github.com/gopherd/gonum@v0.0.4/integrate/quad/hermite_test.go (about) 1 // Copyright ©2016 The Gonum Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package quad 6 7 import ( 8 "fmt" 9 "math" 10 "testing" 11 12 "github.com/gopherd/gonum/floats" 13 "github.com/gopherd/gonum/floats/scalar" 14 ) 15 16 func TestHermite(t *testing.T) { 17 t.Parallel() 18 for cas, test := range []struct { 19 n int 20 f func(float64) float64 21 ev float64 22 tol float64 23 }{ 24 { 25 n: 2, 26 f: func(x float64) float64 { return 1 }, 27 ev: math.SqrtPi, 28 tol: 1e-14, 29 }, 30 { 31 n: 4, 32 f: func(x float64) float64 { return math.Exp(-2 * 0.5 * x) }, 33 ev: math.SqrtPi * math.Exp(0.25), 34 tol: 1e-4, 35 }, 36 { 37 n: 9, 38 f: func(x float64) float64 { return math.Exp(-2 * 0.5 * x) }, 39 ev: math.SqrtPi * math.Exp(0.25), 40 tol: 1e-12, 41 }, 42 { 43 n: 10, 44 f: func(x float64) float64 { return math.Exp(-2 * 0.5 * x) }, 45 ev: math.SqrtPi * math.Exp(0.25), 46 tol: 1e-12, 47 }, 48 { 49 n: 15, 50 f: func(x float64) float64 { return math.Exp(-2 * 2 * x) }, 51 ev: math.SqrtPi * math.Exp(4), 52 tol: 1e-4, 53 }, 54 { 55 n: 22, 56 f: func(x float64) float64 { return math.Exp(-2 * 2 * x) }, 57 ev: math.SqrtPi * math.Exp(4), 58 tol: 1e-12, 59 }, 60 { 61 n: 21, 62 f: func(x float64) float64 { return math.Exp(-2 * 2 * x) }, 63 ev: math.SqrtPi * math.Exp(4), 64 tol: 1e-12, 65 }, 66 { 67 n: 1000, 68 f: func(x float64) float64 { return math.Exp(-2 * 2 * x) }, 69 ev: math.SqrtPi * math.Exp(4), 70 tol: 1e-12, 71 }, 72 } { 73 ev := Fixed(test.f, math.Inf(-1), math.Inf(1), test.n, Hermite{}, 0) 74 if !scalar.EqualWithinAbsOrRel(test.ev, ev, test.tol, test.tol) { 75 t.Errorf("Case %d: expected value mismatch.\nWant %v\ngot %v", cas, test.ev, ev) 76 } 77 } 78 } 79 80 func TestHermiteLocations(t *testing.T) { 81 t.Parallel() 82 // Test the hermite locations and weights against other precomputed table. 83 // Data from http://dlmf.nist.gov/3.5. 84 for _, test := range []struct { 85 n int 86 x []float64 87 w []float64 88 tol float64 89 }{ 90 // Evaluated from Chebfun. 91 { 92 n: 5, 93 x: []float64{-0.202018287045609e1, -0.958572464613819, 0, 0.958572464613819, 0.202018287045609e1}, 94 w: []float64{0.199532420590459e-1, 0.393619323152241, 0.945308720482942, 0.393619323152241, 0.199532420590459e-1}, 95 tol: 1e-14, 96 }, 97 { 98 n: 10, 99 x: []float64{-0.343615911883773760e1, -0.253273167423278980e1, -0.175668364929988177e1, -0.103661082978951365e1, -0.342901327223704609, 0.342901327223704609, 0.103661082978951365e1, 0.175668364929988177e1, 0.253273167423278980e1, 0.343615911883773760e1}, 100 w: []float64{0.764043285523262063e-5, 0.134364574678123269e-2, 0.338743944554810631e-1, 0.240138611082314686, 0.610862633735325799, 0.610862633735325799, 0.240138611082314686, 0.338743944554810631e-1, 0.134364574678123269e-2, 0.764043285523262063e-5}, 101 tol: 1e-14, 102 }, 103 { 104 n: 215, 105 x: []float64{-2.0083110126223993e+01, -1.9573161931385755e+01, -1.9153731166695263e+01, -1.8781558404513735e+01, 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2.1215999344125686e-22, 7.9454711482554462e-23, 2.9449542387975020e-23, 1.0802781850376285e-23, 3.9218067686130826e-24, 1.4090474655086476e-24, 5.0101319085046131e-25, 1.7629987629083774e-25, 6.1394478289562773e-26, 2.1158075825687643e-26, 7.2158518959500610e-27, 2.4353344728003697e-27, 8.1336242788329602e-28, 2.6881837159369457e-28, 8.7918028150808172e-29, 2.8453509035148136e-29, 9.1122854941717965e-30, 2.8876664192770605e-30, 9.0550221579615647e-31, 2.8096311791269716e-31, 8.6262266028303368e-32, 2.6205868311897299e-32, 7.8772879147862415e-33, 2.3428777403438029e-33, 6.8946382222670282e-34, 2.0075040700651605e-34, 5.7833378697531460e-35, 1.6484352599338373e-35, 4.6486878345616557e-36, 1.2970237375676620e-36, 3.5802911787217544e-37, 9.7776710583318967e-38, 2.6417568903758940e-38, 7.0612935196951311e-39, 1.8672533221548388e-39, 4.8847605989668363e-40, 1.2641477416407965e-40, 3.2363856080594989e-41, 8.1964137583105787e-42, 2.0534394826865196e-42, 5.0889423919887406e-43, 1.2475382033165966e-43, 3.0251986512140371e-44, 7.2563902256297714e-45, 1.7216582220922559e-45, 4.0404120146067421e-46, 9.3788484682437942e-47, 2.1533330989172484e-47, 4.8899379879160616e-48, 1.0982936194156852e-48, 2.4397706595195753e-49, 5.3602786943809252e-50, 1.1647316378880106e-50, 2.5029763689774771e-51, 5.3195165510395952e-52, 1.1180576701525420e-52, 2.3239398491612035e-53, 4.7768997974014920e-54, 9.7100129027526196e-55, 1.9518106701136368e-55, 3.8796404008463247e-56, 7.6255782662767904e-57, 1.4820851523028527e-57, 2.8482890022548686e-58, 5.4124867967047064e-59, 1.0169575920927853e-59, 1.8892665906870333e-60, 3.4702373903635070e-61, 6.3021931416666470e-62, 1.1315709177343451e-62, 2.0087239862730963e-63, 3.5253152759474540e-64, 6.1165364987659488e-65, 1.0491406305859313e-65, 1.7789874895279432e-66, 2.9820407337754590e-67, 4.9413553496512498e-68, 8.0939533379932165e-69, 