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doc: Update all documentation for chapter on Numerical Integration * cumtrapz.m, dblquad.m, quadgk.m, quadl.m, quadv.m, trapz.m, triplequad.m, quad.cc, quadcc.cc: Improve docstrings. * Quad-opts.in: Keep code sample together on a single line. * mk-opts.pl: Update quad-options function description * octave.texi: Update order of detailmenu to match order in quad.texi. * quad.txi: Add language about when to use each quad function, add examples of using trapz. * aspell-octave.en.pws: Add new spelling words from quad.texi chapter
author Rik <octave@nomad.inbox5.com>
date Sun, 17 Apr 2011 19:57:07 -0700
parents 7c915d013b9c
children 4e11a87d86e6 f96b9b9f141b
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1 /*
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2
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3 Copyright (C) 2010-2011 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 <stdlib.h>
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28 #include "lo-math.h"
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29 #include "lo-ieee.h"
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30 #include "oct.h"
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31 #include "parse.h"
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32 #include "ov-fcn-handle.h"
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33
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34 #if ! defined (HAVE_COPYSIGN) && defined (HAVE__COPYSIGN)
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35 #define copysign _copysign
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36 #define HAVE_COPYSIGN 1
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37 #endif
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38
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39 /* Define the size of the interval heap. */
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40 #define cquad_heapsize 200
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41
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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
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56 static const double xi[33] = {
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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 0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
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74 -8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
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75 0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
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76 3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
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77 0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
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78 5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
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79 0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
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80 4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
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81 0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
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82 3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
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83 0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
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84 5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
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85 0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
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86 3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
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87 0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
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88 7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
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89 0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
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90 1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
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91 0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
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92 6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
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93 0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
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94 2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
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95 0.00000000000000e+00, 5.40679930965238e-01
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96 };
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97
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98 static const double Lalpha[33] = {
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99 5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
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100 5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
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101 5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
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102 5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
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103 5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
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104 5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
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105 5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
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106 5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
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107 5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
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108 5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
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109 5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
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110 };
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111
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112 static const double Lgamma[33] = {
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113 0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
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114 5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
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115 5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
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116 5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
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117 5.00319182924304e-01, 5.00278009473803e-01, 5.00244319584578e-01,
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118 5.00216403386025e-01, 5.00193012939056e-01, 5.00173220168024e-01,
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parents:
diff changeset
119 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
120 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
121 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
122 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
123 5.00061046334395e-01
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
124 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
125
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
126 static const double V1inv[5 * 5] = {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
127 .47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
128 .37712361663282534635, .47140452079103168293e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
129 -.81649658092772603273e-1, -.46188021535170061160, 0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
130 .46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
131 .12046772038736683169, -.54210474174315074262, .12046772038736683169,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
132 .15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
133 -.30237157840738178177, .21380899352993950775, .10774960475223581324,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
134 -.21549920950447162648, .21549920950447162648, -.21549920950447162648,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
135 .10774960475223581324
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
136 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
137
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
138 static const double V2inv[9 * 9] = {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
139 .11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
140 .25577315077753587922, .27835314560994251755, .25577315077753587922,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
141 .19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
142 -.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
143 -.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
144 .16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
145 .17766815796285469394, .11316664642449611462, -.16306601003711325980,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
146 -.30847037493128779631, -.16306601003711325980, .11316664642449611462,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
147 .17766815796285469394, .26466393115406349388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
148 -.32395302049990834508e-1, -.15521142532414866547,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
149 .88573492664788602740e-1, .29570405784974857322, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
150 -.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
151 .32395302049990834508e-1, .41442155673936851246e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
152 .98186757907405608245e-1, -.23056908429499411784,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
153 -.68047008326360625520e-1, .31797435808002456774,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
154 -.68047008326360625520e-1, -.23056908429499411784,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
155 .98186757907405608245e-1, .41442155673936851246e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
156 -.49981120317798783134e-1, -.24861810572835756217e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
157 .23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
158 -.23561326072010832539, .24861810572835756217e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
159 .49981120317798783134e-1, .79691635865674781228e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
160 -.95725617891693941833e-1, -.57957553356854386344e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
161 .21164072460540271452, -.27529837844505833514, .21164072460540271452,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
162 -.57957553356854386344e-1, -.95725617891693941833e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
163 .79691635865674781228e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
164 -.10894869830716590913, .20131094491947531782, -.15407672674888869038,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
165 .83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
166 .15407672674888869038, -.20131094491947531782, .10894869830716590913,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
167 .54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
168 -.10916211417928767644, .10916211417928767644, -.10916211417928767644,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
169 .10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
170 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
171
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
172 static const double V3inv[17 * 17] = {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
173 .27729677693590098996e-2, .26423663180333065153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
174 .53374068493933898312e-1, .77007854739523195947e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
175 .98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
176 .13612785914022865001, .13888293186236181317, .13612785914022865001,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
177 .12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
178 .77007854739523195947e-1, .53374068493933898312e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
179 .26423663180333065153e-1, .27729677693590098996e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
180 -.48029210642807413690e-2, -.44887724635478800254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
181 -.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
182 -.11102786862182788886, -.85054870109799336515e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
183 -.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
184 .85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
185 .11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
186 .48029210642807413690e-2, .62758546879582030087e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
187 .55561297093529155869e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
188 .93281491021051539742e-1, .92320151237493695139e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
189 .55077987469605684531e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
190 -.96998141716497488255e-2, -.80285961895427405567e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
191 -.13496839655913850224,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
192 -.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
193 -.96998141716497488255e-2, .55077987469605684531e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
194 .92320151237493695139e-1, .93281491021051539742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
195 .55561297093529155869e-1, .62758546879582030087e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
196 -.74850969394858555939e-2, -.61751608943839234096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
197 -.82974150437304275958e-1, -.38437763431942633378e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
198 .45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
199 .98768034347019704401e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
200 -.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
201 -.45745502025779701366e-1, .38437763431942633378e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
202 .82974150437304275958e-1, .61751608943839234096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
203 .74850969394858555939e-2, .86710099994384056338e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
204 .64006230103659573344e-1, .58517426396091675690e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
205 -.29743410528985802680e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
206 -.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
207 .97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
208 -.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
209 -.29743410528985802680e-1, .58517426396091675690e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
210 .64006230103659573344e-1, .86710099994384056338e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
211 -.97486395666294840165e-2, -.62995604908060224672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
212 -.24373234450275529219e-1, .87760984413626872730e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
213 .12205204576993351394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
214 .16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
215 0.0, .13682714580929614678, .12422320942156845775,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
216 -.16216004196864002088e-1, -.12205204576993351394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
217 -.87760984413626872730e-1, .24373234450275529219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
218 .62995604908060224672e-1, .97486395666294840165e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
219 .10956271233750488468e-1, .58613204255294358939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
220 -.13306063940736618859e-1, -.11606666444978454399,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
221 -.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
222 -.44678658254872910434e-1, -.15617684362128533405,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
223 -.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
224 -.52059598001115805639e-1, -.11606666444978454399,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
225 -.13306063940736618859e-1, .58613204255294358939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
226 .10956271233750488468e-1, -.12098893000863087230e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
227 -.51626244709126208453e-1, .48919433304746979330e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
228 .10467644465949427090,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
229 -.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
230 .15434223333238741600, 0.0, -.15434223333238741600,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
231 -.28190838706814496438e-1, .13668732103524749234,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
232 .48729879523084673782e-1, -.10467644465949427090,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
233 -.48919433304746979330e-1, .51626244709126208453e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
234 .12098893000863087230e-1, .13542668300437944822e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
235 .41712033418258689308e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
236 -.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
237 .42121099930651007882e-1, -.14684425840766337756,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
238 -.16108203535058647043e-1, .15698075850757976092,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
239 -.16108203535058647043e-1, -.14684425840766337756,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
240 .42121099930651007882e-1, .12158068748245606853,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
241 -.58303943170068132010e-1, -.76190463272803434388e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
242 .41712033418258689308e-1, .13542668300437944822e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
243 -.14939634995117694417e-1, -.30047246373341564039e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
244 .91624635082546425678e-1, -.79133374319110026377e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
245 -.12292558212072233355, .90013382617762643524e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
246 .84013717196539593395e-1, -.14813033309980695856, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
247 .14813033309980695856, -.84013717196539593395e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
248 -.90013382617762643524e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
249 .12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
250 .30047246373341564039e-1, .14939634995117694417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
251 .16986031342807474208e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
252 .15760203882617033601e-1, -.91494054040950941996e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
253 .70082459207876130806e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
254 .53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
255 .72456667788091316868e-1, -.15564535320096811360,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
256 .72456667788091316868e-1, .84048122493418898508e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
257 -.14340746778352039430, .53390713710144539104e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
258 .70082459207876130806e-1, -.91494054040950941996e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
259 .15760203882617033601e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
260 .16986031342807474208e-1, -.18994065631858742028e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
261 -.82901821370405592927e-3, .77239669773015192888e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
262 -.10850735431039424680, .47524484622086496464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
263 .69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
264 0.0, -.11992057742398672066, .14829314646228194928,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
265 -.69148184871588737021e-1, -.47524484622086496464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
266 .10850735431039424680, -.77239669773015192888e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
267 .82901821370405592927e-3, .18994065631858742028e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
268 .22761703826371535132e-1, -.17728848711449643358e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
269 -.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
270 .63073750910894244526e-1, .32928881123602721303e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
271 -.12280950532497593683, .15926189077282729505, -.12280950532497593683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
272 .32928881123602721303e-1, .63073750910894244526e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
273 -.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
274 -.17728848711449643358e-1, .22761703826371535132e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
275 -.26493215276042203434e-1, .35579780856128386192e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
276 .10447309718398935122e-1, -.68616154085314996709e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
277 .11775363082763954214, -.13918901977011837274, .12312819418827395690,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
278 -.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
279 -.12312819418827395690, .13918901977011837274, -.11775363082763954214,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
280 .68616154085314996709e-1, -.10447309718398935122e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
281 -.35579780856128386192e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
282 .26493215276042203434e-1, .40742523354399706918e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
283 -.73124912999529117195e-1, .49317266444153837821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
284 -.13686605413876015320e-1, -.28342624942191100464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
285 .70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
286 -.13817029659318161476, .12981016288391131812, -.10600251632853603875,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
