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LSST Data Management Base Package
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IntGKPData10.h
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1// -*- lsst-c++ -*-
2
3/*
4 * LSST Data Management System
5 * Copyright 2008, 2009, 2010 LSST Corporation.
6 *
7 * This product includes software developed by the
8 * LSST Project (http://www.lsst.org/).
9 *
10 * This program is free software: you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation, either version 3 of the License, or
13 * (at your option) any later version.
14 *
15 * This program is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 * GNU General Public License for more details.
19 *
20 * You should have received a copy of the LSST License Statement and
21 * the GNU General Public License along with this program. If not,
22 * see <http://www.lsstcorp.org/LegalNotices/>.
23 */
24
25#if !defined(LSST_AFW_MATH_INTGKPDATA10_H)
26#define LSST_AFW_MATH_INTGKPDATA10_H 1
27
28/*
29 * Numeric constants used by the Integrate.h integrator routines.
30 *
31 * @note Gauss-Kronrod-Patterson quadrature coefficients for use in
32 * quadpack routine qng. These coefficients were calculated with
33 * 101 decimal digit arithmetic by L. W. Fullerton, Bell Labs, Nov
34 * 1981.
35 */
36
37#include <vector>
38
39namespace lsst {
40namespace afw {
41namespace math {
42
43namespace details {
44
45static const int NGKPLEVELS = 5;
46
47inline int gkp_n(int level) {
48 assert(level >= 0 && level < NGKPLEVELS);
49 static const int ngkp[NGKPLEVELS] = {5, 5, 11, 22, 44};
50 return ngkp[level];
51}
52
53template <class T>
54inline const std::vector<T>& gkp_x(int level) {
55 // x10, abscissae common to the 10-, 21-, 43- and 87-point rule
56 static const T ax10[5] = {0.973906528517171720077964012084452, 0.865063366688984510732096688423493,
57 0.679409568299024406234327365114874, 0.433395394129247190799265943165784,
58 0.148874338981631210884826001129720};
59 static const std::vector<T> vx10(ax10, ax10 + 5);
60
61 // x21, abscissae common to the 21-, 43- and 87-point rule
62 static const T ax21[5] = {0.995657163025808080735527280689003, 0.930157491355708226001207180059508,
63 0.780817726586416897063717578345042, 0.562757134668604683339000099272694,
64 0.294392862701460198131126603103866};
65 static const std::vector<T> vx21(ax21, ax21 + 5);
66
67 // x43, abscissae common to the 43- and 87-point rule
68 static const T ax43[11] = {0.999333360901932081394099323919911, 0.987433402908088869795961478381209,
69 0.954807934814266299257919200290473, 0.900148695748328293625099494069092,
70 0.825198314983114150847066732588520, 0.732148388989304982612354848755461,
71 0.622847970537725238641159120344323, 0.499479574071056499952214885499755,
72 0.364901661346580768043989548502644, 0.222254919776601296498260928066212,
73 0.074650617461383322043914435796506};
74 static const std::vector<T> vx43(ax43, ax43 + 11);
75
76 // x87, abscissae of the 87-point rule
77 static const T ax87[22] = {0.999902977262729234490529830591582, 0.997989895986678745427496322365960,
78 0.992175497860687222808523352251425, 0.981358163572712773571916941623894,
79 0.965057623858384619128284110607926, 0.943167613133670596816416634507426,
80 0.915806414685507209591826430720050, 0.883221657771316501372117548744163,
81 0.845710748462415666605902011504855, 0.803557658035230982788739474980964,
82 0.757005730685495558328942793432020, 0.706273209787321819824094274740840,
83 0.651589466501177922534422205016736, 0.593223374057961088875273770349144,
84 0.531493605970831932285268948562671, 0.466763623042022844871966781659270,
85 0.399424847859218804732101665817923, 0.329874877106188288265053371824597,
86 0.258503559202161551802280975429025, 0.185695396568346652015917141167606,