1.3105318083913364e-69, 2.0974748886451008e-70, 3.3181673688922034e-71, 5.1885022241593757e-72, 8.0189539522785623e-73, 1.2249408613163427e-73, 1.8493700277748019e-74, 2.7595184467913268e-75, 4.0694244255316937e-76, 5.9307849802130665e-77, 8.5420101452037198e-78, 1.2158102629355303e-78, 1.7100875682708707e-79, 2.3768765122027434e-80, 3.2645205816409649e-81, 4.4304253111256539e-82, 5.9411871493166694e-83, 7.8721132506904387e-84, 1.0305951518623542e-84, 1.3330664066276539e-85, 1.7036114781391146e-86, 2.1509606264107007e-87, 2.6830293789353161e-88, 3.3062621228934451e-89, 4.0249058822982866e-90, 4.8402563555834996e-91, 5.7499313869447363e-92, 6.7472372997026518e-93, 7.8206990104609633e-94, 8.9538238503709081e-95, 1.0125160327802958e-95, 1.1308696244314536e-96, 1.2474616193874682e-97, 1.3590408202563549e-98, 1.4622275809196764e-99, 1.5536778758574346e-100, 1.6302596600457935e-101, 1.6892288684937835e-102, 1.7283914491118722e-103, 1.7462381930467704e-104, 1.7420408695770434e-105, 1.7159011632384579e-106, 1.6687478601660490e-107, 1.6022822189494409e-108, 1.5188759914460687e-109, 1.4214306236084630e-110, 1.3132093168021923e-111, 1.1976555369726998e-112, 1.0782120545724555e-113, 9.5815369347020579e-115, 8.4044484286651008e-116, 7.2762975927456467e-117, 6.2176015753999047e-118, 5.2436098752156138e-119, 4.3643201011221327e-120, 3.5848013541900561e-121, 2.9057566734636031e-122, 2.3242468856634865e-123, 1.8344977691984857e-124, 1.4287193329226953e-125, 1.0978782422293458e-126, 8.3237975699379756e-128, 6.2263179873318509e-129, 4.5947908528904288e-130, 3.3450829826077675e-131, 2.4023517577408972e-132, 1.7019097734602088e-133, 1.1892911728913853e-134, 8.1973391110091452e-136, 5.5727784652837080e-137, 3.7365067262616700e-138, 2.4707887826290998e-139, 1.6112461600760618e-140, 1.0361555453376311e-141, 6.5705990846248260e-143, 4.1084868631522107e-144, 2.5330019418366902e-145, 1.5397329022186058e-146, 9.2276445953465577e-148, 5.4519400815462508e-149, 3.1754477204679572e-150, 1.8231871651497053e-151, 1.0318306794654569e-152, 5.7559205521726687e-154, 3.1646695790053421e-155, 1.7148534423668942e-156, 9.1577398393994249e-158, 4.8193627314441185e-159, 2.4992406762554122e-160, 1.2770873146297890e-161, 6.4298937541404803e-163, 3.1895844350948167e-164, 1.5587902032532034e-165, 7.5048219822215126e-167, 3.5593273811283599e-168, 1.6628216886897738e-169, 7.6515383450168328e-171, 3.4677839663641647e-172, 1.5478543777968840e-173, 6.8038898787652193e-175, 2.9451512664628267e-176, 1.2553211635344571e-177, 5.2683241452994028e-179, 2.1768760700085122e-180, 8.8554655257623945e-182, 3.5463219412740393e-183, 1.3979971540967563e-184, 5.4246006309405095e-186, 2.0717353930894859e-187, 7.7871258963661253e-189, 2.8804977787988646e-190, 1.0485183834985678e-191, 3.7555461091485998e-193, 1.3235146297070864e-194, 4.5889434629100622e-196, 1.5652883428261183e-197, 5.2522174425854836e-199, 1.7335102418187571e-200, 5.6274778917186968e-202, 1.7966885166110605e-203, 5.6411930354623643e-205, 1.7417085836085446e-206, 5.2875341973740781e-208, 1.5782306240050564e-209, 4.6311979145640239e-211, 1.3359414633484673e-212, 3.7880694907273763e-214, 1.0557222065673938e-215, 2.8916581954653459e-217, 7.7834793264643977e-219, 2.0587026324216422e-220, 5.3501942181727508e-222, 1.3660423686167456e-223, 3.4264124275993631e-225, 8.4422388386550666e-227, 2.0430517869416229e-228, 4.8558536412609862e-230, 1.1333825292477732e-231, 2.5975977120672768e-233, 5.8453559227891224e-235, 1.2913751775454810e-236, 2.8006220781933600e-238, 5.9617648426249594e-240, 1.2455769147570116e-241, 2.5538665369453056e-243, 5.1382328650179621e-245, 1.0143147290142510e-246, 1.9643998334224751e-248, 3.7319816642354106e-250, 6.9543286969416096e-252, 1.2709546476364080e-253, 2.2778043641496056e-255, 4.0028201360407956e-257, 6.8965220392645158e-259, 1.1648205513661696e-260, 1.9284240264071905e-262, 3.1290300730289451e-264, 4.9754115871874643e-266, 7.7518975576944083e-268, 1.1832968405584233e-269, 1.7694253405272601e-271, 2.5916065469690241e-273, 3.7174816966218167e-275, 5.2217421416236178e-277, 7.1814456801699481e-279, 9.6689753826506193e-281, 1.2742732003636313e-282, 1.6436097663423948e-284, 2.0745725241264515e-286, 2.5620704080272207e-288, 3.0954507956523426e-290, 3.6581718467738525e-292, 4.2281234022459736e-294, 4.7786980462699519e-296, 5.2806082652713648e-298, 5.7043185644899271e-300, 6.0228361617963862e-302, 6.2145076952356061e-304, 6.2654270878892558e-306, 6.1710869359890172e-308, 5.9370037176434776e-310, 5.5782006898201854e-312, 5.1176127714709937e-314, 4.5836615691792330e-316, 4.0075986642718961e-318, 3.3329668468450492e-320, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00, 0.0000000000000000e+00}, 144 tol: 1e-13, 145 }, 146 } { 147 h := Hermite{} 148 x := make([]float64, test.n) 149 weight := make([]float64, test.n) 150 h.FixedLocations(x, weight, math.Inf(-1), math.Inf(1)) 151 if !floats.EqualApprox(x, test.x, test.tol) { 152 t.Errorf("n = %v, x mismatch", test.n) 153 fmt.Println(x) 154 fmt.Println() 155 fmt.Println(test.x) 156 //t.Errorf("x mismatch. \nWant %v\ngot %v", test.x, x) 157 } 158 if !floats.EqualApprox(weight, test.w, test.tol) { 159 t.Errorf("n = %v, w mismatch", test.n) 160 //t.Errorf("w mismatch. Want %v, got %v", test.w, weight) 161 } 162 } 163 } 164 165 func TestHermiteInitialGuesses(t *testing.T) { 166 t.Parallel() 167 for _, test := range []struct { 168 n int 169 want []float64 170 }{ 171 // Evaluated from Chebfun. 