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annotate libinterp/corefcn/quadcc.cc @ 28930:2883b3d08b7e

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maint: Remove unnecessary parentheses bracketing %!error BIST tests. * bsxfun.cc, call-stack.cc, data.cc, environment.cc, fcn-info.cc, fft.cc, filter.cc, quadcc.cc, sighandlers.cc, sysdep.cc, ov.cc, pt-eval.cc, accumarray.m, repmat.m, beep.m, pchip.m, movfun.m, rosser.m: Remove unnecessary parentheses bracketing %!error BIST tests.
author Rik <rik@octave.org>
date Wed, 14 Oct 2020 13:14:02 -0700
parents bd51beb6205e
children 7854d5752dd2
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rev   line source
27923
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2010-2020 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 {
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112 5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
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113 5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
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114 5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
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115 5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
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116 5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
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117 5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
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118 5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
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119 5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
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120 5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
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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/
Rik <rik@octave.org>
parents: 17744
diff changeset
1190 .36211835346039665762e-1, .11434398255136139683,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1191 -.30033588409423828125e-1, -.10506705408753910481,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1192 .25313077840725783008e-1, .97149327637744872155e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1193 -.21624927200393328444e-1, -.90319582367202122625e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1194 .18688433567711780666e-1, .84372291635345108584e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1195 -.16312261561845420752e-1, -.79149526894804751586e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1196 .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1197 .49607837082461073572, .82265291131801144317, .59621200088559103072,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1198 -.80054302859059362371e-1, -.42612156697795759420,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1199 -.90098145270865592887e-1, .29769623255090078484, .13630307904779758221,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1200 -.21638835185708931831, -.14600247270306082052, .16348801804014290453,
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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
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1487 // The actual integration routine.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1488
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1489 DEFMETHOD (quadcc, interp, args, ,
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1490 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
1491 @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
1492 @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
1493 @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
1494 @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
1495 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
1496 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
1497
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1498 @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
1499 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
1500 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
1501 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
1502
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1503 @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 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
1505 @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
1506
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1507 @noindent
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1508 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
1509
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1510 @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
1511 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
1512 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
1513
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1514 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
1515 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
1516 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
1517 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
1518 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
1519 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
1520 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
1521
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1522 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
1523 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
1524 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
1525 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
1526
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1527 @example
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1528 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
1529 @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
1530
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1531 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
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 @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
1534
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1535 @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
1536
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1537 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
1538 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
1539 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
1540
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1541 @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
1542 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
1543 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
1544 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
1545
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1546 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
1547 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
1548 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
1549
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1550 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
1551 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
1552 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
1553 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
1554 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
1555 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
1556
112b20240c87 move docstrings in C++ files out of C strings and into comments
John W. Eaton <jwe@octave.org>
parents: 21942
diff changeset
1557 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
1558 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
1559 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
1560 @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
1561 @end deftypefn */)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1562 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1563 // Some constants that we will need.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1564 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
1565 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
1566 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
1567 static const double w = M_SQRT2 / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1568 static const int ndiv_max = 20;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1569
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1570 // Arguments left and right.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1571 int nargin = args.length ();
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1572 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
1573 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
1574 bool issingle;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1575
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1576 // 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
1577 bool wrap = false;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1578 double xw;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1579
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1580 // 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
1581 octave_value_list fargs, fvals;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1582
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1583 // Actual variables (as opposed to constants above).
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1584 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
1585 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
1586 int nivals;
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1587 int neval = 0;
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1588 int i, j, d, split;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1589 int nnans, nans[33];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1590 cquad_ival *iv, *ivl, *ivr;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1591 double nc, ncdiff;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1592
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1593 // Parse the input arguments.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1594 if (nargin < 3)
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20232
diff changeset
1595 print_usage ();
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1596
26864
041caa61ed34 use get_function_handle instead of extract_function
John W. Eaton <jwe@octave.org>
parents: 26376
diff changeset
1597 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
1598
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1599 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
1600 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
1601 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
1602 issingle = args(1).is_single_type ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1603
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1604 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
1605 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
1606 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
1607 issingle = (issingle || args(2).is_single_type ());
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1608
23577
80c42f4cca13 maint: Deprecate is_empty and replace with isempty.
