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annotate libinterp/corefcn/quadcc.cc @ 20915:a3359fe50966

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remove unused nargout variables * __ichol__.cc, __ilu__.cc, ellipj.cc, filter.cc, mgorth.cc, nproc.cc, pr-output.cc, quad.cc, quadcc.cc, sylvester.cc: Remove unused nargout from DEFUNs that no longer use it.
author John W. Eaton <jwe@octave.org>
date Wed, 16 Dec 2015 17:02:23 -0500
parents 359476667c4c
children 48b2ad5ee801
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rev   line source
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1 /*
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2
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3 Copyright (C) 2010-2015 Pedro Gonnet
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
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27 #include "lo-ieee.h"
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28 #include "oct-locbuf.h"
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29
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30 #include "defun.h"
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31 #include "error.h"
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32 #include "oct-obj.h"
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33 #include "parse.h"
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34 #include "utils.h"
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35 #include "variables.h"
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36
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37 // Extended debugging.
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38 #define DEBUG_QUADCC 0
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39
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40 // Define the minimum size of the interval heap.
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41 #define min_cquad_heapsize 200
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42
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43 // Data of a single interval.
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44 typedef struct
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45 {
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46 double a, b;
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47 double c[64];
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48 double fx[33];
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49 double igral, err;
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50 int depth, rdepth, ndiv;
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51 } cquad_ival;
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52
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53 // Some constants and matrices that we'll need.
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54
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55 static const double xi[33] =
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56 {
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57 -1., -0.99518472667219688624, -0.98078528040323044912,
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58 -0.95694033573220886493, -0.92387953251128675612,
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59 -0.88192126434835502970, -0.83146961230254523708,
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60 -0.77301045336273696082, -0.70710678118654752440,
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61 -0.63439328416364549822, -0.55557023301960222475,
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62 -0.47139673682599764857, -0.38268343236508977173,
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63 -0.29028467725446236764, -0.19509032201612826785,
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64 -0.098017140329560601995, 0., 0.098017140329560601995,
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65 0.19509032201612826785, 0.29028467725446236764, 0.38268343236508977173,
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66 0.47139673682599764857, 0.55557023301960222475, 0.63439328416364549822,
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67 0.70710678118654752440, 0.77301045336273696082, 0.83146961230254523708,
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68 0.88192126434835502970, 0.92387953251128675612, 0.95694033573220886493,
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69 0.98078528040323044912, 0.99518472667219688624, 1.
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70 };
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71
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72 static const double bee[68] =
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73 {
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74 0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
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75 -8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
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76 0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
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77 3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
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78 0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
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79 5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
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80 0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
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81 4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
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82 0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
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83 3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
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84 0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
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85 5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
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86 0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
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87 3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
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88 0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
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89 7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
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90 0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
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91 1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
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92 0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
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93 6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
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94 0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
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95 2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
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96 0.00000000000000e+00, 5.40679930965238e-01
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97 };
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98
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99 static const double Lalpha[33] =
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100 {
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101 5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
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102 5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
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103 5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
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104 5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
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105 5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
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106 5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
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107 5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
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108 5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
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109 5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
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110 5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
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111 5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
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112 };
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113
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114 static const double Lgamma[33] =
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115 {
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116 0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
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117 5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
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118 5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
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119 5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
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diff changeset
120 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
121 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
122 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
123 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
124 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
125 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
126 5.00061046334395e-01
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
127 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
128
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
129 static const double V1inv[5 * 5] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
130 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
131 .47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
132 .37712361663282534635, .47140452079103168293e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
133 -.81649658092772603273e-1, -.46188021535170061160, 0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
134 .46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
135 .12046772038736683169, -.54210474174315074262, .12046772038736683169,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
136 .15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
137 -.30237157840738178177, .21380899352993950775, .10774960475223581324,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
138 -.21549920950447162648, .21549920950447162648, -.21549920950447162648,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
139 .10774960475223581324
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
140 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
141
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
142 static const double V2inv[9 * 9] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
143 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
144 .11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
145 .25577315077753587922, .27835314560994251755, .25577315077753587922,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
146 .19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
147 -.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
148 -.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
149 .16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
150 .17766815796285469394, .11316664642449611462, -.16306601003711325980,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
151 -.30847037493128779631, -.16306601003711325980, .11316664642449611462,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
152 .17766815796285469394, .26466393115406349388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
153 -.32395302049990834508e-1, -.15521142532414866547,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
154 .88573492664788602740e-1, .29570405784974857322, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
155 -.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
156 .32395302049990834508e-1, .41442155673936851246e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
157 .98186757907405608245e-1, -.23056908429499411784,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
158 -.68047008326360625520e-1, .31797435808002456774,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
159 -.68047008326360625520e-1, -.23056908429499411784,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
160 .98186757907405608245e-1, .41442155673936851246e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
161 -.49981120317798783134e-1, -.24861810572835756217e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
162 .23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
163 -.23561326072010832539, .24861810572835756217e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
164 .49981120317798783134e-1, .79691635865674781228e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
165 -.95725617891693941833e-1, -.57957553356854386344e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
166 .21164072460540271452, -.27529837844505833514, .21164072460540271452,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
167 -.57957553356854386344e-1, -.95725617891693941833e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
168 .79691635865674781228e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
169 -.10894869830716590913, .20131094491947531782, -.15407672674888869038,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
170 .83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
171 .15407672674888869038, -.20131094491947531782, .10894869830716590913,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
172 .54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
173 -.10916211417928767644, .10916211417928767644, -.10916211417928767644,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
174 .10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
175 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
176
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
177 static const double V3inv[17 * 17] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
178 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
179 .27729677693590098996e-2, .26423663180333065153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
180 .53374068493933898312e-1, .77007854739523195947e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
181 .98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
182 .13612785914022865001, .13888293186236181317, .13612785914022865001,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
183 .12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
184 .77007854739523195947e-1, .53374068493933898312e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
185 .26423663180333065153e-1, .27729677693590098996e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
186 -.48029210642807413690e-2, -.44887724635478800254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
187 -.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
188 -.11102786862182788886, -.85054870109799336515e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
189 -.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
190 .85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
191 .11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
192 .48029210642807413690e-2, .62758546879582030087e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
193 .55561297093529155869e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
194 .93281491021051539742e-1, .92320151237493695139e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
195 .55077987469605684531e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
196 -.96998141716497488255e-2, -.80285961895427405567e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
197 -.13496839655913850224,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
198 -.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
199 -.96998141716497488255e-2, .55077987469605684531e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
200 .92320151237493695139e-1, .93281491021051539742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
201 .55561297093529155869e-1, .62758546879582030087e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
202 -.74850969394858555939e-2, -.61751608943839234096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
203 -.82974150437304275958e-1, -.38437763431942633378e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
204 .45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
205 .98768034347019704401e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
206 -.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
207 -.45745502025779701366e-1, .38437763431942633378e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
208 .82974150437304275958e-1, .61751608943839234096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
209 .74850969394858555939e-2, .86710099994384056338e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
210 .64006230103659573344e-1, .58517426396091675690e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
211 -.29743410528985802680e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
212 -.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
213 .97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
214 -.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
215 -.29743410528985802680e-1, .58517426396091675690e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
216 .64006230103659573344e-1, .86710099994384056338e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
217 -.97486395666294840165e-2, -.62995604908060224672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
218 -.24373234450275529219e-1, .87760984413626872730e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
219 .12205204576993351394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
220 .16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
221 0.0, .13682714580929614678, .12422320942156845775,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
222 -.16216004196864002088e-1, -.12205204576993351394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
223 -.87760984413626872730e-1, .24373234450275529219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
224 .62995604908060224672e-1, .97486395666294840165e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
225 .10956271233750488468e-1, .58613204255294358939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
226 -.13306063940736618859e-1, -.11606666444978454399,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
227 -.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
228 -.44678658254872910434e-1, -.15617684362128533405,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
229 -.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
230 -.52059598001115805639e-1, -.11606666444978454399,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
231 -.13306063940736618859e-1, .58613204255294358939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
232 .10956271233750488468e-1, -.12098893000863087230e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
233 -.51626244709126208453e-1, .48919433304746979330e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
234 .10467644465949427090,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
235 -.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
236 .15434223333238741600, 0.0, -.15434223333238741600,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
237 -.28190838706814496438e-1, .13668732103524749234,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
238 .48729879523084673782e-1, -.10467644465949427090,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
239 -.48919433304746979330e-1, .51626244709126208453e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
240 .12098893000863087230e-1, .13542668300437944822e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
241 .41712033418258689308e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
242 -.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
243 .42121099930651007882e-1, -.14684425840766337756,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
244 -.16108203535058647043e-1, .15698075850757976092,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
245 -.16108203535058647043e-1, -.14684425840766337756,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
246 .42121099930651007882e-1, .12158068748245606853,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
247 -.58303943170068132010e-1, -.76190463272803434388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
248 .41712033418258689308e-1, .13542668300437944822e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