87 0.111842213179907468172398359241362, 0.037352123394619870814998165437704};
88 static const std::vector<T> vx87(ax87, ax87 + 22);
89
90 // x175, new abscissae of the 175-point rule
91 static const T ax175[44] = {
92 0.9999863601049729677997719, 0.9996988005421428623760900, 0.9987732473138838303043008,
93 0.9969583851613681945576954, 0.9940679446543307664316419, 0.9899673391741082769960501,
94 0.9845657252243253759726856, 0.9778061574856414566055911, 0.9696573134362640567828241,
95 0.9601075259508299668299148, 0.9491605191933640559839528, 0.9368321320434676982049391,
96 0.9231475266471484946315312, 0.9081385954543932335481458, 0.8918414554201179766275301,
97 0.8742940658668577971868106, 0.8555341249920432726468181, 0.8355974653331171075829366,
98 0.8145171513255796294567278, 0.7923233739697216224661771, 0.7690440708082055924983192,
99 0.7447060413364141221086362, 0.7193362474393392286563226, 0.6929630148748741413274435,
100 0.6656169582351898081906710, 0.6373315753624730450361940, 0.6081435407529742253347887,
101 0.5780927509986774074337714, 0.5472221576559162873479056, 0.5155774001694817879753989,
102 0.4832062516695473663839323, 0.4501579202236101928554315, 0.4164822936334372150371142,
103 0.3822292525735955063074986, 0.3474481818229070516859048, 0.3121877718977455143765043,
104 0.2764961311348905899785770, 0.2404211453027010909070665, 0.2040109589145005126324680,
105 0.1673144327616352753945014, 0.1303814601095591675431696, 0.09326308333660176874846400,
106 0.05601141598806823374241435, 0.01867941779948308845140053};
107 static const std::vector<T> vx175(ax175, ax175 + 44);
108
109 static const std::vector<T>* x[NGKPLEVELS] = {&vx10, &vx21, &vx43, &vx87, &vx175};
110
111 assert(level >= 0 && level < NGKPLEVELS);
112 return *x[level];
113}
114
115template <class T>
116inline const std::vector<T>& gkp_wa(int level) {
117 // w21a, weights of the 21-point formula for abscissae x10
118 static const T aw21a[5] = {0.032558162307964727478818972459390, 0.075039674810919952767043140916190,
119 0.109387158802297641899210590325805, 0.134709217311473325928054001771707,
120 0.147739104901338491374841515972068};
121 static const std::vector<T> vw21a(aw21a, aw21a + 5);
122
123 // w43a, weights of the 43-point formula for abscissae x10,x21
124 static const T aw43a[10] = {0.016296734289666564924281974617663, 0.037522876120869501461613795898115,
125 0.054694902058255442147212685465005, 0.067355414609478086075553166302174,
126 0.073870199632393953432140695251367, 0.005768556059769796184184327908655,
127 0.027371890593248842081276069289151, 0.046560826910428830743339154433824,
128 0.061744995201442564496240336030883, 0.071387267268693397768559114425516};
129 static const std::vector<T> vw43a(aw43a, aw43a + 10);
130
131 // w87a, weights of the 87-point formula for abscissae x10..x43
132 static const T aw87a[21] = {0.008148377384149172900002878448190, 0.018761438201562822243935059003794,
133 0.027347451050052286161582829741283, 0.033677707311637930046581056957588,
134 0.036935099820427907614589586742499, 0.002884872430211530501334156248695,
135 0.013685946022712701888950035273128, 0.023280413502888311123409291030404,
136 0.030872497611713358675466394126442, 0.035693633639418770719351355457044,
137 0.000915283345202241360843392549948, 0.005399280219300471367738743391053,
138 0.010947679601118931134327826856808, 0.016298731696787335262665703223280,
139 0.021081568889203835112433060188190, 0.025370969769253827243467999831710,
140 0.029189697756475752501446154084920, 0.032373202467202789685788194889595,
141 0.034783098950365142750781997949596, 0.036412220731351787562801163687577,
142 0.037253875503047708539592001191226};
143 static const std::vector<T> vw87a(aw87a, aw87a + 21);
144
145 // w175a, weights of the 175-point formula for abscissae x10..x87