287 .70371855298258216249e-1, -.28342624942191100464e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
288 -.13686605413876015320e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
289 .49317266444153837821e-1, -.73124912999529117195e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
290 .40742523354399706918e-1, -.54944368958699908688e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
291 .10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
292 -.77703071757424700773e-1, .61050911730999815031e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
293 -.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
294 -.21438229266251454773e-1, .42052599404498348871e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
295 -.61050911730999815031e-1, .77703071757424700773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
296 -.91369146312596428468e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
297 .10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
298 .27485608464748840573e-1, -.54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
299 .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
300 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
301 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
302 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
303 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
304 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
305 -.54971216929497681146e-1, .54971216929497681146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
306 -.54971216929497681146e-1, .27485608464748840573e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
307 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
308
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
309 static const double V4inv[33 * 33] = {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
310 .69120897476690862600e-3, .66419939766331555194e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
311 .13600665164323186111e-1, .20122785860913684493e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
312 .26583214101668429944e-1, .32712713318999268739e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
313 .38576221976287138036e-1, .44033030938268925133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
314 .49092709529622799673e-1, .53657949874312515646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
315 .57724533144734311859e-1, .61219564530655179096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
316 .64138907503837875026e-1, .66427905189318792009e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
317 .68088956652280022887e-1, .69083051391555695878e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
318 .69422738116739271449e-1, .69083051391555695878e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
319 .68088956652280022887e-1, .66427905189318792009e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
320 .64138907503837875026e-1, .61219564530655179096e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
321 .57724533144734311859e-1, .53657949874312515646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
322 .49092709529622799673e-1, .44033030938268925133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
323 .38576221976287138036e-1, .32712713318999268739e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
324 .26583214101668429944e-1, .20122785860913684493e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
325 .13600665164323186111e-1, .66419939766331555194e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
326 .69120897476690862600e-3, -.11972090629438798134e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
327 -.11448874821643225573e-1, -.23104401104002905904e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
328 -.33352899418646530133e-1, -.42538626424075425908e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
329 -.49969730733911825941e-1, -.55555454015360728353e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
330 -.58955533624852604918e-1, -.60126044219122513907e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
331 -.58959430451175833624e-1, -.55546925396227130606e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
332 -.49984739749347973762e-1, -.42513009141170294365e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
333 -.33399140950669746346e-1, -.23007690803851790829e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
334 -.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
335 .23007690803851790829e-1, .33399140950669746346e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
336 .42513009141170294365e-1, .49984739749347973762e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
337 .55546925396227130606e-1, .58959430451175833624e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
338 .60126044219122513907e-1, .58955533624852604918e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
339 .55555454015360728353e-1, .49969730733911825941e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
340 .42538626424075425908e-1, .33352899418646530133e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
341 .23104401104002905904e-1, .11448874821643225573e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
342 .11972090629438798134e-2, .15501585012936019146e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
343 .14628781502199620482e-1, .28684915921474815271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
344 .39299396074628048026e-1, .46393418975496284204e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
345 .48756902531094699526e-1, .46331333488337494692e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
346 .39012645376980228775e-1, .27452795421085791153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
347 .12430953621169863781e-1, -.47682978056024928800e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
348 -.22825828045428973853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
349 -.40195512090720278312e-1, -.55503004262826221955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
350 -.67424537752827046308e-1, -.75020199300113606452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
351 -.77607844312483656131e-1, -.75020199300113606452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
352 -.67424537752827046308e-1, -.55503004262826221955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
353 -.40195512090720278312e-1, -.22825828045428973853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
354 -.47682978056024928800e-2, .12430953621169863781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
355 .27452795421085791153e-1, .39012645376980228775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
356 .46331333488337494692e-1, .48756902531094699526e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
357 .46393418975496284204e-1, .39299396074628048026e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
358 .28684915921474815271e-1, .14628781502199620482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
359 .15501585012936019146e-2, -.18377757558949194214e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
360 -.17050470050949761565e-1, -.31952119564923250836e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
361 -.40197423449026348155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
362 -.41205649520281371624e-1, -.33909965817492272248e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
363 -.19393664422115332144e-1, .56661049630886784692e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
364 .22948272173686561721e-1, .44489719570904738207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
365 .61790363672287920596e-1, .72121014727028013894e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
366 .73627151185287858579e-1, .65784665375961398923e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
367 .49369676372333667559e-1, .26444326317059715065e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
368 -.26444326317059715065e-1, -.49369676372333667559e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
369 -.65784665375961398923e-1, -.73627151185287858579e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
370 -.72121014727028013894e-1, -.61790363672287920596e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
371 -.44489719570904738207e-1, -.22948272173686561721e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
372 -.56661049630886784692e-3, .19393664422115332144e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
373 .33909965817492272248e-1, .41205649520281371624e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
374 .40197423449026348155e-1, .31952119564923250836e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
375 .17050470050949761565e-1, .18377757558949194214e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
376 .20942714740729767769e-2, .18935902405146518232e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
377 .33335840852491735126e-1, .36770680999102286065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
378 .28873194534132768509e-1, .10267303017729535513e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
379 -.14607738306201572890e-1, -.40139568545572305818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
380 -.59808326733858291561e-1, -.68528358823372627506e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
381 -.63306535387619244879e-1, -.44508601817574921056e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
382 -.15449116105605395357e-1, .17941083795006546367e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
383 .48747356011657242123e-1, .70329553984201665523e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
384 .78106117292526169663e-1, .70329553984201665523e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
385 .48747356011657242123e-1, .17941083795006546367e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
386 -.15449116105605395357e-1, -.44508601817574921056e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
387 -.63306535387619244879e-1, -.68528358823372627506e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
388 -.59808326733858291561e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
389 -.40139568545572305818e-1, -.14607738306201572890e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
390 .10267303017729535513e-1, .28873194534132768509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
391 .36770680999102286065e-1, .33335840852491735126e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
392 .18935902405146518232e-1, .20942714740729767769e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
393 -.23245285491878278419e-2, -.20401404737639389919e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
394 -.33019548231022514097e-1, -.29709828426463720091e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
395 -.11760070922697422156e-1, .15987584743850393793e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
396 .43619012891472813485e-1, .61177322409671487721e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
397 .61144030218486655594e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
398 .41895377620089086167e-1, .80232011820644308033e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
399 -.30574701186675900915e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
400 -.62072243008844865848e-1, -.76336186183574765586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
401 -.68435466095345537115e-1, -.40237669208466966207e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
402 .40237669208466966207e-1, .68435466095345537115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
403 .76336186183574765586e-1, .62072243008844865848e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
404 .30574701186675900915e-1, -.80232011820644308033e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
405 -.41895377620089086167e-1, -.61144030218486655594e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
406 -.61177322409671487721e-1, -.43619012891472813485e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
407 -.15987584743850393793e-1, .11760070922697422156e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
408 .29709828426463720091e-1, .33019548231022514097e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
409 .20401404737639389919e-1, .23245285491878278419e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
410 .25451717261579269307e-2, .21480418595666878775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
411 .31177212469293007998e-1, .19816333607013379373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
412 -.72439496274458793681e-2, -.38404203906598342397e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
413 -.57633632255322221046e-1, -.54070547403585392952e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
414 -.26249823354368866005e-1, .15643058212336881516e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
415 .54539832735118677194e-1, .73283028002473989724e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
416 .62835303524135936213e-1, .26175977027801048141e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
417 -.22193636309998606610e-1, -.62597049956093311234e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
418 -.78206986173170212505e-1, -.62597049956093311234e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
419 -.22193636309998606610e-1, .26175977027801048141e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
420 .62835303524135936213e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
421 .73283028002473989724e-1, .54539832735118677194e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
422 .15643058212336881516e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
423 -.26249823354368866005e-1, -.54070547403585392952e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
424 -.57633632255322221046e-1, -.38404203906598342397e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
425 -.72439496274458793681e-2, .19816333607013379373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
426 .31177212469293007998e-1, .21480418595666878775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
427 .25451717261579269307e-2, -.27506573922483820005e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
428 -.22224442095099251870e-1, -.27949927254215773020e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
429 -.80918481053370034987e-2, .25121859354449306916e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
430 .51563535009373061074e-1, .51936965107145960512e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
431 .22146626648171527753e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
432 -.24172689882103382748e-1, -.61731229104853568296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
433 -.68477262429344201201e-1, -.38311232728303704742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
434 .14160578713659552679e-1, .61248813427564184033e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
435 .77136328841293031805e-1, .52514801765183697988e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
436 -.52514801765183697988e-1, -.77136328841293031805e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
437 -.61248813427564184033e-1, -.14160578713659552679e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
438 .38311232728303704742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
439 .68477262429344201201e-1, .61731229104853568296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
440 .24172689882103382748e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
441 -.22146626648171527753e-1, -.51936965107145960512e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
442 -.51563535009373061074e-1, -.25121859354449306916e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
443 .80918481053370034987e-2, .27949927254215773020e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
444 .22224442095099251870e-1, .27506573922483820005e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
445 .29562461131654311467e-2, .22630271480554450613e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
446 .23547399831373800971e-1, -.43964593440902476642e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
447 -.39055315767504970597e-1, -.52369643937940066804e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
448 -.28506131614971613422e-1, .19906048093338832322e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
449 .60408880866392420279e-1, .62493397473656883090e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
450 .21391278377641297859e-1, -.37302864786623254746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
451 -.73665127933539496872e-1, -.61706142476854010202e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
452 -.78065168882546327888e-2, .52335307373945544428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
453 .78278746279419264777e-1, .52335307373945544428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
454 -.78065168882546327888e-2, -.61706142476854010202e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
455 -.73665127933539496872e-1, -.37302864786623254746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
456 .21391278377641297859e-1, .62493397473656883090e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
457 .60408880866392420279e-1, .19906048093338832322e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
458 -.28506131614971613422e-1, -.52369643937940066804e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
459 -.39055315767504970597e-1, -.43964593440902476642e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
460 .23547399831373800971e-1, .22630271480554450613e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
461 .29562461131654311467e-2, -.31515718415504761303e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
462 -.22739451096655080673e-1, -.18157123602272119779e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
463 .16496480897167303621e-1, .46921166788569301124e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
464 .40644395739978416354e-1, -.46275803430732216900e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
465 -.52883375891308909486e-1, -.61116483226324111734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
466 -.17411698764545629853e-1, .44773430013166822765e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
467 .73441577962383869198e-1, .42127368371995472815e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
468 -.25504645957196772465e-1, -.74126818045972742488e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
469 -.62780077864719287317e-1, 0.0, .62780077864719287317e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
470 .74126818045972742488e-1, .25504645957196772465e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
471 -.42127368371995472815e-1, -.73441577962383869198e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
472 -.44773430013166822765e-1, .17411698764545629853e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
473 .61116483226324111734e-1, .52883375891308909486e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
474 .46275803430732216900e-2, -.40644395739978416354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
475 -.46921166788569301124e-1, -.16496480897167303621e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
476 .18157123602272119779e-1, .22739451096655080673e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
477 .31515718415504761303e-2, .33536559294882188208e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
478 .22535348942792006185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
479 .12048629300953560767e-1, -.27166076791299493403e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
480 -.47492745604230978367e-1, -.19246623430993153174e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
481 .36231297307556299322e-1, .61713617181636122004e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
482 .25928029734266134490e-1, -.40478700752883602818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
483 -.71053889866326412049e-1, -.31870824482961751482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
484 .41515251100219081281e-1, .76481960760098381651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
485 .36726509155999912440e-1, -.40090067032627055969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
486 -.78270742903374539397e-1, -.40090067032627055969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
487 .36726509155999912440e-1, .76481960760098381651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
488 .41515251100219081281e-1, -.31870824482961751482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
489 -.71053889866326412049e-1, -.40478700752883602818e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
490 .25928029734266134490e-1, .61713617181636122004e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
491 .36231297307556299322e-1, -.19246623430993153174e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
492 -.47492745604230978367e-1, -.27166076791299493403e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
493 .12048629300953560767e-1, .22535348942792006185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
494 .33536559294882188208e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
495 -.35481220456925318865e-2, -.22062913693073191150e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
496 -.54487362861834144999e-2, .35438821865804087489e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
497 .40733077820527411302e-1, -.67403098138950720914e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
498 -.55559584405239171054e-1, -.42417050790865158745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
499 .24499901971884704925e-1, .68721232891705409302e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
500 .34086082787461126592e-1, -.43441000373118474002e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
501 -.73878085292669148950e-1, -.18846995664706657127e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
502 .59827776178286834498e-1, .70644634584085901794e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
503 -.70644634584085901794e-1, -.59827776178286834498e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
504 .18846995664706657127e-1, .73878085292669148950e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
505 .43441000373118474002e-1, -.34086082787461126592e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
506 -.68721232891705409302e-1, -.24499901971884704925e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
507 .42417050790865158745e-1, .55559584405239171054e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
508 .67403098138950720914e-2, -.40733077820527411302e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
509 -.35438821865804087489e-1, .54487362861834144999e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