172 { 173 n: 215, 174 want: []float64{0, 0.151326329763712, 0.302660700793398, 0.454011159911720, 0.605385765065948, 0.756792590918330, 0.908239734470234, 1.059735320731617, 1.211287508447394, 1.362904495892717, 1.514594526749157, 1.666365896074552, 1.818226956379164, 1.970186123821706, 2.122251884538916, 2.274432801123240, 2.426737519263548, 2.579174774564779, 2.731753399562905, 2.884482330952826, 3.037370617047366, 3.190427425487010, 3.343662051220745, 3.497083924780193, 3.650702620869949, 3.804527867299248, 3.958569554281313, 4.112837744128784, 4.267342681375636, 4.422094803358200, 4.577104751290402, 4.732383381871004, 4.887941779463563, 5.043791268893151, 5.199943428907478, 5.356410106353889, 5.513203431128299, 5.670335831956713, 5.827820053075521, 5.985669171882509, 6.143896617637219, 6.302516191296349, 6.461542086578262, 6.620988912359293, 6.780871716514890, 6.941206011329554, 7.102007800612191, 7.263293608667420, 7.425080511288993, 7.587386168959320, 7.750228862458692, 7.913627531110426, 8.077601813913194, 8.242172093840729, 8.407359545621334, 8.573186187346858, 8.739674936302684, 8.906849669458699, 9.074735289116129, 9.243357794268617, 9.412744358308792, 9.582923413795772, 9.753924745096450, 9.925779589826769, 10.098520750150884, 10.272182715150265, 10.446801795655594, 10.622416273146731, 10.799066564577450, 10.976795405279171, 11.155648052452676, 11.335672512180423, 11.516919793401330, 11.699444192903831, 11.883303616137852, 12.068559939553955, 12.255279421290370, 12.443533168399910, 12.633397670509774, 12.824955411930718, 13.018295576901773, 13.213514866037960, 13.410718446364541, 13.610021062878001, 13.811548346792373, 14.015438365098394, 14.221843468615116, 14.430932512542578, 14.642893546366283, 14.857937101386424, 15.076300248006383, 15.298251657131900, 15.524097989861344, 15.754192071913305, 15.988943508292977, 16.228832700713156, 16.474429717130270, 16.726420259572109, 16.985642328947012, 17.253139580754688, 17.530241825363181, 17.818691945179868, 18.120857274390474, 18.440107345774539, 18.781555607447057, 19.153723464992801, 19.573128956064245, 20.082675660407357}, 175 }, 176 { 177 n: 216, 178 want: []float64{7.5487718957947841e-02, 2.2646713089416223e-01, 3.7745846761172613e-01, 5.2846968803819716e-01, 6.7950876473020116e-01, 8.3058368936317251e-01, 9.8170247825952706e-01, 1.1328731779663146e+00, 1.2841038708939367e+00, 1.4354026810274640e+00, 1.5867777797225648e+00, 1.7382373915984026e+00, 1.8897898005400910e+00, 2.0414433558240375e+00, 2.1932064783796412e+00, 2.3450876672018457e+00, 2.4970955059292010e+00, 2.6492386696032790e+00, 2.8015259316256671e+00, 2.9539661709299665e+00, 3.1065683793869288e+00, 3.2593416694621893e+00, 3.4122952821469283e+00, 3.5654385951833136e+00, 3.7187811316079062e+00, 3.8723325686377130e+00, 4.0261027469252912e+00, 4.1801016802112088e+00, 4.3343395654041350e+00, 4.4888267931211692e+00, 4.6435739587232687e+00, 4.7985918738836766e+00, 4.9538915787298405e+00, 5.1094843546028494e+00, 5.2653817374818566e+00, 5.4215955321250595e+00, 5.5781378269829656e+00, 5.7350210099447425e+00, 5.8922577849835758e+00, 6.0498611897730488e+00, 6.2078446143528714e+00, 6.3662218209298418e+00, 6.5250069649076838e+00, 6.6842146172486627e+00, 6.8438597882796577e+00, 7.0039579530666876e+00, 7.1645250784943162e+00, 7.3255776522003675e+00, 7.4871327135320032e+00, 7.6492078867069049e+00, 7.8118214163831334e+00, 7.9749922058635363e+00, 8.1387398581859554e+00, 8.3030847203790454e+00, 8.4680479311960379e+00, 8.6336514726757141e+00, 8.7999182259219690e+00, 8.9668720315415094e+00, 9.1345377552342626e+00, 9.3029413590944845e+00, 9.4721099792532808e+00, 9.6420720105775217e+00, 9.8128571992374614e+00, 9.9844967440684584e+00, 1.0157023407784097e+01, 1.0330471639251822e+01, 1.0504877708222864e+01, 1.0680279854120787e+01, 1.0856718450743809e+01, 1.1034236189033734e+01, 1.1212878280418622e+01, 1.1392692683659751e+01, 1.1573730358642214e+01, 1.1756045551162156e+01, 1.1939696113507749e+01, 1.2124743866538131e+01, 1.2311255010076101e+01, 1.2499300589800702e+01, 1.2688957030525529e+01, 1.2880306747870632e+01, 1.3073438853003600e+01, 1.3268449968504161e+01, 1.3465445177719724e+01, 1.3664539135531767e+01, 1.3865857375666192e+01, 1.4069537859142688e+01, 1.4275732821001174e+01, 1.4484610989259913e+01, 1.4696360272885402e+01, 1.4911191046953165e+01, 1.5129340207007946e+01, 1.5351076226802732e+01, 1.5576705543358910e+01, 1.5806580725457744e+01, 1.6041111080581306e+01, 