940252e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
876 -.16014956068786763273e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
877 .21112579608213651273e-1, -.26006877464703437057e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
878 .30650714874402762189e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
879 -.34999369144476467749e-1, .39010960357087507670e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
880 -.42646854695899611372e-1, .45872036510847994332e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
881 -.48655445537990983379e-1, .50970276026831042415e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
882 -.52794234894345577483e-1, .54109756419563083153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
883 -.54904171411058497973e-1, .27584914609096156163e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
884 .13794141262469565740e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
885 .27588282524939131481e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
886 .27588282524939131481e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
887 .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
888 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
889 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
890 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
891 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
892 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
893 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
894 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
895 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
896 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
897 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
898 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
899 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
900 -.27588282524939131481e-1, .13794141262469565740e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
901 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
902
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
903 static const double Tleft[33 * 33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
904 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
905 1., -.86602540378443864678, 0., .33071891388307382381, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
906 -.20728904939721249057, 0., .15128841196122722208, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
907 -.11918864298744029244, 0., .98352013661686631224e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
908 -.83727065404940845733e-1, 0., .72893399403505841203e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
909 -.64544632643375022436e-1, 0., .57913170372415565639e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
910 -.52518242575729562263e-1, 0., .48043311993977520457e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
911 -.44271433659733990243e-1, 0., .41048928022856771981e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
912 -.38263878662008271459e-1, 0., .35832844026365304501e-1, 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
913 .50000000000000000000, -.96824583655185422130, .57282196186948000082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
914 .21650635094610966169, -.35903516540862679125, -.97578093724974971969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
915 .26203921611325660506, .55792409597991015609e-1, -.20644078533943456204,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
916 -.36172381205961199479e-1, .17035068468874958194,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
917 .25371838001497225980e-1, -.14501953125000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
918 -.18786835250972344757e-1, .12625507130328301066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
919 .14473795929590520582e-1, -.11179458309419422675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
920 -.11494434254897626155e-1, .10030855351241635862,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
921 .93498556820544479096e-2, -.90964264465390582629e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
922 -.77546391824364392762e-2, .83213457337452292745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
923 .65358085945588638605e-2, -.76680372422574234569e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
924 -.55835321940047427169e-2, .71098828931825789428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
925 .48253327982967591019e-2, -.66274981937248958553e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
926 -.42118078245337801387e-2, .62064306433355646267e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
927 .37083386598903548973e-2, 0., 0., .25000000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
928 -.73950997288745200531, .83852549156242113615, -.23175620272173946716,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
929 -.37791833195149451496, .25710129174850522325, .21608307321780204633,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
930 -.22844049245646009157, -.14009503000335388415, .19897685605518413847,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
931 .98264706042471226893e-1, -.17445445004279014046,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
932 -.72761100054958328401e-1, .15463589893742108388,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
933 .56056770591708784481e-1, -.13855313872640495158,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
934 -.44517752443294564781e-1, .12534277657695128850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
935 .36211835346039665762e-1, -.11434398255136139683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
936 -.30033588409423828125e-1, .10506705408753910481,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
937 .25313077840725783008e-1, -.97149327637744872155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
938 -.21624927200393328444e-1, .90319582367202122625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
939 .18688433567711780666e-1, -.84372291635345108584e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
940 -.16312261561845420752e-1, .79149526894804751586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
941 .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
942 -.49607837082461073572, .82265291131801144317, -.59621200088559103072,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
943 -.80054302859059362371e-1, .42612156697795759420,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
944 -.90098145270865592887e-1, -.29769623255090078484, .13630307904779758221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
945 .21638835185708931831, -.14600247270306082052, -.16348801804014290453,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
946 .14340708728599057249, .12755243353979286190, -.13661523715071346961,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
947 -.10215585947881057394, .12864248070157166547, .83592528025348693602e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
948 -.12066728689302565222, -.69633728678718053052e-1, .11314245177331919532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
949 .58882939251410088028e-1, -.10621835858758221487,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
950 -.50432266865187597572e-1, .99916834723527771581e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
951 .43672094283057258509e-1, -.94206380251950852413e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
952 -.38181356812697746418e-1, .89035739656537771225e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
953 .33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
954 -.31093357409581873586, .67604086414949799246, -.75644205980613611039,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
955 .28990586430124175741, .30648508196770360914, -.35801372616842500052,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
956 -.91326869828709014708e-1, .31127929687500000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
957 -.90915752838698393094e-2, -.25637381283965534330,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
958 .57601077850322797594e-1, .21019685709225757945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
959 -.81244992138514014256e-1, -.17375078516720988858,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
960 .92289437277967051125e-1, .14527351914265391374,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
961 -.96675340792832019889e-1, -.12289485697108543415,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
962 .97448175340011084006e-1, .10511755943298339844,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
963 -.96242247086378239657e-1, -.90822942272780513537e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
964 .93966350452322132384e-1, .79189411876493712558e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
965 -.91139307067989309325e-1, -.69613039934383197265e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
966 .88062491671135767870e-1, .61646331729340817494e-1, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
967 .31250000000000000000e-1, -.18684782411095934408, .50176689760410660236,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
968 -.74784031498626095398, .56472001151566251186, .14842464993721351203e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
969 -.41162920273003120936, .20243071230196532282, .23772054897172750436,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
970 -.24963810923972235950, -.12116179938394678936, .24330535483519110663,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
971 .47903849781124471359e-1, -.22133299683101224293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
972 -.20542915138527200983e-2, .19653465717678146728,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
973 -.26818172626509178444e-1, -.17319122357631210944,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
974 .45065391411065545445e-1, .15253391395444065941,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
975 -.56543897711725408302e-1, -.13469154928743585367,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
976 .63632471400208840155e-1, .11941684923913523817,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
977 -.67828850207933293098e-1, -.10636309084510652670,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
978 .70095786922999181504e-1, .95187373095150709082e-1, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
979 0., .15625000000000000000e-1, -.10909562534194485289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
980 .34842348626527747318, -.64461114561628111443, .69382480527334683659,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
981 -.29551102358528827763, -.25527584713978439819, .38878771718544715394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
982 -.82956185835347407489e-2, -.31183177761966943912, .12831420840372374767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
983 .22067618205599434368, -.17569196937129496961, -.14598057000132284135,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
984 .18864406621763419484, .89921002550386645767e-1, -.18571835020187122114,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
985 -.48967672227195481777e-1, .17584685670380332798,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
986 .19267984545067426324e-1, -.16335437520503462738,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
987 .22598055455032407594e-2, .15032800884170631129,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
988 -.17883358353754640871e-1, -.13774837869432209951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
