23 #if defined (HAVE_CONFIG_H) 42 #define DEBUG_QUADCC 0 58 static const double DROP_RELTOL = std::numeric_limits<double>::epsilon () * 10;
62 static const double xi[33] =
64 -1., -0.99518472667219688624, -0.98078528040323044912,
65 -0.95694033573220886493, -0.92387953251128675612,
66 -0.88192126434835502970, -0.83146961230254523708,
67 -0.77301045336273696082, -0.70710678118654752440,
68 -0.63439328416364549822, -0.55557023301960222475,
69 -0.47139673682599764857, -0.38268343236508977173,
70 -0.29028467725446236764, -0.19509032201612826785,
71 -0.098017140329560601995, 0., 0.098017140329560601995,
72 0.19509032201612826785, 0.29028467725446236764, 0.38268343236508977173,
73 0.47139673682599764857, 0.55557023301960222475, 0.63439328416364549822,
74 0.70710678118654752440, 0.77301045336273696082, 0.83146961230254523708,
75 0.88192126434835502970, 0.92387953251128675612, 0.95694033573220886493,
76 0.98078528040323044912, 0.99518472667219688624, 1.
79 static const double bee[68] =
81 0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
82 -8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
83 0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
84 3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
85 0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
86 5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
87 0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
88 4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
89 0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
90 3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
91 0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
92 5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
93 0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
94 3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
95 0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
96 7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
97 0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
98 1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
99 0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
100 6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
101 0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
102 2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
103 0.00000000000000e+00, 5.40679930965238e-01
108 5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
109 5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
110 5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
111 5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
112 5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
113 5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
114 5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
115 5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
116 5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
117 5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
118 5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
123 0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
124 5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
125 5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
126 5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
127 5.00319182924304e-01, 5.00278009473803e-01, 5.00244319584578e-01,
128 5.00216403386025e-01, 5.00193012939056e-01, 5.00173220168024e-01,
129 5.00156323280355e-01, 5.00141783641018e-01, 5.00129182278347e-01,
130 5.00118189340972e-01, 5.00108542278496e-01, 5.00100030010003e-01,
131 5.00092481273333e-01, 5.00085755939229e-01, 5.00079738458365e-01,
132 5.00074332862969e-01, 5.00069458915387e-01, 5.00065049112355e-01,
138 .47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
139 .37712361663282534635, .47140452079103168293e-1,
140 -.81649658092772603273e-1, -.46188021535170061160, 0,
141 .46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
142 .12046772038736683169, -.54210474174315074262, .12046772038736683169,
143 .15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
144 -.30237157840738178177, .21380899352993950775, .10774960475223581324,
145 -.21549920950447162648, .21549920950447162648, -.21549920950447162648,
146 .10774960475223581324
151 .11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
152 .25577315077753587922, .27835314560994251755, .25577315077753587922,
153 .19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
154 -.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
155 -.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
156 .16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
157 .17766815796285469394, .11316664642449611462, -.16306601003711325980,
158 -.30847037493128779631, -.16306601003711325980, .11316664642449611462,
159 .17766815796285469394, .26466393115406349388e-1,
160 -.32395302049990834508e-1, -.15521142532414866547,
161 .88573492664788602740e-1, .29570405784974857322, 0.0,
162 -.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
163 .32395302049990834508e-1, .41442155673936851246e-1,
164 .98186757907405608245e-1, -.23056908429499411784,
165 -.68047008326360625520e-1, .31797435808002456774,
166 -.68047008326360625520e-1, -.23056908429499411784,
167 .98186757907405608245e-1, .41442155673936851246e-1,
168 -.49981120317798783134e-1, -.24861810572835756217e-1,
169 .23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
170 -.23561326072010832539, .24861810572835756217e-1,
171 .49981120317798783134e-1, .79691635865674781228e-1,
172 -.95725617891693941833e-1, -.57957553356854386344e-1,
173 .21164072460540271452, -.27529837844505833514, .21164072460540271452,
174 -.57957553356854386344e-1, -.95725617891693941833e-1,
175 .79691635865674781228e-1,
176 -.10894869830716590913, .20131094491947531782, -.15407672674888869038,