1.6280776662107755e+01, 1.6526147125048691e+01, 1.6777907674840002e+01, 1.7036895705202610e+01, 1.7304154114531990e+01, 1.7581011746684457e+01, 1.7869210214084568e+01, 1.8171115120332015e+01, 1.8490093525334313e+01, 1.8831255107137672e+01, 1.9203114954794152e+01, 1.9622178785373663e+01, 2.0131752068311702e+01}, 179 }, 180 } { 181 got := make([]float64, test.n/2+test.n%2) 182 for i := range got { 183 got[i] = Hermite{}.hermiteInitialGuess(i, test.n) 184 } 185 if !floats.EqualApprox(got, test.want, 1e-14) { 186 t.Errorf("n = %v, hermite initial guesses mismatch", test.n) 187 } 188 } 189 } 190 191 func TestHermiteLocationsAsy0(t *testing.T) { 192 t.Parallel() 193 for _, test := range []struct { 194 n int 195 x []float64 196 w []float64 197 }{ 198 // Evaluated from Chebfun. 199 { 200 n: 215, 201 x: []float64{-7.9483151672010196e-15, 1.5132632976672361e-01, 3.0266070079942864e-01, 4.5401115992078167e-01, 6.0538576507805808e-01, 7.5679259093351370e-01, 9.0823973448851325e-01, 1.0597353207530273e+00, 1.2112875084719879e+00, 1.3629044959205205e+00, 1.5145945267802365e+00, 1.6663658961089640e+00, 1.8182269564169717e+00, 1.9701861238629792e+00, 2.1222518845837395e+00, 2.2744328011717010e+00, 2.4267375193157439e+00, 2.5791747746208049e+00, 2.7317533996228827e+00, 2.8844823310168755e+00, 3.0373706171156218e+00, 3.1904274255596032e+00, 3.3436620512978501e+00, 3.4970839248619634e+00, 3.6507026209565665e+00, 3.8045278673909002e+00, 3.9585695543782120e+00, 4.1128377442311503e+00, 4.2673426814837114e+00, 4.4220948034722349e+00, 4.5771047514106780e+00, 4.7323833819978187e+00, 4.8879417795972326e+00, 5.0437912690340267e+00, 5.1999434290559226e+00, 5.3564101065103049e+00, 5.5132034312931157e+00, 5.6703358321303936e+00, 5.8278200532585673e+00, 5.9856691720754620e+00, 6.1438966178406549e+00, 6.3025161915109100e+00, 6.4615420868046280e+00, 6.6209889125982082e+00, 6.7808717167671544e+00, 6.9412060115960434e+00, 7.1020078008938672e+00, 7.2632936089653120e+00, 7.4250805116042331e+00, 7.5873861692931381e+00, 7.7502288628124383e+00, 7.9136275314855800e+00, 8.0776018143113824e+00, 8.2421720942637187e+00, 8.4073595460710955e+00, 8.5731861878255415e+00, 8.7396749368126798e+00, 8.9068496700026394e+00, 9.0747352896969389e+00, 9.2433577948895387e+00, 9.4127443589734394e+00, 9.5829234145081710e+00, 9.7539247458611111e+00, 9.9257795906487338e+00, 1.0098520751035824e+01, 1.0272182716104577e+01, 1.0446801796686490e+01, 1.0622416274262394e+01, 1.0799066565787168e+01, 1.0976795406593546e+01, 1.1155648053883823e+01, 1.1335672513742256e+01, 1.1516919795109878e+01, 1.1699444194777641e+01, 1.1883303618198463e+01, 1.2068559941826503e+01, 1.2255279423804318e+01, 1.2443533171189967e+01, 1.2633397673617059e+01, 1.2824955415404188e+01, 1.3018295580800100e+01, 1.3213514870431910e+01, 1.3410718451340038e+01, 1.3610021068540190e+01, 1.3811548353270942e+01, 1.4015438372554696e+01, 1.4221843477251845e+01, 1.4430932522616979e+01, 1.4642893558208563e+01, 1.4857937115425768e+01, 1.5076300264808333e+01, 1.5298251677453143e+01, 1.5524098014731747e+01, 1.5754192102761674e+01, 1.5988943547145137e+01, 1.6228832750513551e+01, 1.6474429782282726e+01, 1.6726420346886542e+01, 1.6985642449377284e+01, 1.7253139752773148e+01, 1.7530242081974308e+01, 1.7818692349773503e+01, 1.8120857960601569e+01, 1.8440108632764016e+01, 1.8781558404513735e+01, 1.9153731166695263e+01, 1.9573161931385755e+01, 2.0083110126223993e+01}, 202 w: []float64{5.8004562850365771e-04, 5.6692877486338696e-04, 5.2932867305102921e-04, 4.7211368597165944e-04, 4.0223648470876573e-04, 3.2735218319190782e-04, 2.5446548811048362e-04, 1.8892919855999243e-04, 1.3396711152850057e-04, 9.0718165504482523e-05, 5.8661199606591556e-05, 3.6218251240150691e-05, 2.1349054444552587e-05, 1.2013089019084848e-05, 6.4521031002773646e-06, 3.3071925113778075e-06, 1.6175791039359969e-06, 7.5483313427524376e-07, 3.3600239642860852e-07, 1.4264659961771696e-07, 5.7746366478382785e-08, 2.2286582090203475e-08, 8.1983021699506761e-09, 2.8738670556378732e-09, 9.5976924324201262e-10, 3.0529085215378481e-10, 9.2467927287192434e-11, 2.6660996519674056e-11, 7.3154481204350507e-12, 1.9096325566425540e-12, 4.7409073505752031e-13, 1.1189936218333804e-13, 2.5101111888653927e-14, 5.3492761412487281e-15, 1.0825895304391782e-15, 2.0798005039728529e-16, 3.7912539356931888e-17, 6.5547084049896133e-18, 1.0743122119399353e-18, 1.6684093877262400e-19, 2.4538539136228336e-20, 3.4161583900178126e-21, 4.4991409209589655e-22, 5.6023724685401444e-23, 6.5917775903350454e-24, 7.3239791710744789e-25, 7.6792588730186891e-26, 7.5931172671070367e-27, 7.0751732949679160e-28, 6.2078867832748634e-29, 5.1250608797215456e-30, 3.9778286806416675e-31, 2.9000923323091595e-32, 1.9842934651116758e-33, 1.2729744163019100e-34, 7.6493618655638258e-36, 4.3010461850159373e-37, 2.2604572504006732e-38, 1.1091714341886240e-39, 5.0753225126752125e-41, 2.1629552371814077e-42, 8.5739087326714758e-44, 3.1568681170134092e-45, 