989 .29227555960587143675e-1, .12604194747513151053, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
990 0., .78125000000000000000e-2, -.62377810244809812496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
991 .23080781467370883845, -.50841310636012325368, .69834547012574056043,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
992 -.52572723156526459672, .11464215704954976471e-1, .38698869011491210342,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
993 -.26125646622255207507, -.16951698812361607510, .29773875898928782269,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
994 .20130501202570367491e-1, -.26332493149159310198,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
995 .67734613690401207009e-1, .21207315477103762715, -.11541543390889415193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
996 -.16249634759782417533, .13885887405041735068, .11996491328010275427,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
997 -.14810432001630926895, -.85177658352556243411e-1, .14918860659904380587,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
998 .57317789510444151564e-1, -.14569827645586660151,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
999 -.35213090145965327390e-1, .13975998126844578198, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1000 0., 0., .39062500000000000000e-2, -.35101954600803571207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1001 .14761284084133737720, -.37655033076080192966, .62410290231517322776,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1002 -.64335622317683389875, .28188168266139524244, .22488495672137010675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1003 -.39393811089283576186, .75184777995770096714e-1, .28472023119398293003,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1004 -.20410910833705899572, -.15590046962908511750, .23814567544617953125,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1005 .54442805556829031204e-1, -.22855930338589720954,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1006 .16303223615756629897e-1, .20172722433875559213,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1007 -.62723406421217419404e-1, -.17012230831020922010,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1008 .91754642766136561612e-1, .13927644821381121197, -.10886600968068418181,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1009 -.11139075654373395292, .11797455976331702879, 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1010 0., 0., .19531250000000000000e-2, -.19506820659607596598e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1011 .91865676095362231937e-1, -.26604607809696493849, .51425874205091288223,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1012 -.66047561132505329292, .48660109511591303851, -.17575661168678285615e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1013 -.36594333408055703366, .29088854695378694533, .11318677346656537927,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1014 -.31110645235730182168, .60733219161008787341e-1, .24333848233620420826,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1015 -.15254312332655419708, -.15995968483455388613, .19010344455215289289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1016 .86040636766440260000e-1, -.19652589954665259945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1017 -.27633388517205837713e-1, .18660848552712880387,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1018 -.15942583868416775867e-1, -.16902042462382064786,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1019 .47278526495327740646e-1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1020 .97656250000000000000e-3, -.10731084460857378207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1021 .55939644713816406331e-1, -.18118487371914493668, .39914857299829864263,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1022 -.60812322949933902435, .60011887183061967583, -.26002695805835928795,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1023 -.20883922404786010096, .38988130966114638081, -.11797833550782589082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1024 -.25231824756239520077, .24817859972953934712, .90516417677868996417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1025 -.26079073291293066798, .30259468817169480161e-1, .22178195264114178432,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1026 -.10569877864302048175, -.16679648389266977455, .14637718550245050850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1027 .11219272032739559870, -.16359363640525750353, -.64358194509092101393e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1028 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .48828125000000000000e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1029 -.58542865274813470967e-2, .33461741635290096452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1030 -.11979993155896201271, .29580223766987206958, -.51874761979436016742,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1031 .62861483498014306968, -.44868895761051453296, .12567502628371529386e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1032 .35040366183235474275, -.30466868455569500886, -.70903913601490112666e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1033 .30822791893032512740, -.11969443264190207736, -.20764760317621313946,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1034 .20629838355452128532, .95269702915334718507e-1, -.22432624768705133300,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1035 -.33103381593477797101e-2, .20570036048155716333,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1036 -.62208282720094518964e-1, -.17095309330441436348, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1037 0., 0., 0., 0., 0., 0., .24414062500000000000e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1038 -.31714797501871532475e-2, .19721062526127334100e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1039 -.77311181185536498246e-1, .21124871792841566575, -.41777980401893650886,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1040 .59401977834943551650, -.56132417807488349048, .23433675061367565951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1041 .20222775295220942126, -.38280372496506190127, .14443804214023095767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1042 .22268950939178466797, -.27211314150777981984, -.34184876506180717313e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1043 .26006498895669734842, -.97650425186005090107e-1, -.19024527660129101293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1044 .16789164198044635671, .10875811641651905252, -.19276785058805921298, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1045 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .12207031250000000000e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1046 -.17078941137247586143e-2, .11477733754843910060e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1047 -.48887017020924625462e-1, .14634927241421789683, -.32156282683019547854,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1048 .52165811920227223937, -.60001958466396926460, .41208501541480733755,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1049 -.11366945503190350975e-2, -.33968093962672089159, .30955190935923386766,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1050 .40657421856578262210e-1, -.29873400409871531764, .16094481791768257440,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1051 .16876122436206497694, -.23650217045022161255, -.33070260090574765012e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1052 .22985258456375907796, -.68645651043827097771e-1, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1053 0., 0., 0., 0., 0., 0., 0., 0., .61035156250000000000e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1054 -.91501857608428649078e-3, .66085179496951987952e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1055 -.30383171695850355404e-1, .98840838845366876117e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1056 -.23855447246420318989, .43322017468145613917, -.58049033744876107191,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1057 .52533893203742699346, -.20681056202371946180, -.20180000924562504384,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1058 .37503922291962681797, -.15988102869837429062, -.19823558102762374094,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1059 .28393023878803799622, -.11188133439357510403e-1, -.24730368377168229255,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1060 .14731529061377942839, .14878558042884266021, 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1061 0., 0., 0., 0., 0., 0., 0., 0., .30517578125000000000e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1062 -.48804277318479845551e-3, .37696080990601968396e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1063 -.18603912108994738255e-1, .65325006755649582964e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1064 -.17162960707938819795, .34411527956476971322, -.52289350347082497959,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1065 .57319653625674910592, -.37662253421045430413, -.14099055105384663902e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1066 .33265570610216904208, -.30921265572647566661, -.19911390594166455281e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1067 .28738590811031797718, -.18912130469738472647, -.13235936203215819193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1068 .25076406142356675279, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1069 0., 0., 0., .15258789062500000000e-4, -.25928719280954633249e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1070 .21327398937568540428e-2, -.11244626133630732010e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1071 .42375605740664331966e-1, -.12031130345907846211, .26352562258934426830,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1072 -.44590628258512682078, .56682835613700749379, -.49116715128261660395,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1073 .17845943097110339078, .20541650677432497477, -.36739803642257458221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1074 .16776034069210108273, .17920950989905112908, -.28867732805385066532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1075 .46473465543376206337e-1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1076 0., 0., 0., 0., 0., .76293945312500000000e-5, -.13727610943181290891e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1077 .11979683091449349286e-2, -.67195313034570709806e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1078 .27044920779931968175e-1, -.82472196498517457862e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1079 .19570475044896150093, -.36391620788543817693, .52241392782736588032,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1080 -.54727504974907879912, .34211551468813581183, .31580472732719957762e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1081 -.32830006549176759667, .30563797665254420769, .64905014620683140120e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1082 -.27642986248995073032, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1083 0., 0., 0., 0., 0., 0., .38146972656250000000e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1084 -.72454147007837596854e-4, .66859847582761390285e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1085 -.39751311980366118437e-2, .17015198650201528366e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1086 -.55443621868993855715e-1, .14157060481641692131, -.28641242619559616836,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1087 .45610665490966615415, -.55262786406029265394, .45818352706035500108,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1088 -.14984403004611673047, -.21163807462970713245, .36007252928843413718,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1089 -.17030961385712954159, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1090 0., 0., 0., 0., 0., 0., 0., .19073486328125000000e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1091 -.38135049864067468562e-4, .37101393638555730015e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1092 -.23305339886279723213e-2, .10569913448297127219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1093 -.36640175162216897547e-1, .10010476414320235508, -.21860074212675559892,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1094 .38124757096345313719, -.52020999209879669177, .52172632730659212045,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1095 -.30841620620308814614, -.50322546186721500184e-1, .32577618885114899053,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1096 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1097 0., 0., .95367431640625000000e-6, -.20021483206955925244e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1098 .20481807322420625431e-3, -.13553476938058909882e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1099 .64919676350791905019e-2, -.23848725425069251903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1100 .69384632678886421292e-1, -.16249711393618776934, .30736618106830314788,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1101 -.46399909601971539157, .53765031034002467225, -.42598991476520183929,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1102 .12130445348350215652, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1103 0., 0., 0., 0., 0., 0., 0., 0., .47683715820312500000e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1104 -.10487707828484902486e-4, .11254146162337528943e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1105 -.78248929534271987118e-3, .39468337145306794566e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1106 -.15313546659475671763e-1, .47249070825218564146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1107 -.11804374107101480543, .24031796927792491122, -.39629215049166341285,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1108 .51629108968402548545, -.49622372075429782915, 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1109 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1110 .23841857910156250000e-6, -.54823314130625337326e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1111 .61575377321535518154e-4, -.44877834366497538134e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1112 .23774612048621955857e-2, -.97136347645161687796e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1113 .31671599547606636717e-1, -.84028665767000747480e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1114 .18298487576742964949, -.32647878537696945218, .46970971486488895077, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1115 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1116 0., 0., 0., 0., .11920928955078125000e-6, -.28604020001177375838e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1117 .33559227978295551013e-4, -.25583821662860610560e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1118 .14201552747787302339e-2, -.60938046986874414969e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1119 .20930869247951926793e-1, -.58745021125678072911e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1120 .13613725780285953720, -.26083988356030237586, 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1121 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1122 .59604644775390625000e-7, -.14898180663526043291e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1123 .18224991282807693921e-4, -.14504433444608833821e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1124 .84184722720281809548e-3, -.37846965430000478789e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1125 .13656355548211376864e-1, -.40409541997718853934e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1126 .99226988101858325902e-1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1127 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1128 .29802322387695312500e-7, -.77471708843445529468e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1129 .98649879372606876995e-5, -.81814934772838523887e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1130 .49554483992403011328e-3, -.23290922072351413938e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1131 .88068134250844034186e-2, -.27393666952485719070e-1, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1132 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1133 0., 0., 0., .14901161193847656250e-7, -.40226235946098233685e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1134 .53236418690561306700e-5, -.45933829691164002269e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1135 .28982005232838857913e-3, -.14212974043211018374e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1136 .56192363087488842264e-2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1137 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1138 .74505805969238281250e-8, -.20858299254133430408e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1139 .28648457300134381744e-5, -.25677535898258910850e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1140 .16849420429491355445e-3, -.86062824010315834002e-3, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1141 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1142 0., 0., 0., 0., 0., .37252902984619140625e-8, -.10801736017613096861e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1143 .15376606719887104015e-5, -.14296523739727437959e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1144 .97419023656050887203e-4, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1145 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1146 .18626451492309570312e-8, -.55871592916438890146e-7,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1147 .82331193828137454068e-6, -.79302250528382787666e-5, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1148 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1149 0., 0., 0., 0., 0., 0., 0., .93132257461547851562e-9,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1150 -.28867244235852488244e-7, .43982811713864556957e-6, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1151 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1152 0., 0., 0., 0., 0., 0., 0., 0., .46566128730773925781e-9,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1153 -.14899342093408253335e-7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1154 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1155 0., 0., .23283064365386962891e-9
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1156 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1157
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1158 static const double Tright[33 * 33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1159 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1160 1., .86602540378443864678, 0., -.33071891388307382381, 0.,
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1161 .20728904939721249057, 0., -.15128841196122722208, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1162 .11918864298744029244, 0., -.98352013661686631224e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1163 .83727065404940845733e-1, 0., -.72893399403505841203e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1164 .64544632643375022436e-1, 0., -.57913170372415565639e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1165 .52518242575729562263e-1, 0., -.48043311993977520457e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1166 .44271433659733990243e-1, 0., -.41048928022856771981e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1167 .38263878662008271459e-1, 0., -.35832844026365304501e-1, 0., 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1168 .50000000000000000000, .96824583655185422130, .57282196186948000082,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1169 -.21650635094610966169, -.35903516540862679125, .97578093724974971969e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1170 .26203921611325660506, -.55792409597991015609e-1, -.20644078533943456204,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1171 .36172381205961199479e-1, .17035068468874958194,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1172 -.25371838001497225980e-1, -.14501953125000000000,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1173 .18786835250972344757e-1, .12625507130328301066,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1174 -.14473795929590520582e-1, -.11179458309419422675,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1175 .11494434254897626155e-1, .10030855351241635862,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1176 -.93498556820544479096e-2, -.90964264465390582629e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1177 .77546391824364392762e-2, .83213457337452292745e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1178 -.65358085945588638605e-2, -.76680372422574234569e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1179 .55835321940047427169e-2, .71098828931825789428e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1180 -.48253327982967591019e-2, -.66274981937248958553e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1181 .42118078245337801387e-2, .62064306433355646267e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1182 -.37083386598903548973e-2, 0., 0., .25000000000000000000,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1183 .73950997288745200531, .83852549156242113615, .23175620272173946716,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1184 -.37791833195149451496, -.25710129174850522325, .21608307321780204633,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1185 .22844049245646009157, -.14009503000335388415, -.19897685605518413847,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1186 .98264706042471226893e-1, .17445445004279014046,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1187 -.72761100054958328401e-1, -.15463589893742108388,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1188 .56056770591708784481e-1, .13855313872640495158,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1189 -.44517752443294564781e-1, -.12534277657695128850,
175b392e91fe Use GNU style coding conventions for code in libinterp/
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175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1399 0., 0., 0., 0., 0., 0., 0., .93132257461547851562e-9,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1400 .28867244235852488244e-7, .43982811713864556957e-6, 0., 0., 0., 0., 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1401 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1402 0., 0., 0., 0., 0., 0., 0., 0., .46566128730773925781e-9,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1403 .14899342093408253335e-7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1404 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1405 0., 0., .23283064365386962891e-9
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1406 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1407
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1408 // Allocates a workspace for the given maximum number of intervals.