146 static const T aw175a[43] = {
147 0.004074188692082600103872341, 0.009380719100781411819741177, 0.01367372552502614309257226,
148 0.01683885365581896502443513, 0.01846754991021395380770806, 0.001442436294030254510518689,
149 0.006842973011356375224430623, 0.01164020675144415562952859, 0.01543624880585667934076834,
150 0.01784681681970938536027839, 0.0004576754584154192941064591, 0.002699640110136963534043642,
151 0.005473839800559775445647306, 0.008149365848393670964180954, 0.01054078444460191775302900,
152 0.01268548488462691364854167, 0.01459484887823787625642303, 0.01618660123360139484467359,
153 0.01739154947518257137619173, 0.01820611036567589378188459, 0.01862693775152385427017140,
154 0.0001363171844264931156688042, 0.0009035606060432074452289352, 0.002048434635928091782250346,
155 0.003379145025868061092978424, 0.004774978836099393880602724, 0.006164723826122346701274159,
156 0.007505223673194467726814647, 0.008774483993121594091281642, 0.009969018893220443741650500,
157 0.01109746798050614328494604, 0.01216957356300040269315573, 0.01318725270741960360319771,
158 0.01414345539438560032188640, 0.01502629056404634765715107, 0.01582337568571996469999659,
159 0.01652520670998925164398162, 0.01712754985211303089259342, 0.01763120633007834051620255,
160 0.01803849481144435059221422, 0.01834930224922804724856518, 0.01856027463491628805666919,
161 0.01866711437596752016025132};
162 static const std::vector<T> vw175a(aw175a, aw175a + 43);
163
164 static const std::vector<T>* wa[NGKPLEVELS] = {nullptr, &vw21a, &vw43a, &vw87a, &vw175a};
165
166 assert(level >= 1 && level < NGKPLEVELS);
167 return *wa[level];
168}
169
170template <class T>
171inline const std::vector<T>& gkp_wb(int level) {
172 // w10, weights of the 10-point formula
173 static const T aw10b[6] = {0.066671344308688137593568809893332, 0.149451349150580593145776339657697,
174 0.219086362515982043995534934228163, 0.269266719309996355091226921569469,
175 0.295524224714752870173892994651338, 0.0};
176 static const std::vector<T> vw10b(aw10b, aw10b + 6);
177
178 // w21b, weights of the 21-point formula for abscissae x21
179 static const T aw21b[6] = {0.011694638867371874278064396062192, 0.054755896574351996031381300244580,
180 0.093125454583697605535065465083366, 0.123491976262065851077958109831074,
181 0.142775938577060080797094273138717, 0.149445554002916905664936468389821};
182 static const std::vector<T> vw21b(aw21b, aw21b + 6);
183
184 // w43b, weights of the 43-point formula for abscissae x43
185 static const T aw43b[12] = {0.001844477640212414100389106552965, 0.010798689585891651740465406741293,
186 0.021895363867795428102523123075149, 0.032597463975345689443882222526137,
187 0.042163137935191811847627924327955, 0.050741939600184577780189020092084,
188 0.058379395542619248375475369330206, 0.064746404951445885544689259517511,
189 0.069566197912356484528633315038405, 0.072824441471833208150939535192842,
190 0.074507751014175118273571813842889, 0.074722147517403005594425168280423};
191 static const std::vector<T> vw43b(aw43b, aw43b + 12);
192
193 // w87b, weights of the 87-point formula for abscissae x87
194 static const T aw87b[23] = {0.000274145563762072350016527092881, 0.001807124155057942948341311753254,
195 0.004096869282759164864458070683480, 0.006758290051847378699816577897424,
196 0.009549957672201646536053581325377, 0.012329447652244853694626639963780,
197 0.015010447346388952376697286041943, 0.017548967986243191099665352925900,
198 0.019938037786440888202278192730714, 0.022194935961012286796332102959499,
199 0.024339147126000805470360647041454, 0.026374505414839207241503786552615,
200 0.028286910788771200659968002987960, 0.030052581128092695322521110347341,
201 0.031646751371439929404586051078883, 0.033050413419978503290785944862689,
