23 #if defined (HAVE_CONFIG_H)
38 #define DEBUG_QUADCC 0
41 #define MIN_CQUAD_HEAPSIZE 200
55 static const double xi[33] =
57 -1., -0.99518472667219688624, -0.98078528040323044912,
58 -0.95694033573220886493, -0.92387953251128675612,
59 -0.88192126434835502970, -0.83146961230254523708,
60 -0.77301045336273696082, -0.70710678118654752440,
61 -0.63439328416364549822, -0.55557023301960222475,
62 -0.47139673682599764857, -0.38268343236508977173,
63 -0.29028467725446236764, -0.19509032201612826785,
64 -0.098017140329560601995, 0., 0.098017140329560601995,
65 0.19509032201612826785, 0.29028467725446236764, 0.38268343236508977173,
66 0.47139673682599764857, 0.55557023301960222475, 0.63439328416364549822,
67 0.70710678118654752440, 0.77301045336273696082, 0.83146961230254523708,
68 0.88192126434835502970, 0.92387953251128675612, 0.95694033573220886493,
69 0.98078528040323044912, 0.99518472667219688624, 1.
72 static const double bee[68] =
74 0.00000000000000e+00, 2.28868854108532e-01, 0.00000000000000e+00,
75 -8.15740215243451e-01, 0.00000000000000e+00, 5.31212715259731e-01,
76 0.00000000000000e+00, 1.38538036812454e-02, 0.00000000000000e+00,
77 3.74405228908818e-02, 0.00000000000000e+00, 2.12224115039342e-01,
78 0.00000000000000e+00, -8.16362644507898e-01, 0.00000000000000e+00,
79 5.35648426691481e-01, 0.00000000000000e+00, 1.52417902753662e-03,
80 0.00000000000000e+00, 2.63058840550873e-03, 0.00000000000000e+00,
81 4.15292106318904e-03, 0.00000000000000e+00, 6.97106011119775e-03,
82 0.00000000000000e+00, 1.35535708431058e-02, 0.00000000000000e+00,
83 3.52132898424856e-02, 0.00000000000000e+00, 2.06946714741884e-01,
84 0.00000000000000e+00, -8.15674251283876e-01, 0.00000000000000e+00,
85 5.38841175520580e-01, 0.00000000000000e+00, 1.84909689577590e-04,
86 0.00000000000000e+00, 2.90936325007499e-04, 0.00000000000000e+00,
87 3.84877750950089e-04, 0.00000000000000e+00, 4.86436656735046e-04,
88 0.00000000000000e+00, 6.08688640346879e-04, 0.00000000000000e+00,
89 7.66732830740331e-04, 0.00000000000000e+00, 9.82753336104205e-04,
90 0.00000000000000e+00, 1.29359957505615e-03, 0.00000000000000e+00,
91 1.76616363801885e-03, 0.00000000000000e+00, 2.53323433039089e-03,
92 0.00000000000000e+00, 3.88872172121956e-03, 0.00000000000000e+00,
93 6.58635106468291e-03, 0.00000000000000e+00, 1.30326736343254e-02,
94 0.00000000000000e+00, 3.44353850696714e-02, 0.00000000000000e+00,
95 2.05025409531915e-01, 0.00000000000000e+00, -8.14985893995401e-01,
96 0.00000000000000e+00, 5.40679930965238e-01
101 5.77350269189626e-01, 5.16397779494322e-01, 5.07092552837110e-01,
102 5.03952630678970e-01, 5.02518907629606e-01, 5.01745206004255e-01,
103 5.01280411827603e-01, 5.00979432868120e-01, 5.00773395667191e-01,
104 5.00626174321759e-01, 5.00517330712619e-01, 5.00434593736979e-01,
105 5.00370233297676e-01, 5.00319182924304e-01, 5.00278009473803e-01,
106 5.00244319584578e-01, 5.00216403386025e-01, 5.00193012939056e-01,
107 5.00173220168024e-01, 5.00156323280355e-01, 5.00141783641018e-01,
108 5.00129182278347e-01, 5.00118189340972e-01, 5.00108542278496e-01,
109 5.00100030010004e-01, 5.00092481273333e-01, 5.00085755939229e-01,
110 5.00079738458365e-01, 5.00074332862969e-01, 5.00069458915387e-01,
111 5.00065049112355e-01, 5.00061046334395e-01, 5.00057401986298e-01
116 0.0, 0.0, 5.16397779494322e-01, 5.07092552837110e-01, 5.03952630678970e-01,
117 5.02518907629606e-01, 5.01745206004255e-01, 5.01280411827603e-01,
118 5.00979432868120e-01, 5.00773395667191e-01, 5.00626174321759e-01,
119 5.00517330712619e-01, 5.00434593736979e-01, 5.00370233297676e-01,
120 5.00319182924304e-01, 5.00278009473803e-01, 5.00244319584578e-01,
121 5.00216403386025e-01, 5.00193012939056e-01, 5.00173220168024e-01,
122 5.00156323280355e-01, 5.00141783641018e-01, 5.00129182278347e-01,
123 5.00118189340972e-01, 5.00108542278496e-01, 5.00100030010003e-01,
124 5.00092481273333e-01, 5.00085755939229e-01, 5.00079738458365e-01,
125 5.00074332862969e-01, 5.00069458915387e-01, 5.00065049112355e-01,
131 .47140452079103168293e-1, .37712361663282534635, .56568542494923801952,
132 .37712361663282534635, .47140452079103168293e-1,
133 -.81649658092772603273e-1, -.46188021535170061160, 0,
134 .46188021535170061160, .81649658092772603273e-1, .15058465048420853962,
135 .12046772038736683169, -.54210474174315074262, .12046772038736683169,
136 .15058465048420853962, -.21380899352993950775, .30237157840738178177, -0.,
137 -.30237157840738178177, .21380899352993950775, .10774960475223581324,
138 -.21549920950447162648, .21549920950447162648, -.21549920950447162648,
139 .10774960475223581324
144 .11223917161691230546e-1, .10339219839658349826, .19754094204576565761,
145 .25577315077753587922, .27835314560994251755, .25577315077753587922,
146 .19754094204576565761, .10339219839658349826, .11223917161691230546e-1,
147 -.19440394783993476970e-1, -.16544884625069155470, -.24193725566041460608,
148 -.16953338808305493604, 0.0, .16953338808305493604, .24193725566041460608,
149 .16544884625069155470, .19440394783993476970e-1, .26466393115406349388e-1,
150 .17766815796285469394, .11316664642449611462, -.16306601003711325980,
151 -.30847037493128779631, -.16306601003711325980, .11316664642449611462,
152 .17766815796285469394, .26466393115406349388e-1,
153 -.32395302049990834508e-1, -.15521142532414866547,
154 .88573492664788602740e-1, .29570405784974857322, 0.0,
155 -.29570405784974857322, -.88573492664788602740e-1, .15521142532414866547,
156 .32395302049990834508e-1, .41442155673936851246e-1,