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1409 // Note that if the workspace gets filled, the intervals with the lowest
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21724
diff changeset
1410 // error estimates are dropped. The maximum number of intervals is
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1411 // therefore not the maximum number of intervals that will be computed,
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1412 // but merely the size of the buffer.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1413
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1414 // Compute the product of fx with one of the inverse Vandermonde-like matrices.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1415
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1416 static void
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1417 Vinvfx (const double *fx, double *c, const int d)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1418 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1419 int i, j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1420
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1421 switch (d)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1422 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1423 case 0:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1424 for (i = 0; i <= 4; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1425 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1426 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1427 for (j = 0; j <= 4; j++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1428 c[i] += V1inv[i*5 + j] * fx[j * 8];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1429 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1430 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1431 case 1:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1432 for (i = 0; i <= 8; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1433 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1434 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1435 for (j = 0; j <= 8; j++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1436 c[i] += V2inv[i*9 + j] * fx[j * 4];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1437 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1438 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1439 case 2:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1440 for (i = 0; i <= 16; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1441 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1442 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1443 for (j = 0; j <= 16; j++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1444 c[i] += V3inv[i*17 + j] * fx[j * 2];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1445 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1446 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1447 case 3:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1448 for (i = 0; i <= 32; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1449 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1450 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1451 for (j = 0; j <= 32; j++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1452 c[i] += V4inv[i*33 + j] * fx[j];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1453 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1454 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1455 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1456 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1457
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1458 // Downdate the interpolation given by the N coefficients C by removing
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1459 // the nodes with indices in NaNs.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1460
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1461 static void
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1462 downdate (double *c, int n, int d, int *nans, int nnans)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1463 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1464 static const int bidx[4] = { 0, 6, 16, 34 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1465 double b_new[34], alpha;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1466 int i, j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1467
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1468 for (i = 0; i <= n + 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1469 b_new[i] = bee[bidx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1470 for (i = 0; i < nnans; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1471 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1472 b_new[n + 1] = b_new[n + 1] / Lalpha[n];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1473 b_new[n] = (b_new[n] + xi[nans[i]] * b_new[n + 1]) / Lalpha[n - 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1474 for (j = n - 1; j > 0; j--)
27277
db687716fed6 style fixes: generally aim to break long lines before operators, not after
John W. Eaton <jwe@octave.org>
parents: 26864
diff changeset
1475 b_new[j] = (b_new[j] + xi[nans[i]] * b_new[j + 1]
db687716fed6 style fixes: generally aim to break long lines before operators, not after
John W. Eaton <jwe@octave.org>
parents: 26864
diff changeset
1476 - Lgamma[j + 1] * b_new[j + 2]) / Lalpha[j - 1];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1477 for (j = 0; j <= n; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1478 b_new[j] = b_new[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1479 alpha = c[n] / b_new[n];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1480 for (j = 0; j < n; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1481 c[j] -= alpha * b_new[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1482 c[n] = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1483 n--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1484 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1485 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1486
29958
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29359
diff changeset
1487 OCTAVE_NAMESPACE_BEGIN
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29359
diff changeset
1488
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1489 // The actual integration routine.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1490
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1491 DEFMETHOD (quadcc, interp, args, ,
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1492 doc: /* -*- texinfo -*-
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1493 @deftypefn {} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b})
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1494 @deftypefnx {} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1495 @deftypefnx {} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1496 @deftypefnx {} {[@var{q}, @var{err}, @var{nr_points}] =} quadcc (@dots{})
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1497 Numerically evaluate the integral of @var{f} from @var{a} to @var{b} using
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1498 doubly-adaptive @nospell{Clenshaw-Curtis} quadrature.
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1499
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1500 @var{f} is a function handle, inline function, or string containing the name
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1501 of the function to evaluate. The function @var{f} must be vectorized and
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1502 must return a vector of output values if given a vector of input values.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1503 For example,
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1504
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1505 @example
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1506 f = @@(x) x .* sin (1./x) .* sqrt (abs (1 - x));
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1507 @end example
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1508
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1509 @noindent
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1510 which uses the element-by-element ``dot'' form for all operators.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1511
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1512 @var{a} and @var{b} are the lower and upper limits of integration. Either or
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1513 both limits may be infinite. @code{quadcc} handles an infinite limit by
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1514 substituting the variable of integration with @code{x = tan (pi/2*u)}.
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1515
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1516 The optional argument @var{tol} is a 1- or 2-element vector that specifies the
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1517 desired accuracy of the result. The first element of the vector is the desired
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1518 absolute tolerance, and the second element is the desired relative tolerance.
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1519 To choose a relative test only, set the absolute tolerance to zero. To choose
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1520 an absolute test only, set the relative tolerance to zero. The default
24546
d3a507ca2d5d maint: merge stable to default.
Rik <rik@octave.org>
parents: 24534 24545
diff changeset
1521 absolute tolerance is 1e-10 (1e-5 for single), and the default relative
d3a507ca2d5d maint: merge stable to default.
Rik <rik@octave.org>
parents: 24534 24545
diff changeset
1522 tolerance is 1e-6 (1e-4 for single).
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1523
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1524 The optional argument @var{sing} contains a list of points where the integrand
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1525 has known singularities, or discontinuities in any of its derivatives, inside
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1526 the integration interval. For the example above, which has a discontinuity at
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1527 x=1, the call to @code{quadcc} would be as follows
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1528
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1529 @example
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1530 int = quadcc (f, a, b, [], [ 1 ]);
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1531 @end example
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1532
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1533 The result of the integration is returned in @var{q}.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1534
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1535 @var{err} is an estimate of the absolute integration error.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1536
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1537 @var{nr_points} is the number of points at which the integrand was evaluated.
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1538
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1539 If the adaptive integration did not converge, the value of @var{err} will be
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1540 larger than the requested tolerance. Therefore, it is recommended to verify
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1541 this value for difficult integrands.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1542
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1543 @code{quadcc} is capable of dealing with non-numeric values of the integrand
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1544 such as @code{NaN} or @code{Inf}. If the integral diverges, and @code{quadcc}
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1545 detects this, then a warning is issued and @code{Inf} or @code{-Inf} is
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1546 returned.