510 .22062913693073191150e-1, .35481220456925318865e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
511 .37554176816665075631e-2, .21297045781589919482e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
512 -.13327293083183431816e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
513 -.40635299172764596484e-1, -.27659860508374175359e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
514 .31089232744083445986e-1, .56113781541334176109e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
515 .37577840643257763400e-2, -.60511227350664590865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
516 -.46670556446129053853e-1, .33263195878575888247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
517 .72757324720645228775e-1, .15011712351692283635e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
518 -.65601212994924119078e-1, -.60016855838843789772e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
519 .26220858553188665966e-1, .78322776605833552980e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
520 .26220858553188665966e-1, -.60016855838843789772e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
521 -.65601212994924119078e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
522 .15011712351692283635e-1, .72757324720645228775e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
523 .33263195878575888247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
524 -.46670556446129053853e-1, -.60511227350664590865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
525 .37577840643257763400e-2, .56113781541334176109e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
526 .31089232744083445986e-1, -.27659860508374175359e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
527 -.40635299172764596484e-1, -.13327293083183431816e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
528 .21297045781589919482e-1, .37554176816665075631e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
529 -.39566995305720591229e-2, -.20291873414438919995e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
530 .80617453830770930551e-2, .42270189157016547906e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
531 .10332624526759093004e-1, -.48054759547616142024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
532 -.37678032941171643972e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
533 .36617192625732482394e-1, .61009425973424865714e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
534 -.95589113168026591466e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
535 -.71023202645076922361e-1, -.25097788086808784456e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
536 .62406621963267050244e-1, .56907293171100693511e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
537 -.36435383083882206257e-1, -.75790105119208756348e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
538 .75790105119208756348e-1, .36435383083882206257e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
539 -.56907293171100693511e-1, -.62406621963267050244e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
540 .25097788086808784456e-1, .71023202645076922361e-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 -.61009425973424865714e-1, -.36617192625732482394e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
543 .37678032941171643972e-1, .48054759547616142024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
544 -.10332624526759093004e-1, -.42270189157016547906e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
545 -.80617453830770930551e-2, .20291873414438919995e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
546 .39566995305720591229e-2, .41776092289182138591e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
547 .19013221163904414395e-1, -.14420609729849899876e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
548 -.40259160586844441220e-1, .86327811113710831649e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
549 .53564430703021034399e-1, .65469185402150431933e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
550 -.60383116311280629856e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
551 -.25657793784058876939e-1, .58745680576829226900e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
552 .45649937869034420296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
553 -.49167932056844167772e-1, -.62696614328552187977e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
554 .32540234556426699997e-1, .74280410383464269758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
555 -.11425672633410999870e-1, -.78280649404686404903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
556 -.11425672633410999870e-1, .74280410383464269758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
557 .32540234556426699997e-1, -.62696614328552187977e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
558 -.49167932056844167772e-1, .45649937869034420296e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
559 .58745680576829226900e-1, -.25657793784058876939e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
560 -.60383116311280629856e-1, .65469185402150431933e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
561 .53564430703021034399e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
562 .86327811113710831649e-2, -.40259160586844441220e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
563 -.14420609729849899876e-1, .19013221163904414395e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
564 .41776092289182138591e-2, -.43935502082478059199e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
565 -.17528761237509401631e-1, .20208915249153872535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
566 .34734743119040669109e-1, -.26275910172353637955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
567 -.46368003346018878786e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
568 .26800056330709381025e-1, .56681476464606609921e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
569 -.24749011438127255898e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
570 -.64934612189056658992e-1, .20333742247679279535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
571 .71429299070059318651e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
572 -.14452513210428671266e-1, -.75793341281736586582e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
573 .74717094137184935270e-2, .78034921554757317374e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
574 -.78034921554757317374e-1, -.74717094137184935270e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
575 .75793341281736586582e-1, .14452513210428671266e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
576 -.71429299070059318651e-1, -.20333742247679279535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
577 .64934612189056658992e-1, .24749011438127255898e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
578 -.56681476464606609921e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
579 -.26800056330709381025e-1, .46368003346018878786e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
580 .26275910172353637955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
581 -.34734743119040669109e-1, -.20208915249153872535e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
582 .17528761237509401631e-1, .43935502082478059199e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
583 .46379089482818671473e-2, .15791188144791287229e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
584 -.25134290048737455284e-1, -.26249795071946841205e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
585 .39960457575789924651e-1, .28111892450146525404e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
586 -.51026476400767918226e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
587 -.27266747278681831364e-1, .60708796647861610865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
588 .23532306960642115854e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
589 -.68169639871532441111e-1, -.18204924701958312032e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
590 .73822890510656128485e-1, .11373392486424717019e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
591 -.77133324017644609416e-1, -.39295877480342619961e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
592 .78351902829418987960e-1, -.39295877480342619961e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
593 -.77133324017644609416e-1, .11373392486424717019e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
594 .73822890510656128485e-1, -.18204924701958312032e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
595 -.68169639871532441111e-1, .23532306960642115854e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
596 .60708796647861610865e-1, -.27266747278681831364e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
597 -.51026476400767918226e-1, .28111892450146525404e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
598 .39960457575789924651e-1, -.26249795071946841205e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
599 -.25134290048737455284e-1, .15791188144791287229e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
600 .46379089482818671473e-2, -.48780095920069827068e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
601 -.13886961667516983541e-1, .29071311049368895844e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
602 .15480559452075811600e-1, -.47527977686242313065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
603 -.31929089844361042178e-2, .58015667638415922967e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
604 -.14547915466597622925e-1, -.61067668299848923244e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
605 .35093678009090186851e-1, .55378399159800654657e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
606 -.54277226474891610385e-1, -.42023830782434076509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
607 .69197384645944912066e-1, .22610783557709586445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
608 -.77269275900637030185e-1, 0.0, .77269275900637030185e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
609 -.22610783557709586445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
610 -.69197384645944912066e-1, .42023830782434076509e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
611 .54277226474891610385e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
612 -.55378399159800654657e-1, -.35093678009090186851e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
613 .61067668299848923244e-1, .14547915466597622925e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
614 -.58015667638415922967e-1, .31929089844361042178e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
615 .47527977686242313065e-1, -.15480559452075811600e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
616 -.29071311049368895844e-1, .13886961667516983541e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
617 .48780095920069827068e-2, .51591759101720291381e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
618 .11747497650231330965e-1, -.31777863364694653331e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
619 -.34555825499804605557e-2, .47914131921157015198e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
620 -.22573685920142225247e-1, -.45320344390022666738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
621 .49660630547172186418e-1, .25707858143963615736e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
622 -.68132707341917233933e-1, .67534860185243140399e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
623 .69268150370037450063e-1, -.41585011920451477177e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
624 -.51622397460510041271e-1, .68408139576363036148e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
625 .18981259024768933323e-1, -.78265472429342305554e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
626 .18981259024768933323e-1, .68408139576363036148e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
627 -.51622397460510041271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
628 -.41585011920451477177e-1, .69268150370037450063e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
629 .67534860185243140399e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
630 -.68132707341917233933e-1, .25707858143963615736e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
631 .49660630547172186418e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
632 -.45320344390022666738e-1, -.22573685920142225247e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
633 .47914131921157015198e-1, -.34555825499804605557e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
634 -.31777863364694653331e-1, .11747497650231330965e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
635 .51591759101720291381e-2, -.54365757412741340377e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
636 -.94862516619529080191e-2, .33240472093448190877e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
637 -.88698898099681552229e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
638 -.40973252097216337576e-1, .42995673349795657065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
639 .17320914507876958783e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
640 -.62201292691914856803e-1, .24726274174637346693e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
641 .51320859246515407288e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
642 -.62882063373810501763e-1, -.11003569131725622672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
643 .73842261324108943465e-1, -.39240120294802923208e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
644 -.49293966443941122807e-1, .73552644778818223475e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
645 -.73552644778818223475e-1, .49293966443941122807e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
646 .39240120294802923208e-1, -.73842261324108943465e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
647 .11003569131725622672e-1, .62882063373810501763e-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 -.24726274174637346693e-1, .62201292691914856803e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
650 -.17320914507876958783e-1, -.42995673349795657065e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
651 .40973252097216337576e-1, .88698898099681552229e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
652 -.33240472093448190877e-1, .94862516619529080191e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
653 .54365757412741340377e-2, .57750194549356126240e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
654 .69981166020044116791e-2, -.33274982140403110792e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
655 .20297071020698356116e-1, .27898517839646066582e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
656 -.53368678853282030262e-1, .16656482990394548343e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
657 .46342901447260614255e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
658 -.60536796508149003365e-1, .29109107483842596340e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
659 .63224486124385124504e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
660 -.59028872851312033411e-1, -.14783105962696191734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
661 .74269399241069253865e-1, -.49053677339382384625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
662 -.33525466624811186739e-1, .78397349622515386647e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
663 -.33525466624811186739e-1, -.49053677339382384625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
664 .74269399241069253865e-1, -.14783105962696191734e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
665 -.59028872851312033411e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
666 .63224486124385124504e-1, .29109107483842596340e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
667 -.60536796508149003365e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
668 .46342901447260614255e-1, .16656482990394548343e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
669 -.53368678853282030262e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
670 .27898517839646066582e-1, .20297071020698356116e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
671 -.33274982140403110792e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
672 .69981166020044116791e-2, .57750194549356126240e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
673 -.61100308370519200637e-2, -.44383614355738148616e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
674 .32011283412619094811e-1, -.29965011866372897633e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
675 -.10560682331349193348e-1, .51110336443392506342e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
676 -.45012284729681775492e-1, -.94236825555873320102e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
677 .60860695783141264746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
678 -.55014628647083368926e-1, -.73474782382499482121e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
679 .66640148475243034781e-1, -.62533116045749887988e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
680 -.38650525912400102585e-2, .68429769005837003777e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
681 -.66984505412544901945e-1, 0.0, .66984505412544901945e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
682 -.68429769005837003777e-1, .38650525912400102585e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
683 .62533116045749887988e-1, -.66640148475243034781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
684 .73474782382499482121e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
685 .55014628647083368926e-1, -.60860695783141264746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
686 .94236825555873320102e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
687 .45012284729681775492e-1, -.51110336443392506342e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
688 .10560682331349193348e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
689 .29965011866372897633e-1, -.32011283412619094811e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
690 .44383614355738148616e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
691 .61100308370519200637e-2, .65409373892036191538e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
692 .16350101107071157065e-2, -.29301957285983144319e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
693 .36838667173388832579e-1, -.81922703976491586393e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
694 -.36955670021050133434e-1, .58374851095540469865e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
695 -.31977016246946181856e-1, -.25311073698658094646e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
696 .66674413950106952577e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
697 -.54865713324521039571e-1, -.39797027891537985440e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
698 .62830285264808449064e-1, -.72226313251296100676e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
699 .22560232697133353980e-1, .46455784709904033738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
700 -.78200930751070349956e-1, .46455784709904033738e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
701 .22560232697133353980e-1, -.72226313251296100676e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
702 .62830285264808449064e-1, -.39797027891537985440e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
703 -.54865713324521039571e-1, .66674413950106952577e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
704 -.25311073698658094646e-1, -.31977016246946181856e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
705 .58374851095540469865e-1, -.36955670021050133434e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
706 -.81922703976491586393e-2, .36838667173388832579e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
707 -.29301957285983144319e-1, .16350101107071157065e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
708 .65409373892036191538e-2, -.69686180931868703196e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
709 .11849538727632789870e-2, .25452286414610537766e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
710 -.40522480651713943230e-1, .25694679053362813183e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
711 .14057118113748390637e-1, -.52037614725803488893e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
712 .58849342223684035589e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
713 -.25075229077361409271e-1, -.29559771094034181083e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
714 .68296746944165720199e-1, -.62890462146423984955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
715 .14457636466274596445e-1, .45787612031322361496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
716 -.77231759014655809742e-1, .57881203613910543657e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
717 -.57881203613910543657e-1, .77231759014655809742e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
718 -.45787612031322361496e-1, -.14457636466274596445e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
719 .62890462146423984955e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
720 -.68296746944165720199e-1, .29559771094034181083e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
721 .25075229077361409271e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
722 -.58849342223684035589e-1, .52037614725803488893e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
723 -.14057118113748390637e-1, -.25694679053362813183e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
724 .40522480651713943230e-1, -.25452286414610537766e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
725 -.11849538727632789870e-2, .69686180931868703196e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
726 .75611653617520254845e-2, -.43290610418608409141e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
727 -.20277062025115566914e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
728 .40362947027704828926e-1, -.38938808024132120254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
729 .11831186195916702262e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
730 .28476667401744525357e-1, -.59320969056617684621e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
731 .61101629747436200186e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
732 -.29514834848355389223e-1, -.20668001885001084821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
733 .62923592802445122793e-1, -.73558456263588833115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
734 .45314556330160999776e-1, .79031645918426015574e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
