github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/integrate/quad/hermite_test.go

// Copyright ©2016 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package quad

import (
	"fmt"
	"math"
	"testing"

	"github.com/jingcheng-WU/gonum/floats"
	"github.com/jingcheng-WU/gonum/floats/scalar"
)

func TestHermite(t *testing.T) {
	t.Parallel()
	for cas, test := range []struct {
		n   int
		f   func(float64) float64
		ev  float64
		tol float64
	}{
		{
			n:   2,
			f:   func(x float64) float64 { return 1 },
			ev:  math.SqrtPi,
			tol: 1e-14,
		},
		{
			n:   4,
			f:   func(x float64) float64 { return math.Exp(-2 * 0.5 * x) },
			ev:  math.SqrtPi * math.Exp(0.25),
			tol: 1e-4,
		},
		{
			n:   9,
			f:   func(x float64) float64 { return math.Exp(-2 * 0.5 * x) },
			ev:  math.SqrtPi * math.Exp(0.25),
			tol: 1e-12,
		},
		{
			n:   10,
			f:   func(x float64) float64 { return math.Exp(-2 * 0.5 * x) },
			ev:  math.SqrtPi * math.Exp(0.25),
			tol: 1e-12,
		},
		{
			n:   15,
			f:   func(x float64) float64 { return math.Exp(-2 * 2 * x) },
			ev:  math.SqrtPi * math.Exp(4),
			tol: 1e-4,
		},
		{
			n:   22,
			f:   func(x float64) float64 { return math.Exp(-2 * 2 * x) },
			ev:  math.SqrtPi * math.Exp(4),
			tol: 1e-12,
		},
		{
			n:   21,
			f:   func(x float64) float64 { return math.Exp(-2 * 2 * x) },
			ev:  math.SqrtPi * math.Exp(4),
			tol: 1e-12,
		},
	} {
		ev := Fixed(test.f, math.Inf(-1), math.Inf(1), test.n, Hermite{}, 0)
		if !scalar.EqualWithinAbsOrRel(test.ev, ev, test.tol, test.tol) {
			t.Errorf("Case %d: expected value mismatch.\nWant %v\ngot %v", cas, test.ev, ev)
		}
	}
}