157 .98186757907405608245e-1, -.23056908429499411784,
158 -.68047008326360625520e-1, .31797435808002456774,
159 -.68047008326360625520e-1, -.23056908429499411784,
160 .98186757907405608245e-1, .41442155673936851246e-1,
161 -.49981120317798783134e-1, -.24861810572835756217e-1,
162 .23561326072010832539, -.24472785656448415351, 0.0, .24472785656448415351,
163 -.23561326072010832539, .24861810572835756217e-1,
164 .49981120317798783134e-1, .79691635865674781228e-1,
165 -.95725617891693941833e-1, -.57957553356854386344e-1,
166 .21164072460540271452, -.27529837844505833514, .21164072460540271452,
167 -.57957553356854386344e-1, -.95725617891693941833e-1,
168 .79691635865674781228e-1,
169 -.10894869830716590913, .20131094491947531782, -.15407672674888869038,
170 .83385723639789791384e-1, 0.0, -.83385723639789791384e-1,
171 .15407672674888869038, -.20131094491947531782, .10894869830716590913,
172 .54581057089643838221e-1, -.10916211417928767644, .10916211417928767644,
173 -.10916211417928767644, .10916211417928767644, -.10916211417928767644,
174 .10916211417928767644, -.10916211417928767644, .54581057089643838221e-1
177 static const double V3inv[17 * 17] =
179 .27729677693590098996e-2, .26423663180333065153e-1,
180 .53374068493933898312e-1, .77007854739523195947e-1,
181 .98257061072911596869e-1, .11538049741786835604, .12832134344120884559,
182 .13612785914022865001, .13888293186236181317, .13612785914022865001,
183 .12832134344120884559, .11538049741786835604, .98257061072911596869e-1,
184 .77007854739523195947e-1, .53374068493933898312e-1,
185 .26423663180333065153e-1, .27729677693590098996e-2,
186 -.48029210642807413690e-2, -.44887724635478800254e-1,
187 -.85409520147301089416e-1, -.11090267822061423050, -.12033983162705862441,
188 -.11102786862182788886, -.85054870109799336515e-1,
189 -.45998467987742225160e-1, 0.0, .45998467987742225160e-1,
190 .85054870109799336515e-1, .11102786862182788886, .12033983162705862441,
191 .11090267822061423050, .85409520147301089416e-1, .44887724635478800254e-1,
192 .48029210642807413690e-2, .62758546879582030087e-2,
193 .55561297093529155869e-1,
194 .93281491021051539742e-1, .92320151237493695139e-1,
195 .55077987469605684531e-1,
196 -.96998141716497488255e-2, -.80285961895427405567e-1,
197 -.13496839655913850224,
198 -.15512521776684524331, -.13496839655913850224, -.80285961895427405567e-1,
199 -.96998141716497488255e-2, .55077987469605684531e-1,
200 .92320151237493695139e-1, .93281491021051539742e-1,
201 .55561297093529155869e-1, .62758546879582030087e-2,
202 -.74850969394858555939e-2, -.61751608943839234096e-1,
203 -.82974150437304275958e-1, -.38437763431942633378e-1,
204 .45745502025779701366e-1, .12369235652734542162, .14720439712852868239,
205 .98768034347019704401e-1, 0.0,
206 -.98768034347019704401e-1, -.14720439712852868239, -.12369235652734542162,
207 -.45745502025779701366e-1, .38437763431942633378e-1,
208 .82974150437304275958e-1, .61751608943839234096e-1,
209 .74850969394858555939e-2, .86710099994384056338e-2,
210 .64006230103659573344e-1, .58517426396091675690e-1,
211 -.29743410528985802680e-1,
212 -.11934127779157114754, -.12686773515361299409, -.30729137153877447035e-1,
213 .97307836256600731568e-1, .15635811574451401023, .97307836256600731568e-1,
214 -.30729137153877447035e-1, -.12686773515361299409, -.11934127779157114754,
215 -.29743410528985802680e-1, .58517426396091675690e-1,
216 .64006230103659573344e-1, .86710099994384056338e-2,
217 -.97486395666294840165e-2, -.62995604908060224672e-1,
218 -.24373234450275529219e-1, .87760984413626872730e-1,
219 .12205204576993351394,
220 .16216004196864002088e-1, -.12422320942156845775, -.13682714580929614678,
221 0.0, .13682714580929614678, .12422320942156845775,
222 -.16216004196864002088e-1, -.12205204576993351394,
223 -.87760984413626872730e-1, .24373234450275529219e-1,
224 .62995604908060224672e-1, .97486395666294840165e-2,
225 .10956271233750488468e-1, .58613204255294358939e-1,
226 -.13306063940736618859e-1, -.11606666444978454399,
227 -.52059598001115805639e-1, .10868540217796151849, .12594452879014618005,
228 -.44678658254872910434e-1, -.15617684362128533405,
229 -.44678658254872910434e-1, .12594452879014618005, .10868540217796151849,
230 -.52059598001115805639e-1, -.11606666444978454399,
231 -.13306063940736618859e-1, .58613204255294358939e-1,
232 .10956271233750488468e-1, -.12098893000863087230e-1,
233 -.51626244709126208453e-1, .48919433304746979330e-1,
234 .10467644465949427090,
235 -.48729879523084673782e-1, -.13668732103524749234, .28190838706814496438e-1,
236 .15434223333238741600, 0.0, -.15434223333238741600,
237 -.28190838706814496438e-1, .13668732103524749234,
238 .48729879523084673782e-1, -.10467644465949427090,
239 -.48919433304746979330e-1, .51626244709126208453e-1,
240 .12098893000863087230e-1, .13542668300437944822e-1,
241 .41712033418258689308e-1,
242 -.76190463272803434388e-1, -.58303943170068132010e-1, .12158068748245606853,
243 .42121099930651007882e-1, -.14684425840766337756,
244 -.16108203535058647043e-1, .15698075850757976092,
245 -.16108203535058647043e-1, -.14684425840766337756,
246 .42121099930651007882e-1, .12158068748245606853,
247 -.58303943170068132010e-1, -.76190463272803434388e-1,
248 .41712033418258689308e-1, .13542668300437944822e-1,
249 -.14939634995117694417e-1, -.30047246373341564039e-1,
250 .91624635082546425678e-1, -.79133374319110026377e-2,
251 -.12292558212072233355, .90013382617762643524e-1,
252 .84013717196539593395e-1, -.14813033309980695856, 0.0,
253 .14813033309980695856, -.84013717196539593395e-1,