735 -.58136953576334689357e-1, .78538474524006405758e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
736 -.58136953576334689357e-1, .79031645918426015574e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
737 .45314556330160999776e-1, -.73558456263588833115e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
738 .62923592802445122793e-1, -.20668001885001084821e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
739 -.29514834848355389223e-1, .61101629747436200186e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
740 -.59320969056617684621e-1, .28476667401744525357e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
741 .11831186195916702262e-1, -.38938808024132120254e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
742 .40362947027704828926e-1, -.20277062025115566914e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
743 -.43290610418608409141e-2, .75611653617520254845e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
744 -.81505692478987769484e-2, .74297333588288568430e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
745 .14314212513540223314e-1, -.36711242251332751607e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
746 .46240027755503814626e-1, -.34921532671769023773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
747 .46930051972353714773e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
748 .32842770336385381562e-1, -.61317813706529588466e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
749 .67000809902468893103e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
750 -.45337449655535622885e-1, .35794459576271920867e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
751 .41830061526027213385e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
752 -.72091371931944711708e-1, .74150028530317793195e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
753 -.46487632538609942002e-1, 0.0, .46487632538609942002e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
754 -.74150028530317793195e-1, .72091371931944711708e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
755 -.41830061526027213385e-1, -.35794459576271920867e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
756 .45337449655535622885e-1, -.67000809902468893103e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
757 .61317813706529588466e-1, -.32842770336385381562e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
758 -.46930051972353714773e-2, .34921532671769023773e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
759 -.46240027755503814626e-1, .36711242251332751607e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
760 -.14314212513540223314e-1, -.74297333588288568430e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
761 .81505692478987769484e-2, .90693182942442189743e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
762 -.11121000903959576737e-1, -.71308296141317458546e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
763 .29219439765986671645e-1, -.45820286629778129593e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
764 .49088381175879124421e-1, -.35614888785023038938e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
765 .78906970900092777895e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
766 .26262843038404929480e-1, -.56143674270125757857e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
767 .71700220472378350694e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
768 -.66963544500697307945e-1, .42215091779892228883e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
769 -.41338867413966866997e-2, -.36164891772995367321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
770 .66584367783847858225e-1, -.77874712365070098328e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
771 .66584367783847858225e-1, -.36164891772995367321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
772 -.41338867413966866997e-2, .42215091779892228883e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
773 -.66963544500697307945e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
774 .71700220472378350694e-1, -.56143674270125757857e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
775 .26262843038404929480e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
776 .78906970900092777895e-2, -.35614888785023038938e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
777 .49088381175879124421e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
778 -.45820286629778129593e-1, .29219439765986671645e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
779 -.71308296141317458546e-2, -.11121000903959576737e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
780 .90693182942442189743e-2, -.99848472706332791043e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
781 .14701271465939718856e-1, -.32917820356048383366e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
782 -.19201195309873585230e-1, .38409681836626963278e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
783 -.51647324405878909521e-1, .54522171113149311354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
784 -.45040302741689006270e-1, .24183738595685990149e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
785 .42204134165479735097e-2, -.34317295181348742251e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
786 .59542472465494579941e-1, -.74135115907618101263e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
787 .74491937840566532596e-1, -.60042604725161994304e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
788 .33437677409000083169e-1, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
789 -.33437677409000083169e-1, .60042604725161994304e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
790 -.74491937840566532596e-1, .74135115907618101263e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
791 -.59542472465494579941e-1, .34317295181348742251e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
792 -.42204134165479735097e-2, -.24183738595685990149e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
793 .45040302741689006270e-1, -.54522171113149311354e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
794 .51647324405878909521e-1, -.38409681836626963278e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
795 .19201195309873585230e-1, .32917820356048383366e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
796 -.14701271465939718856e-1, .99848472706332791043e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
797 .11775579274769383373e-1, -.19892153937316935880e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
798 .95335114477449041055e-2, .57661528440359081617e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
799 -.23382690532380910781e-1, .40237257037170725321e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
800 -.53280289903551636474e-1, .59974361806023689068e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
801 -.58701684061992853224e-1, .49033407111597129616e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
802 -.31818835267847249219e-1, .90800541261162098886e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
803 .16272906819312603838e-1, -.40863896581186229487e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
804 .61346046297517367703e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
805 -.74896047554167268919e-1, .79632642148310325817e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
806 -.74896047554167268919e-1, .61346046297517367703e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
807 -.40863896581186229487e-1, .16272906819312603838e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
808 .90800541261162098886e-2, -.31818835267847249219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
809 .49033407111597129616e-1, -.58701684061992853224e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
810 .59974361806023689068e-1, -.53280289903551636474e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
811 .40237257037170725321e-1, -.23382690532380910781e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
812 .57661528440359081617e-2, .95335114477449041055e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
813 -.19892153937316935880e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
814 .11775579274769383373e-1, -.13562702617218467450e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
815 .24885419969649845849e-1, -.18368693901908875583e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
816 .81673147806084084638e-2, .47890591326129587131e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
817 -.19313752945227974024e-1, .34065953398362954708e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
818 -.47667045133463415672e-1, .58820377816690514309e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
819 -.66424139824618415970e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
820 .69667606260856092515e-1, -.68102459384364543253e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
821 .61683024923302547971e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
822 -.50771943476441639136e-1, .36110771847327189215e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
823 -.18758028464284563358e-1, 0.0, .18758028464284563358e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
824 -.36110771847327189215e-1, .50771943476441639136e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
825 -.61683024923302547971e-1, .68102459384364543253e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
826 -.69667606260856092515e-1, .66424139824618415970e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
827 -.58820377816690514309e-1, .47667045133463415672e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
828 -.34065953398362954708e-1, .19313752945227974024e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
829 -.47890591326129587131e-2, -.81673147806084084638e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
830 .18368693901908875583e-1, -.24885419969649845849e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
831 .13562702617218467450e-1, .20576545037980523979e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
832 -.40093155172981004337e-1, .36954083167944054826e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
833 -.31856506837591907746e-1, .24996323181546255126e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
834 -.16637165210473614136e-1, .71002706773325085237e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
835 .32478629093205201133e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
836 -.14009562579050569518e-1, .24771262248780618922e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
837 -.35119395835433647559e-1, .44656290368574753171e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
838 -.53015448339647394161e-1, .59875631995693046782e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
839 -.64973208326045193862e-1, .68112280331082143373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
840 -.69172215234062186994e-1, .68112280331082143373e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
841 -.64973208326045193862e-1, .59875631995693046782e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
842 -.53015448339647394161e-1, .44656290368574753171e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
843 -.35119395835433647559e-1, .24771262248780618922e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
844 -.14009562579050569518e-1, .32478629093205201133e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
845 .71002706773325085237e-2, -.16637165210473614136e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
846 .24996323181546255126e-1, -.31856506837591907746e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
847 .36954083167944054826e-1, -.40093155172981004337e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
848 .20576545037980523979e-1, -.27584914609096156163e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
849 .54904171411058497973e-1, -.54109756419563083153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
850 .52794234894345577483e-1, -.50970276026831042415e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
851 .48655445537990983379e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
852 -.45872036510847994332e-1, .42646854695899611372e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
853 -.39010960357087507670e-1, .34999369144476467749e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
854 -.30650714874402762189e-1, .26006877464703437057e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
855 -.21112579608213651273e-1, .16014956068786763273e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
856 -.10763099747751940252e-1, .54075888924374485533e-2, 0.0,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
857 -.54075888924374485533e-2, .10763099747751940252e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
858 -.16014956068786763273e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
859 .21112579608213651273e-1, -.26006877464703437057e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
860 .30650714874402762189e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
861 -.34999369144476467749e-1, .39010960357087507670e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
862 -.42646854695899611372e-1, .45872036510847994332e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
863 -.48655445537990983379e-1, .50970276026831042415e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
864 -.52794234894345577483e-1, .54109756419563083153e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
865 -.54904171411058497973e-1, .27584914609096156163e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
866 .13794141262469565740e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
867 .27588282524939131481e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
868 .27588282524939131481e-1, -.27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
869 .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
870 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
871 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
872 -.27588282524939131481e-1, .27588282524939131481e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
873 -.27588282524939131481e-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, .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, .13794141262469565740e-1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
883 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
884
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
885 static const double Tleft[33 * 33] = {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
886 1., -.86602540378443864678, 0., .33071891388307382381, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
887 -.20728904939721249057, 0., .15128841196122722208, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
888 -.11918864298744029244, 0., .98352013661686631224e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
889 -.83727065404940845733e-1, 0., .72893399403505841203e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
890 -.64544632643375022436e-1, 0., .57913170372415565639e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
891 -.52518242575729562263e-1, 0., .48043311993977520457e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
892 -.44271433659733990243e-1, 0., .41048928022856771981e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
893 -.38263878662008271459e-1, 0., .35832844026365304501e-1, 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
894 .50000000000000000000, -.96824583655185422130, .57282196186948000082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
895 .21650635094610966169, -.35903516540862679125, -.97578093724974971969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
896 .26203921611325660506, .55792409597991015609e-1, -.20644078533943456204,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
897 -.36172381205961199479e-1, .17035068468874958194,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
898 .25371838001497225980e-1, -.14501953125000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
899 -.18786835250972344757e-1, .12625507130328301066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
900 .14473795929590520582e-1, -.11179458309419422675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
901 -.11494434254897626155e-1, .10030855351241635862,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
902 .93498556820544479096e-2, -.90964264465390582629e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
903 -.77546391824364392762e-2, .83213457337452292745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
904 .65358085945588638605e-2, -.76680372422574234569e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
905 -.55835321940047427169e-2, .71098828931825789428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
906 .48253327982967591019e-2, -.66274981937248958553e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
907 -.42118078245337801387e-2, .62064306433355646267e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
908 .37083386598903548973e-2, 0., 0., .25000000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
909 -.73950997288745200531, .83852549156242113615, -.23175620272173946716,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
910 -.37791833195149451496, .25710129174850522325, .21608307321780204633,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
911 -.22844049245646009157, -.14009503000335388415, .19897685605518413847,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
912 .98264706042471226893e-1, -.17445445004279014046,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
913 -.72761100054958328401e-1, .15463589893742108388,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
914 .56056770591708784481e-1, -.13855313872640495158,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
915 -.44517752443294564781e-1, .12534277657695128850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
916 .36211835346039665762e-1, -.11434398255136139683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
917 -.30033588409423828125e-1, .10506705408753910481,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
918 .25313077840725783008e-1, -.97149327637744872155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
919 -.21624927200393328444e-1, .90319582367202122625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
920 .18688433567711780666e-1, -.84372291635345108584e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
921 -.16312261561845420752e-1, .79149526894804751586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
922 .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
923 -.49607837082461073572, .82265291131801144317, -.59621200088559103072,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
924 -.80054302859059362371e-1, .42612156697795759420,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
925 -.90098145270865592887e-1, -.29769623255090078484, .13630307904779758221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
926 .21638835185708931831, -.14600247270306082052, -.16348801804014290453,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
927 .14340708728599057249, .12755243353979286190, -.13661523715071346961,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
928 -.10215585947881057394, .12864248070157166547, .83592528025348693602e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
929 -.12066728689302565222, -.69633728678718053052e-1, .11314245177331919532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
930 .58882939251410088028e-1, -.10621835858758221487,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
931 -.50432266865187597572e-1, .99916834723527771581e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
932 .43672094283057258509e-1, -.94206380251950852413e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
933 -.38181356812697746418e-1, .89035739656537771225e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
934 .33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
935 -.31093357409581873586, .67604086414949799246, -.75644205980613611039,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
936 .28990586430124175741, .30648508196770360914, -.35801372616842500052,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
937 -.91326869828709014708e-1, .31127929687500000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
938 -.90915752838698393094e-2, -.25637381283965534330,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
939 .57601077850322797594e-1, .21019685709225757945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
940 -.81244992138514014256e-1, -.17375078516720988858,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
941 .92289437277967051125e-1, .14527351914265391374,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
942 -.96675340792832019889e-1, -.12289485697108543415,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
943 .97448175340011084006e-1, .10511755943298339844,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
944 -.96242247086378239657e-1, -.90822942272780513537e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
945 .93966350452322132384e-1, .79189411876493712558e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
946 -.91139307067989309325e-1, -.69613039934383197265e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
947 .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
948 .31250000000000000000e-1, -.18684782411095934408, .50176689760410660236,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
949 -.74784031498626095398, .56472001151566251186, .14842464993721351203e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
950 -.41162920273003120936, .20243071230196532282, .23772054897172750436,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
951 -.24963810923972235950, -.12116179938394678936, .24330535483519110663,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
952 .47903849781124471359e-1, -.22133299683101224293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
953 -.20542915138527200983e-2, .19653465717678146728,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
954 -.26818172626509178444e-1, -.17319122357631210944,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
955 .45065391411065545445e-1, .15253391395444065941,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
956 -.56543897711725408302e-1, -.13469154928743585367,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
957 .63632471400208840155e-1, .11941684923913523817,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
958 -.67828850207933293098e-1, -.10636309084510652670,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
959 .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
960 0., .15625000000000000000e-1, -.10909562534194485289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