177 .83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
178 .15407672674888869038, -.20131094491947531782, .10894869830716590913,
179 .54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
180 -.10916211417928767644, .10916211417928767644, -.10916211417928767644,
181 .10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
184 static const double V3inv[17 * 17] =
186 .27729677693590098996e-2, .26423663180333065153e-1,
187 .53374068493933898312e-1, .77007854739523195947e-1,
188 .98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
189 .13612785914022865001, .13888293186236181317, .13612785914022865001,
190 .12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
191 .77007854739523195947e-1, .53374068493933898312e-1,
192 .26423663180333065153e-1, .27729677693590098996e-2,
193 -.48029210642807413690e-2, -.44887724635478800254e-1,
194 -.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
195 -.11102786862182788886, -.85054870109799336515e-1,
196 -.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
197 .85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
198 .11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
199 .48029210642807413690e-2, .62758546879582030087e-2,
200 .55561297093529155869e-1,
201 .93281491021051539742e-1, .92320151237493695139e-1,
202 .55077987469605684531e-1,
203 -.96998141716497488255e-2, -.80285961895427405567e-1,
204 -.13496839655913850224,
205 -.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
206 -.96998141716497488255e-2, .55077987469605684531e-1,
207 .92320151237493695139e-1, .93281491021051539742e-1,
208 .55561297093529155869e-1, .62758546879582030087e-2,
209 -.74850969394858555939e-2, -.61751608943839234096e-1,
210 -.82974150437304275958e-1, -.38437763431942633378e-1,
211 .45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
212 .98768034347019704401e-1, 0.0,
213 -.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
214 -.45745502025779701366e-1, .38437763431942633378e-1,
215 .82974150437304275958e-1, .61751608943839234096e-1,
216 .74850969394858555939e-2, .86710099994384056338e-2,
217 .64006230103659573344e-1, .58517426396091675690e-1,
218 -.29743410528985802680e-1,
219 -.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
220 .97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
221 -.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
222 -.29743410528985802680e-1, .58517426396091675690e-1,
223 .64006230103659573344e-1, .86710099994384056338e-2,
224 -.97486395666294840165e-2, -.62995604908060224672e-1,
225 -.24373234450275529219e-1, .87760984413626872730e-1,
226 .12205204576993351394,
227 .16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
228 0.0, .13682714580929614678, .12422320942156845775,
229 -.16216004196864002088e-1, -.12205204576993351394,
230 -.87760984413626872730e-1, .24373234450275529219e-1,
231 .62995604908060224672e-1, .97486395666294840165e-2,
232 .10956271233750488468e-1, .58613204255294358939e-1,
233 -.13306063940736618859e-1, -.11606666444978454399,
234 -.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
235 -.44678658254872910434e-1, -.15617684362128533405,
236 -.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
237 -.52059598001115805639e-1, -.11606666444978454399,
238 -.13306063940736618859e-1, .58613204255294358939e-1,
239 .10956271233750488468e-1, -.12098893000863087230e-1,
240 -.51626244709126208453e-1, .48919433304746979330e-1,
241 .10467644465949427090,
242 -.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
243 .15434223333238741600, 0.0, -.15434223333238741600,
244 -.28190838706814496438e-1, .13668732103524749234,
245 .48729879523084673782e-1, -.10467644465949427090,
246 -.48919433304746979330e-1, .51626244709126208453e-1,
247 .12098893000863087230e-1, .13542668300437944822e-1,
248 .41712033418258689308e-1,
249 -.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
250 .42121099930651007882e-1, -.14684425840766337756,
251 -.16108203535058647043e-1, .15698075850757976092,
252 -.16108203535058647043e-1, -.14684425840766337756,
253 .42121099930651007882e-1, .12158068748245606853,
254 -.58303943170068132010e-1, -.76190463272803434388e-1,
255 .41712033418258689308e-1, .13542668300437944822e-1,
256 -.14939634995117694417e-1, -.30047246373341564039e-1,
257 .91624635082546425678e-1, -.79133374319110026377e-2,
258 -.12292558212072233355, .90013382617762643524e-1,
259 .84013717196539593395e-1, -.14813033309980695856, 0.0,
260 .14813033309980695856, -.84013717196539593395e-1,
261 -.90013382617762643524e-1,
262 .12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
263 .30047246373341564039e-1, .14939634995117694417e-1,
264 .16986031342807474208e-1,
265 .15760203882617033601e-1, -.91494054040950941996e-1,
266 .70082459207876130806e-1,
267 .53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
268 .72456667788091316868e-1, -.15564535320096811360,
269 .72456667788091316868e-1, .84048122493418898508e-1,
270 -.14340746778352039430, .53390713710144539104e-1,
271 .70082459207876130806e-1, -.91494054040950941996e-1,
272 .15760203882617033601e-1,
273 .16986031342807474208e-1, -.18994065631858742028e-1,
274 -.82901821370405592927e-3, .77239669773015192888e-1,
275 -.10850735431039424680, .47524484622086496464e-1,
276 .69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
277 0.0, -.11992057742398672066, .14829314646228194928,
278 -.69148184871588737021e-1, -.47524484622086496464e-1,
279 .10850735431039424680, -.77239669773015192888e-1,
280 .82901821370405592927e-3, .18994065631858742028e-1,
281 .22761703826371535132e-1, -.17728848711449643358e-1,
282 -.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
283 .63073750910894244526e-1, .32928881123602721303e-1,
284 -.12280950532497593683, .15926189077282729505, -.12280950532497593683,