Rik <rik@octave.org>
parents: 23564
diff changeset
1609 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
1610 {
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1611 if (issingle)
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1612 {
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1613 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
1614 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
1615 }
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1616 else
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 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
1619 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
1620 }
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1621 }
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1622 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
1623 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
1624 else
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1625 {
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1626 NDArray tol = args(3).array_value ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1627
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1628 abstol = tol(0);
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1629 if (abstol < 0)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1630 error ("quadcc: absolute tolerance must be >=0");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1631
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1632 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
1633 {
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1634 if (issingle)
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
1635 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
1636 else
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-6;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1638 }
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1639 else
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 reltol = tol(1);
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1642 if (reltol < 0)
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1643 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
1644 }
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1645 }
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1646
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1647 if (nargin < 5)
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1648 nivals = 1;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1649 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
1650 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
1651 else
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1652 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
1653
21213
f7d1050b9b53 maint: Clean up various usages of #ifdef.
Rik <rik@octave.org>
parents: 21200
diff changeset
1654 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
1655 : MIN_CQUAD_HEAPSIZE);
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1656 // The interval heap.
15996
1aff8c38c53c use octave_local_buffer for temporary arrays in quadcc
John W. Eaton <jwe@octave.org>
parents: 15995
diff changeset
1657 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
1658 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
1659 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
1660
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1661 if (nivals == 1)
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 iivals[0] = a;
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1664 iivals[1] = b;
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1665 }
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1666 else
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1667 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1668 // Intervals around singularities.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1669 sing = args(4).array_value ().fortran_vec ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1670 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
1671 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
1672 iivals[nivals] = b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1673 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1674
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1675 // 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
1676 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
1677 {
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1678 wrap = true;
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1679 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
1680 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
1681 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
1682 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1683 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
1684 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1685
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1686 // Initialize the heaps.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1687 for (i = 0; i < cquad_heapsize; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1688 heap[i] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1689
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1690 // Create the first interval(s).
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1691 igral = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1692 err = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1693 for (j = 0; j < nivals; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1694 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1695 // Initialize the interval.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1696 iv = &(ivals[heap[j]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1697 m = (iivals[j] + iivals[j + 1]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1698 h = (iivals[j + 1] - iivals[j]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1699 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1700 ColumnVector ex (33);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1701 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1702 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1703 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
1704 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
1705 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1706 else
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 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
1709 ex(i) = m + xi[i]*h;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1710 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1711 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
1712 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
1713 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
1714 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
1715
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1716 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
1717 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1718 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
1719
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1720 for (i = 0; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1721 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1722 iv->fx[i] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1723 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1724 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1725 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
1726 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
1727 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1728 neval++;
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
1729 if (! octave::math::isfinite (iv->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1730 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1731 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1732 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1733 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1734 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1735 Vinvfx (iv->fx, &(iv->c[idx[3]]), 3);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1736 Vinvfx (iv->fx, &(iv->c[idx[2]]), 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1737 Vinvfx (iv->fx, &(iv->c[0]), 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1738 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
1739 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
1740 iv->a = iivals[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1741 iv->b = iivals[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1742 iv->depth = 3;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1743 iv->rdepth = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1744 iv->ndiv = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1745 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
1746 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1747 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
1748 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1749 temp = iv->c[idx[3] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1750 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1751 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1752 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1753 for (i = 0; i <= n[2]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1754 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1755 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
1756 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
1757 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
1758 nc += temp * temp;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1759 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1760 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1761 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1762 iv->err = ncdiff * 2 * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1763 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
1764 iv->err = 2 * h * nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1765
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1766 // Tabulate this interval's data.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1767 igral += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1768 err += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1769
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1770 // Sift it up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1771 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1772 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
1773 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1774 std::swap (heap[i], heap[i / 2]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1775 i /= 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1776 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1777 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1778
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1779 // Initialize some global values.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1780 igral_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1781 err_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1782
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1783 // Main loop.