961 .34842348626527747318, -.64461114561628111443, .69382480527334683659,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
962 -.29551102358528827763, -.25527584713978439819, .38878771718544715394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
963 -.82956185835347407489e-2, -.31183177761966943912, .12831420840372374767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
964 .22067618205599434368, -.17569196937129496961, -.14598057000132284135,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
965 .18864406621763419484, .89921002550386645767e-1, -.18571835020187122114,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
966 -.48967672227195481777e-1, .17584685670380332798,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
967 .19267984545067426324e-1, -.16335437520503462738,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
968 .22598055455032407594e-2, .15032800884170631129,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
969 -.17883358353754640871e-1, -.13774837869432209951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
970 .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
971 0., .78125000000000000000e-2, -.62377810244809812496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
972 .23080781467370883845, -.50841310636012325368, .69834547012574056043,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
973 -.52572723156526459672, .11464215704954976471e-1, .38698869011491210342,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
974 -.26125646622255207507, -.16951698812361607510, .29773875898928782269,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
975 .20130501202570367491e-1, -.26332493149159310198,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
976 .67734613690401207009e-1, .21207315477103762715, -.11541543390889415193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
977 -.16249634759782417533, .13885887405041735068, .11996491328010275427,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
978 -.14810432001630926895, -.85177658352556243411e-1, .14918860659904380587,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
979 .57317789510444151564e-1, -.14569827645586660151,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
980 -.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
981 0., 0., .39062500000000000000e-2, -.35101954600803571207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
982 .14761284084133737720, -.37655033076080192966, .62410290231517322776,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
983 -.64335622317683389875, .28188168266139524244, .22488495672137010675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
984 -.39393811089283576186, .75184777995770096714e-1, .28472023119398293003,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
985 -.20410910833705899572, -.15590046962908511750, .23814567544617953125,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
986 .54442805556829031204e-1, -.22855930338589720954,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
987 .16303223615756629897e-1, .20172722433875559213,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
988 -.62723406421217419404e-1, -.17012230831020922010,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
989 .91754642766136561612e-1, .13927644821381121197, -.10886600968068418181,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
990 -.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
991 0., 0., .19531250000000000000e-2, -.19506820659607596598e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
992 .91865676095362231937e-1, -.26604607809696493849, .51425874205091288223,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
993 -.66047561132505329292, .48660109511591303851, -.17575661168678285615e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
994 -.36594333408055703366, .29088854695378694533, .11318677346656537927,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
995 -.31110645235730182168, .60733219161008787341e-1, .24333848233620420826,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
996 -.15254312332655419708, -.15995968483455388613, .19010344455215289289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
997 .86040636766440260000e-1, -.19652589954665259945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
998 -.27633388517205837713e-1, .18660848552712880387,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
999 -.15942583868416775867e-1, -.16902042462382064786,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1000 .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
1001 .97656250000000000000e-3, -.10731084460857378207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1002 .55939644713816406331e-1, -.18118487371914493668, .39914857299829864263,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1003 -.60812322949933902435, .60011887183061967583, -.26002695805835928795,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1004 -.20883922404786010096, .38988130966114638081, -.11797833550782589082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1005 -.25231824756239520077, .24817859972953934712, .90516417677868996417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1006 -.26079073291293066798, .30259468817169480161e-1, .22178195264114178432,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1007 -.10569877864302048175, -.16679648389266977455, .14637718550245050850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1008 .11219272032739559870, -.16359363640525750353, -.64358194509092101393e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1009 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
1010 -.58542865274813470967e-2, .33461741635290096452e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1011 -.11979993155896201271, .29580223766987206958, -.51874761979436016742,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1012 .62861483498014306968, -.44868895761051453296, .12567502628371529386e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1013 .35040366183235474275, -.30466868455569500886, -.70903913601490112666e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1014 .30822791893032512740, -.11969443264190207736, -.20764760317621313946,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1015 .20629838355452128532, .95269702915334718507e-1, -.22432624768705133300,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1016 -.33103381593477797101e-2, .20570036048155716333,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1017 -.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
1018 0., 0., 0., 0., 0., 0., .24414062500000000000e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1019 -.31714797501871532475e-2, .19721062526127334100e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1020 -.77311181185536498246e-1, .21124871792841566575, -.41777980401893650886,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1021 .59401977834943551650, -.56132417807488349048, .23433675061367565951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1022 .20222775295220942126, -.38280372496506190127, .14443804214023095767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1023 .22268950939178466797, -.27211314150777981984, -.34184876506180717313e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1024 .26006498895669734842, -.97650425186005090107e-1, -.19024527660129101293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1025 .16789164198044635671, .10875811641651905252, -.19276785058805921298, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1026 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
1027 -.17078941137247586143e-2, .11477733754843910060e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1028 -.48887017020924625462e-1, .14634927241421789683, -.32156282683019547854,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1029 .52165811920227223937, -.60001958466396926460, .41208501541480733755,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1030 -.11366945503190350975e-2, -.33968093962672089159, .30955190935923386766,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1031 .40657421856578262210e-1, -.29873400409871531764, .16094481791768257440,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1032 .16876122436206497694, -.23650217045022161255, -.33070260090574765012e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1033 .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
1034 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
1035 -.91501857608428649078e-3, .66085179496951987952e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1036 -.30383171695850355404e-1, .98840838845366876117e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1037 -.23855447246420318989, .43322017468145613917, -.58049033744876107191,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1038 .52533893203742699346, -.20681056202371946180, -.20180000924562504384,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1039 .37503922291962681797, -.15988102869837429062, -.19823558102762374094,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1040 .28393023878803799622, -.11188133439357510403e-1, -.24730368377168229255,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1041 .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
1042 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
1043 -.48804277318479845551e-3, .37696080990601968396e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1044 -.18603912108994738255e-1, .65325006755649582964e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1045 -.17162960707938819795, .34411527956476971322, -.52289350347082497959,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1046 .57319653625674910592, -.37662253421045430413, -.14099055105384663902e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1047 .33265570610216904208, -.30921265572647566661, -.19911390594166455281e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1048 .28738590811031797718, -.18912130469738472647, -.13235936203215819193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1049 .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
1050 0., 0., 0., .15258789062500000000e-4, -.25928719280954633249e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1051 .21327398937568540428e-2, -.11244626133630732010e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1052 .42375605740664331966e-1, -.12031130345907846211, .26352562258934426830,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1053 -.44590628258512682078, .56682835613700749379, -.49116715128261660395,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1054 .17845943097110339078, .20541650677432497477, -.36739803642257458221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1055 .16776034069210108273, .17920950989905112908, -.28867732805385066532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1056 .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
1057 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
1058 .11979683091449349286e-2, -.67195313034570709806e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1059 .27044920779931968175e-1, -.82472196498517457862e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1060 .19570475044896150093, -.36391620788543817693, .52241392782736588032,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1061 -.54727504974907879912, .34211551468813581183, .31580472732719957762e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1062 -.32830006549176759667, .30563797665254420769, .64905014620683140120e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1063 -.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
1064 0., 0., 0., 0., 0., 0., .38146972656250000000e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1065 -.72454147007837596854e-4, .66859847582761390285e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1066 -.39751311980366118437e-2, .17015198650201528366e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1067 -.55443621868993855715e-1, .14157060481641692131, -.28641242619559616836,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1068 .45610665490966615415, -.55262786406029265394, .45818352706035500108,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1069 -.14984403004611673047, -.21163807462970713245, .36007252928843413718,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1070 -.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
1071 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
1072 -.38135049864067468562e-4, .37101393638555730015e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1073 -.23305339886279723213e-2, .10569913448297127219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1074 -.36640175162216897547e-1, .10010476414320235508, -.21860074212675559892,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1075 .38124757096345313719, -.52020999209879669177, .52172632730659212045,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1076 -.30841620620308814614, -.50322546186721500184e-1, .32577618885114899053,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1077 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
1078 0., 0., .95367431640625000000e-6, -.20021483206955925244e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1079 .20481807322420625431e-3, -.13553476938058909882e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1080 .64919676350791905019e-2, -.23848725425069251903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1081 .69384632678886421292e-1, -.16249711393618776934, .30736618106830314788,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1082 -.46399909601971539157, .53765031034002467225, -.42598991476520183929,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1083 .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
1084 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
1085 -.10487707828484902486e-4, .11254146162337528943e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1086 -.78248929534271987118e-3, .39468337145306794566e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1087 -.15313546659475671763e-1, .47249070825218564146e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1088 -.11804374107101480543, .24031796927792491122, -.39629215049166341285,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1089 .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
1090 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
1091 .23841857910156250000e-6, -.54823314130625337326e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1092 .61575377321535518154e-4, -.44877834366497538134e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1093 .23774612048621955857e-2, -.97136347645161687796e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1094 .31671599547606636717e-1, -.84028665767000747480e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1095 .18298487576742964949, -.32647878537696945218, .46970971486488895077, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1096 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1097 0., 0., 0., 0., .11920928955078125000e-6, -.28604020001177375838e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1098 .33559227978295551013e-4, -.25583821662860610560e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1099 .14201552747787302339e-2, -.60938046986874414969e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1100 .20930869247951926793e-1, -.58745021125678072911e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1101 .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
1102 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
1103 .59604644775390625000e-7, -.14898180663526043291e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1104 .18224991282807693921e-4, -.14504433444608833821e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1105 .84184722720281809548e-3, -.37846965430000478789e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1106 .13656355548211376864e-1, -.40409541997718853934e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1107 .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
1108 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
1109 .29802322387695312500e-7, -.77471708843445529468e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1110 .98649879372606876995e-5, -.81814934772838523887e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1111 .49554483992403011328e-3, -.23290922072351413938e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1112 .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
1113 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
1114 0., 0., 0., .14901161193847656250e-7, -.40226235946098233685e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1115 .53236418690561306700e-5, -.45933829691164002269e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1116 .28982005232838857913e-3, -.14212974043211018374e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1117 .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
1118 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
1119 .74505805969238281250e-8, -.20858299254133430408e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1120 .28648457300134381744e-5, -.25677535898258910850e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1121 .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
1122 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
1123 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
1124 .15376606719887104015e-5, -.14296523739727437959e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1125 .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
1126 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
1127 .18626451492309570312e-8, -.55871592916438890146e-7,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1128 .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
1129 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
1130 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
1131 -.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
1132 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1133 0., 0., 0., 0., 0., 0., 0., 0., .46566128730773925781e-9,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1134 -.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
1135 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
1136 0., 0., .23283064365386962891e-9
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1137 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1138
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1139 static const double Tright[33 * 33] = {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1140 1., .86602540378443864678, 0., -.33071891388307382381, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1141 .20728904939721249057, 0., -.15128841196122722208, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1142 .11918864298744029244, 0., -.98352013661686631224e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1143 .83727065404940845733e-1, 0., -.72893399403505841203e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1144 .64544632643375022436e-1, 0., -.57913170372415565639e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1145 .52518242575729562263e-1, 0., -.48043311993977520457e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1146 .44271433659733990243e-1, 0., -.41048928022856771981e-1, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1147 .38263878662008271459e-1, 0., -.35832844026365304501e-1, 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1148 .50000000000000000000, .96824583655185422130, .57282196186948000082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1149 -.21650635094610966169, -.35903516540862679125, .97578093724974971969e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1150 .26203921611325660506, -.55792409597991015609e-1, -.20644078533943456204,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1151 .36172381205961199479e-1, .17035068468874958194,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1152 -.25371838001497225980e-1, -.14501953125000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1153 .18786835250972344757e-1, .12625507130328301066,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1154 -.14473795929590520582e-1, -.11179458309419422675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1155 .11494434254897626155e-1, .10030855351241635862,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1156 -.93498556820544479096e-2, -.90964264465390582629e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1157 .77546391824364392762e-2, .83213457337452292745e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1158 -.65358085945588638605e-2, -.76680372422574234569e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1159 .55835321940047427169e-2, .71098828931825789428e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1160 -.48253327982967591019e-2, -.66274981937248958553e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1161 .42118078245337801387e-2, .62064306433355646267e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1162 -.37083386598903548973e-2, 0., 0., .25000000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1163 .73950997288745200531, .83852549156242113615, .23175620272173946716,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1164 -.37791833195149451496, -.25710129174850522325, .21608307321780204633,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1165 .22844049245646009157, -.14009503000335388415, -.19897685605518413847,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1166 .98264706042471226893e-1, .17445445004279014046,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1167 -.72761100054958328401e-1, -.15463589893742108388,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1168 .56056770591708784481e-1, .13855313872640495158,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1169 -.44517752443294564781e-1, -.12534277657695128850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1170 .36211835346039665762e-1, .11434398255136139683,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1171 -.30033588409423828125e-1, -.10506705408753910481,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1172 .25313077840725783008e-1, .97149327637744872155e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1173 -.21624927200393328444e-1, -.90319582367202122625e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1174 .18688433567711780666e-1, .84372291635345108584e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1175 -.16312261561845420752e-1, -.79149526894804751586e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1176 .14362333871852474757e-1, 0., 0., 0., .12500000000000000000,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1177 .49607837082461073572, .82265291131801144317, .59621200088559103072,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1178 -.80054302859059362371e-1, -.42612156697795759420,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1179 -.90098145270865592887e-1, .29769623255090078484, .13630307904779758221,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1180 -.21638835185708931831, -.14600247270306082052, .16348801804014290453,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1181 .14340708728599057249, -.12755243353979286190, -.13661523715071346961,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1182 .10215585947881057394, .12864248070157166547, -.83592528025348693602e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1183 -.12066728689302565222, .69633728678718053052e-1, .11314245177331919532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1184 -.58882939251410088028e-1, -.10621835858758221487,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1185 .50432266865187597572e-1, .99916834723527771581e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1186 -.43672094283057258509e-1, -.94206380251950852413e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1187 .38181356812697746418e-1, .89035739656537771225e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1188 -.33661934598216332678e-1, 0., 0., 0., 0., .62500000000000000000e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1189 .31093357409581873586, .67604086414949799246, .75644205980613611039,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1190 .28990586430124175741, -.30648508196770360914, -.35801372616842500052,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1191 .91326869828709014708e-1, .31127929687500000000, .90915752838698393094e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1192 -.25637381283965534330, -.57601077850322797594e-1, .21019685709225757945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1193 .81244992138514014256e-1, -.17375078516720988858,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1194 -.92289437277967051125e-1, .14527351914265391374,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1195 .96675340792832019889e-1, -.12289485697108543415,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1196 -.97448175340011084006e-1, .10511755943298339844,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1197 .96242247086378239657e-1, -.90822942272780513537e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1198 -.93966350452322132384e-1, .79189411876493712558e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1199 .91139307067989309325e-1, -.69613039934383197265e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1200 -.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