249 -.14939634995117694417e-1, -.30047246373341564039e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
250 .91624635082546425678e-1, -.79133374319110026377e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
251 -.12292558212072233355, .90013382617762643524e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
252 .84013717196539593395e-1, -.14813033309980695856, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
253 .14813033309980695856, -.84013717196539593395e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
254 -.90013382617762643524e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
255 .12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
256 .30047246373341564039e-1, .14939634995117694417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
257 .16986031342807474208e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
258 .15760203882617033601e-1, -.91494054040950941996e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
259 .70082459207876130806e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
260 .53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
261 .72456667788091316868e-1, -.15564535320096811360,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
262 .72456667788091316868e-1, .84048122493418898508e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
263 -.14340746778352039430, .53390713710144539104e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
264 .70082459207876130806e-1, -.91494054040950941996e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
265 .15760203882617033601e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
266 .16986031342807474208e-1, -.18994065631858742028e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
267 -.82901821370405592927e-3, .77239669773015192888e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
268 -.10850735431039424680, .47524484622086496464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
269 .69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
270 0.0, -.11992057742398672066, .14829314646228194928,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
271 -.69148184871588737021e-1, -.47524484622086496464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
272 .10850735431039424680, -.77239669773015192888e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
273 .82901821370405592927e-3, .18994065631858742028e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
274 .22761703826371535132e-1, -.17728848711449643358e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
275 -.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
276 .63073750910894244526e-1, .32928881123602721303e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
277 -.12280950532497593683, .15926189077282729505, -.12280950532497593683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
278 .32928881123602721303e-1, .63073750910894244526e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
279 -.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
280 -.17728848711449643358e-1, .22761703826371535132e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
281 -.26493215276042203434e-1, .35579780856128386192e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
282 .10447309718398935122e-1, -.68616154085314996709e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
283 .11775363082763954214, -.13918901977011837274, .12312819418827395690,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
284 -.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
285 -.12312819418827395690, .13918901977011837274, -.11775363082763954214,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
286 .68616154085314996709e-1, -.10447309718398935122e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
287 -.35579780856128386192e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
288 .26493215276042203434e-1, .40742523354399706918e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
289 -.73124912999529117195e-1, .49317266444153837821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
290 -.13686605413876015320e-1, -.28342624942191100464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
291 .70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
292 -.13817029659318161476, .12981016288391131812, -.10600251632853603875,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
293 .70371855298258216249e-1, -.28342624942191100464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
294 -.13686605413876015320e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
295 .49317266444153837821e-1, -.73124912999529117195e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
296 .40742523354399706918e-1, -.54944368958699908688e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
297 .10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
298 -.77703071757424700773e-1, .61050911730999815031e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
299 -.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
300 -.21438229266251454773e-1, .42052599404498348871e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
301 -.61050911730999815031e-1, .77703071757424700773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
302 -.91369146312596428468e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
303 .10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
304 .27485608464748840573e-1, -.54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
305 .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
306 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
307 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
308 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
309 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
310 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
311 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
312 -.54971216929497681146e-1, .27485608464748840573e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
313 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
314
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
315 static const double V4inv[33 * 33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
316 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
317 .69120897476690862600e-3, .66419939766331555194e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
318 .13600665164323186111e-1, .20122785860913684493e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
319 .26583214101668429944e-1, .32712713318999268739e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
320 .38576221976287138036e-1, .44033030938268925133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
321 .49092709529622799673e-1, .53657949874312515646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
322 .57724533144734311859e-1, .61219564530655179096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
323 .64138907503837875026e-1, .66427905189318792009e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
324 .68088956652280022887e-1, .69083051391555695878e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
325 .69422738116739271449e-1, .69083051391555695878e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
326 .68088956652280022887e-1, .66427905189318792009e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
327 .64138907503837875026e-1, .61219564530655179096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
328 .57724533144734311859e-1, .53657949874312515646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
329 .49092709529622799673e-1, .44033030938268925133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
330 .38576221976287138036e-1, .32712713318999268739e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
331 .26583214101668429944e-1, .20122785860913684493e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
332 .13600665164323186111e-1, .66419939766331555194e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
333 .69120897476690862600e-3, -.11972090629438798134e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
334 -.11448874821643225573e-1, -.23104401104002905904e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
335 -.33352899418646530133e-1, -.42538626424075425908e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
336 -.49969730733911825941e-1, -.55555454015360728353e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
337 -.58955533624852604918e-1, -.60126044219122513907e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
338 -.58959430451175833624e-1, -.55546925396227130606e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
339 -.49984739749347973762e-1, -.42513009141170294365e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
340 -.33399140950669746346e-1, -.23007690803851790829e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
341 -.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
342 .23007690803851790829e-1, .33399140950669746346e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
343 .42513009141170294365e-1, .49984739749347973762e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
344 .55546925396227130606e-1, .58959430451175833624e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
345 .60126044219122513907e-1, .58955533624852604918e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
346 .55555454015360728353e-1, .49969730733911825941e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
347 .42538626424075425908e-1, .33352899418646530133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
348 .23104401104002905904e-1, .11448874821643225573e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
349 .11972090629438798134e-2, .15501585012936019146e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
350 .14628781502199620482e-1, .28684915921474815271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
351 .39299396074628048026e-1, .46393418975496284204e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
352 .48756902531094699526e-1, .46331333488337494692e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
353 .39012645376980228775e-1, .27452795421085791153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
354 .12430953621169863781e-1, -.47682978056024928800e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
355 -.22825828045428973853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
356 -.40195512090720278312e-1, -.55503004262826221955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
357 -.67424537752827046308e-1, -.75020199300113606452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
358 -.77607844312483656131e-1, -.75020199300113606452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
359 -.67424537752827046308e-1, -.55503004262826221955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
360 -.40195512090720278312e-1, -.22825828045428973853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
361 -.47682978056024928800e-2, .12430953621169863781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
362 .27452795421085791153e-1, .39012645376980228775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
363 .46331333488337494692e-1, .48756902531094699526e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
364 .46393418975496284204e-1, .39299396074628048026e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
365 .28684915921474815271e-1, .14628781502199620482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
366 .15501585012936019146e-2, -.18377757558949194214e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
367 -.17050470050949761565e-1, -.31952119564923250836e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
368 -.40197423449026348155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
369 -.41205649520281371624e-1, -.33909965817492272248e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
370 -.19393664422115332144e-1, .56661049630886784692e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
371 .22948272173686561721e-1, .44489719570904738207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
372 .61790363672287920596e-1, .72121014727028013894e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
373 .73627151185287858579e-1, .65784665375961398923e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
374 .49369676372333667559e-1, .26444326317059715065e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
375 -.26444326317059715065e-1, -.49369676372333667559e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
376 -.65784665375961398923e-1, -.73627151185287858579e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
377 -.72121014727028013894e-1, -.61790363672287920596e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
378 -.44489719570904738207e-1, -.22948272173686561721e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
379 -.56661049630886784692e-3, .19393664422115332144e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
380 .33909965817492272248e-1, .41205649520281371624e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
381 .40197423449026348155e-1, .31952119564923250836e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
382 .17050470050949761565e-1, .18377757558949194214e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
383 .20942714740729767769e-2, .18935902405146518232e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
384 .33335840852491735126e-1, .36770680999102286065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
385 .28873194534132768509e-1, .10267303017729535513e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
386 -.14607738306201572890e-1, -.40139568545572305818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
387 -.59808326733858291561e-1, -.68528358823372627506e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
388 -.63306535387619244879e-1, -.44508601817574921056e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
389 -.15449116105605395357e-1, .17941083795006546367e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
390 .48747356011657242123e-1, .70329553984201665523e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
391 .78106117292526169663e-1, .70329553984201665523e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
392 .48747356011657242123e-1, .17941083795006546367e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
393 -.15449116105605395357e-1, -.44508601817574921056e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
394 -.63306535387619244879e-1, -.68528358823372627506e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
395 -.59808326733858291561e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
396 -.40139568545572305818e-1, -.14607738306201572890e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
397 .10267303017729535513e-1, .28873194534132768509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
398 .36770680999102286065e-1, .33335840852491735126e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
399 .18935902405146518232e-1, .20942714740729767769e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
400 -.23245285491878278419e-2, -.20401404737639389919e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
401 -.33019548231022514097e-1, -.29709828426463720091e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
402 -.11760070922697422156e-1, .15987584743850393793e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
403 .43619012891472813485e-1, .61177322409671487721e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
404 .61144030218486655594e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
405 .41895377620089086167e-1, .80232011820644308033e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
406 -.30574701186675900915e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
407 -.62072243008844865848e-1, -.76336186183574765586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
408 -.68435466095345537115e-1, -.40237669208466966207e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
409 .40237669208466966207e-1, .68435466095345537115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
410 .76336186183574765586e-1, .62072243008844865848e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
411 .30574701186675900915e-1, -.80232011820644308033e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
412 -.41895377620089086167e-1, -.61144030218486655594e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
413 -.61177322409671487721e-1, -.43619012891472813485e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
414 -.15987584743850393793e-1, .11760070922697422156e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
415 .29709828426463720091e-1, .33019548231022514097e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
416 .20401404737639389919e-1, .23245285491878278419e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
417 .25451717261579269307e-2, .21480418595666878775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
418 .31177212469293007998e-1, .19816333607013379373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
419 -.72439496274458793681e-2, -.38404203906598342397e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
420 -.57633632255322221046e-1, -.54070547403585392952e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
421 -.26249823354368866005e-1, .15643058212336881516e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
422 .54539832735118677194e-1, .73283028002473989724e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
423 .62835303524135936213e-1, .26175977027801048141e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
424 -.22193636309998606610e-1, -.62597049956093311234e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
425 -.78206986173170212505e-1, -.62597049956093311234e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
426 -.22193636309998606610e-1, .26175977027801048141e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
427 .62835303524135936213e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
428 .73283028002473989724e-1, .54539832735118677194e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
429 .15643058212336881516e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
430 -.26249823354368866005e-1, -.54070547403585392952e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
431 -.57633632255322221046e-1, -.38404203906598342397e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
432 -.72439496274458793681e-2, .19816333607013379373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
433 .31177212469293007998e-1, .21480418595666878775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
434 .25451717261579269307e-2, -.27506573922483820005e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
435 -.22224442095099251870e-1, -.27949927254215773020e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
436 -.80918481053370034987e-2, .25121859354449306916e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
437 .51563535009373061074e-1, .51936965107145960512e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
438 .22146626648171527753e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
439 -.24172689882103382748e-1, -.61731229104853568296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
440 -.68477262429344201201e-1, -.38311232728303704742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
441 .14160578713659552679e-1, .61248813427564184033e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
442 .77136328841293031805e-1, .52514801765183697988e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
443 -.52514801765183697988e-1, -.77136328841293031805e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
444 -.61248813427564184033e-1, -.14160578713659552679e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
445 .38311232728303704742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
446 .68477262429344201201e-1, .61731229104853568296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
447 .24172689882103382748e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
448 -.22146626648171527753e-1, -.51936965107145960512e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
449 -.51563535009373061074e-1, -.25121859354449306916e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
450 .80918481053370034987e-2, .27949927254215773020e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
451 .22224442095099251870e-1, .27506573922483820005e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
452 .29562461131654311467e-2, .22630271480554450613e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
453 .23547399831373800971e-1, -.43964593440902476642e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
454 -.39055315767504970597e-1, -.52369643937940066804e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
455 -.28506131614971613422e-1, .19906048093338832322e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
456 .60408880866392420279e-1, .62493397473656883090e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
457 .21391278377641297859e-1, -.37302864786623254746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
458 -.73665127933539496872e-1, -.61706142476854010202e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
459 -.78065168882546327888e-2, .52335307373945544428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