202 0.034255099704226061787082821046821, 0.035262412660156681033782717998428,
203 0.036076989622888701185500318003895, 0.036698604498456094498018047441094,
204 0.037120549269832576114119958413599, 0.037334228751935040321235449094698,
205 0.037361073762679023410321241766599};
206 static const std::vector<T> vw87b(aw87b, aw87b + 23);
207
208 // w175b, weights of the 175-point formula for abscissae x175
209 static const T aw175b[45] = {
210 0.00003901440664395060055484226, 0.0002787312407993348139961464, 0.0006672934146291138823512275,
211 0.001163051749910003055308177, 0.001738533916888715565420637, 0.002369555040550195269486165,
212 0.003036735036032612976379865, 0.003725394125884235586678819, 0.004424387541776355951933433,
213 0.005125062882078508655875582, 0.005820601038952832388647054, 0.006505667785357412495794539,
214 0.007176258976795165213169074, 0.007829642423806550517967042, 0.008464316525043036555640657,
215 0.009079917879101951192512711, 0.009677029304308397008134699, 0.01025687419430508685393322,
216 0.01082092935368957685380896, 0.01137052956179654620079332, 0.01190655150082017425918844,
217 0.01242924137407215963971061, 0.01293819980598456566872951, 0.01343248644726851711632966,
218 0.01391078107864287587682982, 0.01437154592198526807352501, 0.01481316256915705351874381,
219 0.01523404482122031244940129, 0.01563274056894636856297717, 0.01600802989372176552081826,
220 0.01635901148521841710605397, 0.01668515675646806540972517, 0.01698630892029276765404134,
221 0.01726261506199017604299177, 0.01751439915887340284018269, 0.01774200489411242260549908,
222 0.01794564958245060930824294, 0.01812532816637054898168673, 0.01828078919412312732671357,
223 0.01841158014800801587767163, 0.01851713825962505903167768, 0.01859689376712028821908313,
224 0.01865035760791320287947920, 0.01867717982648033250824110, 0.01868053688133951170552407};
225 static const std::vector<T> vw175b(aw175b, aw175b + 45);
226
227 static const std::vector<T>* wb[NGKPLEVELS] = {&vw10b, &vw21b, &vw43b, &vw87b, &vw175b};
228
229 assert(level >= 0 && level < NGKPLEVELS);
230 return *wb[level];
231}
232
233#ifdef EXTRA_PREC_H
234
235template <>
236inline const std::vector<Quad>& gkp_x<Quad>(int level) {
237 // x10, abscissae common to the 10-, 21-, 43- and 87-point rule
238 static const Quad ax10[5] = {"0.973906528517171720077964012084452", "0.865063366688984510732096688423493",
239 "0.679409568299024406234327365114874", "0.433395394129247190799265943165784",
240 "0.148874338981631210884826001129720"};
241 static const std::vector<Quad> vx10(ax10, ax10 + 5);
242
243 // x21, abscissae common to the 21-, 43- and 87-point rule
244 static const Quad ax21[5] = {"0.995657163025808080735527280689003", "0.930157491355708226001207180059508",
245 "0.780817726586416897063717578345042", "0.562757134668604683339000099272694",
246 "0.294392862701460198131126603103866"};
247 static const std::vector<Quad> vx21(ax21, ax21 + 5);
248
249 // x43, abscissae common to the 43- and 87-point rule
250 static const Quad ax43[11] = {
251 "0.999333360901932081394099323919911", "0.987433402908088869795961478381209",
252 "0.954807934814266299257919200290473", "0.900148695748328293625099494069092",
253 "0.825198314983114150847066732588520", "0.732148388989304982612354848755461",
254 "0.622847970537725238641159120344323", "0.499479574071056499952214885499755",
255 "0.364901661346580768043989548502644", "0.222254919776601296498260928066212",
256 "0.074650617461383322043914435796506"};
257 static const std::vector<Quad> vx43(ax43, ax43 + 11);
258
259 // x87, abscissae of the 87-point rule
260 static const Quad ax87[22] = {
261 "0.999902977262729234490529830591582", "0.997989895986678745427496322365960",
262 "0.992175497860687222808523352251425", "0.981358163572712773571916941623894",
263 "0.965057623858384619128284110607926", "0.943167613133670596816416634507426",