1201 .31250000000000000000e-1, .18684782411095934408, .50176689760410660236,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1202 .74784031498626095398, .56472001151566251186, -.14842464993721351203e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1203 -.41162920273003120936, -.20243071230196532282, .23772054897172750436,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1204 .24963810923972235950, -.12116179938394678936, -.24330535483519110663,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1205 .47903849781124471359e-1, .22133299683101224293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1206 -.20542915138527200983e-2, -.19653465717678146728,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1207 -.26818172626509178444e-1, .17319122357631210944,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1208 .45065391411065545445e-1, -.15253391395444065941,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1209 -.56543897711725408302e-1, .13469154928743585367,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1210 .63632471400208840155e-1, -.11941684923913523817,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1211 -.67828850207933293098e-1, .10636309084510652670,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1212 .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
1213 0., .15625000000000000000e-1, .10909562534194485289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1214 .34842348626527747318, .64461114561628111443, .69382480527334683659,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1215 .29551102358528827763, -.25527584713978439819, -.38878771718544715394,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1216 -.82956185835347407489e-2, .31183177761966943912, .12831420840372374767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1217 -.22067618205599434368, -.17569196937129496961, .14598057000132284135,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1218 .18864406621763419484, -.89921002550386645767e-1, -.18571835020187122114,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1219 .48967672227195481777e-1, .17584685670380332798,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1220 -.19267984545067426324e-1, -.16335437520503462738,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1221 -.22598055455032407594e-2, .15032800884170631129,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1222 .17883358353754640871e-1, -.13774837869432209951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1223 -.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
1224 0., .78125000000000000000e-2, .62377810244809812496e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1225 .23080781467370883845, .50841310636012325368, .69834547012574056043,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1226 .52572723156526459672, .11464215704954976471e-1, -.38698869011491210342,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1227 -.26125646622255207507, .16951698812361607510, .29773875898928782269,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1228 -.20130501202570367491e-1, -.26332493149159310198,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1229 -.67734613690401207009e-1, .21207315477103762715, .11541543390889415193,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1230 -.16249634759782417533, -.13885887405041735068, .11996491328010275427,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1231 .14810432001630926895, -.85177658352556243411e-1, -.14918860659904380587,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1232 .57317789510444151564e-1, .14569827645586660151,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1233 -.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
1234 0., 0., .39062500000000000000e-2, .35101954600803571207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1235 .14761284084133737720, .37655033076080192966, .62410290231517322776,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1236 .64335622317683389875, .28188168266139524244, -.22488495672137010675,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1237 -.39393811089283576186, -.75184777995770096714e-1, .28472023119398293003,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1238 .20410910833705899572, -.15590046962908511750, -.23814567544617953125,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1239 .54442805556829031204e-1, .22855930338589720954, .16303223615756629897e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1240 -.20172722433875559213, -.62723406421217419404e-1, .17012230831020922010,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1241 .91754642766136561612e-1, -.13927644821381121197, -.10886600968068418181,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1242 .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
1243 0., 0., .19531250000000000000e-2, .19506820659607596598e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1244 .91865676095362231937e-1, .26604607809696493849, .51425874205091288223,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1245 .66047561132505329292, .48660109511591303851, .17575661168678285615e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1246 -.36594333408055703366, -.29088854695378694533, .11318677346656537927,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1247 .31110645235730182168, .60733219161008787341e-1, -.24333848233620420826,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1248 -.15254312332655419708, .15995968483455388613, .19010344455215289289,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1249 -.86040636766440260000e-1, -.19652589954665259945,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1250 .27633388517205837713e-1, .18660848552712880387, .15942583868416775867e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1251 -.16902042462382064786, -.47278526495327740646e-1, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1252 0., 0., 0., 0., .97656250000000000000e-3, .10731084460857378207e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1253 .55939644713816406331e-1, .18118487371914493668, .39914857299829864263,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1254 .60812322949933902435, .60011887183061967583, .26002695805835928795,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1255 -.20883922404786010096, -.38988130966114638081, -.11797833550782589082,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1256 .25231824756239520077, .24817859972953934712, -.90516417677868996417e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1257 -.26079073291293066798, -.30259468817169480161e-1, .22178195264114178432,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1258 .10569877864302048175, -.16679648389266977455, -.14637718550245050850,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1259 .11219272032739559870, .16359363640525750353, -.64358194509092101393e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1260 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
1261 .58542865274813470967e-2, .33461741635290096452e-1, .11979993155896201271,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1262 .29580223766987206958, .51874761979436016742, .62861483498014306968,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1263 .44868895761051453296, .12567502628371529386e-1, -.35040366183235474275,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1264 -.30466868455569500886, .70903913601490112666e-1, .30822791893032512740,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1265 .11969443264190207736, -.20764760317621313946, -.20629838355452128532,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1266 .95269702915334718507e-1, .22432624768705133300,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1267 -.33103381593477797101e-2, -.20570036048155716333,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1268 -.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
1269 0., 0., 0., 0., 0., 0., .24414062500000000000e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1270 .31714797501871532475e-2, .19721062526127334100e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1271 .77311181185536498246e-1, .21124871792841566575, .41777980401893650886,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1272 .59401977834943551650, .56132417807488349048, .23433675061367565951,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1273 -.20222775295220942126, -.38280372496506190127, -.14443804214023095767,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1274 .22268950939178466797, .27211314150777981984, -.34184876506180717313e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1275 -.26006498895669734842, -.97650425186005090107e-1, .19024527660129101293,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1276 .16789164198044635671, -.10875811641651905252, -.19276785058805921298, 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1277 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
1278 .17078941137247586143e-2, .11477733754843910060e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1279 .48887017020924625462e-1, .14634927241421789683, .32156282683019547854,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1280 .52165811920227223937, .60001958466396926460, .41208501541480733755,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1281 .11366945503190350975e-2, -.33968093962672089159, -.30955190935923386766,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1282 .40657421856578262210e-1, .29873400409871531764, .16094481791768257440,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1283 -.16876122436206497694, -.23650217045022161255, .33070260090574765012e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1284 .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
1285 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
1286 .91501857608428649078e-3, .66085179496951987952e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1287 .30383171695850355404e-1, .98840838845366876117e-1, .23855447246420318989,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1288 .43322017468145613917, .58049033744876107191, .52533893203742699346,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1289 .20681056202371946180, -.20180000924562504384, -.37503922291962681797,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1290 -.15988102869837429062, .19823558102762374094, .28393023878803799622,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1291 .11188133439357510403e-1, -.24730368377168229255, -.14731529061377942839,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1292 .14878558042884266021, 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
1293 0., 0., .30517578125000000000e-4, .48804277318479845551e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1294 .37696080990601968396e-2, .18603912108994738255e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1295 .65325006755649582964e-1, .17162960707938819795, .34411527956476971322,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1296 .52289350347082497959, .57319653625674910592, .37662253421045430413,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1297 -.14099055105384663902e-1, -.33265570610216904208, -.30921265572647566661,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1298 .19911390594166455281e-1, .28738590811031797718, .18912130469738472647,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1299 -.13235936203215819193, -.25076406142356675279, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1300 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .15258789062500000000e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1301 .25928719280954633249e-3, .21327398937568540428e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1302 .11244626133630732010e-1, .42375605740664331966e-1, .12031130345907846211,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1303 .26352562258934426830, .44590628258512682078, .56682835613700749379,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1304 .49116715128261660395, .17845943097110339078, -.20541650677432497477,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1305 -.36739803642257458221, -.16776034069210108273, .17920950989905112908,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1306 .28867732805385066532, .46473465543376206337e-1, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1307 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .76293945312500000000e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1308 .13727610943181290891e-3, .11979683091449349286e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1309 .67195313034570709806e-2, .27044920779931968175e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1310 .82472196498517457862e-1, .19570475044896150093, .36391620788543817693,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1311 .52241392782736588032, .54727504974907879912, .34211551468813581183,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1312 -.31580472732719957762e-1, -.32830006549176759667, -.30563797665254420769,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1313 .64905014620683140120e-2, .27642986248995073032, 0., 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1314 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .38146972656250000000e-5,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1315 .72454147007837596854e-4, .66859847582761390285e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1316 .39751311980366118437e-2, .17015198650201528366e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1317 .55443621868993855715e-1, .14157060481641692131, .28641242619559616836,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1318 .45610665490966615415, .55262786406029265394, .45818352706035500108,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1319 .14984403004611673047, -.21163807462970713245, -.36007252928843413718,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1320 -.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
1321 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
1322 .38135049864067468562e-4, .37101393638555730015e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1323 .23305339886279723213e-2, .10569913448297127219e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1324 .36640175162216897547e-1, .10010476414320235508, .21860074212675559892,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1325 .38124757096345313719, .52020999209879669177, .52172632730659212045,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1326 .30841620620308814614, -.50322546186721500184e-1, -.32577618885114899053,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1327 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
1328 0., 0., .95367431640625000000e-6, .20021483206955925244e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1329 .20481807322420625431e-3, .13553476938058909882e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1330 .64919676350791905019e-2, .23848725425069251903e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1331 .69384632678886421292e-1, .16249711393618776934, .30736618106830314788,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1332 .46399909601971539157, .53765031034002467225, .42598991476520183929,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1333 .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
1334 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
1335 .10487707828484902486e-4, .11254146162337528943e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1336 .78248929534271987118e-3, .39468337145306794566e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1337 .15313546659475671763e-1, .47249070825218564146e-1, .11804374107101480543,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1338 .24031796927792491122, .39629215049166341285, .51629108968402548545,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1339 .49622372075429782915, 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
1340 0., 0., 0., 0., 0., 0., 0., 0., 0., .23841857910156250000e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1341 .54823314130625337326e-5, .61575377321535518154e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1342 .44877834366497538134e-3, .23774612048621955857e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1343 .97136347645161687796e-2, .31671599547606636717e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1344 .84028665767000747480e-1, .18298487576742964949, .32647878537696945218,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1345 .46970971486488895077, 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
1346 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., .11920928955078125000e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1347 .28604020001177375838e-5, .33559227978295551013e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1348 .25583821662860610560e-3, .14201552747787302339e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1349 .60938046986874414969e-2, .20930869247951926793e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1350 .58745021125678072911e-1, .13613725780285953720, .26083988356030237586,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1351 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
1352 0., 0., 0., 0., 0., 0., .59604644775390625000e-7,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1353 .14898180663526043291e-5, .18224991282807693921e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1354 .14504433444608833821e-3, .84184722720281809548e-3,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1355 .37846965430000478789e-2, .13656355548211376864e-1,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1356 .40409541997718853934e-1, .99226988101858325902e-1, 0., 0., 0., 0., 0.,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1357 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
1358 0., 0., .29802322387695312500e-7, .77471708843445529468e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1359 .98649879372606876995e-5, .81814934772838523887e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1360 .49554483992403011328e-3, .23290922072351413938e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1361 .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
1362 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
1363 0., 0., 0., .14901161193847656250e-7, .40226235946098233685e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1364 .53236418690561306700e-5, .45933829691164002269e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1365 .28982005232838857913e-3, .14212974043211018374e-2,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1366 .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
1367 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
1368 .74505805969238281250e-8, .20858299254133430408e-6,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1369 .28648457300134381744e-5, .25677535898258910850e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1370 .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
1371 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
1372 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
1373 .15376606719887104015e-5, .14296523739727437959e-4,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1374 .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
1375 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
1376 .18626451492309570312e-8, .55871592916438890146e-7,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1377 .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
1378 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
1379 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
1380 .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
1381 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
1382 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
1383 .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
1384 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
1385 0., 0., .23283064365386962891e-9
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1386 };
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1387
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1388 /* Allocates a workspace for the given maximum number of intervals.