1.0780709245918455e-46, 3.4094518277810594e-48, 9.9692987408874913e-50, 2.6905726285477170e-51, 6.6902112757430557e-53, 1.5297458011420645e-54, 3.2099851519180199e-56, 6.1681886704578063e-58, 1.0829083084555836e-59, 1.7328083889009238e-61, 2.5206396804555329e-63, 3.3240965181095399e-65, 3.9623955222122382e-67, 4.2558991248868728e-69, 4.1048947183601511e-71, 3.5424776999043975e-73, 2.7245890408644923e-75, 1.8596929038788086e-77, 1.1213274238978696e-79, 5.9430256314002078e-82, 2.7536336403486887e-84, 1.1087876280230634e-86, 3.8548279808836764e-89, 1.1488445098745636e-91, 2.9118805234147757e-94, 6.2218187764965726e-97, 1.1097458975689325e-99, 1.6341809683598844e-102, 1.9621625424695376e-105, 1.8939702898325753e-108, 1.4459753551186440e-111, 8.5692594596311645e-115, 3.8565449589488849e-118, 1.2843410590864927e-121, 3.0685300780965873e-125, 5.0651104293759753e-129, 5.5131423653412833e-133, 3.7300165435945031e-137, 1.4525522232777015e-141, 2.9352196847507026e-146, 2.6587623615117695e-151, 8.6633861029598960e-157, 7.0653364942986233e-163, 7.2051505413036788e-170, 1.5514139491189097e-178}, 203 }, 204 { 205 n: 216, 206 x: []float64{7.5487718959414210e-02, 2.2646713089859094e-01, 3.7745846761911317e-01, 5.2846968804856509e-01, 6.7950876474356448e-01, 8.3058368937955573e-01, 9.8170247827895785e-01, 1.1328731779888348e+00, 1.2841038709195900e+00, 1.4354026810562848e+00, 1.5867777797546210e+00, 1.7382373916337388e+00, 1.8897898005787916e+00, 2.0414433558661624e+00, 2.1932064784252856e+00, 2.3450876672510903e+00, 2.4970955059821409e+00, 2.6492386696600243e+00, 2.8015259316863266e+00, 2.9539661709946619e+00, 3.1065683794558021e+00, 3.2593416695353823e+00, 3.4122952822245907e+00, 3.5654385952656149e+00, 3.7187811316950210e+00, 3.8723325687298416e+00, 4.0261027470226392e+00, 4.1801016803139959e+00, 4.3343395655126109e+00, 4.4888267932355790e+00, 4.6435739588438905e+00, 4.7985918740108131e+00, 4.9538915788638089e+00, 5.1094843547439881e+00, 5.2653817376305465e+00, 5.4215955322816969e+00, 5.5781378271479722e+00, 5.7350210101185848e+00, 5.8922577851667635e+00, 6.0498611899661094e+00, 6.2078446145563948e+00, 6.3662218211444577e+00, 6.5250069651340752e+00, 6.6842146174875827e+00, 6.8438597885318986e+00, 7.0039579533331269e+00, 7.1645250787759087e+00, 7.3255776524981444e+00, 7.4871327138470951e+00, 7.6492078870405447e+00, 7.8118214167366684e+00, 7.9749922062384426e+00, 8.1387398585838486e+00, 8.3030847208017082e+00, 8.4680479316454296e+00, 8.6336514731539875e+00, 8.7999182264315081e+00, 8.9668720320849413e+00, 9.1345377558145096e+00, 9.3029413597147883e+00, 9.4721099799172528e+00, 9.6420720112891818e+00, 9.8128572000013108e+00, 9.9844967448895385e+00, 1.0157023408668081e+01, 1.0330471640205081e+01, 1.0504877709252620e+01, 1.0680279855235202e+01, 1.0856718451952171e+01, 1.1034236190346626e+01, 1.1212878281848150e+01, 1.1392692685219812e+01, 1.1573730360348824e+01, 1.1756045553033841e+01, 1.1939696115566026e+01, 1.2124743868808109e+01, 1.2311255012587219e+01, 1.2499300592587632e+01, 1.2688957033629340e+01, 1.2880306751340244e+01, 1.3073438856897617e+01, 1.3268449972893279e+01, 1.3465445182689793e+01, 1.3664539141187824e+01, 1.3865857382137794e+01, 1.4069537866591046e+01, 1.4275732829628778e+01, 1.4484610999323769e+01, 1.4696360284715409e+01, 1.4911191060978103e+01, 1.5129340223792830e+01, 1.5351076247103551e+01, 1.5576705568204593e+01, 1.5806580756275796e+01, 1.6041111119395726e+01, 1.6280776711860355e+01, 1.6526147190139376e+01, 1.6777907762072694e+01, 1.7036895825521608e+01, 1.7304154286393636e+01, 1.7581012003064874e+01, 1.7869210618319627e+01, 1.8171115805943941e+01, 1.8490094811217439e+01, 1.8831257901839155e+01, 1.9203122650098184e+01, 1.9622211733828486e+01, 2.0131752068397390e+01}, 207 w: []float64{5.7408951238509774e-04, 5.4853385977693967e-04, 5.0077995633045094e-04, 4.3681926493182888e-04, 3.6404534695321319e-04, 2.8986205027358900e-04, 2.2048980967270541e-04, 1.6022189177224014e-04, 1.1121464501100074e-04, 7.3735261435177744e-05, 4.6689968632275442e-05, 2.8233496634858870e-05, 1.6302404527221912e-05, 8.9873835313609794e-06, 4.7299184092204348e-06, 2.3760322139117827e-06, 1.1391060264678187e-06, 5.2109775739704647e-07, 2.2742736124678848e-07, 9.4679280581569520e-08, 3.7589897335857270e-08, 1.4229883676778969e-08, 5.1351173480468011e-09, 1.7661093963625318e-09, 5.7875785413194057e-10, 1.8066600901602130e-10, 5.3707955985666741e-11, 1.5200567246892033e-11, 4.0945877360252466e-12, 1.0494304449814065e-12, 2.5582770078364328e-13, 5.9298335011290506e-14, 1.3064177735039720e-14, 2.7346561920969734e-15, 5.4366757055637182e-16, 1.0261135273171614e-16, 1.8378155831501011e-17, 3.1221798154524404e-18, 5.0287455392773255e-19, 7.6752848097550855e-20, 1.1095334788910946e-20, 1.5183281292392555e-21, 1.9657499371912346e-22, 2.4064442018314010e-23, 2.7838422576260478e-24, 3.0413021389695441e-25, 3.1356913424697775e-26, 3.0490587561112177e-27, 2.7941107980138270e-28, 