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1547
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1548 Note: @code{quadcc} is a general purpose quadrature algorithm and, as such,
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1549 may be less efficient for a smooth or otherwise well-behaved integrand than
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1550 other methods such as @code{quadgk}.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1551
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1552 The algorithm uses @nospell{Clenshaw-Curtis} quadrature rules of increasing
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1553 degree in each interval and bisects the interval if either the function does
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1554 not appear to be smooth or a rule of maximum degree has been reached. The
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1555 error estimate is computed from the L2-norm of the difference between two
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1556 successive interpolations of the integrand over the nodes of the respective
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1557 quadrature rules.
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1558
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1559 Reference: @nospell{P. Gonnet}, @cite{Increasing the Reliability of Adaptive
25003
2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release.
Rik <rik@octave.org>
parents: 24986
diff changeset
1560 Quadrature Using Explicit Interpolants}, @nospell{ACM} Transactions on
27800
5a6a19a4e3da doc: Use Texinfo non-sentence ending periods in citations.
Rik <rik@octave.org>
parents: 27277
diff changeset
1561 Mathematical Software, Vol.@: 37, Issue 3, Article No.@: 3, 2010.
21966
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1562 @seealso{quad, quadv, quadl, quadgk, trapz, dblquad, triplequad}
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1563 @end deftypefn */)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1564 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1565 // Some constants that we will need.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1566 static const int n[4] = { 4, 8, 16, 32 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1567 static const int skip[4] = { 8, 4, 2, 1 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1568 static const int idx[4] = { 0, 5, 14, 31 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1569 static const double w = M_SQRT2 / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1570 static const int ndiv_max = 20;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1571
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1572 // Arguments left and right.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1573 int nargin = args.length ();
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1574 octave_value fcn;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1575 double a, b, abstol, reltol, *sing;
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1576 bool issingle;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1577
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1578 // Variables needed for transforming the integrand.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1579 bool wrap = false;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1580 double xw;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1581
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1582 // Stuff we will need to call the integrand.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1583 octave_value_list fargs, fvals;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1584
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1585 // Actual variables (as opposed to constants above).
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1586 double m, h, ml, hl, mr, hr, temp;
13219
cf5ebc0e47e4 fix warnings for unused but set variables and shadowed variables
John W. Eaton <jwe@octave.org>
parents: 13141
diff changeset
1587 double igral, err, igral_final, err_final;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1588 int nivals;
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1589 int neval = 0;
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1590 int i, j, d, split;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1591 int nnans, nans[33];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1592 cquad_ival *iv, *ivl, *ivr;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1593 double nc, ncdiff;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1594
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1595 // Parse the input arguments.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1596 if (nargin < 3)
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20232
diff changeset
1597 print_usage ();
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1598
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1599 fcn = octave::get_function_handle (interp, args(0), "x");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1600
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1601 if (! args(1).is_real_scalar ())
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1602 error ("quadcc: lower limit of integration (A) must be a real scalar");
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1603 a = args(1).double_value ();
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1604 issingle = args(1).is_single_type ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1605
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1606 if (! args(2).is_real_scalar ())
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1607 error ("quadcc: upper limit of integration (B) must be a real scalar");
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1608 b = args(2).double_value ();
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1609 issingle = (issingle || args(2).is_single_type ());
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1610
23577
80c42f4cca13 maint: Deprecate is_empty and replace with isempty.
Rik <rik@octave.org>
parents: 23564
diff changeset
1611 if (nargin < 4 || args(3).isempty ())
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1612 {
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1613 if (issingle)
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1614 {
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1615 abstol = 1.0e-5;
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1616 reltol = 1.0e-4;
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1617 }
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1618 else
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1619 {
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1620 abstol = 1.0e-10;
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1621 reltol = 1.0e-6;
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1622 }
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1623 }
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1624 else if (! args(3).isnumeric () || args(3).numel () > 2)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1625 error ("quadcc: TOL must be a 1- or 2-element vector [AbsTol, RelTol]");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1626 else
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1627 {
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1628 NDArray tol = args(3).array_value ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1629
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1630 abstol = tol(0);
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1631 if (abstol < 0)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1632 error ("quadcc: absolute tolerance must be >=0");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1633
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1634 if (tol.numel () == 1)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1635 {
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1636 if (issingle)
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1637 reltol = 1.0e-4;
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1638 else
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1639 reltol = 1.0e-6;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1640 }
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1641 else
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1642 {
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1643 reltol = tol(1);
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1644 if (reltol < 0)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1645 error ("quadcc: relative tolerance must be >=0");
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1646 }
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1647 }
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1648
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1649 if (nargin < 5)
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1650 nivals = 1;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1651 else if (! (args(4).is_real_scalar () || args(4).is_real_matrix ()))
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1652 error ("quadcc: list of singularities (SING) must be a vector of real values");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1653 else
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1654 nivals = 1 + args(4).numel ();
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1655
21213
f7d1050b9b53 maint: Clean up various usages of #ifdef.
Rik <rik@octave.org>
parents: 21200
diff changeset
1656 int cquad_heapsize = (nivals >= MIN_CQUAD_HEAPSIZE ? nivals + 1
f7d1050b9b53 maint: Clean up various usages of #ifdef.
Rik <rik@octave.org>
parents: 21200
diff changeset
1657 : MIN_CQUAD_HEAPSIZE);
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1658 // The interval heap.
15996
1aff8c38c53c use octave_local_buffer for temporary arrays in quadcc
John W. Eaton <jwe@octave.org>
parents: 15995
diff changeset
1659 OCTAVE_LOCAL_BUFFER (cquad_ival, ivals, cquad_heapsize);
1aff8c38c53c use octave_local_buffer for temporary arrays in quadcc
John W. Eaton <jwe@octave.org>
parents: 15995
diff changeset
1660 OCTAVE_LOCAL_BUFFER (double, iivals, cquad_heapsize);
1aff8c38c53c use octave_local_buffer for temporary arrays in quadcc
John W. Eaton <jwe@octave.org>
parents: 15995
diff changeset
1661 OCTAVE_LOCAL_BUFFER (int, heap, cquad_heapsize);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1662
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1663 if (nivals == 1)
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1664 {
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1665 iivals[0] = a;
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1666 iivals[1] = b;
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1667 }
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1668 else
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1669 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1670 // Intervals around singularities.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1671 sing = args(4).array_value ().fortran_vec ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1672 iivals[0] = a;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1673 std::copy_n (sing, nivals-1, iivals+1);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1674 iivals[nivals] = b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1675 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1676
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1677 // If a or b are +/-Inf, transform the integral.