264 "0.915806414685507209591826430720050", "0.883221657771316501372117548744163",
265 "0.845710748462415666605902011504855", "0.803557658035230982788739474980964",
266 "0.757005730685495558328942793432020", "0.706273209787321819824094274740840",
267 "0.651589466501177922534422205016736", "0.593223374057961088875273770349144",
268 "0.531493605970831932285268948562671", "0.466763623042022844871966781659270",
269 "0.399424847859218804732101665817923", "0.329874877106188288265053371824597",
270 "0.258503559202161551802280975429025", "0.185695396568346652015917141167606",
271 "0.111842213179907468172398359241362", "0.037352123394619870814998165437704"};
272 static const std::vector<Quad> vx87(ax87, ax87 + 22);
273
274 // x175, new abscissae of the 175-point rule
275 static const Quad ax175[44] = {
276 "0.9999863601049729677997719", "0.9996988005421428623760900", "0.9987732473138838303043008",
277 "0.9969583851613681945576954", "0.9940679446543307664316419", "0.9899673391741082769960501",
278 "0.9845657252243253759726856", "0.9778061574856414566055911", "0.9696573134362640567828241",
279 "0.9601075259508299668299148", "0.9491605191933640559839528", "0.9368321320434676982049391",
280 "0.9231475266471484946315312", "0.9081385954543932335481458", "0.8918414554201179766275301",
281 "0.8742940658668577971868106", "0.8555341249920432726468181", "0.8355974653331171075829366",
282 "0.8145171513255796294567278", "0.7923233739697216224661771", "0.7690440708082055924983192",
283 "0.7447060413364141221086362", "0.7193362474393392286563226", "0.6929630148748741413274435",
284 "0.6656169582351898081906710", "0.6373315753624730450361940", "0.6081435407529742253347887",
285 "0.5780927509986774074337714", "0.5472221576559162873479056", "0.5155774001694817879753989",
286 "0.4832062516695473663839323", "0.4501579202236101928554315", "0.4164822936334372150371142",
287 "0.3822292525735955063074986", "0.3474481818229070516859048", "0.3121877718977455143765043",
288 "0.2764961311348905899785770", "0.2404211453027010909070665", "0.2040109589145005126324680",
289 "0.1673144327616352753945014", "0.1303814601095591675431696", "0.09326308333660176874846400",
290 "0.05601141598806823374241435", "0.01867941779948308845140053"};
291 static const std::vector<Quad> vx175(ax175, ax175 + 44);
292
293 static const std::vector<Quad>* x[NGKPLEVELS] = {&vx10, &vx21, &vx43, &vx87, &vx175};
294
295 assert(level >= 0 && level < NGKPLEVELS);
296 return *x[level];
297}
298
299template <>
300inline const std::vector<Quad>& gkp_wa<Quad>(int level) {
301 // w21a, weights of the 21-point formula for abscissae x10
302 static const Quad aw21a[5] = {
303 "0.032558162307964727478818972459390", "0.075039674810919952767043140916190",
304 "0.109387158802297641899210590325805", "0.134709217311473325928054001771707",
305 "0.147739104901338491374841515972068"};
306 static const std::vector<Quad> vw21a(aw21a, aw21a + 5);
307
308 // w43a, weights of the 43-point formula for abscissae x10,x21
309 static const Quad aw43a[10] = {
310 "0.016296734289666564924281974617663", "0.037522876120869501461613795898115",
311 "0.054694902058255442147212685465005", "0.067355414609478086075553166302174",
312 "0.073870199632393953432140695251367", "0.005768556059769796184184327908655",
313 "0.027371890593248842081276069289151", "0.046560826910428830743339154433824",
314 "0.061744995201442564496240336030883", "0.071387267268693397768559114425516"};
315 static const std::vector<Quad> vw43a(aw43a, aw43a + 10);
316
317 // w87a, weights of the 87-point formula for abscissae x10..x43
318 static const Quad aw87a[21] = {
319 "0.008148377384149172900002878448190", "0.018761438201562822243935059003794",
320 "0.027347451050052286161582829741283", "0.033677707311637930046581056957588",