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1389 Note that if the workspace gets filled, the intervals with the
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1390 lowest error estimates are dropped. The maximum number of
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1391 intervals is therefore not the maximum number of intervals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1392 that will be computed, but merely the size of the buffer.
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1393 */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1394
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1395 /* Compute the product of the fx with one of the inverse
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1396 Vandermonde-like matrices. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1397
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1398 void
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1399 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
1400 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1401
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1402 int i, j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1403
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1404 switch (d)
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 case 0:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1407 for (i = 0; i <= 4; i++)
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 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1410 for (j = 0; j <= 4; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1411 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
1412 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1413 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1414 case 1:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1415 for (i = 0; i <= 8; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1416 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1417 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1418 for (j = 0; j <= 8; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1419 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
1420 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1421 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1422 case 2:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1423 for (i = 0; i <= 16; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1424 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1425 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1426 for (j = 0; j <= 16; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1427 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
1428 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1429 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1430 case 3:
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1431 for (i = 0; i <= 32; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1432 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1433 c[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1434 for (j = 0; j <= 32; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1435 c[i] += V4inv[i * 33 + j] * fx[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1436 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1437 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1438 }
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 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1441
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1442
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1443 /* Downdate the interpolation given by the n coefficients c
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1444 by removing the nodes with indices in nans. */
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 void
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1447 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
1448 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1449
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1450 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
1451 double b_new[34], alpha;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1452 int i, j;
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 for (i = 0; i <= n + 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1455 b_new[i] = bee[bidx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1456 for (i = 0; i < nnans; i++)
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 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
1459 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
1460 for (j = n - 1; j > 0; j--)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1461 b_new[j] =
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1462 (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
1463 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
1464 for (j = 0; j <= n; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1465 b_new[j] = b_new[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1466 alpha = c[n] / b_new[n];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1467 for (j = 0; j < n; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1468 c[j] -= alpha * b_new[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1469 c[n] = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1470 n--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1471 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1472
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1473 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1474
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 /* The actual integration routine.
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1478 */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1479
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
1480 DEFUN_DLD (quadcc, args, nargout,
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1481 "-*- texinfo -*-\n\
12612
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1482 @deftypefn {Function File} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b})\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1483 @deftypefnx {Function File} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1484 @deftypefnx {Function File} {@var{q} =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1485 @deftypefnx {Function File} {[@var{q}, @var{err}, @var{nr_points}] =} quadcc (@dots{})\n\
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\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1487 using the doubly-adaptive Clenshaw-Curtis quadrature described by P. Gonnet\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1488 in @cite{Increasing the Reliability of Adaptive Quadrature Using Explicit\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1489 Interpolants}.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1490 @var{f} is a function handle, inline function, or string\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1491 containing the name of the function to evaluate.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1492 The function @var{f} must be vectorized and must return a vector of output\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1493 values if given a vector of input values. For example,\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1494 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1495 @example\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1496 f = @@(x) x .* sin (1./x) .* sqrt (abs (1 - x));\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1497 @end example\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1498 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1499 @noindent\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1500 which uses the element-by-element `dot' form for all operators.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1501 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1502 @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
1503 or both limits may be infinite. @code{quadcc} handles an inifinite limit\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1504 by substituting the variable of integration with @code{x=tan(pi/2*u)}.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1505 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1506 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
1507 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
1508 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1509 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
1510 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
1511 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
1512 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
1513 @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
1514 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1515 @example\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1516 int = quadcc (f, a, b, 1.0e-6, [ 1 ]);\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1517 @end example\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1518 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1519 The result of the integration is returned in @var{q}.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1520 @var{err} is an estimate of the absolute integration error and\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1521 @var{nr_points} is the number of points at which the integrand was evaluated.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1522 If the adaptive integration did not converge, the value of\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1523 @var{err} will be larger than the requested tolerance. Therefore, it is\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1524 recommended to verify this value for difficult integrands.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1525 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1526 @code{quadcc} is capable of dealing with non-numeric\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1527 values of the integrand such as @code{NaN} or @code{Inf}.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1528 If the integral diverges, and @code{quadcc} detects this, \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1529 then a warning is issued and @code{Inf} or @code{-Inf} is returned.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1530 \n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1531 Note: @code{quadcc} is a general purpose quadrature algorithm\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1532 and, as such, may be less efficient for a smooth or otherwise\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1533 well-behaved integrand than other methods such as @code{quadgk}.\n\
16cca721117b doc: Update all documentation for chapter on Numerical Integration
Rik <octave@nomad.inbox5.com>
parents: 12553
diff changeset
1534 \n\
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1535 The algorithm uses Clenshaw-Curtis quadrature rules of increasing\n\
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1536 degree in each interval and bisects the interval if either the\n\
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1537 function does not appear to be smooth or a rule of maximum\n\
12553
7c915d013b9c quadcc: Add reference to original paper in docstring.
Rik <octave@nomad.inbox5.com>
parents: 11590
diff changeset
1538 degree has been reached. The error estimate is computed from the\n\
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1539 L2-norm of the difference between two successive interpolations\n\
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1540 of the integrand over the nodes of the respective quadrature rules.\n\
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1541 \n\
12553
7c915d013b9c quadcc: Add reference to original paper in docstring.
Rik <octave@nomad.inbox5.com>
parents: 11590
diff changeset
1542 Reference: P. Gonnet, @cite{Increasing the Reliability of Adaptive\n\
7c915d013b9c quadcc: Add reference to original paper in docstring.
Rik <octave@nomad.inbox5.com>
parents: 11590
diff changeset
1543 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
1544 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
1545 @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
1546 @end deftypefn")
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1547 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1548
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1549 /* Some constants that we will need. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1550 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
1551 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
1552 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
1553 static const double w = M_SQRT2 / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1554 static const int ndiv_max = 20;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1555
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1556 /* The interval heap. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1557 cquad_ival ivals[cquad_heapsize];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1558 int heap[cquad_heapsize];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1559
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1560 /* Arguments left and right */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1561 int nargin = args.length ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1562 octave_function *fcn;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1563 double a, b, tol, iivals[cquad_heapsize], *sing;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1564
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1565 /* Variables needed for transforming the integrand. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1566 int wrap = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1567 double xw;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1568
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1569 /* Stuff we will need to call the integrand. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1570 octave_value_list fargs, retval;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1571
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1572 /* Actual variables (as opposed to constants above). */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1573 double m, h, ml, hl, mr, hr, temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1574 double igral, err, igral_final, err_final, err_excess;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1575 int nivals, neval = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1576 int i, j, d, split, t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1577 int nnans, nans[33];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1578 cquad_ival *iv, *ivl, *ivr;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1579 double nc, ncdiff;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1580
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1581
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1582 /* Parse the input arguments. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1583 if (nargin < 1)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1584 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1585 error
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1586 ("quadcc: first argument (integrand) of type function handle required");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1587 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1588 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1589 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1590 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1591 if (args (0).is_function_handle () || args (0).is_inline_function ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1592 fcn = args (0).function_value ();
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1593 else
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1594 {
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1595 error ("quadcc: first argument (integrand) must be a function handle or an inline function");
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1596 return octave_value_list();
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1597 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1598 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1599
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1600 if (nargin < 2 || !args (1).is_real_scalar ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1601 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1602 error ("quadcc: second argument (left interval edge) must be a single real scalar");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1603 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1604 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1605 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1606 a = args (1).double_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1607
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1608 if (nargin < 3 || !args (2).is_real_scalar ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1609 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1610 error ("quadcc: third argument (right interval edge) must be a single real scalar");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1611 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1612 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1613 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1614 b = args (2).double_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1615
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1616 if (nargin < 4)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1617 tol = 1.0e-6;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1618 else if (!args (3).is_real_scalar ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1619 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1620 error ("quadcc: fourth argument (tolerance) must be a single real scalar");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1621 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1622 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1623 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1624 tol = args (3).double_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1625
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1626 if (nargin < 5)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1627 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1628 nivals = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1629 iivals[0] = a;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1630 iivals[1] = b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1631 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1632 else if (!(args (4).is_real_scalar () || args (4).is_real_matrix ()))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1633 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1634 error ("quadcc: fifth argument (singularities) must be a vector of real values");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1635 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1636 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1637 else
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 nivals = 1 + args (4).length ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1640 if ( nivals > cquad_heapsize ) {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1641 error ("quadcc: maximum number of singular points is limited to %i",
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1642 cquad_heapsize-1);
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1643 return octave_value_list();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1644 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1645 sing = args (4).array_value ().fortran_vec ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1646 iivals[0] = a;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1647 for (i = 0; i < nivals - 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1648 iivals[i + 1] = sing[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1649 iivals[nivals] = b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1650 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1651
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1652 /* If a or b are +/-Inf, transform the integral. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1653 if (xisinf (a) || xisinf (b))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1654 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1655 wrap = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1656 for (i = 0; i <= nivals; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1657 if (xisinf (iivals[i]))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1658 iivals[i] = copysign (1.0, iivals[i]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1659 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1660 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
1661 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1662
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1663
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1664 /* Initialize the heaps. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1665 for (i = 0; i < cquad_heapsize; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1666 heap[i] = i;
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
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1669 /* Create the first interval(s). */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1670 igral = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1671 err = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1672 for (j = 0; j < nivals; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1673 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1674
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1675 /* Initialize the interval. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1676 iv = &(ivals[heap[j]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1677 m = (iivals[j] + iivals[j + 1]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1678 h = (iivals[j + 1] - iivals[j]) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1679 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1680 ColumnVector ex (33);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1681 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1682 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1683 for (i = 0; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1684 ex (i) = tan (M_PI / 2 * (m + xi[i] * h));
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1685 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1686 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1687 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1688 for (i = 0; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1689 ex (i) = m + xi[i] * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1690 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1691 fargs (0) = ex;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1692 retval = feval (fcn, fargs, 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1693 if (retval.length () != 1 || !retval (0).is_real_matrix ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1694 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1695 error
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1696 ("quadcc: integrand must return a single, real-valued vector");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1697 return octave_value_list ();
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 Matrix effex = retval (0).matrix_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1700 if (effex.length () != ex.length ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1701 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1702 error ("quadcc: integrand must return a single, real-valued vector of the same size as the input");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1703 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1704 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1705 for (i = 0; i <= n[3]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1706 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1707 iv->fx[i] = effex (i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1708 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1709 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1710 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1711 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
1712 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1713 neval++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1714 if (!xfinite (iv->fx[i]))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1715 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1716 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1717 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1718 }
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 Vinvfx (iv->fx, &(iv->c[idx[3]]), 3);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1721 Vinvfx (iv->fx, &(iv->c[idx[2]]), 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1722 Vinvfx (iv->fx, &(iv->c[0]), 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1723 for (i = 0; i < nnans; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1724 iv->fx[i] = octave_NaN;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1725 iv->a = iivals[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1726 iv->b = iivals[j + 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1727 iv->depth = 3;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1728 iv->rdepth = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1729 iv->ndiv = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1730 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
1731 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1732 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
1733 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1734 temp = iv->c[idx[3] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1735 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1736 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1737 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1738 for (i = 0; i <= n[2]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1739 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1740 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
1741 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1742 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
1743 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1744 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1745 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1746 iv->err = ncdiff * 2 * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1747 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
1748 iv->err = 2 * h * nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1749
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1750 /* Tabulate this interval's data. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1751 igral += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1752 err += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1753
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1754 /* Sift it up the heap. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1755 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1756 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
1757 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1758 temp = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1759 heap[i] = heap[i / 2];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1760 heap[i / 2] = temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1761 i /= 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1762 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1763
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1764 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1765
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1766
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1767 /* Initialize some global values. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1768 igral_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1769 err_final = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1770 err_excess = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1771
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1772
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1773 /* Main loop. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1774 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
1775 && !(err_final > fabs (igral) * tol
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1776 && err - err_final < fabs (igral) * tol))
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
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1779 /* Allow the user to interrupt. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1780 OCTAVE_QUIT;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1781
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1782 /* Put our finger on the interval with the largest error. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1783 iv = &(ivals[heap[0]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1784 m = (iv->a + iv->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1785 h = (iv->b - iv->a) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1786
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1787 /* printf
11562
1811f4f8b3b5 Rename cquad to quadcc and add to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11553
diff changeset
1788 ("quadcc: processing ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1789 heap[0], nivals, iv->a, iv->b, iv->igral, iv->err, iv->depth);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1790 */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1791 /* Should we try to increase the degree? */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1792 if (iv->depth < 3)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1793 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1794
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1795 /* Keep tabs on some variables. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1796 d = ++iv->depth;
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 /* Get the new (missing) function values */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1799 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1800 ColumnVector ex (n[d] / 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1801 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1802 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1803 for (i = 0; i < n[d] / 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1804 ex (i) =