2.4112340295373517e-29, 1.9579916032501855e-30, 1.4948591683644822e-31, 1.0720958700672810e-32, 7.2163812209007653e-34, 4.5545782039839515e-35, 2.6927171840186886e-36, 1.4896964129251313e-37, 7.7036780004272946e-39, 3.7196117693798106e-40, 1.6748563396289038e-41, 7.0241404150854973e-43, 2.7401344340734534e-44, 9.9291319468776600e-46, 3.3371619908503302e-47, 1.0387276524925886e-48, 2.9893704843803614e-50, 7.9408570659652511e-52, 1.9434716944530867e-53, 4.3740144067322860e-55, 9.0342460240718143e-57, 1.7087495134365174e-58, 2.9528859528856670e-60, 4.6509376421165100e-62, 6.6593952486160953e-64, 8.6442830921042970e-66, 1.0142381095581560e-67, 1.0722439547251424e-69, 1.0179251007077803e-71, 8.6461259693742430e-74, 6.5448969088799971e-76, 4.3965762236216239e-78, 2.6089085327841006e-80, 1.3607099985773063e-82, 6.2039892663366641e-85, 2.4580575133840935e-87, 8.4080554628125066e-90, 2.4652597109139967e-92, 6.1467455174872763e-95, 1.2918545805718045e-97, 2.2661732049781124e-100, 3.2815976681148591e-103, 3.8741015126651295e-106, 3.6760977386321105e-109, 2.7584831111443303e-112, 1.6064052012003602e-115, 7.1024252453209961e-119, 2.3230796238780657e-122, 5.4494213912665180e-126, 8.8284366174946482e-130, 9.4271378060446301e-134, 6.2539251873936211e-138, 2.3865140957941506e-142, 4.7220323342515999e-147, 4.1840743138172546e-152, 1.3319161291512504e-157, 1.0592510752538756e-163, 1.0503755670967946e-170, 2.1869674690632971e-179}, 208 }, 209 } { 210 n := test.n 211 x := make([]float64, n/2+n%2) 212 w := make([]float64, n/2+n%2) 213 for i := range x { 214 x[i], w[i] = Hermite{}.locationsAsy0(i, n) 215 } 216 if !floats.EqualApprox(x, test.x, 1e-13) { 217 t.Errorf("n = %v, x mismatch", n) 218 fmt.Println(x[107]) 219 fmt.Println(test.x[107]) 220 } 221 if !floats.EqualApprox(w, test.w, 1e-13) { 222 t.Errorf("n = %v, w mismatch", n) 223 } 224 } 225 } 226 227 func TestHermiteAsyAiry(t *testing.T) { 228 t.Parallel() 229 for _, test := range []struct { 230 n int 231 theta []float64 232 val []float64 233 dval []float64 234 }{ 235 { 236 n: 215, 237 theta: []float64{1.5707963267948966e+00, 1.5635071294267224e+00, 1.5562171573546757e+00, 1.5489256352159648e+00, 1.5416317863284521e+00, 1.5343348320272066e+00, 1.5270339909965103e+00, 1.5197284785957685e+00, 1.5124175061777518e+00, 1.5051002803975593e+00, 1.4977760025106577e+00, 1.4904438676582881e+00, 1.4831030641384946e+00, 1.4757527726609410e+00, 1.4683921655836265e+00, 1.4610204061295120e+00, 1.4536366475809854e+00, 1.4462400324499760e+00, 1.4388296916214274e+00, 1.4314047434676882e+00, 1.4239642929312548e+00, 1.4165074305731233e+00, 1.4090332315838545e+00, 1.4015407547542300e+00, 1.3940290414022056e+00, 1.3864971142525955e+00, 1.3789439762656834e+00, 1.3713686094106747e+00, 1.3637699733795743e+00, 1.3561470042367485e+00, 1.3484986129990375e+00, 1.3408236841408716e+00, 1.3331210740183812e+00, 1.3253896092059803e+00, 1.3176280847383373e+00, 1.3098352622500289e+00, 1.3020098680044709e+00, 1.2941505908029671e+00, 1.2862560797638511e+00, 1.2783249419607658e+00, 1.2703557399080556e+00, 1.2623469888800907e+00, 1.2542971540500127e+00, 1.2462046474319508e+00, 1.2380678246090893e+00, 1.2298849812281600e+00, 1.2216543492388388e+00, 1.2133740928542220e+00, 1.2050423042059359e+00, 1.1966569986644591e+00, 1.1882161097919153e+00, 1.1797174838907749e+00, 1.1711588741076131e+00, 1.1625379340461441e+00, 1.1538522108381697e+00, 1.1450991376146524e+00, 1.1362760253118058e+00, 1.1273800537386238e+00, 1.1184082618225748e+00, 1.1093575369389341e+00, 1.1002246032162142e+00, 1.0910060086950395e+00, 1.0816981112001869e+00, 1.0722970627649082e+00, 1.0627987924225111e+00, 1.0531989871517369e+00, 1.0434930707289145e+00, 1.0336761802000907e+00, 1.0237431396389916e+00, 1.0136884308001370e+00, 1.0035061602085740e+00, 9.9319002214595331e-01, 9.8273325689369295e-01, 9.7212860347355579e-01, 9.6136824597870241e-01, 9.5044375240720391e-01, 9.3934600468605900e-01, 9.2806511829511895e-01, 9.1659034955139063e-01, 9.0490998817422319e-01, 8.9301123219309975e-01, 8.8088004154453947e-01, 8.6850096578161351e-01, 8.5585694011780433e-01, 8.4292904244735056e-01, 8.2969620188675874e-01, 8.1613484656631152e-01, 8.0221847457494289e-01, 7.8791712669745728e-01, 7.7319673223616503e-01, 7.5801828879746735e-01, 7.4233682191908168e-01, 7.2610004838413222e-01, 7.0924663405346811e-01, 6.9170388642137270e-01, 6.7338464244284535e-01, 6.5418298314185364e-01, 6.3396819041411068e-01, 6.1257598542667102e-01, 5.8979540387821172e-01, 5.6534835113739590e-01, 5.3885619819698471e-01, 5.0978185232293227e-01, 4.7732127920035572e-01, 4.4017830784988765e-01, 3.9602307074600884e-01, 3.3985069280702440e-01, 2.5624520569356829e-01}, 238 val: []float64{-2.7524590607067879e-13, -1.2484792737707130e-10, 2.5043777255407545e-10, -3.7621487726711831e-10, 5.0266571286479591e-10, -6.3022107051014496e-10, 7.5847898514904004e-10, -8.8850597267422281e-10, 1.0201287099545048e-09, -1.1532700149758681e-09, 