21782
2aef506f3fec use namespace for lo-mappers.h functions
John W. Eaton <jwe@octave.org>
parents: 21751
diff changeset
1678 if (octave::math::isinf (a) || octave::math::isinf (b))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1679 {
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1680 wrap = true;
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1681 for (i = 0; i < nivals + 1; i++)
21782
2aef506f3fec use namespace for lo-mappers.h functions
John W. Eaton <jwe@octave.org>
parents: 21751
diff changeset
1682 if (octave::math::isinf (iivals[i]))
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21782
diff changeset
1683 iivals[i] = std::copysign (1.0, iivals[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1684 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1685 iivals[i] = 2.0 * atan (iivals[i]) / M_PI;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1686 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1687
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1688 // Initialize the heaps.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1689 for (i = 0; i < cquad_heapsize; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1690 heap[i] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1691
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1692 // Create the first interval(s).
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1693 igral = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1694 err = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1695 for (j = 0; j < nivals; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1696 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1697 // Initialize the interval.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1698 iv = &(ivals[heap[j]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1699 m = (iivals[j] + iivals[j + 1]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1700 h = (iivals[j + 1] - iivals[j]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1701 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1702 ColumnVector ex (33);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1703 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1704 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1705 for (i = 0; i <= n[3]; i++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1706 ex(i) = tan (M_PI/2 * (m + xi[i]*h));
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1707 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1708 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1709 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1710 for (i = 0; i <= n[3]; i++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1711 ex(i) = m + xi[i]*h;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1712 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1713 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
1714 fvals = octave::feval (fcn, fargs, 1);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1715 if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1716 error ("quadcc: integrand F must return a single, real-valued vector");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1717
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1718 Matrix effex = fvals(0).matrix_value ();
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1719 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1720 error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1721
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1722 for (i = 0; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1723 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1724 iv->fx[i] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1725 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1726 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1727 xw = ex(i);
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1728 iv->fx[i] *= (1.0 + xw*xw) * M_PI/2;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1729 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1730 neval++;
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
1731 if (! octave::math::isfinite (iv->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1732 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1733 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1734 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1735 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1736 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1737 Vinvfx (iv->fx, &(iv->c[idx[3]]), 3);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1738 Vinvfx (iv->fx, &(iv->c[idx[2]]), 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1739 Vinvfx (iv->fx, &(iv->c[0]), 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1740 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
1741 iv->fx[nans[i]] = octave::numeric_limits<double>::NaN ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1742 iv->a = iivals[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1743 iv->b = iivals[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1744 iv->depth = 3;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1745 iv->rdepth = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1746 iv->ndiv = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1747 iv->igral = 2 * h * iv->c[idx[3]] * w;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1748 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1749 for (i = n[2] + 1; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1750 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1751 temp = iv->c[idx[3] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1752 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1753 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1754 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1755 for (i = 0; i <= n[2]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1756 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1757 temp = iv->c[idx[2] + i] - iv->c[idx[3] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1758 ncdiff += temp * temp;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1759 temp = iv->c[idx[3] + i];
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1760 nc += temp * temp;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1761 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1762 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1763 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1764 iv->err = ncdiff * 2 * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1765 if (ncdiff / nc > 0.1 && iv->err < 2 * h * nc)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1766 iv->err = 2 * h * nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1767
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1768 // Tabulate this interval's data.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1769 igral += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1770 err += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1771
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1772 // Sift it up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1773 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1774 while (i > 0 && ivals[heap[i / 2]].err < ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1775 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1776 std::swap (heap[i], heap[i / 2]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1777 i /= 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1778 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1779 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1780
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1781 // Initialize some global values.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1782 igral_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1783 err_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1784
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1785 // Main loop.
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1786 while (nivals > 0
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1787 && err > std::max (abstol, fabs (igral) * reltol)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1788 && ! (err_final > std::max (abstol, fabs (igral) * reltol)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1789 && err - err_final < std::max (abstol, fabs (igral) * reltol)))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1790 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1791 // Allow the user to interrupt.
22860
0b1e25cc4457 eliminate use of OCTAVE_QUIT macro in C++ sources
John W. Eaton <jwe@octave.org>
parents: 22755
diff changeset
1792 octave_quit ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1793
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1794 // Put our finger on the interval with the largest error.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1795 iv = &(ivals[heap[0]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1796 m = (iv->a + iv->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1797 h = (iv->b - iv->a) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1798
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1799 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1800 printf ("quadcc: processing ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1801 heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1802 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1803
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1804 // Should we try to increase the degree?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1805 if (iv->depth < 3)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1806 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1807 // Keep tabs on some variables.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1808 d = ++iv->depth;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1809
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1810 // Get the new (missing) function values.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1811 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1812 ColumnVector ex (n[d] / 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1813 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1814 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1815 for (i = 0; i < n[d] / 2; i++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1816 ex(i) = tan (M_PI/2 * (m + xi[(2*i + 1) * skip[d]] * h));
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1817 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1818 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1819 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1820 for (i = 0; i < n[d] / 2; i++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1821 ex(i) = m + xi[(2*i + 1) * skip[d]] * h;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1822 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1823 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
1824 fvals = octave::feval (fcn, fargs, 1);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1825 if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1826 error ("quadcc: integrand F must return a single, real-valued vector");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1827
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1828 Matrix effex = fvals(0).matrix_value ();
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1829 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1830 error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1831
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1832 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1833 for (i = 0; i < n[d] / 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1834 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1835 j = (2*i + 1) * skip[d];
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1836 iv->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1837 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1838 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1839 xw = ex(i);
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1840 iv->fx[j] *= (1.0 + xw*xw) * M_PI/2;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1841 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1842 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1843 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1844 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1845 for (i = 0; i <= 32; i += skip[d])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1846 {
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
1847 if (! octave::math::isfinite (iv->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1848 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1849 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1850 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1851 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1852 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1853
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1854 // Compute the new coefficients.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1855 Vinvfx (iv->fx, &(iv->c[idx[d]]), d);
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1856 // Downdate any NaNs.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1857 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1858 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1859 downdate (&(iv->c[idx[d]]), n[d], d, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1860 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
1861 iv->fx[nans[i]] = octave::numeric_limits<double>::NaN ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1862 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1863
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1864 // Compute the error estimate.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1865 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1866 for (i = n[d - 1] + 1; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1867 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1868 temp = iv->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1869 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1870 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1871 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1872 for (i = 0; i <= n[d - 1]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1873 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1874 temp = iv->c[idx[d - 1] + i] - iv->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1875 ncdiff += temp * temp;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1876 temp = iv->c[idx[d] + i];
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1877 nc += temp * temp;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1878 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1879 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1880 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1881 iv->err = ncdiff * 2 * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1882 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1883 iv->igral = 2 * h * w * iv->c[idx[d]];
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1884 // Split the interval prematurely?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1885 split = (nc > 0 && ncdiff / nc > 0.1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1886 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1887 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1888 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1889 // Maximum degree reached, just split.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1890 split = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1891 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1892
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1893 // Should we drop this interval?