460 .78278746279419264777e-1, .52335307373945544428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
461 -.78065168882546327888e-2, -.61706142476854010202e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
462 -.73665127933539496872e-1, -.37302864786623254746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
463 .21391278377641297859e-1, .62493397473656883090e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
464 .60408880866392420279e-1, .19906048093338832322e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
465 -.28506131614971613422e-1, -.52369643937940066804e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
466 -.39055315767504970597e-1, -.43964593440902476642e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
467 .23547399831373800971e-1, .22630271480554450613e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
468 .29562461131654311467e-2, -.31515718415504761303e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
469 -.22739451096655080673e-1, -.18157123602272119779e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
470 .16496480897167303621e-1, .46921166788569301124e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
471 .40644395739978416354e-1, -.46275803430732216900e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
472 -.52883375891308909486e-1, -.61116483226324111734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
473 -.17411698764545629853e-1, .44773430013166822765e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
474 .73441577962383869198e-1, .42127368371995472815e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
475 -.25504645957196772465e-1, -.74126818045972742488e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
476 -.62780077864719287317e-1, 0.0, .62780077864719287317e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
477 .74126818045972742488e-1, .25504645957196772465e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
478 -.42127368371995472815e-1, -.73441577962383869198e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
479 -.44773430013166822765e-1, .17411698764545629853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
480 .61116483226324111734e-1, .52883375891308909486e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
481 .46275803430732216900e-2, -.40644395739978416354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
482 -.46921166788569301124e-1, -.16496480897167303621e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
483 .18157123602272119779e-1, .22739451096655080673e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
484 .31515718415504761303e-2, .33536559294882188208e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
485 .22535348942792006185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
486 .12048629300953560767e-1, -.27166076791299493403e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
487 -.47492745604230978367e-1, -.19246623430993153174e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
488 .36231297307556299322e-1, .61713617181636122004e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
489 .25928029734266134490e-1, -.40478700752883602818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
490 -.71053889866326412049e-1, -.31870824482961751482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
491 .41515251100219081281e-1, .76481960760098381651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
492 .36726509155999912440e-1, -.40090067032627055969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
493 -.78270742903374539397e-1, -.40090067032627055969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
494 .36726509155999912440e-1, .76481960760098381651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
495 .41515251100219081281e-1, -.31870824482961751482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
496 -.71053889866326412049e-1, -.40478700752883602818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
497 .25928029734266134490e-1, .61713617181636122004e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
498 .36231297307556299322e-1, -.19246623430993153174e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
499 -.47492745604230978367e-1, -.27166076791299493403e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
500 .12048629300953560767e-1, .22535348942792006185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
501 .33536559294882188208e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
502 -.35481220456925318865e-2, -.22062913693073191150e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
503 -.54487362861834144999e-2, .35438821865804087489e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
504 .40733077820527411302e-1, -.67403098138950720914e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
505 -.55559584405239171054e-1, -.42417050790865158745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
506 .24499901971884704925e-1, .68721232891705409302e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
507 .34086082787461126592e-1, -.43441000373118474002e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
508 -.73878085292669148950e-1, -.18846995664706657127e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
509 .59827776178286834498e-1, .70644634584085901794e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
510 -.70644634584085901794e-1, -.59827776178286834498e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
511 .18846995664706657127e-1, .73878085292669148950e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
512 .43441000373118474002e-1, -.34086082787461126592e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
513 -.68721232891705409302e-1, -.24499901971884704925e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
514 .42417050790865158745e-1, .55559584405239171054e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
515 .67403098138950720914e-2, -.40733077820527411302e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
516 -.35438821865804087489e-1, .54487362861834144999e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
517 .22062913693073191150e-1, .35481220456925318865e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
518 .37554176816665075631e-2, .21297045781589919482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
519 -.13327293083183431816e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
520 -.40635299172764596484e-1, -.27659860508374175359e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
521 .31089232744083445986e-1, .56113781541334176109e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
522 .37577840643257763400e-2, -.60511227350664590865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
523 -.46670556446129053853e-1, .33263195878575888247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
524 .72757324720645228775e-1, .15011712351692283635e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
525 -.65601212994924119078e-1, -.60016855838843789772e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
526 .26220858553188665966e-1, .78322776605833552980e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
527 .26220858553188665966e-1, -.60016855838843789772e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
528 -.65601212994924119078e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
529 .15011712351692283635e-1, .72757324720645228775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
530 .33263195878575888247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
531 -.46670556446129053853e-1, -.60511227350664590865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
532 .37577840643257763400e-2, .56113781541334176109e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
533 .31089232744083445986e-1, -.27659860508374175359e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
534 -.40635299172764596484e-1, -.13327293083183431816e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
535 .21297045781589919482e-1, .37554176816665075631e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
536 -.39566995305720591229e-2, -.20291873414438919995e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
537 .80617453830770930551e-2, .42270189157016547906e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
538 .10332624526759093004e-1, -.48054759547616142024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
539 -.37678032941171643972e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
540 .36617192625732482394e-1, .61009425973424865714e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
541 -.95589113168026591466e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
542 -.71023202645076922361e-1, -.25097788086808784456e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
543 .62406621963267050244e-1, .56907293171100693511e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
544 -.36435383083882206257e-1, -.75790105119208756348e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
545 .75790105119208756348e-1, .36435383083882206257e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
546 -.56907293171100693511e-1, -.62406621963267050244e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
547 .25097788086808784456e-1, .71023202645076922361e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
548 .95589113168026591466e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
549 -.61009425973424865714e-1, -.36617192625732482394e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
550 .37678032941171643972e-1, .48054759547616142024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
551 -.10332624526759093004e-1, -.42270189157016547906e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
552 -.80617453830770930551e-2, .20291873414438919995e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
553 .39566995305720591229e-2, .41776092289182138591e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
554 .19013221163904414395e-1, -.14420609729849899876e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
555 -.40259160586844441220e-1, .86327811113710831649e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
556 .53564430703021034399e-1, .65469185402150431933e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
557 -.60383116311280629856e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
558 -.25657793784058876939e-1, .58745680576829226900e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
559 .45649937869034420296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
560 -.49167932056844167772e-1, -.62696614328552187977e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
561 .32540234556426699997e-1, .74280410383464269758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
562 -.11425672633410999870e-1, -.78280649404686404903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
563 -.11425672633410999870e-1, .74280410383464269758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
564 .32540234556426699997e-1, -.62696614328552187977e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
565 -.49167932056844167772e-1, .45649937869034420296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
566 .58745680576829226900e-1, -.25657793784058876939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
567 -.60383116311280629856e-1, .65469185402150431933e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
568 .53564430703021034399e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
569 .86327811113710831649e-2, -.40259160586844441220e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
570 -.14420609729849899876e-1, .19013221163904414395e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
571 .41776092289182138591e-2, -.43935502082478059199e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
572 -.17528761237509401631e-1, .20208915249153872535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
573 .34734743119040669109e-1, -.26275910172353637955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
574 -.46368003346018878786e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
575 .26800056330709381025e-1, .56681476464606609921e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
576 -.24749011438127255898e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
577 -.64934612189056658992e-1, .20333742247679279535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
578 .71429299070059318651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
579 -.14452513210428671266e-1, -.75793341281736586582e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
580 .74717094137184935270e-2, .78034921554757317374e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
581 -.78034921554757317374e-1, -.74717094137184935270e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
582 .75793341281736586582e-1, .14452513210428671266e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
583 -.71429299070059318651e-1, -.20333742247679279535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
584 .64934612189056658992e-1, .24749011438127255898e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
585 -.56681476464606609921e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
586 -.26800056330709381025e-1, .46368003346018878786e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
587 .26275910172353637955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
588 -.34734743119040669109e-1, -.20208915249153872535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
589 .17528761237509401631e-1, .43935502082478059199e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
590 .46379089482818671473e-2, .15791188144791287229e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
591 -.25134290048737455284e-1, -.26249795071946841205e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
592 .39960457575789924651e-1, .28111892450146525404e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
593 -.51026476400767918226e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
594 -.27266747278681831364e-1, .60708796647861610865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
595 .23532306960642115854e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
596 -.68169639871532441111e-1, -.18204924701958312032e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
597 .73822890510656128485e-1, .11373392486424717019e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
598 -.77133324017644609416e-1, -.39295877480342619961e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
599 .78351902829418987960e-1, -.39295877480342619961e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
600 -.77133324017644609416e-1, .11373392486424717019e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
601 .73822890510656128485e-1, -.18204924701958312032e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
602 -.68169639871532441111e-1, .23532306960642115854e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
603 .60708796647861610865e-1, -.27266747278681831364e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
604 -.51026476400767918226e-1, .28111892450146525404e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
605 .39960457575789924651e-1, -.26249795071946841205e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
606 -.25134290048737455284e-1, .15791188144791287229e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
607 .46379089482818671473e-2, -.48780095920069827068e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
608 -.13886961667516983541e-1, .29071311049368895844e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
609 .15480559452075811600e-1, -.47527977686242313065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
610 -.31929089844361042178e-2, .58015667638415922967e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
611 -.14547915466597622925e-1, -.61067668299848923244e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
612 .35093678009090186851e-1, .55378399159800654657e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
613 -.54277226474891610385e-1, -.42023830782434076509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
614 .69197384645944912066e-1, .22610783557709586445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
615 -.77269275900637030185e-1, 0.0, .77269275900637030185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
616 -.22610783557709586445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
617 -.69197384645944912066e-1, .42023830782434076509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
618 .54277226474891610385e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
619 -.55378399159800654657e-1, -.35093678009090186851e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
620 .61067668299848923244e-1, .14547915466597622925e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
621 -.58015667638415922967e-1, .31929089844361042178e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
622 .47527977686242313065e-1, -.15480559452075811600e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
623 -.29071311049368895844e-1, .13886961667516983541e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
624 .48780095920069827068e-2, .51591759101720291381e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
625 .11747497650231330965e-1, -.31777863364694653331e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
626 -.34555825499804605557e-2, .47914131921157015198e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
627 -.22573685920142225247e-1, -.45320344390022666738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
628 .49660630547172186418e-1, .25707858143963615736e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
629 -.68132707341917233933e-1, .67534860185243140399e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
630 .69268150370037450063e-1, -.41585011920451477177e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
631 -.51622397460510041271e-1, .68408139576363036148e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
632 .18981259024768933323e-1, -.78265472429342305554e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
633 .18981259024768933323e-1, .68408139576363036148e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
634 -.51622397460510041271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
635 -.41585011920451477177e-1, .69268150370037450063e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
636 .67534860185243140399e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
637 -.68132707341917233933e-1, .25707858143963615736e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
638 .49660630547172186418e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
639 -.45320344390022666738e-1, -.22573685920142225247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
640 .47914131921157015198e-1, -.34555825499804605557e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
641 -.31777863364694653331e-1, .11747497650231330965e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
642 .51591759101720291381e-2, -.54365757412741340377e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
643 -.94862516619529080191e-2, .33240472093448190877e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
644 -.88698898099681552229e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
645 -.40973252097216337576e-1, .42995673349795657065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
646 .17320914507876958783e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
647 -.62201292691914856803e-1, .24726274174637346693e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
648 .51320859246515407288e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
649 -.62882063373810501763e-1, -.11003569131725622672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
650 .73842261324108943465e-1, -.39240120294802923208e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
651 -.49293966443941122807e-1, .73552644778818223475e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
652 -.73552644778818223475e-1, .49293966443941122807e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
653 .39240120294802923208e-1, -.73842261324108943465e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
654 .11003569131725622672e-1, .62882063373810501763e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
655 -.51320859246515407288e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
656 -.24726274174637346693e-1, .62201292691914856803e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
657 -.17320914507876958783e-1, -.42995673349795657065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
658 .40973252097216337576e-1, .88698898099681552229e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
659 -.33240472093448190877e-1, .94862516619529080191e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
660 .54365757412741340377e-2, .57750194549356126240e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
661 .69981166020044116791e-2, -.33274982140403110792e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
662 .20297071020698356116e-1, .27898517839646066582e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
663 -.53368678853282030262e-1, .16656482990394548343e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
664 .46342901447260614255e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