1.2885402426941860e-09, -1.4262514564750722e-09, 1.5667774694950304e-09, -1.7098460348004283e-09, 1.8563663242006209e-09, -2.0060430373954962e-09, 2.1597272205910619e-09, -2.3174687646872261e-09, 2.4795270439737100e-09, -2.6462815453642877e-09, 2.8188431716836157e-09, -2.9962948915230151e-09, 3.1805879826447352e-09, -3.3709772507788239e-09, 3.5681573894354513e-09, -3.7732681484183285e-09, 3.9863813736176932e-09, -4.2080297462347532e-09, 4.4391671460302399e-09, -4.6802436355831232e-09, 4.9322546933533433e-09, -5.1957881449299223e-09, 5.4715433664057677e-09, -5.7608265327475837e-09, 6.0644153161437157e-09, -6.3835515563504339e-09, 6.7192819880764795e-09, -7.0729371214636086e-09, 7.4458702579674617e-09, -7.8396410076078555e-09, 8.2556088536449877e-09, -8.6960989460562939e-09, 9.1626310723815202e-09, -9.6575986146054327e-09, 1.0182896152806950e-08, -1.0741758184989815e-08, 1.1337214303287172e-08, -1.1971481080324528e-08, 1.2648762056240369e-08, -1.3372488830525768e-08, 1.4147041859097387e-08, -1.4977276046958432e-08, 1.5868475891599271e-08, -1.6825823997480545e-08, 1.7856900524878266e-08, -1.8967833880184117e-08, 2.0167708166421882e-08, -2.1465280681285451e-08, 2.2870631970634630e-08, -2.4395881051717265e-08, 2.6054060647767539e-08, -2.7859818527100110e-08, 2.9830454146699167e-08, -3.1984835487787522e-08, 3.4345470368342559e-08, -3.6937900081988413e-08, 3.9790883510012329e-08, -4.2938418365980210e-08, 4.6419377177480922e-08, -5.0279213559974237e-08, 5.4570799296449321e-08, -5.9356303125081130e-08, 6.4708755363671345e-08, -7.0714511032393380e-08, 7.7475892426711618e-08, -8.5115456468135130e-08, 9.3779863576446978e-08, -1.0364644483987255e-07, 1.1493006182865740e-07, -1.2789317815470753e-07, 1.4285900893044798e-07, -1.6022759919461249e-07, 1.8049814080062288e-07, -2.0429953256541455e-07, 2.3243044535889061e-07, -2.6591504027157263e-07, 3.0608147425737922e-07, -3.5467098673335754e-07, 4.1399606056878556e-07, -4.8716979156405424e-07, 5.7844824292016844e-07, -6.9374768843585542e-07, 8.4144962449118331e-07, -1.0336795693201387e-06, 1.2884020459910342e-06, -1.6329629222918408e-06, 2.1103031286712709e-06, -2.7903321871954755e-06, 3.7918023218017778e-06, -5.3269144947324421e-06, 7.7989206456257246e-06, -1.2034979469568085e-05, 1.9905658561076196e-05, -3.6224899321604820e-05, 7.5828952282754516e-05, -1.9870421394114517e-04, 7.9136577883937422e-04, -9.1266148556594703e-03}, 239 dval: []float64{-2.9359856130945122e+01, 2.9359466144908318e+01, -2.9358296010652477e+01, 2.9356345199427643e+01, -2.9353612829040124e+01, 2.9350097662433203e+01, -2.9345798105693621e+01, 2.9340712205476308e+01, -2.9334837645838910e+01, 2.9328171744474840e+01, -2.9320711448331572e+01, 2.9312453328598885e+01, -2.9303393575049100e+01, 2.9293527989709109e+01, -2.9282851979841201e+01, 2.9271360550207458e+01, -2.9259048294588819e+01, 2.9245909386527540e+01, -2.9231937569258221e+01, 2.9217126144788914e+01, -2.9201467962090302e+01, 2.9184955404346876e+01, -2.9167580375219231e+01, 2.9149334284062498e+01, -2.9130208030040425e+01, 2.9110191985068752e+01, -2.9089275975516287e+01, 2.9067449262584436e+01, -2.9044700521279459e+01, 2.9021017817883425e+01, -2.8996388585821325e+01, 2.8970799599811933e+01, -2.8944236948180023e+01, 2.8916686003195348e+01, -2.8888131389291605e+01, 2.8858556949003951e+01, -2.8827945706448649e+01, 2.8796279828150279e+01, -2.8763540581003511e+01, 2.8729708287134507e+01, -2.8694762275403512e+01, 2.8658680829263385e+01, -2.8621441130659093e+01, 2.8583019199620328e+01, -2.8543389829161509e+01, 2.8502526515061927e+01, -2.8460401380051497e+01, 2.8416985091874277e+01, -2.8372246774642264e+01, 2.8326153912823031e+01, -2.8278672247129006e+01, 2.8229765661486788e+01, -2.8179396060166667e+01, 2.8127523234037287e+01, -2.8074104714780372e+01, 2.8019095615750665e+01, -2.7962448457994284e+01, 2.7904112979739956e+01, -2.7844035927448619e+01, 2.7782160826241125e+01, -2.7718427727214667e+01, 2.7652772928798932e+01, -2.7585128668881747e+01, 2.7515422783940370e+01, -2.7443578330833645e+01, 2.7369513166223737e+01, -2.7293139477783004e+01, 2.7214363260373997e+01, -2.7133083729234610e+01, 2.7049192660814331e+01, -2.6962573650237655e+01, 2.6873101272350414e+01, -2.6780640130847800e+01, 2.6685043776981303e+01, -2.6586153475654008e+01, 2.6483796792158788e+01, -2.6377785967154090e+01, 2.6267916040395331e+01, -2.6153962674834343e+01, 2.6035679621411951e+01, -2.5912795750458177e+01, 2.5785011557068390e+01, -2.5651995023754676e+01, 2.5513376692151432e+01, -2.5368743753874771e+01, 2.5217632914945654e+01, -2.5059521712941240e+01, 2.4893817863127197e+01, -2.4719846067215368e+01, 2.4536831517922174e+01, -2.4343879046260469e+01, 2.4139946442705973e+01, -2.3923809867871942e+01, 2.3694018337866666e+01, -2.3448832829666316e+01, 2.3186143264519330e+01, -2.2903352884396824e+01, 2.2597213200674400e+01, -2.2263581543467414e+01, 2.1897052703993687e+01, -2.1490376258364485e+01, 2.1033488463000687e+01, -2.0511802124454178e+01, 