254 -.90013382617762643524e-1,
255 .12292558212072233355, .79133374319110026377e-2, -.91624635082546425678e-1,
256 .30047246373341564039e-1, .14939634995117694417e-1,
257 .16986031342807474208e-1,
258 .15760203882617033601e-1, -.91494054040950941996e-1,
259 .70082459207876130806e-1,
260 .53390713710144539104e-1, -.14340746778352039430, .84048122493418898508e-1,
261 .72456667788091316868e-1, -.15564535320096811360,
262 .72456667788091316868e-1, .84048122493418898508e-1,
263 -.14340746778352039430, .53390713710144539104e-1,
264 .70082459207876130806e-1, -.91494054040950941996e-1,
265 .15760203882617033601e-1,
266 .16986031342807474208e-1, -.18994065631858742028e-1,
267 -.82901821370405592927e-3, .77239669773015192888e-1,
268 -.10850735431039424680, .47524484622086496464e-1,
269 .69148184871588737021e-1, -.14829314646228194928, .11992057742398672066,
270 0.0, -.11992057742398672066, .14829314646228194928,
271 -.69148184871588737021e-1, -.47524484622086496464e-1,
272 .10850735431039424680, -.77239669773015192888e-1,
273 .82901821370405592927e-3, .18994065631858742028e-1,
274 .22761703826371535132e-1, -.17728848711449643358e-1,
275 -.47496371572480503788e-1, .10659958402328690063, -.11696013966166296514,
276 .63073750910894244526e-1, .32928881123602721303e-1,
277 -.12280950532497593683, .15926189077282729505, -.12280950532497593683,
278 .32928881123602721303e-1, .63073750910894244526e-1,
279 -.11696013966166296514, .10659958402328690063, -.47496371572480503788e-1,
280 -.17728848711449643358e-1, .22761703826371535132e-1,
281 -.26493215276042203434e-1, .35579780856128386192e-1,
282 .10447309718398935122e-1, -.68616154085314996709e-1,
283 .11775363082763954214, -.13918901977011837274, .12312819418827395690,
284 -.72053565748259077905e-1, 0.0, .72053565748259077905e-1,
285 -.12312819418827395690, .13918901977011837274, -.11775363082763954214,
286 .68616154085314996709e-1, -.10447309718398935122e-1,
287 -.35579780856128386192e-1,
288 .26493215276042203434e-1, .40742523354399706918e-1,
289 -.73124912999529117195e-1, .49317266444153837821e-1,
290 -.13686605413876015320e-1, -.28342624942191100464e-1,
291 .70371855298258216249e-1, -.10600251632853603875, .12981016288391131812,
292 -.13817029659318161476, .12981016288391131812, -.10600251632853603875,
293 .70371855298258216249e-1, -.28342624942191100464e-1,
294 -.13686605413876015320e-1,
295 .49317266444153837821e-1, -.73124912999529117195e-1,
296 .40742523354399706918e-1, -.54944368958699908688e-1,
297 .10777725663147408190, -.10152395581538265428, .91369146312596428468e-1,
298 -.77703071757424700773e-1, .61050911730999815031e-1,
299 -.42052599404498348871e-1, .21438229266251454773e-1, 0.0,
300 -.21438229266251454773e-1, .42052599404498348871e-1,
301 -.61050911730999815031e-1, .77703071757424700773e-1,
302 -.91369146312596428468e-1,
303 .10152395581538265428, -.10777725663147408190, .54944368958699908688e-1,
304 .27485608464748840573e-1, -.54971216929497681146e-1,
305 .54971216929497681146e-1,
306 -.54971216929497681146e-1, .54971216929497681146e-1,
307 -.54971216929497681146e-1, .54971216929497681146e-1,
308 -.54971216929497681146e-1, .54971216929497681146e-1,
309 -.54971216929497681146e-1, .54971216929497681146e-1,
310 -.54971216929497681146e-1, .54971216929497681146e-1,
311 -.54971216929497681146e-1, .54971216929497681146e-1,
312 -.54971216929497681146e-1, .27485608464748840573e-1
315 static const double V4inv[33 * 33] =
317 .69120897476690862600e-3, .66419939766331555194e-2,
318 .13600665164323186111e-1, .20122785860913684493e-1,
319 .26583214101668429944e-1, .32712713318999268739e-1,
320 .38576221976287138036e-1, .44033030938268925133e-1,
321 .49092709529622799673e-1, .53657949874312515646e-1,
322 .57724533144734311859e-1, .61219564530655179096e-1,
323 .64138907503837875026e-1, .66427905189318792009e-1,
324 .68088956652280022887e-1, .69083051391555695878e-1,
325 .69422738116739271449e-1, .69083051391555695878e-1,
326 .68088956652280022887e-1, .66427905189318792009e-1,
327 .64138907503837875026e-1, .61219564530655179096e-1,
328 .57724533144734311859e-1, .53657949874312515646e-1,
329 .49092709529622799673e-1, .44033030938268925133e-1,
330 .38576221976287138036e-1, .32712713318999268739e-1,
331 .26583214101668429944e-1, .20122785860913684493e-1,
332 .13600665164323186111e-1, .66419939766331555194e-2,
333 .69120897476690862600e-3, -.11972090629438798134e-2,
334 -.11448874821643225573e-1, -.23104401104002905904e-1,
335 -.33352899418646530133e-1, -.42538626424075425908e-1,
336 -.49969730733911825941e-1, -.55555454015360728353e-1,
337 -.58955533624852604918e-1, -.60126044219122513907e-1,
338 -.58959430451175833624e-1, -.55546925396227130606e-1,
339 -.49984739749347973762e-1, -.42513009141170294365e-1,
340 -.33399140950669746346e-1, -.23007690803851790829e-1,
341 -.11728275717520066169e-1, 0.0, .11728275717520066169e-1,
342 .23007690803851790829e-1, .33399140950669746346e-1,
343 .42513009141170294365e-1, .49984739749347973762e-1,
344 .55546925396227130606e-1, .58959430451175833624e-1,
345 .60126044219122513907e-1, .58955533624852604918e-1,
346 .55555454015360728353e-1, .49969730733911825941e-1,
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629 -.68132707341917233933e-1, .67534860185243140399e-2,
630 .69268150370037450063e-1, -.41585011920451477177e-1,
631 -.51622397460510041271e-1, .68408139576363036148e-1,
632 .18981259024768933323e-1, -.78265472429342305554e-1,
633 .18981259024768933323e-1, .68408139576363036148e-1,
634 -.51622397460510041271e-1,