665 -.60536796508149003365e-1, .29109107483842596340e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
666 .63224486124385124504e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
667 -.59028872851312033411e-1, -.14783105962696191734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
668 .74269399241069253865e-1, -.49053677339382384625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
669 -.33525466624811186739e-1, .78397349622515386647e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
670 -.33525466624811186739e-1, -.49053677339382384625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
671 .74269399241069253865e-1, -.14783105962696191734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
672 -.59028872851312033411e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
673 .63224486124385124504e-1, .29109107483842596340e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
674 -.60536796508149003365e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
675 .46342901447260614255e-1, .16656482990394548343e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
676 -.53368678853282030262e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
677 .27898517839646066582e-1, .20297071020698356116e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
678 -.33274982140403110792e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
679 .69981166020044116791e-2, .57750194549356126240e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
680 -.61100308370519200637e-2, -.44383614355738148616e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
681 .32011283412619094811e-1, -.29965011866372897633e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
682 -.10560682331349193348e-1, .51110336443392506342e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
683 -.45012284729681775492e-1, -.94236825555873320102e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
684 .60860695783141264746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
685 -.55014628647083368926e-1, -.73474782382499482121e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
686 .66640148475243034781e-1, -.62533116045749887988e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
687 -.38650525912400102585e-2, .68429769005837003777e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
688 -.66984505412544901945e-1, 0.0, .66984505412544901945e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
689 -.68429769005837003777e-1, .38650525912400102585e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
690 .62533116045749887988e-1, -.66640148475243034781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
691 .73474782382499482121e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
692 .55014628647083368926e-1, -.60860695783141264746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
693 .94236825555873320102e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
694 .45012284729681775492e-1, -.51110336443392506342e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
695 .10560682331349193348e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
696 .29965011866372897633e-1, -.32011283412619094811e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
697 .44383614355738148616e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
698 .61100308370519200637e-2, .65409373892036191538e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
699 .16350101107071157065e-2, -.29301957285983144319e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
700 .36838667173388832579e-1, -.81922703976491586393e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
701 -.36955670021050133434e-1, .58374851095540469865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
702 -.31977016246946181856e-1, -.25311073698658094646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
703 .66674413950106952577e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
704 -.54865713324521039571e-1, -.39797027891537985440e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
705 .62830285264808449064e-1, -.72226313251296100676e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
706 .22560232697133353980e-1, .46455784709904033738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
707 -.78200930751070349956e-1, .46455784709904033738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
708 .22560232697133353980e-1, -.72226313251296100676e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
709 .62830285264808449064e-1, -.39797027891537985440e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
710 -.54865713324521039571e-1, .66674413950106952577e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
711 -.25311073698658094646e-1, -.31977016246946181856e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
712 .58374851095540469865e-1, -.36955670021050133434e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
713 -.81922703976491586393e-2, .36838667173388832579e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
714 -.29301957285983144319e-1, .16350101107071157065e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
715 .65409373892036191538e-2, -.69686180931868703196e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
716 .11849538727632789870e-2, .25452286414610537766e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
717 -.40522480651713943230e-1, .25694679053362813183e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
718 .14057118113748390637e-1, -.52037614725803488893e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
719 .58849342223684035589e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
720 -.25075229077361409271e-1, -.29559771094034181083e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
721 .68296746944165720199e-1, -.62890462146423984955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
722 .14457636466274596445e-1, .45787612031322361496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
723 -.77231759014655809742e-1, .57881203613910543657e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
724 -.57881203613910543657e-1, .77231759014655809742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
725 -.45787612031322361496e-1, -.14457636466274596445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
726 .62890462146423984955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
727 -.68296746944165720199e-1, .29559771094034181083e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
728 .25075229077361409271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
729 -.58849342223684035589e-1, .52037614725803488893e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
730 -.14057118113748390637e-1, -.25694679053362813183e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
731 .40522480651713943230e-1, -.25452286414610537766e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
732 -.11849538727632789870e-2, .69686180931868703196e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
733 .75611653617520254845e-2, -.43290610418608409141e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
734 -.20277062025115566914e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
735 .40362947027704828926e-1, -.38938808024132120254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
736 .11831186195916702262e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
737 .28476667401744525357e-1, -.59320969056617684621e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
738 .61101629747436200186e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
739 -.29514834848355389223e-1, -.20668001885001084821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
740 .62923592802445122793e-1, -.73558456263588833115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
741 .45314556330160999776e-1, .79031645918426015574e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
742 -.58136953576334689357e-1, .78538474524006405758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
743 -.58136953576334689357e-1, .79031645918426015574e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
744 .45314556330160999776e-1, -.73558456263588833115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
745 .62923592802445122793e-1, -.20668001885001084821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
746 -.29514834848355389223e-1, .61101629747436200186e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
747 -.59320969056617684621e-1, .28476667401744525357e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
748 .11831186195916702262e-1, -.38938808024132120254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
749 .40362947027704828926e-1, -.20277062025115566914e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
750 -.43290610418608409141e-2, .75611653617520254845e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
751 -.81505692478987769484e-2, .74297333588288568430e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
752 .14314212513540223314e-1, -.36711242251332751607e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
753 .46240027755503814626e-1, -.34921532671769023773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
754 .46930051972353714773e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
755 .32842770336385381562e-1, -.61317813706529588466e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
756 .67000809902468893103e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
757 -.45337449655535622885e-1, .35794459576271920867e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
758 .41830061526027213385e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
759 -.72091371931944711708e-1, .74150028530317793195e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
760 -.46487632538609942002e-1, 0.0, .46487632538609942002e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
761 -.74150028530317793195e-1, .72091371931944711708e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
762 -.41830061526027213385e-1, -.35794459576271920867e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
763 .45337449655535622885e-1, -.67000809902468893103e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
764 .61317813706529588466e-1, -.32842770336385381562e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
765 -.46930051972353714773e-2, .34921532671769023773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
766 -.46240027755503814626e-1, .36711242251332751607e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
767 -.14314212513540223314e-1, -.74297333588288568430e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
768 .81505692478987769484e-2, .90693182942442189743e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
769 -.11121000903959576737e-1, -.71308296141317458546e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
770 .29219439765986671645e-1, -.45820286629778129593e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
771 .49088381175879124421e-1, -.35614888785023038938e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
772 .78906970900092777895e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
773 .26262843038404929480e-1, -.56143674270125757857e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
774 .71700220472378350694e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
775 -.66963544500697307945e-1, .42215091779892228883e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
776 -.41338867413966866997e-2, -.36164891772995367321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
777 .66584367783847858225e-1, -.77874712365070098328e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
778 .66584367783847858225e-1, -.36164891772995367321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
779 -.41338867413966866997e-2, .42215091779892228883e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
780 -.66963544500697307945e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
781 .71700220472378350694e-1, -.56143674270125757857e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
782 .26262843038404929480e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
783 .78906970900092777895e-2, -.35614888785023038938e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
784 .49088381175879124421e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
785 -.45820286629778129593e-1, .29219439765986671645e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
786 -.71308296141317458546e-2, -.11121000903959576737e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
787 .90693182942442189743e-2, -.99848472706332791043e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
788 .14701271465939718856e-1, -.32917820356048383366e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
789 -.19201195309873585230e-1, .38409681836626963278e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
790 -.51647324405878909521e-1, .54522171113149311354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
791 -.45040302741689006270e-1, .24183738595685990149e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
792 .42204134165479735097e-2, -.34317295181348742251e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
793 .59542472465494579941e-1, -.74135115907618101263e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
794 .74491937840566532596e-1, -.60042604725161994304e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
795 .33437677409000083169e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
796 -.33437677409000083169e-1, .60042604725161994304e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
797 -.74491937840566532596e-1, .74135115907618101263e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
798 -.59542472465494579941e-1, .34317295181348742251e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
799 -.42204134165479735097e-2, -.24183738595685990149e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
800 .45040302741689006270e-1, -.54522171113149311354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
801 .51647324405878909521e-1, -.38409681836626963278e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
802 .19201195309873585230e-1, .32917820356048383366e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
803 -.14701271465939718856e-1, .99848472706332791043e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
804 .11775579274769383373e-1, -.19892153937316935880e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
805 .95335114477449041055e-2, .57661528440359081617e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
806 -.23382690532380910781e-1, .40237257037170725321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
807 -.53280289903551636474e-1, .59974361806023689068e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
808 -.58701684061992853224e-1, .49033407111597129616e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
809 -.31818835267847249219e-1, .90800541261162098886e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
810 .16272906819312603838e-1, -.40863896581186229487e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
811 .61346046297517367703e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
812 -.74896047554167268919e-1, .79632642148310325817e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
813 -.74896047554167268919e-1, .61346046297517367703e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
814 -.40863896581186229487e-1, .16272906819312603838e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
815 .90800541261162098886e-2, -.31818835267847249219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
816 .49033407111597129616e-1, -.58701684061992853224e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
817 .59974361806023689068e-1, -.53280289903551636474e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
818 .40237257037170725321e-1, -.23382690532380910781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
819 .57661528440359081617e-2, .95335114477449041055e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
820 -.19892153937316935880e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
821 .11775579274769383373e-1, -.13562702617218467450e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
822 .24885419969649845849e-1, -.18368693901908875583e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
823 .81673147806084084638e-2, .47890591326129587131e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
824 -.19313752945227974024e-1, .34065953398362954708e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
825 -.47667045133463415672e-1, .58820377816690514309e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
826 -.66424139824618415970e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
827 .69667606260856092515e-1, -.68102459384364543253e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
828 .61683024923302547971e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
829 -.50771943476441639136e-1, .36110771847327189215e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
830 -.18758028464284563358e-1, 0.0, .18758028464284563358e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
831 -.36110771847327189215e-1, .50771943476441639136e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
832 -.61683024923302547971e-1, .68102459384364543253e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
833 -.69667606260856092515e-1, .66424139824618415970e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
834 -.58820377816690514309e-1, .47667045133463415672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
835 -.34065953398362954708e-1, .19313752945227974024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
836 -.47890591326129587131e-2, -.81673147806084084638e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
837 .18368693901908875583e-1, -.24885419969649845849e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
838 .13562702617218467450e-1, .20576545037980523979e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
839 -.40093155172981004337e-1, .36954083167944054826e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
840 -.31856506837591907746e-1, .24996323181546255126e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
841 -.16637165210473614136e-1, .71002706773325085237e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
842 .32478629093205201133e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
843 -.14009562579050569518e-1, .24771262248780618922e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
844 -.35119395835433647559e-1, .44656290368574753171e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
845 -.53015448339647394161e-1, .59875631995693046782e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
846 -.64973208326045193862e-1, .68112280331082143373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
847 -.69172215234062186994e-1, .68112280331082143373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
848 -.64973208326045193862e-1, .59875631995693046782e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
849 -.53015448339647394161e-1, .44656290368574753171e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
850 -.35119395835433647559e-1, .24771262248780618922e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
851 -.14009562579050569518e-1, .32478629093205201133e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
852 .71002706773325085237e-2, -.16637165210473614136e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
853 .24996323181546255126e-1, -.31856506837591907746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
854 .36954083167944054826e-1, -.40093155172981004337e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
855 .20576545037980523979e-1, -.27584914609096156163e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
856 .54904171411058497973e-1, -.54109756419563083153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
857 .52794234894345577483e-1, -.50970276026831042415e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
858 .48655445537990983379e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
859 -.45872036510847994332e-1, .42646854695899611372e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
860 -.39010960357087507670e-1, .34999369144476467749e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
861 -.30650714874402762189e-1, .26006877464703437057e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
862 -.21112579608213651273e-1, .16014956068786763273e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
863 -.10763099747751940252e-1, .54075888924374485533e-2, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
864 -.54075888924374485533e-2, .10763099747751940252e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
865 -.16014956068786763273e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
866 .21112579608213651273e-1, -.26006877464703437057e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
867 .30650714874402762189e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
868 -.34999369144476467749e-1, .39010960357087507670e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
869 -.42646854695899611372e-1, .45872036510847994332e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
870 -.48655445537990983379e-1, .50970276026831042415e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