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1894 if ((m + h*xi[0]) >= (m + h*xi[1])
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1895 || (m + h*xi[31]) >= (m + h*xi[32])
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1896 || iv->err < fabs (iv->igral) * DROP_RELTOL)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1897 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1898 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1899 printf ("quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1900 heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1901 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1902
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1903 // Keep this interval's contribution.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1904 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1905 igral_final += iv->igral;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1906 // Swap with the last element on the heap.
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1907 std::swap (heap[nivals - 1], heap[0]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1908 nivals--;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1909 // Fix up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1910 i = 0;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1911 while (2*i + 1 < nivals)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1912 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1913 // Get the kids.
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1914 j = 2*i + 1;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1915 // If the j+1st entry exists and is larger than the jth,
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1916 // use it instead.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1917 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1918 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1919 j++;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1920 // Do we need to move the ith entry up?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1921 if (ivals[heap[j]].err <= ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1922 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1923 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1924 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1925 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1926 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1927 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1928 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1929 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1930 else if (split)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1931 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1932 // Some values we will need often...
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1933 d = iv->depth;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1934 // Generate the interval on the left.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1935 ivl = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1936 ivl->a = iv->a;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1937 ivl->b = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1938 ml = (ivl->a + ivl->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1939 hl = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1940 ivl->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1941 ivl->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1942 ivl->fx[0] = iv->fx[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1943 ivl->fx[32] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1944 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1945 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1946 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1947 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1948 for (i = 0; i < n[0] - 1; i++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1949 ex(i) = tan (M_PI/2 * (ml + xi[(i + 1) * skip[0]] * hl));
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1950 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1951 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1952 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1953 for (i = 0; i < n[0] - 1; i++)
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1954 ex(i) = ml + xi[(i + 1) * skip[0]] * hl;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1955 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1956 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
1957 fvals = octave::feval (fcn, fargs, 1);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1958 if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1959 error ("quadcc: integrand F must return a single, real-valued vector");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1960
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1961 Matrix effex = fvals(0).matrix_value ();
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1962 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1963 error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1964
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1965 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1966 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1967 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1968 j = (i + 1) * skip[0];
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1969 ivl->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1970 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1971 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1972 xw = ex(i);
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1973 ivl->fx[j] *= (1.0 + xw*xw) * M_PI/2;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1974 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1975 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1976 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1977 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1978 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1979 {
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
1980 if (! octave::math::isfinite (ivl->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1981 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1982 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1983 ivl->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1984 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1985 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1986 Vinvfx (ivl->fx, ivl->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1987 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1988 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1989 downdate (ivl->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1990 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
1991 ivl->fx[nans[i]] = octave::numeric_limits<double>::NaN ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1992 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1993 for (i = 0; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1994 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1995 ivl->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1996 for (j = i; j <= n[d]; j++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1997 ivl->c[idx[d] + i] += Tleft[i*33 + j] * iv->c[idx[d] + j];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1998 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1999 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2000 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2001 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2002 temp = ivl->c[i] - ivl->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2003 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2004 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2005 for (i = n[0] + 1; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2006 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2007 temp = ivl->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2008 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2009 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2010 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2011 ivl->err = ncdiff * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2012 // Check for divergence.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2013 ivl->ndiv = iv->ndiv + (fabs (iv->c[0]) > 0
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2014 && ivl->c[0] / iv->c[0] > 2);
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2015 if (ivl->ndiv > ndiv_max && 2*ivl->ndiv > ivl->rdepth)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2016 {
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21782
diff changeset
2017 igral = std::copysign (octave::numeric_limits<double>::Inf (), igral);
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
2018 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2019 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2020 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2021
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2022 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2023 ivl->igral = h * w * ivl->c[0];
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
2024
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2025 // Generate the interval on the right.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2026 ivr = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2027 ivr->a = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2028 ivr->b = iv->b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2029 mr = (ivr->a + ivr->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2030 hr = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2031 ivr->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2032 ivr->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2033 ivr->fx[0] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2034 ivr->fx[32] = iv->fx[32];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2035 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2036 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2037 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2038 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2039 for (i = 0; i < n[0] - 1; i++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2040 ex(i) = tan (M_PI/2 * (mr + xi[(i + 1) * skip[0]] * hr));
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2041 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2042 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2043 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2044 for (i = 0; i < n[0] - 1; i++)
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2045 ex(i) = mr + xi[(i + 1) * skip[0]] * hr;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2046 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2047 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
2048 fvals = octave::feval (fcn, fargs, 1);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2049 if (fvals.length () != 1 || ! fvals(0).is_real_matrix ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
2050 error ("quadcc: integrand F must return a single, real-valued vector");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
2051
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2052 Matrix effex = fvals(0).matrix_value ();
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
2053 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
2054 error ("quadcc: integrand F must return a single, real-valued vector of the same size as the input");
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
2055
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
2056 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2057 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2058 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2059 j = (i + 1) * skip[0];
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2060 ivr->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2061 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2062 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2063 xw = ex(i);
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2064 ivr->fx[j] *= (1.0 + xw*xw) * M_PI/2;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2065 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2066 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2067 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2068 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2069 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2070 {
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
2071 if (! octave::math::isfinite (ivr->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2072 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2073 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2074 ivr->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2075 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2076 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2077 Vinvfx (ivr->fx, ivr->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2078 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2079 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2080 downdate (ivr->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2081 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
2082 ivr->fx[nans[i]] = octave::numeric_limits<double>::NaN ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2083 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2084 for (i = 0; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2085 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2086 ivr->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2087 for (j = i; j <= n[d]; j++)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2088 ivr->c[idx[d] + i] += Tright[i*33 + j] * iv->c[idx[d] + j];
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2089 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2090 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2091 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2092 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2093 temp = ivr->c[i] - ivr->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2094 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2095 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2096 for (i = n[0] + 1; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2097 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2098 temp = ivr->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2099 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2100 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2101 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2102 ivr->err = ncdiff * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2103 // Check for divergence.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2104 ivr->ndiv = iv->ndiv + (fabs (iv->c[0]) > 0
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2105 && ivr->c[0] / iv->c[0] > 2);
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2106 if (ivr->ndiv > ndiv_max && 2*ivr->ndiv > ivr->rdepth)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2107 {
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21782
diff changeset
2108 igral = std::copysign (octave::numeric_limits<double>::Inf (), igral);
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
2109 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2110 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2111 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2112
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2113 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2114 ivr->igral = h * w * ivr->c[0];
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
2115
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2116 // Fix-up the heap: we now have one interval on top that we
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2117 // don't need any more and two new, unsorted ones at the bottom.