635 -.41585011920451477177e-1, .69268150370037450063e-1,
636 .67534860185243140399e-2,
637 -.68132707341917233933e-1, .25707858143963615736e-1,
638 .49660630547172186418e-1,
639 -.45320344390022666738e-1, -.22573685920142225247e-1,
640 .47914131921157015198e-1, -.34555825499804605557e-2,
641 -.31777863364694653331e-1, .11747497650231330965e-1,
642 .51591759101720291381e-2, -.54365757412741340377e-2,
643 -.94862516619529080191e-2, .33240472093448190877e-1,
644 -.88698898099681552229e-2,
645 -.40973252097216337576e-1, .42995673349795657065e-1,
646 .17320914507876958783e-1,
647 -.62201292691914856803e-1, .24726274174637346693e-1,
648 .51320859246515407288e-1,
649 -.62882063373810501763e-1, -.11003569131725622672e-1,
650 .73842261324108943465e-1, -.39240120294802923208e-1,
651 -.49293966443941122807e-1, .73552644778818223475e-1, 0.0,
652 -.73552644778818223475e-1, .49293966443941122807e-1,
653 .39240120294802923208e-1, -.73842261324108943465e-1,
654 .11003569131725622672e-1, .62882063373810501763e-1,
655 -.51320859246515407288e-1,
656 -.24726274174637346693e-1, .62201292691914856803e-1,
657 -.17320914507876958783e-1, -.42995673349795657065e-1,
658 .40973252097216337576e-1, .88698898099681552229e-2,
659 -.33240472093448190877e-1, .94862516619529080191e-2,
660 .54365757412741340377e-2, .57750194549356126240e-2,
661 .69981166020044116791e-2, -.33274982140403110792e-1,
662 .20297071020698356116e-1, .27898517839646066582e-1,
663 -.53368678853282030262e-1, .16656482990394548343e-1,
664 .46342901447260614255e-1,
665 -.60536796508149003365e-1, .29109107483842596340e-2,
666 .63224486124385124504e-1,
667 -.59028872851312033411e-1, -.14783105962696191734e-1,
668 .74269399241069253865e-1, -.49053677339382384625e-1,
669 -.33525466624811186739e-1, .78397349622515386647e-1,
670 -.33525466624811186739e-1, -.49053677339382384625e-1,
671 .74269399241069253865e-1, -.14783105962696191734e-1,
672 -.59028872851312033411e-1,
673 .63224486124385124504e-1, .29109107483842596340e-2,
674 -.60536796508149003365e-1,
675 .46342901447260614255e-1, .16656482990394548343e-1,
676 -.53368678853282030262e-1,
677 .27898517839646066582e-1, .20297071020698356116e-1,
678 -.33274982140403110792e-1,
679 .69981166020044116791e-2, .57750194549356126240e-2,
680 -.61100308370519200637e-2, -.44383614355738148616e-2,
681 .32011283412619094811e-1, -.29965011866372897633e-1,
682 -.10560682331349193348e-1, .51110336443392506342e-1,
683 -.45012284729681775492e-1, -.94236825555873320102e-2,
684 .60860695783141264746e-1,
685 -.55014628647083368926e-1, -.73474782382499482121e-2,
686 .66640148475243034781e-1, -.62533116045749887988e-1,
687 -.38650525912400102585e-2, .68429769005837003777e-1,
688 -.66984505412544901945e-1, 0.0, .66984505412544901945e-1,
689 -.68429769005837003777e-1, .38650525912400102585e-2,
690 .62533116045749887988e-1, -.66640148475243034781e-1,
691 .73474782382499482121e-2,
692 .55014628647083368926e-1, -.60860695783141264746e-1,
693 .94236825555873320102e-2,
694 .45012284729681775492e-1, -.51110336443392506342e-1,
695 .10560682331349193348e-1,
696 .29965011866372897633e-1, -.32011283412619094811e-1,
697 .44383614355738148616e-2,
698 .61100308370519200637e-2, .65409373892036191538e-2,
699 .16350101107071157065e-2, -.29301957285983144319e-1,
700 .36838667173388832579e-1, -.81922703976491586393e-2,
701 -.36955670021050133434e-1, .58374851095540469865e-1,
702 -.31977016246946181856e-1, -.25311073698658094646e-1,
703 .66674413950106952577e-1,
704 -.54865713324521039571e-1, -.39797027891537985440e-2,
705 .62830285264808449064e-1, -.72226313251296100676e-1,
706 .22560232697133353980e-1, .46455784709904033738e-1,
707 -.78200930751070349956e-1, .46455784709904033738e-1,
708 .22560232697133353980e-1, -.72226313251296100676e-1,
709 .62830285264808449064e-1, -.39797027891537985440e-2,
710 -.54865713324521039571e-1, .66674413950106952577e-1,
711 -.25311073698658094646e-1, -.31977016246946181856e-1,
712 .58374851095540469865e-1, -.36955670021050133434e-1,
713 -.81922703976491586393e-2, .36838667173388832579e-1,
714 -.29301957285983144319e-1, .16350101107071157065e-2,
715 .65409373892036191538e-2, -.69686180931868703196e-2,
716 .11849538727632789870e-2, .25452286414610537766e-1,
717 -.40522480651713943230e-1, .25694679053362813183e-1,
718 .14057118113748390637e-1, -.52037614725803488893e-1,
719 .58849342223684035589e-1,
720 -.25075229077361409271e-1, -.29559771094034181083e-1,
721 .68296746944165720199e-1, -.62890462146423984955e-1,
722 .14457636466274596445e-1, .45787612031322361496e-1,
723 -.77231759014655809742e-1, .57881203613910543657e-1, 0.0,
724 -.57881203613910543657e-1, .77231759014655809742e-1,
725 -.45787612031322361496e-1, -.14457636466274596445e-1,
726 .62890462146423984955e-1,
727 -.68296746944165720199e-1, .29559771094034181083e-1,
728 .25075229077361409271e-1,
729 -.58849342223684035589e-1, .52037614725803488893e-1,
730 -.14057118113748390637e-1, -.25694679053362813183e-1,
731 .40522480651713943230e-1, -.25452286414610537766e-1,
732 -.11849538727632789870e-2, .69686180931868703196e-2,
733 .75611653617520254845e-2, -.43290610418608409141e-2,
734 -.20277062025115566914e-1,
735 .40362947027704828926e-1, -.38938808024132120254e-1,
736 .11831186195916702262e-1,
737 .28476667401744525357e-1, -.59320969056617684621e-1,
738 .61101629747436200186e-1,
739 -.29514834848355389223e-1, -.20668001885001084821e-1,
740 .62923592802445122793e-1, -.73558456263588833115e-1,
741 .45314556330160999776e-1, .79031645918426015574e-2,
742 -.58136953576334689357e-1, .78538474524006405758e-1,