871 -.52794234894345577483e-1, .54109756419563083153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
872 -.54904171411058497973e-1, .27584914609096156163e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
873 .13794141262469565740e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
874 .27588282524939131481e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
875 .27588282524939131481e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
876 .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
877 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
878 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
879 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
880 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
881 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
882 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
883 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
884 -.27588282524939131481e-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, .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, .13794141262469565740e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
890 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
891
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
892 static const double Tleft[33 * 33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
893 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
894 1., -.86602540378443864678, 0., .33071891388307382381, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
895 -.20728904939721249057, 0., .15128841196122722208, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
896 -.11918864298744029244, 0., .98352013661686631224e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
897 -.83727065404940845733e-1, 0., .72893399403505841203e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
898 -.64544632643375022436e-1, 0., .57913170372415565639e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
899 -.52518242575729562263e-1, 0., .48043311993977520457e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
900 -.44271433659733990243e-1, 0., .41048928022856771981e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
901 -.38263878662008271459e-1, 0., .35832844026365304501e-1, 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
902 .50000000000000000000, -.96824583655185422130, .57282196186948000082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
903 .21650635094610966169, -.35903516540862679125, -.97578093724974971969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
904 .26203921611325660506, .55792409597991015609e-1, -.20644078533943456204,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
905 -.36172381205961199479e-1, .17035068468874958194,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
906 .25371838001497225980e-1, -.14501953125000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
907 -.18786835250972344757e-1, .12625507130328301066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
908 .14473795929590520582e-1, -.11179458309419422675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
909 -.11494434254897626155e-1, .10030855351241635862,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
910 .93498556820544479096e-2, -.90964264465390582629e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
911 -.77546391824364392762e-2, .83213457337452292745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
912 .65358085945588638605e-2, -.76680372422574234569e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
913 -.55835321940047427169e-2, .71098828931825789428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
914 .48253327982967591019e-2, -.66274981937248958553e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
915 -.42118078245337801387e-2, .62064306433355646267e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
916 .37083386598903548973e-2, 0., 0., .25000000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
917 -.73950997288745200531, .83852549156242113615, -.23175620272173946716,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
918 -.37791833195149451496, .25710129174850522325, .21608307321780204633,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
919 -.22844049245646009157, -.14009503000335388415, .19897685605518413847,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
920 .98264706042471226893e-1, -.17445445004279014046,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
921 -.72761100054958328401e-1, .15463589893742108388,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
922 .56056770591708784481e-1, -.13855313872640495158,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
923 -.44517752443294564781e-1, .12534277657695128850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
924 .36211835346039665762e-1, -.11434398255136139683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
925 -.30033588409423828125e-1, .10506705408753910481,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
926 .25313077840725783008e-1, -.97149327637744872155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
927 -.21624927200393328444e-1, .90319582367202122625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
928 .18688433567711780666e-1, -.84372291635345108584e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
929 -.16312261561845420752e-1, .79149526894804751586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
930 .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
931 -.49607837082461073572, .82265291131801144317, -.59621200088559103072,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
932 -.80054302859059362371e-1, .42612156697795759420,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
933 -.90098145270865592887e-1, -.29769623255090078484, .13630307904779758221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
934 .21638835185708931831, -.14600247270306082052, -.16348801804014290453,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
935 .14340708728599057249, .12755243353979286190, -.13661523715071346961,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
936 -.10215585947881057394, .12864248070157166547, .83592528025348693602e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
937 -.12066728689302565222, -.69633728678718053052e-1, .11314245177331919532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
938 .58882939251410088028e-1, -.10621835858758221487,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
939 -.50432266865187597572e-1, .99916834723527771581e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
940 .43672094283057258509e-1, -.94206380251950852413e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
941 -.38181356812697746418e-1, .89035739656537771225e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
942 .33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
943 -.31093357409581873586, .67604086414949799246, -.75644205980613611039,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
944 .28990586430124175741, .30648508196770360914, -.35801372616842500052,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
945 -.91326869828709014708e-1, .31127929687500000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
946 -.90915752838698393094e-2, -.25637381283965534330,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
947 .57601077850322797594e-1, .21019685709225757945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
948 -.81244992138514014256e-1, -.17375078516720988858,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
949 .92289437277967051125e-1, .14527351914265391374,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
950 -.96675340792832019889e-1, -.12289485697108543415,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
951 .97448175340011084006e-1, .10511755943298339844,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
952 -.96242247086378239657e-1, -.90822942272780513537e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
953 .93966350452322132384e-1, .79189411876493712558e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
954 -.91139307067989309325e-1, -.69613039934383197265e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
955 .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
956 .31250000000000000000e-1, -.18684782411095934408, .50176689760410660236,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
957 -.74784031498626095398, .56472001151566251186, .14842464993721351203e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
958 -.41162920273003120936, .20243071230196532282, .23772054897172750436,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
959 -.24963810923972235950, -.12116179938394678936, .24330535483519110663,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
960 .47903849781124471359e-1, -.22133299683101224293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
961 -.20542915138527200983e-2, .19653465717678146728,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
962 -.26818172626509178444e-1, -.17319122357631210944,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
963 .45065391411065545445e-1, .15253391395444065941,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
964 -.56543897711725408302e-1, -.13469154928743585367,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
965 .63632471400208840155e-1, .11941684923913523817,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
966 -.67828850207933293098e-1, -.10636309084510652670,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
967 .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
968 0., .15625000000000000000e-1, -.10909562534194485289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
969 .34842348626527747318, -.64461114561628111443, .69382480527334683659,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
970 -.29551102358528827763, -.25527584713978439819, .38878771718544715394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
971 -.82956185835347407489e-2, -.31183177761966943912, .12831420840372374767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
972 .22067618205599434368, -.17569196937129496961, -.14598057000132284135,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
973 .18864406621763419484, .89921002550386645767e-1, -.18571835020187122114,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
974 -.48967672227195481777e-1, .17584685670380332798,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
975 .19267984545067426324e-1, -.16335437520503462738,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
976 .22598055455032407594e-2, .15032800884170631129,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
977 -.17883358353754640871e-1, -.13774837869432209951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
978 .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
979 0., .78125000000000000000e-2, -.62377810244809812496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
980 .23080781467370883845, -.50841310636012325368, .69834547012574056043,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
981 -.52572723156526459672, .11464215704954976471e-1, .38698869011491210342,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
982 -.26125646622255207507, -.16951698812361607510, .29773875898928782269,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
983 .20130501202570367491e-1, -.26332493149159310198,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
984 .67734613690401207009e-1, .21207315477103762715, -.11541543390889415193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
985 -.16249634759782417533, .13885887405041735068, .11996491328010275427,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
986 -.14810432001630926895, -.85177658352556243411e-1, .14918860659904380587,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
987 .57317789510444151564e-1, -.14569827645586660151,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
988 -.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
989 0., 0., .39062500000000000000e-2, -.35101954600803571207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
990 .14761284084133737720, -.37655033076080192966, .62410290231517322776,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
991 -.64335622317683389875, .28188168266139524244, .22488495672137010675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
992 -.39393811089283576186, .75184777995770096714e-1, .28472023119398293003,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
993 -.20410910833705899572, -.15590046962908511750, .23814567544617953125,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
994 .54442805556829031204e-1, -.22855930338589720954,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
995 .16303223615756629897e-1, .20172722433875559213,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
996 -.62723406421217419404e-1, -.17012230831020922010,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
997 .91754642766136561612e-1, .13927644821381121197, -.10886600968068418181,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
998 -.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
999 0., 0., .19531250000000000000e-2, -.19506820659607596598e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1000 .91865676095362231937e-1, -.26604607809696493849, .51425874205091288223,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1001 -.66047561132505329292, .48660109511591303851, -.17575661168678285615e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1002 -.36594333408055703366, .29088854695378694533, .11318677346656537927,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1003 -.31110645235730182168, .60733219161008787341e-1, .24333848233620420826,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1004 -.15254312332655419708, -.15995968483455388613, .19010344455215289289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1005 .86040636766440260000e-1, -.19652589954665259945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1006 -.27633388517205837713e-1, .18660848552712880387,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1007 -.15942583868416775867e-1, -.16902042462382064786,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1008 .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
1009 .97656250000000000000e-3, -.10731084460857378207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1010 .55939644713816406331e-1, -.18118487371914493668, .39914857299829864263,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1011 -.60812322949933902435, .60011887183061967583, -.26002695805835928795,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1012 -.20883922404786010096, .38988130966114638081, -.11797833550782589082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1013 -.25231824756239520077, .24817859972953934712, .90516417677868996417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1014 -.26079073291293066798, .30259468817169480161e-1, .22178195264114178432,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1015 -.10569877864302048175, -.16679648389266977455, .14637718550245050850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1016 .11219272032739559870, -.16359363640525750353, -.64358194509092101393e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1017 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
1018 -.58542865274813470967e-2, .33461741635290096452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1019 -.11979993155896201271, .29580223766987206958, -.51874761979436016742,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1020 .62861483498014306968, -.44868895761051453296, .12567502628371529386e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1021 .35040366183235474275, -.30466868455569500886, -.70903913601490112666e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1022 .30822791893032512740, -.11969443264190207736, -.20764760317621313946,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1023 .20629838355452128532, .95269702915334718507e-1, -.22432624768705133300,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1024 -.33103381593477797101e-2, .20570036048155716333,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1025 -.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
1026 0., 0., 0., 0., 0., 0., .24414062500000000000e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1027 -.31714797501871532475e-2, .19721062526127334100e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1028 -.77311181185536498246e-1, .21124871792841566575, -.41777980401893650886,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1029 .59401977834943551650, -.56132417807488349048, .23433675061367565951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1030 .20222775295220942126, -.38280372496506190127, .14443804214023095767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1031 .22268950939178466797, -.27211314150777981984, -.34184876506180717313e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1032 .26006498895669734842, -.97650425186005090107e-1, -.19024527660129101293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1033 .16789164198044635671, .10875811641651905252, -.19276785058805921298, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1034 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
1035 -.17078941137247586143e-2, .11477733754843910060e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1036 -.48887017020924625462e-1, .14634927241421789683, -.32156282683019547854,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1037 .52165811920227223937, -.60001958466396926460, .41208501541480733755,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1038 -.11366945503190350975e-2, -.33968093962672089159, .30955190935923386766,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1039 .40657421856578262210e-1, -.29873400409871531764, .16094481791768257440,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1040 .16876122436206497694, -.23650217045022161255, -.33070260090574765012e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1041 .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
1042 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
1043 -.91501857608428649078e-3, .66085179496951987952e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1044 -.30383171695850355404e-1, .98840838845366876117e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1045 -.23855447246420318989, .43322017468145613917, -.58049033744876107191,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1046 .52533893203742699346, -.20681056202371946180, -.20180000924562504384,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1047 .37503922291962681797, -.15988102869837429062, -.19823558102762374094,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1048 .28393023878803799622, -.11188133439357510403e-1, -.24730368377168229255,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1049 .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
1050 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
1051 -.48804277318479845551e-3, .37696080990601968396e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1052 -.18603912108994738255e-1, .65325006755649582964e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1053 -.17162960707938819795, .34411527956476971322, -.52289350347082497959,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1054 .57319653625674910592, -.37662253421045430413, -.14099055105384663902e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1055 .33265570610216904208, -.30921265572647566661, -.19911390594166455281e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1056 .28738590811031797718, -.18912130469738472647, -.13235936203215819193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1057 .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
1058 0., 0., 0., .15258789062500000000e-4, -.25928719280954633249e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1059 .21327398937568540428e-2, -.11244626133630732010e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1060 .42375605740664331966e-1, -.12031130345907846211, .26352562258934426830,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1061 -.44590628258512682078, .56682835613700749379, -.49116715128261660395,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1062 .17845943097110339078, .20541650677432497477, -.36739803642257458221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1063 .16776034069210108273, .17920950989905112908, -.28867732805385066532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1064 .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
1065 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
1066 .11979683091449349286e-2, -.67195313034570709806e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1067 .27044920779931968175e-1, -.82472196498517457862e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1068 .19570475044896150093, -.36391620788543817693, .52241392782736588032,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1069 -.54727504974907879912, .34211551468813581183, .31580472732719957762e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1070 -.32830006549176759667, .30563797665254420769, .64905014620683140120e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1071 -.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