285 .32928881123602721303e-1, .63073750910894244526e-1,
286 -.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
287 -.17728848711449643358e-1, .22761703826371535132e-1,
288 -.26493215276042203434e-1, .35579780856128386192e-1,
289 .10447309718398935122e-1, -.68616154085314996709e-1,
290 .11775363082763954214, -.13918901977011837274, .12312819418827395690,
291 -.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
292 -.12312819418827395690, .13918901977011837274, -.11775363082763954214,
293 .68616154085314996709e-1, -.10447309718398935122e-1,
294 -.35579780856128386192e-1,
295 .26493215276042203434e-1, .40742523354399706918e-1,
296 -.73124912999529117195e-1, .49317266444153837821e-1,
297 -.13686605413876015320e-1, -.28342624942191100464e-1,
298 .70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
299 -.13817029659318161476, .12981016288391131812, -.10600251632853603875,
300 .70371855298258216249e-1, -.28342624942191100464e-1,
301 -.13686605413876015320e-1,
302 .49317266444153837821e-1, -.73124912999529117195e-1,
303 .40742523354399706918e-1, -.54944368958699908688e-1,
304 .10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
305 -.77703071757424700773e-1, .61050911730999815031e-1,
306 -.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
307 -.21438229266251454773e-1, .42052599404498348871e-1,
308 -.61050911730999815031e-1, .77703071757424700773e-1,
309 -.91369146312596428468e-1,
310 .10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
311 .27485608464748840573e-1, -.54971216929497681146e-1,
312 .54971216929497681146e-1,
313 -.54971216929497681146e-1, .54971216929497681146e-1,
314 -.54971216929497681146e-1, .54971216929497681146e-1,
315 -.54971216929497681146e-1, .54971216929497681146e-1,
316 -.54971216929497681146e-1, .54971216929497681146e-1,
317 -.54971216929497681146e-1, .54971216929497681146e-1,
318 -.54971216929497681146e-1, .54971216929497681146e-1,
319 -.54971216929497681146e-1, .27485608464748840573e-1
322 static const double V4inv[33 * 33] =
324 .69120897476690862600e-3, .66419939766331555194e-2,
325 .13600665164323186111e-1, .20122785860913684493e-1,
326 .26583214101668429944e-1, .32712713318999268739e-1,
327 .38576221976287138036e-1, .44033030938268925133e-1,
328 .49092709529622799673e-1, .53657949874312515646e-1,
329 .57724533144734311859e-1, .61219564530655179096e-1,
330 .64138907503837875026e-1, .66427905189318792009e-1,
331 .68088956652280022887e-1, .69083051391555695878e-1,
332 .69422738116739271449e-1, .69083051391555695878e-1,
333 .68088956652280022887e-1, .66427905189318792009e-1,
334 .64138907503837875026e-1, .61219564530655179096e-1,
335 .57724533144734311859e-1, .53657949874312515646e-1,
336 .49092709529622799673e-1, .44033030938268925133e-1,
337 .38576221976287138036e-1, .32712713318999268739e-1,
338 .26583214101668429944e-1, .20122785860913684493e-1,
339 .13600665164323186111e-1, .66419939766331555194e-2,
340 .69120897476690862600e-3, -.11972090629438798134e-2,
341 -.11448874821643225573e-1, -.23104401104002905904e-1,
342 -.33352899418646530133e-1, -.42538626424075425908e-1,
343 -.49969730733911825941e-1, -.55555454015360728353e-1,
344 -.58955533624852604918e-1, -.60126044219122513907e-1,
345 -.58959430451175833624e-1, -.55546925396227130606e-1,
346 -.49984739749347973762e-1, -.42513009141170294365e-1,
347 -.33399140950669746346e-1, -.23007690803851790829e-1,
348 -.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
349 .23007690803851790829e-1, .33399140950669746346e-1,
350 .42513009141170294365e-1, .49984739749347973762e-1,
351 .55546925396227130606e-1, .58959430451175833624e-1,
352 .60126044219122513907e-1, .58955533624852604918e-1,
353 .55555454015360728353e-1, .49969730733911825941e-1,
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636 -.68132707341917233933e-1, .67534860185243140399e-2,
637 .69268150370037450063e-1, -.41585011920451477177e-1,
638 -.51622397460510041271e-1, .68408139576363036148e-1,
639 .18981259024768933323e-1, -.78265472429342305554e-1,
640 .18981259024768933323e-1, .68408139576363036148e-1,
641 -.51622397460510041271e-1,
642 -.41585011920451477177e-1, .69268150370037450063e-1,
643 .67534860185243140399e-2,
644 -.68132707341917233933e-1, .25707858143963615736e-1,
645 .49660630547172186418e-1,
646 -.45320344390022666738e-1, -.22573685920142225247e-1,
647 .47914131921157015198e-1, -.34555825499804605557e-2,
648 -.31777863364694653331e-1, .11747497650231330965e-1,
649 .51591759101720291381e-2, -.54365757412741340377e-2,
650 -.94862516619529080191e-2, .33240472093448190877e-1,
651 -.88698898099681552229e-2,
652 -.40973252097216337576e-1, .42995673349795657065e-1,
653 .17320914507876958783e-1,
654 -.62201292691914856803e-1, .24726274174637346693e-1,
655 .51320859246515407288e-1,
656 -.62882063373810501763e-1, -.11003569131725622672e-1,
657 .73842261324108943465e-1, -.39240120294802923208e-1,
658 -.49293966443941122807e-1, .73552644778818223475e-1, 0.0,
659 -.73552644778818223475e-1, .49293966443941122807e-1,
660 .39240120294802923208e-1, -.73842261324108943465e-1,
661 .11003569131725622672e-1, .62882063373810501763e-1,
662 -.51320859246515407288e-1,
663 -.24726274174637346693e-1, .62201292691914856803e-1,
664 -.17320914507876958783e-1, -.42995673349795657065e-1,
665 .40973252097216337576e-1, .88698898099681552229e-2,
666 -.33240472093448190877e-1, .94862516619529080191e-2,
667 .54365757412741340377e-2, .57750194549356126240e-2,
668 .69981166020044116791e-2, -.33274982140403110792e-1,
669 .20297071020698356116e-1, .27898517839646066582e-1,
670 -.53368678853282030262e-1, .16656482990394548343e-1,
671 .46342901447260614255e-1,
672 -.60536796508149003365e-1, .29109107483842596340e-2,
673 .63224486124385124504e-1,