321 "0.036935099820427907614589586742499", "0.002884872430211530501334156248695",
322 "0.013685946022712701888950035273128", "0.023280413502888311123409291030404",
323 "0.030872497611713358675466394126442", "0.035693633639418770719351355457044",
324 "0.000915283345202241360843392549948", "0.005399280219300471367738743391053",
325 "0.010947679601118931134327826856808", "0.016298731696787335262665703223280",
326 "0.021081568889203835112433060188190", "0.025370969769253827243467999831710",
327 "0.029189697756475752501446154084920", "0.032373202467202789685788194889595",
328 "0.034783098950365142750781997949596", "0.036412220731351787562801163687577",
329 "0.037253875503047708539592001191226"};
330 static const std::vector<Quad> vw87a(aw87a, aw87a + 21);
331
332 // w175a, weights of the 175-point formula for abscissae x10..x87
333 static const Quad aw175a[43] = {"0.004074188692082600103872341", "0.009380719100781411819741177",
334 "0.01367372552502614309257226", "0.01683885365581896502443513",
335 "0.01846754991021395380770806", "0.001442436294030254510518689",
336 "0.006842973011356375224430623", "0.01164020675144415562952859",
337 "0.01543624880585667934076834", "0.01784681681970938536027839",
338 "0.0004576754584154192941064591", "0.002699640110136963534043642",
339 "0.005473839800559775445647306", "0.008149365848393670964180954",
340 "0.01054078444460191775302900", "0.01268548488462691364854167",
341 "0.01459484887823787625642303", "0.01618660123360139484467359",
342 "0.01739154947518257137619173", "0.01820611036567589378188459",
343 "0.01862693775152385427017140", "0.0001363171844264931156688042",
344 "0.0009035606060432074452289352", "0.002048434635928091782250346",
345 "0.003379145025868061092978424", "0.004774978836099393880602724",
346 "0.006164723826122346701274159", "0.007505223673194467726814647",
347 "0.008774483993121594091281642", "0.009969018893220443741650500",
348 "0.01109746798050614328494604", "0.01216957356300040269315573",
349 "0.01318725270741960360319771", "0.01414345539438560032188640",
350 "0.01502629056404634765715107", "0.01582337568571996469999659",
351 "0.01652520670998925164398162", "0.01712754985211303089259342",
352 "0.01763120633007834051620255", "0.01803849481144435059221422",
353 "0.01834930224922804724856518", "0.01856027463491628805666919",
354 "0.01866711437596752016025132"};
355 static const std::vector<Quad> vw175a(aw175a, aw175a + 43);
356
357 static const std::vector<Quad>* wa[NGKPLEVELS] = {0, &vw21a, &vw43a, &vw87a, &vw175a};
358
359 assert(level >= 1 && level < NGKPLEVELS);
360 return *wa[level];
361}
362
363template <>
364inline const std::vector<Quad>& gkp_wb<Quad>(int level) {
365 // w10, weights of the 10-point formula
366 static const Quad aw10b[6] = {
367 "0.066671344308688137593568809893332", "0.149451349150580593145776339657697",
368 "0.219086362515982043995534934228163", "0.269266719309996355091226921569469",
369 "0.295524224714752870173892994651338", "0.0"};
370 static const std::vector<Quad> vw10b(aw10b, aw10b + 6);
371
372 // w21b, weights of the 21-point formula for abscissae x21
373 static const Quad aw21b[6] = {
374 "0.011694638867371874278064396062192", "0.054755896574351996031381300244580",
375 "0.093125454583697605535065465083366", "0.123491976262065851077958109831074",
376 "0.142775938577060080797094273138717", "0.149445554002916905664936468389821"};
377 static const std::vector<Quad> vw21b(aw21b, aw21b + 6);
378
379 // w43b, weights of the 43-point formula for abscissae x43
380 static const Quad aw43b[12] = {
381 "0.001844477640212414100389106552965", "0.010798689585891651740465406741293",
382 "0.021895363867795428102523123075149", "0.032597463975345689443882222526137",
383 "0.042163137935191811847627924327955", "0.050741939600184577780189020092084",