1.9902938182242686e+01, -1.9169784832381577e+01, 1.8243381598901596e+01, -1.6969663168974311e+01, 1.4853826851969115e+01}, 240 }, 241 { 242 n: 215, 243 theta: []float64{1.5707963267948968e+00, 1.5635071294265777e+00, 1.5562171573543850e+00, 1.5489256352155283e+00, 1.5416317863278686e+00, 1.5343348320264747e+00, 1.5270339909956292e+00, 1.5197284785947358e+00, 1.5124175061765655e+00, 1.5051002803962170e+00, 1.4977760025091569e+00, 1.4904438676566254e+00, 1.4831030641366665e+00, 1.4757527726589439e+00, 1.4683921655814560e+00, 1.4610204061271637e+00, 1.4536366475784539e+00, 1.4462400324472560e+00, 1.4388296916185130e+00, 1.4314047434645731e+00, 1.4239642929279313e+00, 1.4165074305695844e+00, 1.4090332315800913e+00, 1.4015407547502341e+00, 1.3940290413979675e+00, 1.3864971142481046e+00, 1.3789439762609286e+00, 1.3713686094056443e+00, 1.3637699733742550e+00, 1.3561470042311266e+00, 1.3484986129930978e+00, 1.3408236841345980e+00, 1.3331210740117563e+00, 1.3253896091989852e+00, 1.3176280847309516e+00, 1.3098352622422307e+00, 1.3020098679962364e+00, 1.2941505907942705e+00, 1.2862560797546647e+00, 1.2783249419510594e+00, 1.2703557398977969e+00, 1.2623469888692436e+00, 1.2542971540385390e+00, 1.2462046474198085e+00, 1.2380678245962331e+00, 1.2298849812145400e+00, 1.2216543492243996e+00, 1.2133740928389052e+00, 1.2050423041896758e+00, 1.1966569986471847e+00, 1.1882161097735480e+00, 1.1797174838712285e+00, 1.1711588740867924e+00, 1.1625379340239450e+00, 1.1538522108144755e+00, 1.1450991375893356e+00, 1.1362760252847235e+00, 1.1273800537096179e+00, 1.1184082617914692e+00, 1.1093575369055320e+00, 1.1002246031802951e+00, 1.0910060086563567e+00, 1.0816981111584625e+00, 1.0722970627198296e+00, 1.0627987923737243e+00, 1.0531989870988405e+00, 1.0434930706714527e+00, 1.0336761801375436e+00, 1.0237431395707643e+00, 1.0136884307255469e+00, 1.0035061601268345e+00, 9.9319002205615470e-01, 9.8273325679477930e-01, 9.7212860336429585e-01, 9.6136824585765468e-01, 9.5044375227267230e-01, 9.3934600453603823e-01, 9.2806511812722514e-01, 9.1659034936277473e-01, 9.0490998796145916e-01, 8.9301123195204113e-01, 8.8088004127013353e-01, 8.6850096546765831e-01, 8.5585693975662547e-01, 8.4292904202937069e-01, 8.2969620139991496e-01, 8.1613484599525510e-01, 8.0221847389992995e-01, 7.8791712589278218e-01, 7.7319673126791522e-01, 7.5801828762024448e-01, 7.4233682047111893e-01, 7.2610004657985505e-01, 7.0924663177187774e-01, 6.9170388348738876e-01, 6.7338463859636577e-01, 6.5418297798453895e-01, 6.3396818331389482e-01, 6.1257597533770680e-01, 5.8979538898074346e-01, 5.6534832806423485e-01, 5.3885616021897675e-01, 5.0978178458826806e-01, 4.7732114425935024e-01, 4.4017799165717791e-01, 3.9602210904603868e-01, 3.3984592789666196e-01, 2.5616263514373872e-01}, 244 val: []float64{-2.7524577037687927e-13, -1.3157296144588393e-13, -1.4217705189589319e-13, -9.3051784272423659e-14, 6.2263913433904649e-14, -7.2338165854311426e-14, 1.6489823942055246e-13, 8.2086154015730068e-14, 1.7030857773598118e-13, 1.9200825273544764e-13, 3.4144423192398587e-13, -1.3350292964848512e-13, 7.7406393378692183e-16, 3.0802286839980475e-15, 1.0626665274130983e-13, 9.7508116816654928e-14, -1.2286283979350783e-13, 1.6602061523803380e-13, 1.2145800400612989e-14, -2.0125760394077007e-13, 1.1752853222876857e-13, 1.5246361311903834e-13, -1.7100196342840500e-13, -9.0852635256292980e-14, -7.8101776477326909e-14, -8.6215405399587178e-14, -1.8424041061507494e-13, -1.7748959370373156e-13, 1.6659488983250428e-14, -2.3029664495695825e-14, 4.9882044749360307e-14, -1.6935708059066857e-13, -1.6889419531778083e-14, -1.5488691966202885e-13, 4.7496471682336465e-15, -6.0236075531674274e-14, -4.7790439973748918e-14, 1.0528243973915236e-14, -1.4481370116381506e-13, 4.8870674172048881e-14, 5.9145722182844837e-14, -3.6252017525118028e-14, -1.4799821290649442e-13, 7.8483748114372226e-14, -3.1698431394015554e-14, -2.1250000650523357e-13, -1.2207160366356720e-13, -4.4799710774576449e-14, -6.6076225108040054e-14, 4.9432907671096125e-14, 1.1714372287574581e-13, 7.1071624668919607e-14, -1.4699620399669987e-13, 4.9028118279404591e-14, 5.6995970859340297e-15, 1.8655926516135062e-14, 3.2409175615798361e-14, 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-2.2299378247087898e+01, 2.1932149880590437e+01, -2.1524711604350518e+01, 2.1066983868178077e+01, -2.0544356598759389e+01, 1.9934415684120079e+01, -1.9199991281861426e+01, 1.8272015261833435e+01, -1.6996182557157578e+01, 1.4876958810870862e+01}, 264 }, 265 } { 266 got := make([]float64, len(test.theta)) 267 gotD := make([]float64, len(test.theta)) 268 for i := range got { 269 got[i], gotD[i] = Hermite{}.hermpolyAsyAiry(i, test.n, test.theta[i]) 270 } 271 if !floats.EqualApprox(test.val, got, 1e-12) { 272 t.Errorf("n = %v, hermpolyAsyAiry mismatch", test.n) 273 } 274 if !floats.EqualApprox(test.dval, gotD, 1e-12) { 275 t.Errorf("n = %v, hermpolyAsyAiry deriv mismatch", test.n) 276 } 277 } 278 }