674 -.59028872851312033411e-1, -.14783105962696191734e-1,
675 .74269399241069253865e-1, -.49053677339382384625e-1,
676 -.33525466624811186739e-1, .78397349622515386647e-1,
677 -.33525466624811186739e-1, -.49053677339382384625e-1,
678 .74269399241069253865e-1, -.14783105962696191734e-1,
679 -.59028872851312033411e-1,
680 .63224486124385124504e-1, .29109107483842596340e-2,
681 -.60536796508149003365e-1,
682 .46342901447260614255e-1, .16656482990394548343e-1,
683 -.53368678853282030262e-1,
684 .27898517839646066582e-1, .20297071020698356116e-1,
685 -.33274982140403110792e-1,
686 .69981166020044116791e-2, .57750194549356126240e-2,
687 -.61100308370519200637e-2, -.44383614355738148616e-2,
688 .32011283412619094811e-1, -.29965011866372897633e-1,
689 -.10560682331349193348e-1, .51110336443392506342e-1,
690 -.45012284729681775492e-1, -.94236825555873320102e-2,
691 .60860695783141264746e-1,
692 -.55014628647083368926e-1, -.73474782382499482121e-2,
693 .66640148475243034781e-1, -.62533116045749887988e-1,
694 -.38650525912400102585e-2, .68429769005837003777e-1,
695 -.66984505412544901945e-1, 0.0, .66984505412544901945e-1,
696 -.68429769005837003777e-1, .38650525912400102585e-2,
697 .62533116045749887988e-1, -.66640148475243034781e-1,
698 .73474782382499482121e-2,
699 .55014628647083368926e-1, -.60860695783141264746e-1,
700 .94236825555873320102e-2,
701 .45012284729681775492e-1, -.51110336443392506342e-1,
702 .10560682331349193348e-1,
703 .29965011866372897633e-1, -.32011283412619094811e-1,
704 .44383614355738148616e-2,
705 .61100308370519200637e-2, .65409373892036191538e-2,
706 .16350101107071157065e-2, -.29301957285983144319e-1,
707 .36838667173388832579e-1, -.81922703976491586393e-2,
708 -.36955670021050133434e-1, .58374851095540469865e-1,
709 -.31977016246946181856e-1, -.25311073698658094646e-1,
710 .66674413950106952577e-1,
711 -.54865713324521039571e-1, -.39797027891537985440e-2,
712 .62830285264808449064e-1, -.72226313251296100676e-1,
713 .22560232697133353980e-1, .46455784709904033738e-1,
714 -.78200930751070349956e-1, .46455784709904033738e-1,
715 .22560232697133353980e-1, -.72226313251296100676e-1,
716 .62830285264808449064e-1, -.39797027891537985440e-2,
717 -.54865713324521039571e-1, .66674413950106952577e-1,
718 -.25311073698658094646e-1, -.31977016246946181856e-1,
719 .58374851095540469865e-1, -.36955670021050133434e-1,
720 -.81922703976491586393e-2, .36838667173388832579e-1,
721 -.29301957285983144319e-1, .16350101107071157065e-2,
722 .65409373892036191538e-2, -.69686180931868703196e-2,
723 .11849538727632789870e-2, .25452286414610537766e-1,
724 -.40522480651713943230e-1, .25694679053362813183e-1,
725 .14057118113748390637e-1, -.52037614725803488893e-1,
726 .58849342223684035589e-1,
727 -.25075229077361409271e-1, -.29559771094034181083e-1,
728 .68296746944165720199e-1, -.62890462146423984955e-1,
729 .14457636466274596445e-1, .45787612031322361496e-1,
730 -.77231759014655809742e-1, .57881203613910543657e-1, 0.0,
731 -.57881203613910543657e-1, .77231759014655809742e-1,
732 -.45787612031322361496e-1, -.14457636466274596445e-1,
733 .62890462146423984955e-1,
734 -.68296746944165720199e-1, .29559771094034181083e-1,
735 .25075229077361409271e-1,
736 -.58849342223684035589e-1, .52037614725803488893e-1,
737 -.14057118113748390637e-1, -.25694679053362813183e-1,
738 .40522480651713943230e-1, -.25452286414610537766e-1,
739 -.11849538727632789870e-2, .69686180931868703196e-2,
740 .75611653617520254845e-2, -.43290610418608409141e-2,
741 -.20277062025115566914e-1,
742 .40362947027704828926e-1, -.38938808024132120254e-1,
743 .11831186195916702262e-1,
744 .28476667401744525357e-1, -.59320969056617684621e-1,
745 .61101629747436200186e-1,
746 -.29514834848355389223e-1, -.20668001885001084821e-1,
747 .62923592802445122793e-1, -.73558456263588833115e-1,
748 .45314556330160999776e-1, .79031645918426015574e-2,
749 -.58136953576334689357e-1, .78538474524006405758e-1,
750 -.58136953576334689357e-1, .79031645918426015574e-2,
751 .45314556330160999776e-1, -.73558456263588833115e-1,
752 .62923592802445122793e-1, -.20668001885001084821e-1,
753 -.29514834848355389223e-1, .61101629747436200186e-1,
754 -.59320969056617684621e-1, .28476667401744525357e-1,
755 .11831186195916702262e-1, -.38938808024132120254e-1,
756 .40362947027704828926e-1, -.20277062025115566914e-1,
757 -.43290610418608409141e-2, .75611653617520254845e-2,
758 -.81505692478987769484e-2, .74297333588288568430e-2,
759 .14314212513540223314e-1, -.36711242251332751607e-1,
760 .46240027755503814626e-1, -.34921532671769023773e-1,
761 .46930051972353714773e-2,
762 .32842770336385381562e-1, -.61317813706529588466e-1,
763 .67000809902468893103e-1,
764 -.45337449655535622885e-1, .35794459576271920867e-2,
765 .41830061526027213385e-1,
766 -.72091371931944711708e-1, .74150028530317793195e-1,
767 -.46487632538609942002e-1, 0.0, .46487632538609942002e-1,
768 -.74150028530317793195e-1, .72091371931944711708e-1,
769 -.41830061526027213385e-1, -.35794459576271920867e-2,
770 .45337449655535622885e-1, -.67000809902468893103e-1,
771 .61317813706529588466e-1, -.32842770336385381562e-1,
772 -.46930051972353714773e-2, .34921532671769023773e-1,
773 -.46240027755503814626e-1, .36711242251332751607e-1,
774 -.14314212513540223314e-1, -.74297333588288568430e-2,
775 .81505692478987769484e-2, .90693182942442189743e-2,
776 -.11121000903959576737e-1, -.71308296141317458546e-2,
777 .29219439765986671645e-1, -.45820286629778129593e-1,
778 .49088381175879124421e-1, -.35614888785023038938e-1,
779 .78906970900092777895e-2,
780 .26262843038404929480e-1, -.56143674270125757857e-1,
781 .71700220472378350694e-1,
782 -.66963544500697307945e-1, .42215091779892228883e-1,
783 -.41338867413966866997e-2, -.36164891772995367321e-1,