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
2118
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2119 // Flip the last interval to the top of the heap and sift down.
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2120 std::swap (heap[nivals - 1], heap[0]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2121 nivals--;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2122 // Sift this interval back down the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2123 i = 0;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2124 while (2*i + 1 < nivals - 1)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2125 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2126 j = 2*i + 1;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2127 if (j + 1 < nivals - 1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2128 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2129 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2130 if (ivals[heap[j]].err <= ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2131 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2132 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2133 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2134 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2135 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2136 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2137 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2138
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2139 // Now grab the last interval and sift it up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2140 i = nivals - 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2141 while (i > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2142 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2143 j = (i - 1) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2144 if (ivals[heap[j]].err < ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2145 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2146 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2147 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2148 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2149 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2150 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2151 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2152 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2153 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2154 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2155 // Otherwise, just fix-up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2156 i = 0;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2157 while (2*i + 1 < nivals)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2158 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2159 j = 2*i + 1;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2160 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2161 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2162 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2163 if (ivals[heap[j]].err <= ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2164 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2165 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2166 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2167 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2168 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2169 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2170 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2171 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2172
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2173 // If the heap is about to overflow, remove the last two intervals.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2174 while (nivals > cquad_heapsize - 2)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2175 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2176 iv = &(ivals[heap[nivals - 1]]);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2177 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2178 printf ("quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2179 heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2180 #endif
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2181 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2182 igral_final += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2183 nivals--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2184 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2185
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2186 // Collect the value of the integral and error.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2187 igral = igral_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2188 err = err_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2189 for (i = 0; i < nivals; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2190 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2191 igral += ivals[heap[i]].igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2192 err += ivals[heap[i]].err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2193 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2194 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2195
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2196 #if (DEBUG_QUADCC)
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2197 // Dump the contents of the heap.
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2198 for (i = 0; i < nivals; i++)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2199 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2200 iv = &(ivals[heap[i]]);
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2201 printf ("quadcc: ival %i (%i) with [%e,%e], int=%e, err=%e, depth=%i, rdepth=%i, ndiv=%i\n",
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2202 i, heap[i], iv->a, iv->b, iv->igral, iv->err, iv->depth,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2203 iv->rdepth, iv->ndiv);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2204 }
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2205 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2206
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2207 if (issingle)
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2208 return ovl (static_cast<float> (igral), err, neval);
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2209 else
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2210 return ovl (igral, err, neval);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2211 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2212
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 12653
diff changeset
2213 /*
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2214 %!assert (quadcc (@sin, -pi, pi), 0, 1e-10)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2215 %!assert (quadcc (inline ("sin"), -pi, pi), 0, 1e-10)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2216 %!assert (quadcc ("sin", -pi, pi), 0, 1e-10)
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2217
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2218 %!assert (quadcc (@sin, -pi, 0), -2, 1e-10)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2219 %!assert (quadcc (@sin, 0, pi), 2, 1e-10)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2220 %!assert (quadcc (@(x) 1./sqrt (x), 0, 1), 2, -1e-6)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2221 %!assert (quadcc (@(x) 1./(sqrt (x).*(x+1)), 0, Inf), pi, -1e-6)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2222 %!assert (quadcc (@(x) 1./(sqrt (x).*(x+1)), 0, Inf, [0, 1e-8]), pi, -1e-8)
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2223
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2224 %!assert (quadcc (@(x) exp (-x .^ 2), -Inf, Inf), sqrt (pi), 1e-10)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2225 %!assert (quadcc (@(x) exp (-x .^ 2), -Inf, 0), sqrt (pi)/2, 1e-10)
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2226
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2227 ## Test function with NaNs in interval
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2228 %!function y = __nansin (x)
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2229 %! nan_locs = [-3*pi/4, -pi/4, 0, pi/3, pi/2, pi];
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2230 %! y = sin (x);
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2231 %! idx = min (abs (bsxfun (@minus, x(:), nan_locs)), [], 2);
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2232 %! y(idx < 1e-10) = NaN;
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2233 %!endfunction
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2234
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2235 %!test
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2236 %! [q, err, npoints] = quadcc ("__nansin", -pi, pi, [0, 1e-6]);
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2237 %! assert (q, 0, -1e-6);
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2238 %! assert (err, 0, 15*eps);
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2239
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2240 %!test
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2241 %! assert (class (quadcc (@sin, 0, 1)), "double");
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2242 %! assert (class (quadcc (@sin, single (0), 1)), "single");
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2243 %! assert (class (quadcc (@sin, 0, single (1))), "single");
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2244 %! assert (class (quadcc (@sin, single (0), single (1))), "single");
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2245
22737
7abc25e6206a maint: Clean up code base to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 22407
diff changeset
2246 ## Test input validation
28930
2883b3d08b7e maint: Remove unnecessary parentheses bracketing %!error BIST tests.
Rik <rik@octave.org>
parents: 27923
diff changeset
2247 %!error quadcc ()
2883b3d08b7e maint: Remove unnecessary parentheses bracketing %!error BIST tests.
Rik <rik@octave.org>
parents: 27923
diff changeset
2248 %!error quadcc (@sin)
2883b3d08b7e maint: Remove unnecessary parentheses bracketing %!error BIST tests.
Rik <rik@octave.org>
parents: 27923
diff changeset
2249 %!error quadcc (@sin, 0)
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2250 %!error <lower limit .* must be a .* scalar> (quadcc (@sin, ones (2), pi))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2251 %!error <lower limit .* must be a real scalar> (quadcc (@sin, -i, pi))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2252 %!error <upper limit .* must be a .* scalar> (quadcc (@sin, 0, ones (2)))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2253 %!error <upper limit .* must be a real scalar> (quadcc (@sin, 0, i))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2254 %!error <TOL must be a 1- or 2-element vector> (quadcc (@sin, 0, pi, {1}))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2255 %!error <TOL must be a 1- or 2-element vector> (quadcc (@sin, 0, pi, [1,2,3]))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2256 %!error <absolute tolerance must be .=0> (quadcc (@sin, 0, pi, -1))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2257 %!error <relative tolerance must be .=0> (quadcc (@sin, 0, pi, [1, -1]))
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2258 %!error <SING.* must be .* real values> (quadcc (@sin, 0, pi, 1e-6, [ i ]))
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2259 */
29958
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29359
diff changeset
2260
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29359
diff changeset
2261 OCTAVE_NAMESPACE_END