1072 0., 0., 0., 0., 0., 0., .38146972656250000000e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1073 -.72454147007837596854e-4, .66859847582761390285e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1074 -.39751311980366118437e-2, .17015198650201528366e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1075 -.55443621868993855715e-1, .14157060481641692131, -.28641242619559616836,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1076 .45610665490966615415, -.55262786406029265394, .45818352706035500108,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1077 -.14984403004611673047, -.21163807462970713245, .36007252928843413718,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1078 -.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
1079 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
1080 -.38135049864067468562e-4, .37101393638555730015e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1081 -.23305339886279723213e-2, .10569913448297127219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1082 -.36640175162216897547e-1, .10010476414320235508, -.21860074212675559892,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1083 .38124757096345313719, -.52020999209879669177, .52172632730659212045,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1084 -.30841620620308814614, -.50322546186721500184e-1, .32577618885114899053,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1085 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
1086 0., 0., .95367431640625000000e-6, -.20021483206955925244e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1087 .20481807322420625431e-3, -.13553476938058909882e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1088 .64919676350791905019e-2, -.23848725425069251903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1089 .69384632678886421292e-1, -.16249711393618776934, .30736618106830314788,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1090 -.46399909601971539157, .53765031034002467225, -.42598991476520183929,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1091 .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
1092 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
1093 -.10487707828484902486e-4, .11254146162337528943e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1094 -.78248929534271987118e-3, .39468337145306794566e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1095 -.15313546659475671763e-1, .47249070825218564146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1096 -.11804374107101480543, .24031796927792491122, -.39629215049166341285,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1097 .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
1098 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
1099 .23841857910156250000e-6, -.54823314130625337326e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1100 .61575377321535518154e-4, -.44877834366497538134e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1101 .23774612048621955857e-2, -.97136347645161687796e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1102 .31671599547606636717e-1, -.84028665767000747480e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1103 .18298487576742964949, -.32647878537696945218, .46970971486488895077, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1104 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
1105 0., 0., 0., 0., .11920928955078125000e-6, -.28604020001177375838e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1106 .33559227978295551013e-4, -.25583821662860610560e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1107 .14201552747787302339e-2, -.60938046986874414969e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1108 .20930869247951926793e-1, -.58745021125678072911e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1109 .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
1110 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
1111 .59604644775390625000e-7, -.14898180663526043291e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1112 .18224991282807693921e-4, -.14504433444608833821e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1113 .84184722720281809548e-3, -.37846965430000478789e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1114 .13656355548211376864e-1, -.40409541997718853934e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1115 .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
1116 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
1117 .29802322387695312500e-7, -.77471708843445529468e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1118 .98649879372606876995e-5, -.81814934772838523887e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1119 .49554483992403011328e-3, -.23290922072351413938e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1120 .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
1121 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
1122 0., 0., 0., .14901161193847656250e-7, -.40226235946098233685e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1123 .53236418690561306700e-5, -.45933829691164002269e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1124 .28982005232838857913e-3, -.14212974043211018374e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1125 .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
1126 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
1127 .74505805969238281250e-8, -.20858299254133430408e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1128 .28648457300134381744e-5, -.25677535898258910850e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1129 .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
1130 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
1131 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
1132 .15376606719887104015e-5, -.14296523739727437959e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1133 .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
1134 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
1135 .18626451492309570312e-8, -.55871592916438890146e-7,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1136 .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
1137 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
1138 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
1139 -.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
1140 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
1141 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
1142 -.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
1143 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
1144 0., 0., .23283064365386962891e-9
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1145 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1146
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1147 static const double Tright[33 * 33] =
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1148 {
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1149 1., .86602540378443864678, 0., -.33071891388307382381, 0.,
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1150 .20728904939721249057, 0., -.15128841196122722208, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1151 .11918864298744029244, 0., -.98352013661686631224e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1152 .83727065404940845733e-1, 0., -.72893399403505841203e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1153 .64544632643375022436e-1, 0., -.57913170372415565639e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1154 .52518242575729562263e-1, 0., -.48043311993977520457e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1155 .44271433659733990243e-1, 0., -.41048928022856771981e-1, 0.,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1156 .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
1157 .50000000000000000000, .96824583655185422130, .57282196186948000082,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1158 -.21650635094610966169, -.35903516540862679125, .97578093724974971969e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1159 .26203921611325660506, -.55792409597991015609e-1, -.20644078533943456204,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1160 .36172381205961199479e-1, .17035068468874958194,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1161 -.25371838001497225980e-1, -.14501953125000000000,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1162 .18786835250972344757e-1, .12625507130328301066,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1163 -.14473795929590520582e-1, -.11179458309419422675,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1164 .11494434254897626155e-1, .10030855351241635862,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1165 -.93498556820544479096e-2, -.90964264465390582629e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1166 .77546391824364392762e-2, .83213457337452292745e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1167 -.65358085945588638605e-2, -.76680372422574234569e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1168 .55835321940047427169e-2, .71098828931825789428e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1169 -.48253327982967591019e-2, -.66274981937248958553e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1170 .42118078245337801387e-2, .62064306433355646267e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1171 -.37083386598903548973e-2, 0., 0., .25000000000000000000,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1172 .73950997288745200531, .83852549156242113615, .23175620272173946716,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1173 -.37791833195149451496, -.25710129174850522325, .21608307321780204633,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1174 .22844049245646009157, -.14009503000335388415, -.19897685605518413847,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1175 .98264706042471226893e-1, .17445445004279014046,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1176 -.72761100054958328401e-1, -.15463589893742108388,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1177 .56056770591708784481e-1, .13855313872640495158,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1178 -.44517752443294564781e-1, -.12534277657695128850,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1179 .36211835346039665762e-1, .11434398255136139683,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1180 -.30033588409423828125e-1, -.10506705408753910481,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1181 .25313077840725783008e-1, .97149327637744872155e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1182 -.21624927200393328444e-1, -.90319582367202122625e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1183 .18688433567711780666e-1, .84372291635345108584e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1184 -.16312261561845420752e-1, -.79149526894804751586e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1185 .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1186 .49607837082461073572, .82265291131801144317, .59621200088559103072,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1187 -.80054302859059362371e-1, -.42612156697795759420,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1188 -.90098145270865592887e-1, .29769623255090078484, .13630307904779758221,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1189 -.21638835185708931831, -.14600247270306082052, .16348801804014290453,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1190 .14340708728599057249, -.12755243353979286190, -.13661523715071346961,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1191 .10215585947881057394, .12864248070157166547, -.83592528025348693602e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1192 -.12066728689302565222, .69633728678718053052e-1, .11314245177331919532,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1193 -.58882939251410088028e-1, -.10621835858758221487,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1194 .50432266865187597572e-1, .99916834723527771581e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1195 -.43672094283057258509e-1, -.94206380251950852413e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1196 .38181356812697746418e-1, .89035739656537771225e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1197 -.33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1198 .31093357409581873586, .67604086414949799246, .75644205980613611039,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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diff changeset
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parents: 17744
diff changeset
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diff changeset
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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diff changeset
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
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parents: 17744
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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parents: 17744
diff changeset
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Rik <rik@octave.org>
parents: 17744
diff changeset
1394 0., 0., .23283064365386962891e-9
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1395 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1396
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1397 // Allocates a workspace for the given maximum number of intervals.
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1398 // Note that if the workspace gets filled, the intervals with the lowest
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1399 // error estimates are dropped. The maximum number of intervals is
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1400 // 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
1401 // but merely the size of the buffer.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1402
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1403 // Compute the product of the fx with one of the inverse
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1404 // Vandermonde-like matrices.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1405
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1406 void
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1407 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
1408 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1409 int i, j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1410
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1411 switch (d)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1412 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1413 case 0:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1414 for (i = 0; i <= 4; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1415 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1416 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1417 for (j = 0; j <= 4; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1418 c[i] += V1inv[i * 5 + j] * fx[j * 8];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1419 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1420 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1421 case 1:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1422 for (i = 0; i <= 8; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1423 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1424 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1425 for (j = 0; j <= 8; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1426 c[i] += V2inv[i * 9 + j] * fx[j * 4];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1427 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1428 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1429 case 2:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1430 for (i = 0; i <= 16; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1431 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1432 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1433 for (j = 0; j <= 16; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1434 c[i] += V3inv[i * 17 + j] * fx[j * 2];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1435 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1436 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1437 case 3:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1438 for (i = 0; i <= 32; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1439 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1440 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1441 for (j = 0; j <= 32; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1442 c[i] += V4inv[i * 33 + j] * fx[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1443 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1444 break;
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 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1447
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1448 // Downdate the interpolation given by the N coefficients C by removing
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1449 // the nodes with indices in nans.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1450
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1451 void
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1452 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
1453 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1454 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
1455 double b_new[34], alpha;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1456 int i, j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1457
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1458 for (i = 0; i <= n + 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1459 b_new[i] = bee[bidx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1460 for (i = 0; i < nnans; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1461 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1462 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
1463 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
1464 for (j = n - 1; j > 0; j--)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1465 b_new[j] =
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1466 (b_new[j] + xi[nans[i]] * b_new[j + 1] -
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1467 Lgamma[j + 1] * b_new[j + 2]) / Lalpha[j - 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1468 for (j = 0; j <= n; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1469 b_new[j] = b_new[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1470 alpha = c[n] / b_new[n];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1471 for (j = 0; j < n; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1472 c[j] -= alpha * b_new[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1473 c[n] = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1474 n--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1475 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1476 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1477
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1478 // The actual integration routine.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1479
20915
a3359fe50966 remove unused nargout variables
John W. Eaton <jwe@octave.org>
parents: 20910
diff changeset
1480 DEFUN (quadcc, args, ,
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1481 "-*- texinfo -*-\n\
20853
1142cf6abc0d 2015 Code Sprint: remove class of function from docstring for all C++ files.
Rik <rik@octave.org>
parents: 20831
diff changeset
1482 @deftypefn {} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b})\n\
1142cf6abc0d 2015 Code Sprint: remove class of function from docstring for all C++ files.
Rik <rik@octave.org>
parents: 20831
diff changeset
1483 @deftypefnx {} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})\n\
1142cf6abc0d 2015 Code Sprint: remove class of function from docstring for all C++ files.
Rik <rik@octave.org>
parents: 20831
diff changeset
1484 @deftypefnx {} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\
1142cf6abc0d 2015 Code Sprint: remove class of function from docstring for all C++ files.
Rik <rik@octave.org>
parents: 20831
diff changeset
1485 @deftypefnx {} {[@var{q}, @var{err}, @var{nr_points}] =} quadcc (@dots{})\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1486 Numerically evaluate the integral of @var{f} from @var{a} to @var{b}\n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1487 using doubly-adaptive @nospell{Clenshaw-Curtis} quadrature.\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1488 \n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1489 @var{f} is a function handle, inline function, or string containing the name\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1490 of the function to evaluate. The function @var{f} must be vectorized and\n\
20181
aa36fb998a4d maint: Remove unnecessary whitespace at end of lines.