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1784 while (nivals > 0
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1785 && 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
1786 && ! (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
1787 && 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
1788 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1789 // 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
1790 octave_quit ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1791
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1792 // 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
1793 iv = &(ivals[heap[0]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1794 m = (iv->a + iv->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1795 h = (iv->b - iv->a) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1796
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1797 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1798 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
1799 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
1800 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1801
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1802 // Should we try to increase the degree?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1803 if (iv->depth < 3)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1804 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1805 // Keep tabs on some variables.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1806 d = ++iv->depth;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1807
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1808 // Get the new (missing) function values.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1809 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1810 ColumnVector ex (n[d] / 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1811 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1812 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1813 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
1814 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
1815 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1816 else
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 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
1819 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
1820 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1821 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
1822 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
1823 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
1824 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
1825
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1826 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
1827 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1828 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
1829
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1830 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1831 for (i = 0; i < n[d] / 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1832 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1833 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
1834 iv->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1835 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1836 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1837 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
1838 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
1839 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1840 }
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 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1843 for (i = 0; i <= 32; i += skip[d])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1844 {
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
1845 if (! octave::math::isfinite (iv->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1846 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1847 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1848 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1849 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1850 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1851
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1852 // Compute the new coefficients.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1853 Vinvfx (iv->fx, &(iv->c[idx[d]]), d);
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1854 // Downdate any NaNs.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1855 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1856 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1857 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
1858 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
1859 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
1860 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1861
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1862 // Compute the error estimate.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1863 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1864 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
1865 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1866 temp = iv->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1867 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1868 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1869 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1870 for (i = 0; i <= n[d - 1]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1871 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1872 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
1873 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
1874 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
1875 nc += temp * temp;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1876 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1877 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1878 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1879 iv->err = ncdiff * 2 * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1880 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1881 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
1882 // Split the interval prematurely?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1883 split = (nc > 0 && ncdiff / nc > 0.1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1884 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1885 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1886 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1887 // Maximum degree reached, just split.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1888 split = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1889 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1890
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1891 // 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
1892 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
1893 || (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
1894 || iv->err < fabs (iv->igral) * DROP_RELTOL)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1895 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1896 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1897 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
1898 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
1899 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1900
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1901 // Keep this interval's contribution.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1902 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1903 igral_final += iv->igral;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1904 // 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
1905 std::swap (heap[nivals - 1], heap[0]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1906 nivals--;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1907 // Fix up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1908 i = 0;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1909 while (2*i + 1 < nivals)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1910 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1911 // 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
1912 j = 2*i + 1;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1913 // 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
1914 // use it instead.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1915 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1916 && 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
1917 j++;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1918 // 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
1919 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
1920 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1921 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1922 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
1923 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1924 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1925 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1926 }
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 else if (split)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1929 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1930 // Some values we will need often...
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1931 d = iv->depth;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1932 // Generate the interval on the left.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1933 ivl = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1934 ivl->a = iv->a;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1935 ivl->b = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1936 ml = (ivl->a + ivl->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1937 hl = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1938 ivl->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1939 ivl->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1940 ivl->fx[0] = iv->fx[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1941 ivl->fx[32] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1942 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1943 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1944 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1945 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1946 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
1947 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
1948 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1949 else
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 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
1952 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
1953 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1954 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
1955 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
1956 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
1957 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
1958
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1959 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
1960 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1961 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
1962
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1963 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1964 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1965 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1966 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
1967 ivl->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1968 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1969 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1970 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
1971 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
1972 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1973 }
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 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1976 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1977 {
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
1978 if (! octave::math::isfinite (ivl->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1979 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1980 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1981 ivl->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1982 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1983 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1984 Vinvfx (ivl->fx, ivl->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1985 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1986 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1987 downdate (ivl->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1988 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
1989 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
1990 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1991 for (i = 0; i <= n[d]; i++)
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 ivl->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1994 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
1995 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
1996 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1997 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1998 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1999 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2000 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
2001 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2002 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2003 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
2004 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2005 temp = ivl->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2006 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2007 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2008 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2009 ivl->err = ncdiff * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2010 // Check for divergence.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2011 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
2012 && 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
2013 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
2014 {
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21782
diff changeset
2015 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
2016 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2017 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2018 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2019
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2020 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2021 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
2022
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2023 // Generate the interval on the right.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2024 ivr = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2025 ivr->a = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2026 ivr->b = iv->b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2027 mr = (ivr->a + ivr->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2028 hr = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2029 ivr->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2030 ivr->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2031 ivr->fx[0] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2032 ivr->fx[32] = iv->fx[32];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2033 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2034 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2035 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2036 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2037 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
2038 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
2039 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2040 else
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 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
2043 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
2044 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2045 fargs(0) = ex;
23075
4e3d47dc7e25 move parse tree classes inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 22860
diff changeset
2046 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
2047 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
2048 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
2049
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2050 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
2051 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
2052 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
2053
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
2054 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2055 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2056 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2057 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
2058 ivr->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2059 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2060 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2061 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
2062 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
2063 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2064 }
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 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2067 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2068 {
23564
7049da1648c0 Deprecate octave::math::finite in favor of octave::math::isfinite.