743 -.58136953576334689357e-1, .79031645918426015574e-2,
744 .45314556330160999776e-1, -.73558456263588833115e-1,
745 .62923592802445122793e-1, -.20668001885001084821e-1,
746 -.29514834848355389223e-1, .61101629747436200186e-1,
747 -.59320969056617684621e-1, .28476667401744525357e-1,
748 .11831186195916702262e-1, -.38938808024132120254e-1,
749 .40362947027704828926e-1, -.20277062025115566914e-1,
750 -.43290610418608409141e-2, .75611653617520254845e-2,
751 -.81505692478987769484e-2, .74297333588288568430e-2,
752 .14314212513540223314e-1, -.36711242251332751607e-1,
753 .46240027755503814626e-1, -.34921532671769023773e-1,
754 .46930051972353714773e-2,
755 .32842770336385381562e-1, -.61317813706529588466e-1,
756 .67000809902468893103e-1,
757 -.45337449655535622885e-1, .35794459576271920867e-2,
758 .41830061526027213385e-1,
759 -.72091371931944711708e-1, .74150028530317793195e-1,
760 -.46487632538609942002e-1, 0.0, .46487632538609942002e-1,
761 -.74150028530317793195e-1, .72091371931944711708e-1,
762 -.41830061526027213385e-1, -.35794459576271920867e-2,
763 .45337449655535622885e-1, -.67000809902468893103e-1,
764 .61317813706529588466e-1, -.32842770336385381562e-1,
765 -.46930051972353714773e-2, .34921532671769023773e-1,
766 -.46240027755503814626e-1, .36711242251332751607e-1,
767 -.14314212513540223314e-1, -.74297333588288568430e-2,
768 .81505692478987769484e-2, .90693182942442189743e-2,
769 -.11121000903959576737e-1, -.71308296141317458546e-2,
770 .29219439765986671645e-1, -.45820286629778129593e-1,
771 .49088381175879124421e-1, -.35614888785023038938e-1,
772 .78906970900092777895e-2,
773 .26262843038404929480e-1, -.56143674270125757857e-1,
774 .71700220472378350694e-1,
775 -.66963544500697307945e-1, .42215091779892228883e-1,
776 -.41338867413966866997e-2, -.36164891772995367321e-1,
777 .66584367783847858225e-1, -.77874712365070098328e-1,
778 .66584367783847858225e-1, -.36164891772995367321e-1,
779 -.41338867413966866997e-2, .42215091779892228883e-1,
780 -.66963544500697307945e-1,
781 .71700220472378350694e-1, -.56143674270125757857e-1,
782 .26262843038404929480e-1,
783 .78906970900092777895e-2, -.35614888785023038938e-1,
784 .49088381175879124421e-1,
785 -.45820286629778129593e-1, .29219439765986671645e-1,
786 -.71308296141317458546e-2, -.11121000903959576737e-1,
787 .90693182942442189743e-2, -.99848472706332791043e-2,
788 .14701271465939718856e-1, -.32917820356048383366e-3,
789 -.19201195309873585230e-1, .38409681836626963278e-1,
790 -.51647324405878909521e-1, .54522171113149311354e-1,
791 -.45040302741689006270e-1, .24183738595685990149e-1,
792 .42204134165479735097e-2, -.34317295181348742251e-1,
793 .59542472465494579941e-1, -.74135115907618101263e-1,
794 .74491937840566532596e-1, -.60042604725161994304e-1,
795 .33437677409000083169e-1, 0.0,
796 -.33437677409000083169e-1, .60042604725161994304e-1,
797 -.74491937840566532596e-1, .74135115907618101263e-1,
798 -.59542472465494579941e-1, .34317295181348742251e-1,
799 -.42204134165479735097e-2, -.24183738595685990149e-1,
800 .45040302741689006270e-1, -.54522171113149311354e-1,
801 .51647324405878909521e-1, -.38409681836626963278e-1,
802 .19201195309873585230e-1, .32917820356048383366e-3,
803 -.14701271465939718856e-1, .99848472706332791043e-2,
804 .11775579274769383373e-1, -.19892153937316935880e-1,
805 .95335114477449041055e-2, .57661528440359081617e-2,
806 -.23382690532380910781e-1, .40237257037170725321e-1,
807 -.53280289903551636474e-1, .59974361806023689068e-1,
808 -.58701684061992853224e-1, .49033407111597129616e-1,
809 -.31818835267847249219e-1, .90800541261162098886e-2,
810 .16272906819312603838e-1, -.40863896581186229487e-1,
811 .61346046297517367703e-1,
812 -.74896047554167268919e-1, .79632642148310325817e-1,
813 -.74896047554167268919e-1, .61346046297517367703e-1,
814 -.40863896581186229487e-1, .16272906819312603838e-1,
815 .90800541261162098886e-2, -.31818835267847249219e-1,
816 .49033407111597129616e-1, -.58701684061992853224e-1,
817 .59974361806023689068e-1, -.53280289903551636474e-1,
818 .40237257037170725321e-1, -.23382690532380910781e-1,
819 .57661528440359081617e-2, .95335114477449041055e-2,
820 -.19892153937316935880e-1,
821 .11775579274769383373e-1, -.13562702617218467450e-1,
822 .24885419969649845849e-1, -.18368693901908875583e-1,
823 .81673147806084084638e-2, .47890591326129587131e-2,
824 -.19313752945227974024e-1, .34065953398362954708e-1,
825 -.47667045133463415672e-1, .58820377816690514309e-1,
826 -.66424139824618415970e-1,
827 .69667606260856092515e-1, -.68102459384364543253e-1,
828 .61683024923302547971e-1,
829 -.50771943476441639136e-1, .36110771847327189215e-1,
830 -.18758028464284563358e-1, 0.0, .18758028464284563358e-1,
831 -.36110771847327189215e-1, .50771943476441639136e-1,
832 -.61683024923302547971e-1, .68102459384364543253e-1,
833 -.69667606260856092515e-1, .66424139824618415970e-1,
834 -.58820377816690514309e-1, .47667045133463415672e-1,
835 -.34065953398362954708e-1, .19313752945227974024e-1,
836 -.47890591326129587131e-2, -.81673147806084084638e-2,
837 .18368693901908875583e-1, -.24885419969649845849e-1,
838 .13562702617218467450e-1, .20576545037980523979e-1,
839 -.40093155172981004337e-1, .36954083167944054826e-1,
840 -.31856506837591907746e-1, .24996323181546255126e-1,
841 -.16637165210473614136e-1, .71002706773325085237e-2,
842 .32478629093205201133e-2,
843 -.14009562579050569518e-1, .24771262248780618922e-1,
844 -.35119395835433647559e-1, .44656290368574753171e-1,
845 -.53015448339647394161e-1, .59875631995693046782e-1,