Rik <rik@octave.org>
parents: 20172
diff changeset
1491 must return a vector of output values if given a vector of input values.\n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1492 For example,\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1493 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1494 @example\n\
14360
97883071e8e4 doc: Correct off-by-1 spacings in all .cc docstrings
Rik <octave@nomad.inbox5.com>
parents: 14151
diff changeset
1495 f = @@(x) x .* sin (1./x) .* sqrt (abs (1 - x));\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1496 @end example\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1497 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1498 @noindent\n\
16766
7268845c0a1e avoid backquote in error messages, some uses in doc strings
John W. Eaton <jwe@octave.org>
parents: 15996
diff changeset
1499 which uses the element-by-element ``dot'' form for all operators.\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1500 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1501 @var{a} and @var{b} are the lower and upper limits of integration. Either\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1502 or both limits may be infinite. @code{quadcc} handles an inifinite limit\n\
14854
5ae9f0f77635 maint: Use Octave coding conventions for coddling parenthis is DLD-FUNCTIONS directory
Rik <octave@nomad.inbox5.com>
parents: 14501
diff changeset
1503 by substituting the variable of integration with @code{x = tan (pi/2*u)}.\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1504 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1505 The optional argument @var{tol} defines the relative tolerance used to stop\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1506 the integration procedure. The default value is @math{1e^{-6}}.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1507 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1508 The optional argument @var{sing} contains a list of points where the\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1509 integrand has known singularities, or discontinuities\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1510 in any of its derivatives, inside the integration interval.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1511 For the example above, which has a discontinuity at x=1, the call to\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1512 @code{quadcc} would be as follows\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1513 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1514 @example\n\
14360
97883071e8e4 doc: Correct off-by-1 spacings in all .cc docstrings
Rik <octave@nomad.inbox5.com>
parents: 14151
diff changeset
1515 int = quadcc (f, a, b, 1.0e-6, [ 1 ]);\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1516 @end example\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1517 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1518 The result of the integration is returned in @var{q}.\n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1519 \n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1520 @var{err} is an estimate of the absolute integration error.\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1521 \n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1522 @var{nr_points} is the number of points at which the integrand was evaluated.\n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1523 \n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1524 If the adaptive integration did not converge, the value of @var{err} will be\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1525 larger than the requested tolerance. Therefore, it is recommended to verify\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1526 this value for difficult integrands.\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1527 \n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1528 @code{quadcc} is capable of dealing with non-numeric values of the integrand\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1529 such as @code{NaN} or @code{Inf}. If the integral diverges, and\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1530 @code{quadcc} detects this, then a warning is issued and @code{Inf} or\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1531 @code{-Inf} is returned.\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1532 \n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1533 Note: @code{quadcc} is a general purpose quadrature algorithm and, as such,\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1534 may be less efficient for a smooth or otherwise well-behaved integrand than\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1535 other methods such as @code{quadgk}.\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1536 \n\
19040
0850b5212619 doc: Add @nospell macro around proper names in documentation.
Rik <rik@octave.org>
parents: 17787
diff changeset
1537 The algorithm uses @nospell{Clenshaw-Curtis} quadrature rules of increasing\n\
20172
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1538 degree in each interval and bisects the interval if either the function does\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1539 not appear to be smooth or a rule of maximum degree has been reached. The\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1540 error estimate is computed from the L2-norm of the difference between two\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1541 successive interpolations of the integrand over the nodes of the respective\n\
4f45eaf83908 doc: Update more docstrings to have one sentence summary as first line.
Rik <rik@octave.org>
parents: 19697
diff changeset
1542 quadrature rules.\n\
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1543 \n\
19040
0850b5212619 doc: Add @nospell macro around proper names in documentation.
Rik <rik@octave.org>
parents: 17787
diff changeset
1544 Reference: @nospell{P. Gonnet}, @cite{Increasing the Reliability of Adaptive\n\
12553
7c915d013b9c quadcc: Add reference to original paper in docstring.
Rik <octave@nomad.inbox5.com>
parents: 11590
diff changeset
1545 Quadrature Using Explicit Interpolants}, ACM Transactions on\n\
7c915d013b9c quadcc: Add reference to original paper in docstring.
Rik <octave@nomad.inbox5.com>
parents: 11590
diff changeset
1546 Mathematical Software, Vol. 37, Issue 3, Article No. 3, 2010.\n\
11572
7d6d8c1e471f Grammarcheck Texinfo for files in src directory.
Rik <octave@nomad.inbox5.com>
parents: 11562
diff changeset
1547 @seealso{quad, quadv, quadl, quadgk, trapz, dblquad, triplequad}\n\
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1548 @end deftypefn")
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1549 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1550 // Some constants that we will need.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1551 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
1552 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
1553 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
1554 static const double w = M_SQRT2 / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1555 static const int ndiv_max = 20;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1556
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1557 // Arguments left and right.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1558 int nargin = args.length ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1559 octave_function *fcn;
15996
1aff8c38c53c use octave_local_buffer for temporary arrays in quadcc
John W. Eaton <jwe@octave.org>
parents: 15995
diff changeset
1560 double a, b, tol, *sing;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1561
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1562 // 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
1563 bool wrap = false;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1564 double xw;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1565
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1566 // 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
1567 octave_value_list fargs, fvals;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1568
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1569 // Actual variables (as opposed to constants above).
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1570 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
1571 double igral, err, igral_final, err_final;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1572 int nivals, neval = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1573 int i, j, d, split, t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1574 int nnans, nans[33];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1575 cquad_ival *iv, *ivl, *ivr;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1576 double nc, ncdiff;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1577
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1578 // Parse the input arguments.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1579 if (nargin < 3)
20801
a542a9bf177e eliminate return statements after calls to print_usage
John W. Eaton <jwe@octave.org>
parents: 20232
diff changeset
1580 print_usage ();
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1581
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1582 if (args(0).is_function_handle () || args(0).is_inline_function ())
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1583 fcn = args(0).function_value ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1584 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1585 {
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1586 std::string fcn_name = unique_symbol_name ("__quadcc_fcn__");
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1587 std::string fname = "function y = ";
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1588 fname.append (fcn_name);
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1589 fname.append ("(x) y = ");
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1590 fcn = extract_function (args(0), "quadcc", fcn_name, fname,
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1591 "; endfunction");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1592 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1593
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1594 if (! args(1).is_real_scalar ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1595 error ("quadcc: lower limit of integration (A) must be a single real scalar");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1596 else
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1597 a = args(1).double_value ();
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(2).is_real_scalar ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1600 error ("quadcc: upper limit of integration (B) must be a single real scalar");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1601 else
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1602 b = args(2).double_value ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1603
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1604 if (nargin < 4 || args(3).is_empty ())
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1605 tol = 1.0e-6;
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1606 else if (! args(3).is_real_scalar () || args(3).double_value () <= 0)
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1607 error ("quadcc: tolerance (TOL) must be a single real scalar > 0");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1608 else
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1609 tol = args(3).double_value ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1610
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1611 if (nargin < 5)
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1612 nivals = 1;
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1613 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
1614 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
1615 else
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1616 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
1617
19593
446c46af4b42 strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 17787
diff changeset
1618 int cquad_heapsize = (nivals >= min_cquad_heapsize ? nivals + 1
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1619 : min_cquad_heapsize);
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1620 // The interval heap.
15996
1aff8c38c53c use octave_local_buffer for temporary arrays in quadcc
John W. Eaton <jwe@octave.org>
parents: 15995
diff changeset
1621 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
1622 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
1623 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
1624
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1625 if (nivals == 1)
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1626 {
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1627 iivals[0] = a;
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1628 iivals[1] = b;
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1629 }
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1630 else
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1631 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1632 // Intervals around singularities.
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1633 sing = args(4).array_value ().fortran_vec ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1634 iivals[0] = a;
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1635 for (i = 0; i < nivals - 1; i++)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1636 iivals[i + 1] = sing[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1637 iivals[nivals] = b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1638 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1639
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1640 // If a or b are +/-Inf, transform the integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1641 if (xisinf (a) || xisinf (b))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1642 {
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1643 wrap = true;
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1644 for (i = 0; i < nivals + 1; i++)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1645 if (xisinf (iivals[i]))
14151
e8bad0dc263c quadcc: use gnulib::copysign
John W. Eaton <jwe@octave.org>
parents: 14138
diff changeset
1646 iivals[i] = gnulib::copysign (1.0, iivals[i]);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1647 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1648 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
1649 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1650
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1651 // Initialize the heaps.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1652 for (i = 0; i < cquad_heapsize; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1653 heap[i] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1654
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1655 // Create the first interval(s).
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1656 igral = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1657 err = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1658 for (j = 0; j < nivals; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1659 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1660 // Initialize the interval.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1661 iv = &(ivals[heap[j]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1662 m = (iivals[j] + iivals[j + 1]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1663 h = (iivals[j + 1] - iivals[j]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1664 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1665 ColumnVector ex (33);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1666 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1667 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1668 for (i = 0; i <= n[3]; i++)
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1669 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
1670 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1671 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1672 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1673 for (i = 0; i <= n[3]; i++)
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1674 ex(i) = m + xi[i] * h;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1675 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1676 fargs(0) = ex;
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1677 fvals = 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
1678 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
1679 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
1680
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1681 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
1682 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1683 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
1684
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1685 for (i = 0; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1686 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1687 iv->fx[i] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1688 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1689 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1690 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1691 iv->fx[i] *= (1.0 + xw * xw) * M_PI / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1692 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1693 neval++;
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1694 if (! xfinite (iv->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1695 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1696 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1697 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1698 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1699 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1700 Vinvfx (iv->fx, &(iv->c[idx[3]]), 3);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1701 Vinvfx (iv->fx, &(iv->c[idx[2]]), 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1702 Vinvfx (iv->fx, &(iv->c[0]), 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1703 for (i = 0; i < nnans; i++)
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
1704 iv->fx[nans[i]] = octave_NaN;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1705 iv->a = iivals[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1706 iv->b = iivals[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1707 iv->depth = 3;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1708 iv->rdepth = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1709 iv->ndiv = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1710 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
1711 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1712 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
1713 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1714 temp = iv->c[idx[3] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1715 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1716 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1717 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1718 for (i = 0; i <= n[2]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1719 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1720 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
1721 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1722 nc += iv->c[idx[3] + i] * iv->c[idx[3] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1723 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1724 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1725 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1726 iv->err = ncdiff * 2 * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1727 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
1728 iv->err = 2 * h * nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1729
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1730 // Tabulate this interval's data.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1731 igral += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1732 err += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1733
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1734 // Sift it up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1735 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1736 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
1737 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1738 temp = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1739 heap[i] = heap[i / 2];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1740 heap[i / 2] = temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1741 i /= 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1742 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1743 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1744
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1745 // Initialize some global values.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1746 igral_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1747 err_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1748
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1749 // Main loop.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1750 while (nivals > 0 && err > 0.0 && err > fabs (igral) * tol
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1751 && !(err_final > fabs (igral) * tol
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1752 && err - err_final < fabs (igral) * tol))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1753 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1754 // Allow the user to interrupt.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1755 OCTAVE_QUIT;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1756
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1757 // 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
1758 iv = &(ivals[heap[0]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1759 m = (iv->a + iv->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1760 h = (iv->b - iv->a) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1761
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1762 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1763 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
1764 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
1765 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1766
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1767 // Should we try to increase the degree?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1768 if (iv->depth < 3)
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 // Keep tabs on some variables.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1771 d = ++iv->depth;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1772
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1773 // Get the new (missing) function values.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1774 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1775 ColumnVector ex (n[d] / 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1776 if (wrap)
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 for (i = 0; i < n[d] / 2; i++)
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1779 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
1780 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1781 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1782 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1783 for (i = 0; i < n[d] / 2; i++)
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1784 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
1785 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1786 fargs(0) = ex;
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1787 fvals = 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
1788 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
1789 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
1790
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1791 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
1792 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1793 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
1794
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1795 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1796 for (i = 0; i < n[d] / 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1797 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1798 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
1799 iv->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1800 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1801 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1802 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1803 iv->fx[j] *= (1.0 + xw * xw) * M_PI / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1804 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1805 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1806 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1807 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1808 for (i = 0; i <= 32; i += skip[d])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1809 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1810 if (! xfinite (iv->fx[i]))
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1811 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1812 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1813 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1814 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1815 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1816
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1817 // Compute the new coefficients.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1818 Vinvfx (iv->fx, &(iv->c[idx[d]]), d);
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1819 // Downdate any NaNs.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1820 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1821 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1822 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
1823 for (i = 0; i < nnans; i++)
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
1824 iv->fx[nans[i]] = octave_NaN;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1825 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1826
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1827 // Compute the error estimate.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1828 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1829 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
1830 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1831 temp = iv->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1832 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1833 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1834 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1835 for (i = 0; i <= n[d - 1]; i++)
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 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
1838 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1839 nc += iv->c[idx[d] + i] * iv->c[idx[d] + i];
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 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1842 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1843 iv->err = ncdiff * 2 * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1844 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1845 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
1846 // Split the interval prematurely?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1847 split = (nc > 0 && ncdiff / nc > 0.1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1848 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1849 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1850 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1851 // Maximum degree reached, just split.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1852 split = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1853 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1854
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1855 // Should we drop this interval?