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1805 tan (M_PI / 2 * (m + xi[(2 * i + 1) * skip[d]] * h));
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 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1808 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1809 for (i = 0; i < n[d] / 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1810 ex (i) = m + xi[(2 * i + 1) * skip[d]] * h;
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 fargs (0) = ex;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1813 retval = feval (fcn, fargs, 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1814 if (retval.length () != 1 || !retval (0).is_real_matrix ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1815 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1816 error ("quadcc: integrand must return a single, real-valued vector");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1817 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1818 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1819 Matrix effex = retval (0).matrix_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1820 if (effex.length () != ex.length ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1821 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1822 error ("quadcc: integrand must return a single, real-valued vector of the same size as the input");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1823 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1824 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1825 neval += effex.length ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1826 for (i = 0; i < n[d] / 2; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1827 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1828 j = (2 * i + 1) * skip[d];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1829 iv->fx[j] = effex (i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1830 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1831 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1832 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1833 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
1834 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1835 }
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 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1838 for (i = 0; i <= 32; i += skip[d])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1839 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1840 if (!xfinite (iv->fx[i]))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1841 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1842 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1843 iv->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1844 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1845 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1846
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1847 /* Compute the new coefficients. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1848 Vinvfx (iv->fx, &(iv->c[idx[d]]), d);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1849 /* Downdate any NaNs. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1850 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1851 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1852 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
1853 for (i = 0; i < nnans; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1854 iv->fx[i] = octave_NaN;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1855 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1856
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1857 /* Compute the error estimate. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1858 nc = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1859 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
1860 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1861 temp = iv->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1862 nc += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1863 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1864 ncdiff = nc;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1865 for (i = 0; i <= n[d - 1]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1866 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1867 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
1868 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1869 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
1870 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1871 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1872 nc = sqrt (nc);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1873 iv->err = ncdiff * 2 * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1874 /* Compute the local integral. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1875 iv->igral = 2 * h * w * iv->c[idx[d]];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1876 /* Split the interval prematurely? */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1877 split = (nc > 0 && ncdiff / nc > 0.1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1878 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1879
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1880 /* Maximum degree reached, just split. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1881 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1882 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1883 split = 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1884 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1885
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1886
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1887 /* Should we drop this interval? */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1888 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
1889 || (m + h * xi[31]) >= (m + h * xi[32])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1890 || iv->err < fabs (iv->igral) * DBL_EPSILON * 10)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1891 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1892
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1893 /* printf
11562
1811f4f8b3b5 Rename cquad to quadcc and add to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11553
diff changeset
1894 ("quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1895 heap[0], nivals, iv->a, iv->b, iv->igral, iv->err,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1896 iv->depth);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1897 */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1898 /* Keep this interval's contribution */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1899 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1900 igral_final += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1901 /* Swap with the last element on the heap */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1902 t = heap[nivals - 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1903 heap[nivals - 1] = heap[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1904 heap[0] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1905 nivals--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1906 /* Fix up the heap */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1907 i = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1908 while (2 * i + 1 < nivals)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1909 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1910
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1911 /* Get the kids */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1912 j = 2 * i + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1913 /* If the j+1st entry exists and is larger than the jth,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1914 use it instead. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1915 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1916 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1917 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1918 /* Do we need to move the ith entry up? */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1919 if (ivals[heap[j]].err <= ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1920 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1921 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1922 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1923 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1924 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1925 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1926 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1927 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1928 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1929
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1930 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1931
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1932 /* Do we need to split this interval? */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1933 else if (split)
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
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1936 /* Some values we will need often... */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1937 d = iv->depth;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1938 /* Generate the interval on the left */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1939 ivl = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1940 ivl->a = iv->a;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1941 ivl->b = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1942 ml = (ivl->a + ivl->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1943 hl = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1944 ivl->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1945 ivl->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1946 ivl->fx[0] = iv->fx[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1947 ivl->fx[32] = iv->fx[16];
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 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1950 if (wrap)
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 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1953 ex (i) = tan (M_PI / 2 * (ml + xi[(i + 1) * skip[0]] * hl));
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1954 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1955 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1956 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1957 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1958 ex (i) = ml + xi[(i + 1) * skip[0]] * hl;
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 fargs (0) = ex;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1961 retval = feval (fcn, fargs, 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1962 if (retval.length () != 1 || !retval (0).is_real_matrix ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1963 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1964 error ("quadcc: integrand must return a single, real-valued vector");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1965 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1966 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1967 Matrix effex = retval (0).matrix_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1968 if (effex.length () != ex.length ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1969 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
1970 error ("quadcc: integrand must return a single, real-valued vector of the same size as the input");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1971 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1972 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1973 neval += effex.length ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1974 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1975 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1976 j = (i + 1) * skip[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1977 ivl->fx[j] = effex (i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1978 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1979 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1980 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1981 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
1982 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1983 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1984 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1985 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1986 for (i = 0; i <= 32; i += skip[0])
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 if (!xfinite (ivl->fx[i]))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1989 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1990 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1991 ivl->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1992 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1993 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1994 Vinvfx (ivl->fx, ivl->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1995 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1996 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1997 downdate (ivl->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1998 for (i = 0; i < nnans; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
1999 ivl->fx[i] = octave_NaN;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2000 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2001 for (i = 0; i <= n[d]; i++)
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 ivl->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2004 for (j = i; j <= n[d]; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2005 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
2006 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2007 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2008 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2009 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2010 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
2011 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2012 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2013 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
2014 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2015 temp = ivl->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2016 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2017 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2018 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2019 ivl->err = ncdiff * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2020 /* Check for divergence. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2021 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
2022 && ivl->c[0] / iv->c[0] > 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2023 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
2024 {
11178
c08e9d4e54c7 cquad.cc (Fcquad): use octave_Inf, not INFINITY
John W. Eaton <jwe@octave.org>
parents: 10944
diff changeset
2025 igral = 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
2026 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2027 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2028 }
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 /* Compute the local integral. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2031 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
2032
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
2033
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2034 /* Generate the interval on the right */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2035 ivr = &(ivals[heap[nivals++]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2036 ivr->a = m;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2037 ivr->b = iv->b;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2038 mr = (ivr->a + ivr->b) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2039 hr = h / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2040 ivr->depth = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2041 ivr->rdepth = iv->rdepth + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2042 ivr->fx[0] = iv->fx[16];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2043 ivr->fx[32] = iv->fx[32];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2044 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2045 ColumnVector ex (n[0] - 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2046 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2047 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2048 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2049 ex (i) = tan (M_PI / 2 * (mr + xi[(i + 1) * skip[0]] * hr));
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 else
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 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2054 ex (i) = mr + xi[(i + 1) * skip[0]] * hr;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2055 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2056 fargs (0) = ex;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2057 retval = feval (fcn, fargs, 1);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2058 if (retval.length () != 1 || !retval (0).is_real_matrix ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2059 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
2060 error ("quadcc: integrand must return a single, real-valued vector");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2061 return octave_value_list ();
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 Matrix effex = retval (0).matrix_value ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2064 if (effex.length () != ex.length ())
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2065 {
11590
4ced6b90fffb style fixes for warning and error messages in source files
John W. Eaton <jwe@octave.org>
parents: 11586
diff changeset
2066 error ("quadcc: integrand must return a single, real-valued vector of the same size as the input");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2067 return octave_value_list ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2068 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2069 neval += effex.length ();
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2070 for (i = 0; i < n[0] - 1; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2071 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2072 j = (i + 1) * skip[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2073 ivr->fx[j] = effex (i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2074 if (wrap)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2075 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2076 xw = ex(i);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2077 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
2078 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2079 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2080 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2081 nnans = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2082 for (i = 0; i <= 32; i += skip[0])
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2083 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2084 if (!xfinite (ivr->fx[i]))
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2085 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2086 nans[nnans++] = i;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2087 ivr->fx[i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2088 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2089 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2090 Vinvfx (ivr->fx, ivr->c, 0);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2091 if (nnans > 0)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2092 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2093 downdate (ivr->c, n[0], 0, nans, nnans);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2094 for (i = 0; i < nnans; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2095 ivr->fx[i] = octave_NaN;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2096 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2097 for (i = 0; i <= n[d]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2098 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2099 ivr->c[idx[d] + i] = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2100 for (j = i; j <= n[d]; j++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2101 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
2102 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2103 ncdiff = 0.0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2104 for (i = 0; i <= n[0]; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2105 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2106 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
2107 ncdiff += temp * temp;
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 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
2110 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2111 temp = ivr->c[idx[d] + i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2112 ncdiff += temp * temp;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2113 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2114 ncdiff = sqrt (ncdiff);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2115 ivr->err = ncdiff * h;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2116 /* Check for divergence. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2117 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
2118 && ivr->c[0] / iv->c[0] > 2);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2119 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
2120 {
11178
c08e9d4e54c7 cquad.cc (Fcquad): use octave_Inf, not INFINITY
John W. Eaton <jwe@octave.org>
parents: 10944
diff changeset
2121 igral = 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
2122 warning ("quadcc: divergent integral detected");
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2123 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2124 }
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 /* Compute the local integral. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2127 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
2128
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11572
diff changeset
2129
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2130 /* Fix-up the heap: we now have one interval on top
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2131 that we don't need any more and two new, unsorted
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2132 ones at the bottom. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2133 /* Flip the last interval to the top of the heap and
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2134 sift down. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2135 t = heap[nivals - 1];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2136 heap[nivals - 1] = heap[0];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2137 heap[0] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2138 nivals--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2139 /* Sift this interval back down the heap. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2140 i = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2141 while (2 * i + 1 < nivals - 1)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2142 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2143 j = 2 * i + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2144 if (j + 1 < nivals - 1
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2145 && 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
2146 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2147 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
2148 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2149 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2150 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2151 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2152 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2153 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2154 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2155 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2156 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2157
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2158 /* Now grab the last interval and sift it up the heap. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2159 i = nivals - 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2160 while (i > 0)
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 j = (i - 1) / 2;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2163 if (ivals[heap[j]].err < ivals[heap[i]].err)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2164 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2165 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2166 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2167 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2168 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2169 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2170 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2171 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2172 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2173
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2174
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2175 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2176
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2177 /* Otherwise, just fix-up the heap. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2178 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2179 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2180 i = 0;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2181 while (2 * i + 1 < nivals)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2182 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2183 j = 2 * i + 1;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2184 if (j + 1 < nivals
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2185 && 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
2186 j++;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2187 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
2188 break;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2189 else
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2190 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2191 t = heap[j];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2192 heap[j] = heap[i];
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2193 heap[i] = t;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2194 i = j;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2195 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2196 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2197
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2198 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2199
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2200 /* If the heap is about to overflow, remove the last two
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2201 intervals. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2202 while (nivals > cquad_heapsize - 2)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2203 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2204 iv = &(ivals[heap[nivals - 1]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2205 /* printf
11562
1811f4f8b3b5 Rename cquad to quadcc and add to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11553
diff changeset
2206 ("quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2207 heap[0], nivals, iv->a, iv->b, iv->igral, iv->err,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2208 iv->depth);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2209 */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2210 err_final += iv->err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2211 igral_final += iv->igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2212 nivals--;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2213 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2214
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2215 /* Collect the value of the integral and error. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2216 igral = igral_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2217 err = err_final;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2218 for (i = 0; i < nivals; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2219 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2220 igral += ivals[heap[i]].igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2221 err += ivals[heap[i]].err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2222 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2223
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2224 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2225
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2226 /* Dump the contents of the heap. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2227 /* for (i = 0; i < nivals; i++)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2228 {
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2229 iv = &(ivals[heap[i]]);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2230 printf
11562
1811f4f8b3b5 Rename cquad to quadcc and add to documentation.
Rik <octave@nomad.inbox5.com>
parents: 11553
diff changeset
2231 ("quadcc: ival %i (%i) with [%e,%e], int=%e, err=%e, depth=%i, rdepth=%i, ndiv=%i\n",
10944
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2232 i, heap[i], iv->a, iv->b, iv->igral, iv->err, iv->depth,
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2233 iv->rdepth, iv->ndiv);
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2234 }
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2235 */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2236 /* Clean up and present the results. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2237 retval (0) = igral;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2238 if (nargout > 1)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2239 retval (1) = err;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2240 if (nargout > 2)
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2241 retval (2) = neval;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2242 /* All is well that ends well. */
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2243 return retval;
a7655cdba470 add the cquad integrator, by Pedro Gonnet
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
2244 }