384 "0.058379395542619248375475369330206", "0.064746404951445885544689259517511",
385 "0.069566197912356484528633315038405", "0.072824441471833208150939535192842",
386 "0.074507751014175118273571813842889", "0.074722147517403005594425168280423"};
387 static const std::vector<Quad> vw43b(aw43b, aw43b + 12);
388
389 // w87b, weights of the 87-point formula for abscissae x87
390 static const Quad aw87b[23] = {
391 "0.000274145563762072350016527092881", "0.001807124155057942948341311753254",
392 "0.004096869282759164864458070683480", "0.006758290051847378699816577897424",
393 "0.009549957672201646536053581325377", "0.012329447652244853694626639963780",
394 "0.015010447346388952376697286041943", "0.017548967986243191099665352925900",
395 "0.019938037786440888202278192730714", "0.022194935961012286796332102959499",
396 "0.024339147126000805470360647041454", "0.026374505414839207241503786552615",
397 "0.028286910788771200659968002987960", "0.030052581128092695322521110347341",
398 "0.031646751371439929404586051078883", "0.033050413419978503290785944862689",
399 "0.034255099704226061787082821046821", "0.035262412660156681033782717998428",
400 "0.036076989622888701185500318003895", "0.036698604498456094498018047441094",
401 "0.037120549269832576114119958413599", "0.037334228751935040321235449094698",
402 "0.037361073762679023410321241766599"};
403 static const std::vector<Quad> vw87b(aw87b, aw87b + 23);
404
405 // w175b, weights of the 175-point formula for abscissae x175
406 static const Quad aw175b[45] = {"0.00003901440664395060055484226", "0.0002787312407993348139961464",
407 "0.0006672934146291138823512275", "0.001163051749910003055308177",
408 "0.001738533916888715565420637", "0.002369555040550195269486165",
409 "0.003036735036032612976379865", "0.003725394125884235586678819",
410 "0.004424387541776355951933433", "0.005125062882078508655875582",
411 "0.005820601038952832388647054", "0.006505667785357412495794539",
412 "0.007176258976795165213169074", "0.007829642423806550517967042",
413 "0.008464316525043036555640657", "0.009079917879101951192512711",
414 "0.009677029304308397008134699", "0.01025687419430508685393322",
415 "0.01082092935368957685380896", "0.01137052956179654620079332",
416 "0.01190655150082017425918844", "0.01242924137407215963971061",
417 "0.01293819980598456566872951", "0.01343248644726851711632966",
418 "0.01391078107864287587682982", "0.01437154592198526807352501",
419 "0.01481316256915705351874381", "0.01523404482122031244940129",
420 "0.01563274056894636856297717", "0.01600802989372176552081826",
421 "0.01635901148521841710605397", "0.01668515675646806540972517",
422 "0.01698630892029276765404134", "0.01726261506199017604299177",
423 "0.01751439915887340284018269", "0.01774200489411242260549908",
424 "0.01794564958245060930824294", "0.01812532816637054898168673",
425 "0.01828078919412312732671357", "0.01841158014800801587767163",
426 "0.01851713825962505903167768", "0.01859689376712028821908313",
427 "0.01865035760791320287947920", "0.01867717982648033250824110",
428 "0.01868053688133951170552407"};
429 static const std::vector<Quad> vw175b(aw175b, aw175b + 45);
430
431 static const std::vector<Quad>* wb[NGKPLEVELS] = {&vw10b, &vw21b, &vw43b, &vw87b, &vw175b};
432
433 assert(level >= 0 && level < NGKPLEVELS);
434 return *wb[level];
435}
436
437#endif
438
439} // end of namespace details
440} // namespace math
441} // namespace afw
442} // namespace lsst
443
444#endif
lsst::afw::math::details::gkp_x
const std::vector< T > & gkp_x(int level)
Definition IntGKPData10.h:54
lsst::afw::math::details::gkp_wa
const std::vector< T > & gkp_wa(int level)
Definition IntGKPData10.h:116
lsst::afw::math::details::gkp_wb
const std::vector< T > & gkp_wb(int level)
Definition IntGKPData10.h:171
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