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1856 if ((m + h * xi[0]) >= (m + h * xi[1])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1857 || (m + h * xi[31]) >= (m + h * xi[32])
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1858 || iv->err < fabs (iv->igral)
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1859 * std::numeric_limits<double>::epsilon () * 10)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1860 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1861 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
1862 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
1863 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
1864 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1865
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1866 // Keep this interval's contribution.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1867 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1868 igral_final += iv->igral;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1869 // Swap with the last element on the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1870 t = heap[nivals - 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1871 heap[nivals - 1] = heap[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1872 heap[0] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1873 nivals--;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1874 // Fix up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1875 i = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1876 while (2 * i + 1 < nivals)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1877 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1878 // Get the kids.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1879 j = 2 * i + 1;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1880 // 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
1881 // use it instead.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1882 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1883 && 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
1884 j++;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1885 // 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
1886 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
1887 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1888 else
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 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1891 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1892 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1893 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1894 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1895 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1896 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1897 else if (split)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1898 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1899 // Some values we will need often...
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1900 d = iv->depth;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1901 // Generate the interval on the left.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1902 ivl = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1903 ivl->a = iv->a;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1904 ivl->b = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1905 ml = (ivl->a + ivl->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1906 hl = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1907 ivl->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1908 ivl->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1909 ivl->fx[0] = iv->fx[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1910 ivl->fx[32] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1911 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1912 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1913 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1914 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1915 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
1916 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
1917 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1918 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1919 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1920 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
1921 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
1922 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1923 fargs(0) = ex;
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1924 fvals = 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
1925 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
1926 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
1927
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
1928 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
1929 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
1930 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
1931
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
1932 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1933 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1934 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1935 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
1936 ivl->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1937 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1938 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1939 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1940 ivl->fx[j] *= (1.0 + xw * xw) * M_PI / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1941 }
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 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1944 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1945 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1946 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
1947 if (! xfinite (ivl->fx[i]))
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 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1950 ivl->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1951 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1952 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1953 Vinvfx (ivl->fx, ivl->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1954 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1955 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1956 downdate (ivl->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1957 for (i = 0; i < nnans; i++)
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
1958 ivl->fx[nans[i]] = octave_NaN;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1959 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1960 for (i = 0; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1961 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1962 ivl->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1963 for (j = i; j <= n[d]; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1964 ivl->c[idx[d] + i] += Tleft[i * 33 + j] * iv->c[idx[d] + j];
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 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1967 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1968 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1969 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
1970 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1971 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1972 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
1973 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1974 temp = ivl->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1975 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1976 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1977 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1978 ivl->err = ncdiff * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1979 // Check for divergence.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1980 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
1981 && ivl->c[0] / iv->c[0] > 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1982 if (ivl->ndiv > ndiv_max && 2 * ivl->ndiv > ivl->rdepth)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1983 {
14151
e8bad0dc263c quadcc: use gnulib::copysign
John W. Eaton <jwe@octave.org>
parents: 14138
diff changeset
1984 igral = gnulib::copysign (octave_Inf, igral);
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1985 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1986 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1987 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1988
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1989 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1990 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
1991
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
1992 // Generate the interval on the right.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1993 ivr = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1994 ivr->a = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1995 ivr->b = iv->b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1996 mr = (ivr->a + ivr->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1997 hr = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1998 ivr->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1999 ivr->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2000 ivr->fx[0] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2001 ivr->fx[32] = iv->fx[32];
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 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2004 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2005 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2006 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
2007 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
2008 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2009 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2010 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2011 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
2012 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
2013 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2014 fargs(0) = ex;
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2015 fvals = 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
2016 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
2017 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
2018
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2019 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
2020 if (effex.numel () != ex.numel ())
20831
35241c4b696c eliminate return statements after calls to error
John W. Eaton <jwe@octave.org>
parents: 20801
diff changeset
2021 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
2022
20232
a9574e3c6e9e Deprecate Array::length() and Sparse::length() in favour of ::numel().
Carnë Draug <carandraug@octave.org>
parents: 20181
diff changeset
2023 neval += effex.numel ();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2024 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2025 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2026 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
2027 ivr->fx[j] = effex(i);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2028 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2029 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2030 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2031 ivr->fx[j] *= (1.0 + xw * xw) * M_PI / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2032 }
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 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2035 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2036 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2037 {
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2038 if (! xfinite (ivr->fx[i]))
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 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2041 ivr->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2042 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2043 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2044 Vinvfx (ivr->fx, ivr->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2045 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2046 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2047 downdate (ivr->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2048 for (i = 0; i < nnans; i++)
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2049 ivr->fx[nans[i]] = octave_NaN;
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2050 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2051 for (i = 0; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2052 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2053 ivr->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2054 for (j = i; j <= n[d]; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2055 ivr->c[idx[d] + i] += Tright[i * 33 + j] * iv->c[idx[d] + j];
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 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2058 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2059 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2060 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
2061 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2062 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2063 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
2064 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2065 temp = ivr->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2066 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2067 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2068 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2069 ivr->err = ncdiff * h;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2070 // Check for divergence.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2071 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
2072 && ivr->c[0] / iv->c[0] > 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2073 if (ivr->ndiv > ndiv_max && 2 * ivr->ndiv > ivr->rdepth)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2074 {
14151
e8bad0dc263c quadcc: use gnulib::copysign
John W. Eaton <jwe@octave.org>
parents: 14138
diff changeset
2075 igral = gnulib::copysign (octave_Inf, igral);
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
2076 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2077 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2078 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2079
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2080 // Compute the local integral.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2081 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
2082
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2083 // Fix-up the heap: we now have one interval on top that we
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2084 // don't need any more and two new, unsorted ones at the
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2085 // bottom.
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
2086
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2087 // Flip the last interval to the top of the heap and sift down.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2088 t = heap[nivals - 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2089 heap[nivals - 1] = heap[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2090 heap[0] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2091 nivals--;
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2092 // Sift this interval back down the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2093 i = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2094 while (2 * i + 1 < nivals - 1)
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 j = 2 * i + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2097 if (j + 1 < nivals - 1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2098 && 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
2099 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2100 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
2101 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2102 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2103 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2104 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2105 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2106 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2107 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2108 }
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 // 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
2112 i = nivals - 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2113 while (i > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2114 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2115 j = (i - 1) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2116 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
2117 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2118 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2119 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2120 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2121 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2122 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2123 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2124 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2125 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2126 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2127 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2128 {
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2129 // Otherwise, just fix-up the heap.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2130 i = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2131 while (2 * i + 1 < nivals)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2132 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2133 j = 2 * i + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2134 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2135 && 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
2136 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2137 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
2138 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2139 else
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 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2142 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2143 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2144 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2145 }
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 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2148
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2149 // If the heap is about to overflow, remove the last two
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2150 // intervals.
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2151 while (nivals > cquad_heapsize - 2)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2152 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2153 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
2154 #if (DEBUG_QUADCC)
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2155 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
2156 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
2157 #endif
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2158 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2159 igral_final += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2160 nivals--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2161 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2162
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2163 // 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
2164 igral = igral_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2165 err = err_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2166 for (i = 0; i < nivals; i++)
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 igral += ivals[heap[i]].igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2169 err += ivals[heap[i]].err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2170 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2171 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2172
20910
359476667c4c * quadcc.cc: Style fixes.
John W. Eaton <jwe@octave.org>
parents: 20909
diff changeset
2173 // 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
2174 #if (DEBUG_QUADCC)
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2175 for (i = 0; i < nivals; i++)
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2176 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2177 iv = &(ivals[heap[i]]);
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2178 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
2179 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
2180 iv->rdepth, iv->ndiv);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2181 }
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2182 #endif
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2183
20909
03e4ddd49396 omit unnecessary nargout checks
John W. Eaton <jwe@octave.org>
parents: 20898
diff changeset
2184 return ovl (igral, err, neval);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2185 }
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2186
13141
e81ddf9cacd5 maint: untabify and remove trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 12653
diff changeset
2187 /*
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2188 %!assert (quadcc (@sin, -pi, pi), 0, 1e-6)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2189 %!assert (quadcc (inline ("sin"),- pi, pi), 0, 1e-6)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2190 %!assert (quadcc ("sin", -pi, pi), 0, 1e-6)
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2191
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2192 %!assert (quadcc (@sin, -pi, 0), -2, 1e-6)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2193 %!assert (quadcc (@sin, 0, pi), 2, 1e-6)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2194 %!assert (quadcc (@(x) 1./sqrt (x), 0, 1), 2, 1e-6)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2195 %!assert (quadcc (@(x) 1./(sqrt (x).*(x+1)), 0, Inf), pi, 1e-6)
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2196
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2197 %!assert (quadcc (@(x) exp (-x .^ 2), -Inf, Inf), sqrt (pi), 1e-6)
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2198 %!assert (quadcc (@(x) exp (-x .^ 2), -Inf, 0), sqrt (pi)/2, 1e-6)
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2199
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2200 ## 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
2201 %!function y = __nansin (x)
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2202 %! 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
2203 %! y = sin (x);
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2204 %! 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
2205 %! y(idx < 1e-10) = NaN;
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2206 %!endfunction
15437
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2207
c9954a15bc03 Fix quadcc when there are NaNs in the integrand (bug #37414)
Rik <rik@octave.org>
parents: 14151
diff changeset
2208 %!test
17787
175b392e91fe Use GNU style coding conventions for code in libinterp/
Rik <rik@octave.org>
parents: 17744
diff changeset
2209 %! [q, err, npoints] = quadcc ("__nansin", -pi, pi);
15995
906ae1705522 quadcc.cc: Use heap instead of stack for large temporary variables.
Rik <rik@octave.org>
parents: 15994
diff changeset
2210 %! 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
2211 %! 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
2212
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2213 %% Test input validation
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2214 %!error (quadcc ())
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2215 %!error (quadcc (@sin))
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2216 %!error (quadcc (@sin, 0))
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2217 %!error (quadcc (@sin, ones (2), pi))
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2218 %!error (quadcc (@sin, -i, pi))
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14360
diff changeset
2219 %!error (quadcc (@sin, 0, ones (2)))
12614
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2220 %!error (quadcc (@sin, 0, i))
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2221 %!error (quadcc (@sin, 0, pi, 0))
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2222 %!error (quadcc (@sin, 0, pi, 1e-6, [ i ]))
4e11a87d86e6 quadcc.cc: Recode input validation and add tests.
Rik <octave@nomad.inbox5.com>
parents: 12612
diff changeset
2223 */