846 -.64973208326045193862e-1, .68112280331082143373e-1,
847 -.69172215234062186994e-1, .68112280331082143373e-1,
848 -.64973208326045193862e-1, .59875631995693046782e-1,
849 -.53015448339647394161e-1, .44656290368574753171e-1,
850 -.35119395835433647559e-1, .24771262248780618922e-1,
851 -.14009562579050569518e-1, .32478629093205201133e-2,
852 .71002706773325085237e-2, -.16637165210473614136e-1,
853 .24996323181546255126e-1, -.31856506837591907746e-1,
854 .36954083167944054826e-1, -.40093155172981004337e-1,
855 .20576545037980523979e-1, -.27584914609096156163e-1,
856 .54904171411058497973e-1, -.54109756419563083153e-1,
857 .52794234894345577483e-1, -.50970276026831042415e-1,
858 .48655445537990983379e-1,
859 -.45872036510847994332e-1, .42646854695899611372e-1,
860 -.39010960357087507670e-1, .34999369144476467749e-1,
861 -.30650714874402762189e-1, .26006877464703437057e-1,
862 -.21112579608213651273e-1, .16014956068786763273e-1,
863 -.10763099747751940252e-1, .54075888924374485533e-2, 0.0,
864 -.54075888924374485533e-2, .10763099747751940252e-1,
865 -.16014956068786763273e-1,
866 .21112579608213651273e-1, -.26006877464703437057e-1,
867 .30650714874402762189e-1,
868 -.34999369144476467749e-1, .39010960357087507670e-1,
869 -.42646854695899611372e-1, .45872036510847994332e-1,
870 -.48655445537990983379e-1, .50970276026831042415e-1,
871 -.52794234894345577483e-1, .54109756419563083153e-1,
872 -.54904171411058497973e-1, .27584914609096156163e-1,
873 .13794141262469565740e-1, -.27588282524939131481e-1,
874 .27588282524939131481e-1, -.27588282524939131481e-1,
875 .27588282524939131481e-1, -.27588282524939131481e-1,
876 .27588282524939131481e-1,
877 -.27588282524939131481e-1, .27588282524939131481e-1,
878 -.27588282524939131481e-1, .27588282524939131481e-1,
879 -.27588282524939131481e-1, .27588282524939131481e-1,
880 -.27588282524939131481e-1, .27588282524939131481e-1,
881 -.27588282524939131481e-1, .27588282524939131481e-1,
882 -.27588282524939131481e-1, .27588282524939131481e-1,
883 -.27588282524939131481e-1, .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, .13794141262469565740e-1
892 static const double Tleft[33 * 33] =
894 1., -.86602540378443864678, 0., .33071891388307382381, 0.,
895 -.20728904939721249057, 0., .15128841196122722208, 0.,
896 -.11918864298744029244, 0., .98352013661686631224e-1, 0.,
897 -.83727065404940845733e-1, 0., .72893399403505841203e-1, 0.,
898 -.64544632643375022436e-1, 0., .57913170372415565639e-1, 0.,
899 -.52518242575729562263e-1, 0., .48043311993977520457e-1, 0.,
900 -.44271433659733990243e-1, 0., .41048928022856771981e-1, 0.,
901 -.38263878662008271459e-1, 0., .35832844026365304501e-1, 0., 0.,
902 .50000000000000000000, -.96824583655185422130, .57282196186948000082,
903 .21650635094610966169, -.35903516540862679125, -.97578093724974971969e-1,
904 .26203921611325660506, .55792409597991015609e-1, -.20644078533943456204,
905 -.36172381205961199479e-1, .17035068468874958194,
906 .25371838001497225980e-1, -.14501953125000000000,
907 -.18786835250972344757e-1, .12625507130328301066,
908 .14473795929590520582e-1, -.11179458309419422675,
909 -.11494434254897626155e-1, .10030855351241635862,
910 .93498556820544479096e-2, -.90964264465390582629e-1,
911 -.77546391824364392762e-2, .83213457337452292745e-1,
912 .65358085945588638605e-2, -.76680372422574234569e-1,
913 -.55835321940047427169e-2, .71098828931825789428e-1,
914 .48253327982967591019e-2, -.66274981937248958553e-1,
915 -.42118078245337801387e-2, .62064306433355646267e-1,
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1414 for (i = 0; i <= 4; i++)
1417 for (j = 0; j <= 4; j++)
1418 c[i] +=
V1inv[i * 5 + j] * fx[j * 8];
1422 for (i = 0; i <= 8; i++)
1425 for (j = 0; j <= 8; j++)
1426 c[i] +=
V2inv[i * 9 + j] * fx[j * 4];
1430 for (i = 0; i <= 16; i++)
1433 for (j = 0; j <= 16; j++)
1434 c[i] +=
V3inv[i * 17 + j] * fx[j * 2];
1438 for (i = 0; i <= 32; i++)
1441 for (j = 0; j <= 32; j++)
1442 c[i] +=
V4inv[i * 33 + j] * fx[j];
1454 static const int bidx[4] = { 0, 6, 16, 34 };
1455 double b_new[34], alpha;
1458 for (i = 0; i <= n + 1; i++)
1459 b_new[i] =
bee[bidx[d] + i];
1460 for (i = 0; i < nnans; i++)
1462 b_new[n + 1] = b_new[n + 1] /
Lalpha[n];
1463 b_new[n] = (b_new[n] +
xi[nans[
i]] * b_new[n + 1]) /
Lalpha[n - 1];
1464 for (j = n - 1; j > 0; j--)
1466 (b_new[j] +
xi[nans[i]] * b_new[j + 1] -
1468 for (j = 0; j <= n; j++)
1469 b_new[j] = b_new[j + 1];
1470 alpha = c[n] / b_new[n];
1471 for (j = 0; j < n; j++)
1472 c[j] -= alpha * b_new[j];
1552 static const int n[4] = { 4, 8, 16, 32 };
1553 static const int skip[4] = { 8, 4, 2, 1 };
1554 static const int idx[4] = { 0, 5, 14, 31 };
1555 static const double w = M_SQRT2 / 2;
1556 static const int ndiv_max = 20;
1561 double a,
b, tol, *sing;
1571 double m,
h, ml, hl, mr, hr, temp;
1572 double igral,
err, igral_final, err_final;
1573 int nivals, neval = 0;
1574 int i, j,
d, split,
t;
1575 int nnans, nans[33];
1583 if (
args(0).is_function_handle () ||
args(0).is_inline_function ())
1584 fcn =
args(0).function_value ();
1589 fname.append (fcn_name);
1590 fname.append (
"(x) y = ");
1595 if (!
args(1).is_real_scalar ())
1596 error (
"quadcc: lower limit of integration (A) must be a single real scalar");
1598 a =
args(1).double_value ();
1600 if (!
args(2).is_real_scalar ())
1601 error (
"quadcc: upper limit of integration (B) must be a single real scalar");
1603 b =
args(2).double_value ();
1605 if (nargin < 4 ||
args(3).is_empty ())
1607 else if (!