784 .66584367783847858225e-1, -.77874712365070098328e-1,
785 .66584367783847858225e-1, -.36164891772995367321e-1,
786 -.41338867413966866997e-2, .42215091779892228883e-1,
787 -.66963544500697307945e-1,
788 .71700220472378350694e-1, -.56143674270125757857e-1,
789 .26262843038404929480e-1,
790 .78906970900092777895e-2, -.35614888785023038938e-1,
791 .49088381175879124421e-1,
792 -.45820286629778129593e-1, .29219439765986671645e-1,
793 -.71308296141317458546e-2, -.11121000903959576737e-1,
794 .90693182942442189743e-2, -.99848472706332791043e-2,
795 .14701271465939718856e-1, -.32917820356048383366e-3,
796 -.19201195309873585230e-1, .38409681836626963278e-1,
797 -.51647324405878909521e-1, .54522171113149311354e-1,
798 -.45040302741689006270e-1, .24183738595685990149e-1,
799 .42204134165479735097e-2, -.34317295181348742251e-1,
800 .59542472465494579941e-1, -.74135115907618101263e-1,
801 .74491937840566532596e-1, -.60042604725161994304e-1,
802 .33437677409000083169e-1, 0.0,
803 -.33437677409000083169e-1, .60042604725161994304e-1,
804 -.74491937840566532596e-1, .74135115907618101263e-1,
805 -.59542472465494579941e-1, .34317295181348742251e-1,
806 -.42204134165479735097e-2, -.24183738595685990149e-1,
807 .45040302741689006270e-1, -.54522171113149311354e-1,
808 .51647324405878909521e-1, -.38409681836626963278e-1,
809 .19201195309873585230e-1, .32917820356048383366e-3,
810 -.14701271465939718856e-1, .99848472706332791043e-2,
811 .11775579274769383373e-1, -.19892153937316935880e-1,
812 .95335114477449041055e-2, .57661528440359081617e-2,
813 -.23382690532380910781e-1, .40237257037170725321e-1,
814 -.53280289903551636474e-1, .59974361806023689068e-1,
815 -.58701684061992853224e-1, .49033407111597129616e-1,
816 -.31818835267847249219e-1, .90800541261162098886e-2,
817 .16272906819312603838e-1, -.40863896581186229487e-1,
818 .61346046297517367703e-1,
819 -.74896047554167268919e-1, .79632642148310325817e-1,
820 -.74896047554167268919e-1, .61346046297517367703e-1,
821 -.40863896581186229487e-1, .16272906819312603838e-1,
822 .90800541261162098886e-2, -.31818835267847249219e-1,
823 .49033407111597129616e-1, -.58701684061992853224e-1,
824 .59974361806023689068e-1, -.53280289903551636474e-1,
825 .40237257037170725321e-1, -.23382690532380910781e-1,
826 .57661528440359081617e-2, .95335114477449041055e-2,
827 -.19892153937316935880e-1,
828 .11775579274769383373e-1, -.13562702617218467450e-1,
829 .24885419969649845849e-1, -.18368693901908875583e-1,
830 .81673147806084084638e-2, .47890591326129587131e-2,
831 -.19313752945227974024e-1, .34065953398362954708e-1,
832 -.47667045133463415672e-1, .58820377816690514309e-1,
833 -.66424139824618415970e-1,
834 .69667606260856092515e-1, -.68102459384364543253e-1,
835 .61683024923302547971e-1,
836 -.50771943476441639136e-1, .36110771847327189215e-1,
837 -.18758028464284563358e-1, 0.0, .18758028464284563358e-1,
838 -.36110771847327189215e-1, .50771943476441639136e-1,
839 -.61683024923302547971e-1, .68102459384364543253e-1,
840 -.69667606260856092515e-1, .66424139824618415970e-1,
841 -.58820377816690514309e-1, .47667045133463415672e-1,
842 -.34065953398362954708e-1, .19313752945227974024e-1,
843 -.47890591326129587131e-2, -.81673147806084084638e-2,
844 .18368693901908875583e-1, -.24885419969649845849e-1,
845 .13562702617218467450e-1, .20576545037980523979e-1,
846 -.40093155172981004337e-1, .36954083167944054826e-1,
847 -.31856506837591907746e-1, .24996323181546255126e-1,
848 -.16637165210473614136e-1, .71002706773325085237e-2,
849 .32478629093205201133e-2,
850 -.14009562579050569518e-1, .24771262248780618922e-1,
851 -.35119395835433647559e-1, .44656290368574753171e-1,
852 -.53015448339647394161e-1, .59875631995693046782e-1,
853 -.64973208326045193862e-1, .68112280331082143373e-1,
854 -.69172215234062186994e-1, .68112280331082143373e-1,
855 -.64973208326045193862e-1, .59875631995693046782e-1,
856 -.53015448339647394161e-1, .44656290368574753171e-1,
857 -.35119395835433647559e-1, .24771262248780618922e-1,
858 -.14009562579050569518e-1, .32478629093205201133e-2,
859 .71002706773325085237e-2, -.16637165210473614136e-1,
860 .24996323181546255126e-1, -.31856506837591907746e-1,
861 .36954083167944054826e-1, -.40093155172981004337e-1,
862 .20576545037980523979e-1, -.27584914609096156163e-1,
863 .54904171411058497973e-1, -.54109756419563083153e-1,
864 .52794234894345577483e-1, -.50970276026831042415e-1,
865 .48655445537990983379e-1,
866 -.45872036510847994332e-1, .42646854695899611372e-1,
867 -.39010960357087507670e-1, .34999369144476467749e-1,
868 -.30650714874402762189e-1, .26006877464703437057e-1,
869 -.21112579608213651273e-1, .16014956068786763273e-1,
870 -.10763099747751940252e-1, .54075888924374485533e-2, 0.0,
871 -.54075888924374485533e-2, .10763099747751940252e-1,
872 -.16014956068786763273e-1,
873 .21112579608213651273e-1, -.26006877464703437057e-1,
874 .30650714874402762189e-1,
875 -.34999369144476467749e-1, .39010960357087507670e-1,
876 -.42646854695899611372e-1, .45872036510847994332e-1,
877 -.48655445537990983379e-1, .50970276026831042415e-1,
878 -.52794234894345577483e-1, .54109756419563083153e-1,
879 -.54904171411058497973e-1, .27584914609096156163e-1,
880 .13794141262469565740e-1, -.27588282524939131481e-1,
881 .27588282524939131481e-1, -.27588282524939131481e-1,
882 .27588282524939131481e-1, -.27588282524939131481e-1,
883 .27588282524939131481e-1,
884 -.27588282524939131481e-1, .27588282524939131481e-1,
885 -.27588282524939131481e-1, .27588282524939131481e-1,
886 -.27588282524939131481e-1, .27588282524939131481e-1,
887 -.27588282524939131481e-1, .27588282524939131481e-1,
888 -.27588282524939131481e-1, .27588282524939131481e-1,
889 -.27588282524939131481e-1, .27588282524939131481e-1,
890 -.27588282524939131481e-1, .27588282524939131481e-1,