Rik <rik@octave.org>
parents: 23220
diff changeset
2069 if (! octave::math::isfinite (ivr->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2070 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2071 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2072 ivr->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2073 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2074 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2075 Vinvfx (ivr->fx, ivr->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2076 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2077 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2078 downdate (ivr->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2079 for (i = 0; i < nnans; i++)
21723
bae585228161 use namespace for numeric_limits
John W. Eaton <jwe@octave.org>
parents: 21721
diff changeset
2080 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
2081 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2082 for (i = 0; i <= n[d]; i++)
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 ivr->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2085 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
2086 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
2087 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2088 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2089 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2090 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2091 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
2092 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2093 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2094 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
2095 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2096 temp = ivr->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2097 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2098 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2099 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2100 ivr->err = ncdiff * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2101 // Check for divergence.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2102 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
2103 && 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
2104 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
2105 {
21942
aab79a1885cc limit gnulib headers to liboctave/wrappers directory
John W. Eaton <jwe@octave.org>
parents: 21782
diff changeset
2106 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
2107 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2108 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2109 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2110
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2111 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2112 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
2113
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2114 // 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
2115 // 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
2116
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2117 // 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
2118 std::swap (heap[nivals - 1], heap[0]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2119 nivals--;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2120 // Sift this interval back down the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2121 i = 0;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2122 while (2*i + 1 < nivals - 1)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2123 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2124 j = 2*i + 1;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2125 if (j + 1 < nivals - 1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2126 && 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
2127 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2128 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
2129 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2130 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2131 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2132 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2133 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2134 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2135 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2136
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2137 // 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
2138 i = nivals - 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2139 while (i > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2140 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2141 j = (i - 1) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2142 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
2143 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2144 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2145 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2146 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2147 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2148 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2149 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2150 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2151 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2152 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2153 // Otherwise, just fix-up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2154 i = 0;
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2155 while (2*i + 1 < nivals)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2156 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2157 j = 2*i + 1;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2158 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2159 && 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
2160 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2161 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
2162 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2163 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2164 {
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2165 std::swap (heap[j], heap[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2166 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2167 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2168 }
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
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2171 // 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
2172 while (nivals > cquad_heapsize - 2)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2173 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2174 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
2175 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2176 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
2177 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
2178 #endif
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2179 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2180 igral_final += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2181 nivals--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2182 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2183
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2184 // 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
2185 igral = igral_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2186 err = err_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2187 for (i = 0; i < nivals; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2188 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2189 igral += ivals[heap[i]].igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2190 err += ivals[heap[i]].err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2191 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2192 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2193
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2194 #if (DEBUG_QUADCC)
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2195 // 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
2196 for (i = 0; i < nivals; i++)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2197 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2198 iv = &(ivals[heap[i]]);
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2199 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
2200 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
2201 iv->rdepth, iv->ndiv);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2202 }
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2203 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2204
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2205 if (issingle)
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2206 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
2207 else
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2208 return ovl (igral, err, neval);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2209 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2210
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 12653
diff changeset
2211 /*
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2212 %!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
2213 %!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
2214 %!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
2215
24098
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, 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
2217 %!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
2218 %!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
2219 %!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
2220 %!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
2221
24098
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) 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
2223 %!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
2224
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2225 ## 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
2226 %!function y = __nansin (x)
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2227 %! 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
2228 %! y = sin (x);
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2229 %! 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
2230 %! y(idx < 1e-10) = NaN;
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2231 %!endfunction
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2232
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2233 %!test
24098
71dad5be765a quadcc.cc: Use an Absolute Tolerance, as well as RelTol (Bug #46349).
Rik <rik@octave.org>
parents: 23577
diff changeset
2234 %! [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
2235 %! 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
2236 %! 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
2237
24157
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2238 %!test
5fc5c1a49aa1 quadcc: Preserve output of type single when input is single (bug #52243).
Rik <rik@octave.org>
parents: 24098
diff changeset
2239 %! 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
2240 %! 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
2241 %! 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
2242 %! 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
2243
22737
7abc25e6206a maint: Clean up code base to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 22407
diff changeset
2244 ## Test input validation
28930
2883b3d08b7e maint: Remove unnecessary parentheses bracketing %!error BIST tests.
Rik <rik@octave.org>
parents: 27923
diff changeset
2245 %!error quadcc ()
2883b3d08b7e maint: Remove unnecessary parentheses bracketing %!error BIST tests.
Rik <rik@octave.org>
parents: 27923
diff changeset
2246 %!error quadcc (@sin)
2883b3d08b7e maint: Remove unnecessary parentheses bracketing %!error BIST tests.
Rik <rik@octave.org>
parents: 27923
diff changeset
2247 %!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
2248 %!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
2249 %!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
2250 %!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
2251 %!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
2252 %!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
2253 %!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
2254 %!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
2255 %!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
2256 %!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
2257 */