args(3).is_real_scalar () ||
args(3).double_value () <= 0)
1608 error (
"quadcc: tolerance (TOL) must be a single real scalar > 0");
1610 tol =
args(3).double_value ();
1614 else if (!(
args(4).is_real_scalar () ||
args(4).is_real_matrix ()))
1615 error (
"quadcc: list of singularities (SING) must be a vector of real values");
1617 nivals = 1 +
args(4).numel ();
1634 sing =
args(4).array_value ().fortran_vec ();
1636 for (i = 0; i < nivals - 1; i++)
1637 iivals[i + 1] = sing[i];
1645 for (i = 0; i < nivals + 1; i++)
1649 iivals[
i] = 2.0 *
atan (iivals[i]) / M_PI;
1653 for (i = 0; i < cquad_heapsize; i++)
1659 for (j = 0; j < nivals; j++)
1662 iv = &(ivals[heap[j]]);
1663 m = (iivals[j] + iivals[j + 1]) / 2;
1664 h = (iivals[j + 1] - iivals[j]) / 2;
1669 for (i = 0; i <= n[3]; i++)
1670 ex(i) = tan (M_PI / 2 * (m +
xi[i] * h));
1674 for (i = 0; i <= n[3]; i++)
1675 ex(i) = m +
xi[
i] *
h;
1678 fvals =
feval (fcn, fargs, 1);
1679 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
1680 error (
"quadcc: integrand F must return a single, real-valued vector");
1682 Matrix effex = fvals(0).matrix_value ();
1684 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
1686 for (i = 0; i <= n[3]; i++)
1688 iv->
fx[
i] = effex(i);
1692 iv->
fx[
i] *= (1.0 + xw * xw) * M_PI / 2;
1704 for (i = 0; i < nnans; i++)
1707 iv->
b = iivals[j + 1];
1711 iv->
igral = 2 * h * iv->
c[idx[3]] *
w;
1713 for (i = n[2] + 1; i <= n[3]; i++)
1715 temp = iv->
c[idx[3] +
i];
1719 for (i = 0; i <= n[2]; i++)
1721 temp = iv->
c[idx[2] +
i] - iv->
c[idx[3] +
i];
1722 ncdiff += temp * temp;
1723 nc += iv->
c[idx[3] +
i] * iv->
c[idx[3] +
i];
1725 ncdiff = sqrt (ncdiff);
1727 iv->
err = ncdiff * 2 *
h;
1728 if (ncdiff / nc > 0.1 && iv->
err < 2 * h * nc)
1729 iv->
err = 2 * h * nc;
1737 while (i > 0 && ivals[heap[i / 2]].err < ivals[heap[i]].err)
1740 heap[
i] = heap[i / 2];
1751 while (nivals > 0 && err > 0.0 && err > fabs (igral) * tol
1752 && !(err_final > fabs (igral) * tol
1753 && err - err_final < fabs (igral) * tol))
1759 iv = &(ivals[heap[0]]);
1760 m = (iv->
a + iv->
b) / 2;
1761 h = (iv->
b - iv->
a) / 2;
1764 printf (
"quadcc: processing ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
1779 for (i = 0; i < n[
d] / 2; i++)
1780 ex(i) = tan (M_PI / 2 * (m +
xi[(2 * i + 1) * skip[d]] * h));
1784 for (i = 0; i < n[
d] / 2; i++)
1785 ex(i) = m +
xi[(2 * i + 1) * skip[d]] * h;
1788 fvals =
feval (fcn, fargs, 1);
1789 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
1790 error (
"quadcc: integrand F must return a single, real-valued vector");
1792 Matrix effex = fvals(0).matrix_value ();
1794 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
1796 neval += effex.
numel ();
1797 for (i = 0; i < n[
d] / 2; i++)
1799 j = (2 * i + 1) * skip[d];
1800 iv->
fx[j] = effex(i);
1804 iv->
fx[j] *= (1.0 + xw * xw) * M_PI / 2;
1809 for (i = 0; i <= 32; i += skip[
d])
1823 downdate (&(iv->
c[idx[d]]), n[d], d, nans, nnans);
1824 for (i = 0; i < nnans; i++)
1830 for (i = n[d - 1] + 1; i <= n[
d]; i++)
1832 temp = iv->
c[idx[
d] +
i];
1836 for (i = 0; i <= n[d - 1]; i++)
1838 temp = iv->
c[idx[d - 1] +
i] - iv->
c[idx[
d] +
i];
1839 ncdiff += temp * temp;
1840 nc += iv->
c[idx[
d] +
i] * iv->
c[idx[
d] +
i];
1842 ncdiff = sqrt (ncdiff);
1844 iv->
err = ncdiff * 2 *
h;
1846 iv->
igral = 2 * h * w * iv->
c[idx[
d]];
1848 split = (nc > 0 && ncdiff / nc > 0.1);
1857 if ((m + h *
xi[0]) >= (m + h * xi[1])
1858 || (m + h * xi[31]) >= (m + h * xi[32])
1860 * std::numeric_limits<double>::epsilon () * 10)
1863 printf (
"quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
1868 err_final += iv->
err;
1869 igral_final += iv->
igral;
1871 t = heap[nivals - 1];
1872 heap[nivals - 1] = heap[0];
1877 while (2 * i + 1 < nivals)
1884 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
1887 if (ivals[heap[j]].err <= ivals[heap[i]].err)
1903 ivl = &(ivals[heap[nivals++]]);
1906 ml = (ivl->
a + ivl->
b) / 2;
1910 ivl->
fx[0] = iv->
fx[0];
1911 ivl->
fx[32] = iv->
fx[16];
1916 for (i = 0; i < n[0] - 1; i++)
1917 ex(i) = tan (M_PI / 2 * (ml + xi[(i + 1) * skip[0]] * hl));
1921 for (i = 0; i < n[0] - 1; i++)
1922 ex(i) = ml + xi[(i + 1) * skip[0]] * hl;
1925 fvals =
feval (fcn, fargs, 1);
1926 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
1927 error (
"quadcc: integrand F must return a single, real-valued vector");
1929 Matrix effex = fvals(0).matrix_value ();
1931 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
1933 neval += effex.