891 -.27588282524939131481e-1, .27588282524939131481e-1,
892 -.27588282524939131481e-1, .27588282524939131481e-1,
893 -.27588282524939131481e-1, .27588282524939131481e-1,
894 -.27588282524939131481e-1, .27588282524939131481e-1,
895 -.27588282524939131481e-1, .27588282524939131481e-1,
896 -.27588282524939131481e-1, .13794141262469565740e-1
899 static const double Tleft[33 * 33] =
901 1., -.86602540378443864678, 0., .33071891388307382381, 0.,
902 -.20728904939721249057, 0., .15128841196122722208, 0.,
903 -.11918864298744029244, 0., .98352013661686631224e-1, 0.,
904 -.83727065404940845733e-1, 0., .72893399403505841203e-1, 0.,
905 -.64544632643375022436e-1, 0., .57913170372415565639e-1, 0.,
906 -.52518242575729562263e-1, 0., .48043311993977520457e-1, 0.,
907 -.44271433659733990243e-1, 0., .41048928022856771981e-1, 0.,
908 -.38263878662008271459e-1, 0., .35832844026365304501e-1, 0., 0.,
909 .50000000000000000000, -.96824583655185422130, .57282196186948000082,
910 .21650635094610966169, -.35903516540862679125, -.97578093724974971969e-1,
911 .26203921611325660506, .55792409597991015609e-1, -.20644078533943456204,
912 -.36172381205961199479e-1, .17035068468874958194,
913 .25371838001497225980e-1, -.14501953125000000000,
914 -.18786835250972344757e-1, .12625507130328301066,
915 .14473795929590520582e-1, -.11179458309419422675,
916 -.11494434254897626155e-1, .10030855351241635862,
917 .93498556820544479096e-2, -.90964264465390582629e-1,
918 -.77546391824364392762e-2, .83213457337452292745e-1,
919 .65358085945588638605e-2, -.76680372422574234569e-1,
920 -.55835321940047427169e-2, .71098828931825789428e-1,
921 .48253327982967591019e-2, -.66274981937248958553e-1,
922 -.42118078245337801387e-2, .62064306433355646267e-1,
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i <= 4;
i++)
1423 for (j = 0; j <= 4; j++)
1424 c[
i] +=
V1inv[
i*5 + j] * fx[j * 8];
1428 for (
i = 0;
i <= 8;
i++)
1431 for (j = 0; j <= 8; j++)
1432 c[
i] +=
V2inv[
i*9 + j] * fx[j * 4];
1436 for (
i = 0;
i <= 16;
i++)
1439 for (j = 0; j <= 16; j++)
1440 c[
i] +=
V3inv[
i*17 + j] * fx[j * 2];
1444 for (
i = 0;
i <= 32;
i++)
1447 for (j = 0; j <= 32; j++)
1460 static const int bidx[4] = { 0, 6, 16, 34 };
1461 double b_new[34], alpha;
1464 for (
i = 0;
i <= n + 1;
i++)
1465 b_new[
i] =
bee[bidx[
d] +
i];
1466 for (
i = 0;
i < nnans;
i++)
1468 b_new[n + 1] = b_new[n + 1] /
Lalpha[n];
1469 b_new[n] = (b_new[n] +
xi[nans[
i]] * b_new[n + 1]) /
Lalpha[n - 1];
1470 for (j = n - 1; j > 0; j--)
1472 (b_new[j] +
xi[nans[
i]] * b_new[j + 1] -
1474 for (j = 0; j <= n; j++)
1475 b_new[j] = b_new[j + 1];
1476 alpha =
c[n] / b_new[n];
1477 for (j = 0; j < n; j++)
1478 c[j] -= alpha * b_new[j];
1486 DEFUN (quadcc, args, ,
1570 static const int n[4] = { 4, 8, 16, 32 };
1571 static const int skip[4] = { 8, 4, 2, 1 };
1572 static const int idx[4] = { 0, 5, 14, 31 };
1573 static const double w = M_SQRT2 / 2;
1574 static const int ndiv_max = 20;
1577 int nargin = args.length ();
1579 double a,
b, abstol, reltol, *sing;
1590 double m,
h, ml, hl, mr, hr, temp;
1591 double igral,
err, igral_final, err_final;
1595 int nnans, nans[33];
1603 if (args(0).is_function_handle () || args(0).is_inline_function ())
1609 fname.append (fcn_name);
1610 fname.append (
"(x) y = ");
1615 if (! args(1).is_real_scalar ())
1616 error (
"quadcc: lower limit of integration (A) must be a real scalar");
1617 a = args(1).double_value ();
1618 issingle = args(1).is_single_type ();
1620 if (! args(2).is_real_scalar ())
1621 error (
"quadcc: upper limit of integration (B) must be a real scalar");
1622 b = args(2).double_value ();
1623 issingle = (issingle || args(2).is_single_type ());
1625 if (
nargin < 4 || args(3).isempty ())
1638 else if (! args(3).isnumeric () || args(3).numel () > 2)
1639 error (
"quadcc: TOL must be a 1- or 2-element vector [AbsTol, RelTol]");
1642 NDArray tol = args(3).array_value ();
1646 error (
"quadcc: absolute tolerance must be >=0");
1648 if (tol.
numel () == 1)
1651 static bool do_warn =
true;
1655 "A single tolerance input now sets AbsTol, not RelTol");
1668 error (
"quadcc: relative tolerance must be >=0");
1674 else if (! (args(4).is_real_scalar () || args(4).is_real_matrix ()))
1675 error (
"quadcc: list of singularities (SING) must be a vector of real values");
1677 nivals = 1 + args(4).numel ();
1694 sing = args(4).array_value ().fortran_vec ();
1696 std::copy_n (sing, nivals-1, iivals+1);
1704 for (
i = 0;
i < nivals + 1;
i++)
1708 iivals[
i] = 2.0 *
atan (iivals[
i]) / M_PI;
1712 for (
i = 0;
i < cquad_heapsize;
i++)
1718 for (j = 0; j < nivals; j++)
1721 iv = &(ivals[heap[j]]);
1722 m = (iivals[j] + iivals[j + 1]) / 2;
1723 h = (iivals[j + 1] - iivals[j]) / 2;
1728 for (
i = 0;
i <= n[3];
i++)
1729 ex(
i) = tan (M_PI/2 * (m +
xi[
i]*
h));
1733 for (
i = 0;
i <= n[3];
i++)
1734 ex(
i) = m +
xi[
i]*
h;
1738 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
1739 error (
"quadcc: integrand F must return a single, real-valued vector");
1741 Matrix effex = fvals(0).matrix_value ();
1743 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
1745 for (
i = 0;
i <= n[3];
i++)
1747 iv->
fx[
i] = effex(
i);
1751 iv->
fx[
i] *= (1.0 + xw*xw) * M_PI/2;
1763 for (
i = 0;
i < nnans;
i++)
1766 iv->
b = iivals[j + 1];
1770 iv->
igral = 2 *
h * iv->
c[idx[3]] *
w;
1772 for (
i = n[2] + 1;
i <= n[3];
i++)
1774 temp = iv->
c[idx[3] +
i];
1778 for (
i = 0;
i <= n[2];
i++)
1780 temp = iv->
c[idx[2] +
i] - iv->
c[idx[3] +
i];
1781 ncdiff += temp * temp;
1782 temp = iv->
c[idx[3] +
i];
1785 ncdiff = sqrt (ncdiff);
1787 iv->
err = ncdiff * 2 *
h;
1788 if (ncdiff / nc > 0.1 && iv->
err < 2 *
h * nc)
1789 iv->
err = 2 *
h * nc;
1797 while (
i > 0 && ivals[heap[
i / 2]].