numel ();
1934 for (i = 0; i < n[0] - 1; i++)
1936 j = (i + 1) * skip[0];
1937 ivl->
fx[j] = effex(i);
1941 ivl->
fx[j] *= (1.0 + xw * xw) * M_PI / 2;
1946 for (i = 0; i <= 32; i += skip[0])
1957 downdate (ivl->
c, n[0], 0, nans, nnans);
1958 for (i = 0; i < nnans; i++)
1961 for (i = 0; i <= n[
d]; i++)
1963 ivl->
c[idx[
d] +
i] = 0.0;
1964 for (j = i; j <= n[
d]; j++)
1965 ivl->
c[idx[d] + i] +=
Tleft[i * 33 + j] * iv->
c[idx[d] + j];
1968 for (i = 0; i <= n[0]; i++)
1970 temp = ivl->
c[
i] - ivl->
c[idx[
d] +
i];
1971 ncdiff += temp * temp;
1973 for (i = n[0] + 1; i <= n[
d]; i++)
1975 temp = ivl->
c[idx[
d] +
i];
1976 ncdiff += temp * temp;
1978 ncdiff = sqrt (ncdiff);
1979 ivl->
err = ncdiff *
h;
1981 ivl->
ndiv = iv->
ndiv + (fabs (iv->
c[0]) > 0
1982 && ivl->
c[0] / iv->
c[0] > 2);
1986 warning (
"quadcc: divergent integral detected");
1991 ivl->
igral = h * w * ivl->
c[0];
1994 ivr = &(ivals[heap[nivals++]]);
1997 mr = (ivr->
a + ivr->
b) / 2;
2001 ivr->
fx[0] = iv->
fx[16];
2002 ivr->
fx[32] = iv->
fx[32];
2007 for (i = 0; i < n[0] - 1; i++)
2008 ex(i) = tan (M_PI / 2 * (mr + xi[(i + 1) * skip[0]] * hr));
2012 for (i = 0; i < n[0] - 1; i++)
2013 ex(i) = mr + xi[(i + 1) * skip[0]] * hr;
2016 fvals =
feval (fcn, fargs, 1);
2017 if (fvals.
length () != 1 || ! fvals(0).is_real_matrix ())
2018 error (
"quadcc: integrand F must return a single, real-valued vector");
2020 Matrix effex = fvals(0).matrix_value ();
2022 error (
"quadcc: integrand F must return a single, real-valued vector of the same size as the input");
2024 neval += effex.
numel ();
2025 for (i = 0; i < n[0] - 1; i++)
2027 j = (i + 1) * skip[0];
2028 ivr->
fx[j] = effex(i);
2032 ivr->
fx[j] *= (1.0 + xw * xw) * M_PI / 2;
2037 for (i = 0; i <= 32; i += skip[0])
2048 downdate (ivr->
c, n[0], 0, nans, nnans);
2049 for (i = 0; i < nnans; i++)
2052 for (i = 0; i <= n[
d]; i++)
2054 ivr->
c[idx[
d] +
i] = 0.0;
2055 for (j = i; j <= n[
d]; j++)
2056 ivr->
c[idx[d] + i] +=
Tright[i * 33 + j] * iv->
c[idx[d] + j];
2059 for (i = 0; i <= n[0]; i++)
2061 temp = ivr->
c[
i] - ivr->
c[idx[
d] +
i];
2062 ncdiff += temp * temp;
2064 for (i = n[0] + 1; i <= n[
d]; i++)
2066 temp = ivr->
c[idx[
d] +
i];
2067 ncdiff += temp * temp;
2069 ncdiff = sqrt (ncdiff);
2070 ivr->
err = ncdiff *
h;
2072 ivr->
ndiv = iv->
ndiv + (fabs (iv->
c[0]) > 0
2073 && ivr->
c[0] / iv->
c[0] > 2);
2077 warning (
"quadcc: divergent integral detected");
2082 ivr->
igral = h * w * ivr->
c[0];
2089 t = heap[nivals - 1];
2090 heap[nivals - 1] = heap[0];
2095 while (2 * i + 1 < nivals - 1)
2098 if (j + 1 < nivals - 1
2099 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
2101 if (ivals[heap[j]].err <= ivals[heap[i]].err)
2117 if (ivals[heap[j]].err < ivals[heap[i]].err)
2132 while (2 * i + 1 < nivals)
2136 && ivals[heap[j + 1]].err >= ivals[heap[j]].err)
2138 if (ivals[heap[j]].err <= ivals[heap[i]].err)
2152 while (nivals > cquad_heapsize - 2)
2154 iv = &(ivals[heap[nivals - 1]]);
2156 printf (
"quadcc: dropping ival %i (of %i) with [%e,%e] int=%e, err=%e, depth=%i\n",
2159 err_final += iv->
err;
2160 igral_final += iv->
igral;
2165 igral = igral_final;
2167 for (i = 0; i < nivals; i++)
2169 igral += ivals[heap[
i]].igral;
2170 err += ivals[heap[
i]].err;
2176 for (i = 0; i < nivals; i++)
2178 iv = &(ivals[heap[
i]]);
2179 printf (
"quadcc: ival %i (%i) with [%e,%e], int=%e, err=%e, depth=%i, rdepth=%i, ndiv=%i\n",
2185 return ovl (igral, err, neval);
static const double Lgamma[33]
static const double Tright[33 *33]
OCTAVE_EXPORT octave_value_list isa nd deftypefn *return ovl(args(0).is_integer_type())
nd group nd example oindent or xample printf("%s\n", nthargout(2,"system","cmd"))
OCTINTERP_API void print_usage(void)
octave_idx_type numel(void) const
Number of elements in the array.
octave_idx_type length(void) const
#define DEFUN(name, args_name, nargout_name, doc)
void error(const char *fmt,...)
OCTAVE_EXPORT octave_value_list return the number of command line arguments passed to Octave If called with the optional argument the function t
F77_RET_T F77_REAL &F77_RET_T F77_DBLE &F77_RET_T F77_REAL &F77_RET_T F77_DBLE &F77_RET_T F77_REAL &F77_RET_T F77_DBLE &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 F77_REAL &F77_RET_T F77_DBLE &F77_RET_T F77_DBLE &F77_RET_T F77_REAL &F77_RET_T F77_REAL &F77_RET_T F77_DBLE &F77_RET_T const F77_DBLE F77_DBLE &F77_RET_T const F77_REAL F77_REAL &F77_RET_T F77_REAL F77_REAL &F77_RET_T F77_DBLE F77_DBLE &F77_RET_T const F77_DBLE const F77_DBLE F77_DBLE * d
static const double V2inv[9 *9]
#define MIN_CQUAD_HEAPSIZE
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 const double bee[68]
static const double Tleft[33 *33]
Complex atan(const Complex &x)
double copysign(double x, double y)
static const double V3inv[17 *17]
nd deftypefn *octave_map m
std::complex< double > w(std::complex< double > z, double relerr=0)
the sparsity preserving column transformation such that that defines the pivoting threshold can be given in which case it defines the c
static const double V1inv[5 *5]
void downdate(double *c, int n, int d, int *nans, int nnans)
static const double V4inv[33 *33]
void warning(const char *fmt,...)
=val(i)}if ode{val(i)}occurs in table i
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_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 $)
#define OCTAVE_LOCAL_BUFFER(T, buf, size)
OCTAVE_EXPORT octave_value_list error nd deftypefn *const octave_scalar_map err
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]
void Vinvfx(const double *fx, double *c, const int d)