err < ivals[heap[
i]].
err)
1811 && ! (err_final >
std::max (abstol, fabs (igral) * reltol)
1812 &&
err - err_final <
std::max (abstol, fabs (igral) * reltol)))
1818 iv = &(ivals[heap[0]]);
1819 m = (iv->
a + iv->
b) / 2;
1820 h = (iv->
b - iv->
a) / 2;
1823 printf (
"quadcc: processing ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
1838 for (
i = 0;
i < n[
d] / 2;
i++)
1839 ex(
i) = tan (M_PI/2 * (m +
xi[(2*
i + 1) * skip[
d]] *
h));
1843 for (
i = 0;
i < n[
d] / 2;
i++)
1844 ex(
i) = m +
xi[(2*
i + 1) * skip[
d]] *
h;
1848 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
1849 error (
"quadcc: integrand F must return a single, real-valued vector");
1851 Matrix effex = fvals(0).matrix_value ();
1853 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
1855 neval += effex.
numel ();
1856 for (
i = 0;
i < n[
d] / 2;
i++)
1858 j = (2*
i + 1) * skip[
d];
1859 iv->
fx[j] = effex(
i);
1863 iv->
fx[j] *= (1.0 + xw*xw) * M_PI/2;
1868 for (
i = 0;
i <= 32;
i += skip[
d])
1883 for (
i = 0;
i < nnans;
i++)
1889 for (
i = n[
d - 1] + 1;
i <= n[
d];
i++)
1891 temp = iv->
c[idx[
d] +
i];
1895 for (
i = 0;
i <= n[
d - 1];
i++)
1897 temp = iv->
c[idx[
d - 1] +
i] - iv->
c[idx[
d] +
i];
1898 ncdiff += temp * temp;
1899 temp = iv->
c[idx[
d] +
i];
1902 ncdiff = sqrt (ncdiff);
1904 iv->
err = ncdiff * 2 *
h;
1908 split = (nc > 0 && ncdiff / nc > 0.1);
1917 if ((m +
h*
xi[0]) >= (m +
h*
xi[1])
1918 || (m +
h*
xi[31]) >= (m +
h*
xi[32])
1922 printf (
"quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
1927 err_final += iv->
err;
1928 igral_final += iv->
igral;
1934 while (2*
i + 1 < nivals)
1941 && ivals[heap[j + 1]].
err >= ivals[heap[j]].
err)
1944 if (ivals[heap[j]].
err <= ivals[heap[
i]].
err)
1958 ivl = &(ivals[heap[nivals++]]);
1961 ml = (ivl->
a + ivl->
b) / 2;
1965 ivl->
fx[0] = iv->
fx[0];
1966 ivl->
fx[32] = iv->
fx[16];
1971 for (
i = 0;
i < n[0] - 1;
i++)
1972 ex(
i) = tan (M_PI/2 * (ml +
xi[(
i + 1) * skip[0]] * hl));
1976 for (
i = 0;
i < n[0] - 1;
i++)
1977 ex(
i) = ml +
xi[(
i + 1) * skip[0]] * hl;
1981 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
1982 error (
"quadcc: integrand F must return a single, real-valued vector");
1984 Matrix effex = fvals(0).matrix_value ();
1986 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
1988 neval += effex.
numel ();
1989 for (
i = 0;
i < n[0] - 1;
i++)
1991 j = (
i + 1) * skip[0];
1992 ivl->
fx[j] = effex(
i);
1996 ivl->
fx[j] *= (1.0 + xw*xw) * M_PI/2;
2001 for (
i = 0;
i <= 32;
i += skip[0])
2012 downdate (ivl->
c, n[0], 0, nans, nnans);
2013 for (
i = 0;
i < nnans;
i++)
2016 for (
i = 0;
i <= n[
d];
i++)
2018 ivl->
c[idx[
d] +
i] = 0.0;
2019 for (j =
i; j <= n[
d]; j++)
2020 ivl->
c[idx[
d] +
i] +=
Tleft[
i*33 + j] * iv->
c[idx[
d] + j];
2023 for (
i = 0;
i <= n[0];
i++)
2025 temp = ivl->
c[
i] - ivl->
c[idx[
d] +
i];
2026 ncdiff += temp * temp;
2028 for (
i = n[0] + 1;
i <= n[
d];
i++)
2030 temp = ivl->
c[idx[
d] +
i];
2031 ncdiff += temp * temp;
2033 ncdiff = sqrt (ncdiff);
2034 ivl->
err = ncdiff *
h;
2036 ivl->
ndiv = iv->
ndiv + (fabs (iv->
c[0]) > 0
2037 && ivl->
c[0] / iv->
c[0] > 2);
2041 warning (
"quadcc: divergent integral detected");
2049 ivr = &(ivals[heap[nivals++]]);
2052 mr = (ivr->
a + ivr->
b) / 2;
2056 ivr->
fx[0] = iv->
fx[16];
2057 ivr->
fx[32] = iv->
fx[32];
2062 for (
i = 0;
i < n[0] - 1;
i++)
2063 ex(
i) = tan (M_PI/2 * (mr +
xi[(
i + 1) * skip[0]] * hr));
2067 for (
i = 0;
i < n[0] - 1;
i++)
2068 ex(
i) = mr +
xi[(
i + 1) * skip[0]] * hr;
2072 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
2073 error (
"quadcc: integrand F must return a single, real-valued vector");
2075 Matrix effex = fvals(0).matrix_value ();
2077 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
2079 neval += effex.
numel ();
2080 for (
i = 0;
i < n[0] - 1;
i++)
2082 j = (
i + 1) * skip[0];
2083 ivr->
fx[j] = effex(
i);
2087 ivr->
fx[j] *= (1.0 + xw*xw) * M_PI/2;
2092 for (
i = 0;
i <= 32;
i += skip[0])
2103 downdate (ivr->
c, n[0], 0, nans, nnans);
2104 for (
i = 0;
i < nnans;
i++)
2107 for (
i = 0;
i <= n[
d];
i++)
2109 ivr->
c[idx[
d] +
i] = 0.0;
2110 for (j =
i; j <= n[
d]; j++)
2111 ivr->
c[idx[
d] +
i] +=
Tright[
i*33 + j] * iv->
c[idx[
d] + j];
2114 for (
i = 0;
i <= n[0];
i++)
2116 temp = ivr->
c[
i] - ivr->
c[idx[
d] +
i];
2117 ncdiff += temp * temp;
2119 for (
i = n[0] + 1;
i <= n[
d];
i++)
2121 temp = ivr->
c[idx[
d] +
i];
2122 ncdiff += temp * temp;
2124 ncdiff = sqrt (ncdiff);
2125 ivr->
err = ncdiff *
h;
2127 ivr->
ndiv = iv->
ndiv + (fabs (iv->
c[0]) > 0
2128 && ivr->
c[0] / iv->
c[0] > 2);
2132 warning (
"quadcc: divergent integral detected");
2147 while (2*
i + 1 < nivals - 1)
2150 if (j + 1 < nivals - 1
2151 && ivals[heap[j + 1]].
err >= ivals[heap[j]].
err)
2153 if (ivals[heap[j]].
err <= ivals[heap[
i]].
err)
2167 if (ivals[heap[j]].
err < ivals[heap[
i]].
err)
2180 while (2*
i + 1 < nivals)
2184 && ivals[heap[j + 1]].
err >= ivals[heap[j]].
err)
2186 if (ivals[heap[j]].
err <= ivals[heap[
i]].
err)
2197 while (nivals > cquad_heapsize - 2)
2199 iv = &(ivals[heap[nivals - 1]]);
2201 printf (
"quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
2204 err_final += iv->
err;
2205 igral_final += iv->
igral;
2210 igral = igral_final;
2212 for (
i = 0;
i < nivals;
i++)
2214 igral += ivals[heap[
i]].igral;
2215 err += ivals[heap[
i]].err;
2221 for (
i = 0;
i < nivals;
i++)
2223 iv = &(ivals[heap[
i]]);
2224 printf (
"quadcc: ival %i (%i) with [%e,%e], int=%e, err=%e, depth=%i, rdepth=%i, ndiv=%i\n",
2231 return ovl (static_cast<float> (igral),
err, neval);
2233 return ovl (igral,
err, neval);
OCTINTERP_API octave_value_list feval(const std::string &name, const octave_value_list &args=octave_value_list(), int nargout=0)
void warning_with_id(const char *id, const char *fmt,...)
static const double Lgamma[33]
static const double Tright[33 *33]
OCTINTERP_API void print_usage(void)
static void Vinvfx(const double *fx, double *c, const int d)
printf("%s\, nthargout(2, "system", "cmd"))
#define DEFUN(name, args_name, nargout_name, doc)
Macro to define a builtin function.
void error(const char *fmt,...)
Complex atan(const Complex &x)
nd example oindent opens the file binary numeric values will be read assuming they are stored in IEEE format with the least significant bit and then converted to the native representation Opening a file that is already open simply opens it again and returns a separate file id It is not an error to open a file several though writing to the same file through several different file ids may produce unexpected results The possible values of text mode reading and writing automatically converts linefeeds to the appropriate line end character for the you may append a you must also open the file in binary mode The parameter conversions are currently only supported for and permissions will be set to and then everything is written in a single operation This is very efficient and improves performance c
static const double DROP_RELTOL
F77_RET_T const F77_REAL const F77_REAL F77_REAL &F77_RET_T const F77_DBLE const F77_DBLE F77_DBLE &F77_RET_T const F77_DBLE F77_DBLE &F77_RET_T const F77_REAL F77_REAL &F77_RET_T const F77_DBLE const F77_DBLE F77_DBLE * d
static const double V2inv[9 *9]
std::string unique_symbol_name(const std::string &basename)
calling an anonymous function involves an overhead quite comparable to the overhead of an m file function Passing a handle to a built in function is because the interpreter is not involved in the internal loop For a
static void downdate(double *c, int n, int d, int *nans, int nnans)
static const double bee[68]
static const double Tleft[33 *33]
static const double V3inv[17 *17]
std::complex< double > w(std::complex< double > z, double relerr=0)
static const double V1inv[5 *5]
static const double V4inv[33 *33]
void warning(const char *fmt,...)
charNDArray max(char d, const charNDArray &m)
OCTAVE_EXPORT octave_value_list isa nd deftypefn *return ovl(args(0).isinteger())
OCTAVE_EXPORT octave_value_list or N dimensional array whose elements are all equal to the IEEE symbol NaN(Not a Number). NaN is the result of operations which do not produce a well defined 0 result. Common operations which produce a NaN are arithmetic with infinity ex($\infty - \infty$)
static const double Lalpha[33]
octave_function * extract_function(const octave_value &arg, const std::string &warn_for, const std::string &fname, const std::string &header, const std::string &trailer)
octave_idx_type length(void) const
#define OCTAVE_LOCAL_BUFFER(T, buf, size)
OCTAVE_EXPORT octave_value_list error nd deftypefn *const octave_scalar_map err
virtual octave_function * function_value(bool silent=false)
octave_idx_type numel(void) const
Number of elements in the array.
double copysign(double x, double y)
static const int MIN_CQUAD_HEAPSIZE
If this string is the system will ring the terminal sometimes it is useful to be able to print the original representation of the string
static const double xi[33]