func TestHermiteLocations(t *testing.T) {
	t.Parallel()
	// Test the hermite locations and weights against other precomputed table.
	// Data from http://dlmf.nist.gov/3.5.
	for _, test := range []struct {
		n int
		x []float64
		w []float64
	}{
		// Evaluated from Chebfun.
		{
			n: 5,
			x: []float64{-0.202018287045609e1, -0.958572464613819, 0, 0.958572464613819, 0.202018287045609e1},
			w: []float64{0.199532420590459e-1, 0.393619323152241, 0.945308720482942, 0.393619323152241, 0.199532420590459e-1},
		},
		{
			n: 10,
			x: []float64{-0.343615911883773760e1, -0.253273167423278980e1, -0.175668364929988177e1, -0.103661082978951365e1, -0.342901327223704609, 0.342901327223704609, 0.103661082978951365e1, 0.175668364929988177e1, 0.253273167423278980e1, 0.343615911883773760e1},
			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},
		},
		{
			n: 215,
			x: []float64{-2.0083110126223993e+01, -1.9573161931385755e+01, -1.9153731166695263e+01, -1.8781558404513735e+01, -1.8440108632764016e+01, -1.8120857960601569e+01, -1.7818692349773503e+01, -1.7530242081974308e+01, -1.7253139752773148e+01, -1.6985642449377284e+01, -1.6726420346886542e+01, -1.6474429782282726e+01, -1.6228832750513551e+01, -1.5988943547145137e+01, -1.5754192102761674e+01, -1.5524098014731747e+01, -1.5298251677453143e+01, -1.5076300264808333e+01, -1.4857937115425768e+01, -1.4642893558208563e+01, -1.4430932522616979e+01, -1.4221843477251845e+01, -1.4015438372554696e+01, -1.3811548353270942e+01, -1.3610021068540190e+01, -1.3410718451340038e+01, -1.3213514870431910e+01, -1.3018295580800100e+01, -1.2824955415404188e+01, -1.2633397673617059e+01, -1.2443533171189967e+01, -1.2255279423804318e+01, -1.2068559941826503e+01, -1.1883303618198463e+01, -1.1699444194777641e+01, -1.1516919795109878e+01, -1.1335672513742256e+01, -1.1155648053883823e+01, -1.0976795406593546e+01, -1.0799066565787168e+01, -1.0622416274262394e+01, -1.0446801796686490e+01, -1.0272182716104577e+01, -1.0098520751035824e+01, -9.9257795906487338e+00, -9.7539247458611111e+00, -9.5829234145081710e+00, -9.4127443589734394e+00, -9.2433577948895387e+00, -9.0747352896969389e+00, -8.9068496700026394e+00, -8.7396749368126798e+00, -8.5731861878255415e+00, -8.4073595460710955e+00, -8.2421720942637187e+00, -8.0776018143113824e+00, -7.9136275314855800e+00, -7.7502288628124383e+00, -7.5873861692931381e+00, -7.4250805116042331e+00, -7.2632936089653120e+00, -7.1020078008938672e+00, -6.9412060115960434e+00, -6.7808717167671544e+00, -6.6209889125982082e+00, -6.4615420868046280e+00, -6.3025161915109100e+00, -6.1438966178406549e+00, -5.9856691720754620e+00, -5.8278200532585673e+00, -5.6703358321303936e+00, -5.5132034312931157e+00, -5.3564101065103049e+00, -5.1999434290559226e+00, -5.0437912690340267e+00, -4.8879417795972326e+00, -4.7323833819978187e+00, -4.5771047514106780e+00, -4.4220948034722349e+00, -4.2673426814837114e+00, -4.1128377442311503e+00, -3.9585695543782120e+00, -3.8045278673909002e+00, -3.6507026209565665e+00, -3.4970839248619634e+00, -3.3436620512978501e+00, -3.1904274255596032e+00, -3.0373706171156218e+00, -2.8844823310168755e+00, -2.7317533996228827e+00, -2.5791747746208049e+00, -2.4267375193157439e+00, -2.2744328011717010e+00, -2.1222518845837395e+00, -1.9701861238629792e+00, -1.8182269564169717e+00, -1.6663658961089640e+00, -1.5145945267802365e+00, -1.3629044959205205e+00, -1.2112875084719879e+00, -1.0597353207530273e+00, -9.0823973448851325e-01, -7.5679259093351370e-01, -6.0538576507805808e-01, -4.5401115992078167e-01, -3.0266070079942864e-01, -1.5132632976672361e-01, 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},
			w: []float64{4.0474005560499094e-176, 1.8797130400856443e-167, 1.8432377040276421e-160, 2.2601442864626069e-154, 6.9363023753259492e-149, 7.6575370428605554e-144, 3.7894855074137878e-139, 9.7310398950542353e-135, 1.4382941114934084e-130, 1.3214094652141891e-126, 8.0053233705919762e-123, 3.3506484324551954e-119, 1.0061133084529732e-115, 2.2355880918528976e-112, 3.7723274691873339e-109, 4.9410774014014167e-106, 5.1189805080467357e-103, 4.2633269887655389e-100, 2.8951564896303124e-97, 1.6231768954981774e-94, 7.5966487579367170e-92, 2.9971587600601123e-89, 1.0056653752640396e-86, 2.8926565116618279e-84, 7.1838069610206879e-82, 1.5504440487214177e-79, 2.9253709118548054e-77, 4.8516529695481360e-75, 7.1080340648382430e-73, 9.2417798747589595e-71, 1.0709039437896534e-68, 1.1102986726619406e-66, 1.0337280935884043e-64, 8.6720569345151135e-63, 6.5759615285599325e-61, 4.5206307708839604e-59, 2.8251413443094276e-57, 1.6091856250751163e-55, 8.3743579179261028e-54, 3.9908716881614503e-52, 1.7453732998154445e-50, 7.0192904730947679e-49, 2.6008368230936308e-47, 8.8947358191690260e-46, 2.8125213532676820e-44, 8.2357837374304705e-43, 2.2368010157343200e-41, 5.6428177886700861e-40, 1.3240736407971940e-38, 2.8936578029605094e-37, 5.8971855560501346e-36, 1.1220768467833071e-34, 1.9956009474900652e-33, 3.3209946083724174e-32, 5.1767166839129889e-31, 7.5658951790722304e-30, 1.0377543674300410e-28, 1.3370496163293642e-27, 1.6195422525877890e-26, 1.8458039741402227e-25, 1.9809275961773415e-24, 2.0034006172471768e-23, 1.9107136033126365e-22, 1.7196934641222891e-21, 1.4615728740382834e-20, 1.1737567188678477e-19, 8.9122322093114715e-19, 6.4017277272147784e-18, 4.3526236743179514e-17, 2.8027154496363443e-16, 1.7100226833829111e-15, 9.8907988394494626e-15, 5.4258798698008971e-14, 2.8243097014577004e-13, 1.3955439320917938e-12, 6.5484943121277863e-12, 2.9192823809511808e-11, 1.2368298646403665e-10, 4.9819378483709125e-10, 1.9084879833147422e-09, 6.9554442384546823e-09, 2.4123461087320678e-08, 7.9645691304111948e-08, 2.5038904484412268e-07, 7.4974774628062337e-07, 2.1388110362272039e-06, 5.8142267442915587e-06, 1.5065139508846480e-05, 3.7214305501073257e-05, 8.7657861198914500e-05, 1.9692436368292282e-04, 4.2200152760283493e-04, 8.6279569789330843e-04, 1.6832545363270029e-03, 3.1340302956109622e-03, 5.5696401904272858e-03, 9.4487851093380676e-03, 1.5303805411902717e-02, 2.3666975130344652e-02, 3.4949960453868167e-02, 4.9288724246681882e-02, 6.6386134961517171e-02, 8.5401153510804823e-02, 1.0493731687783339e-01, 1.2316720474285285e-01, 1.3809371553328023e-01, 1.4790300421921079e-01, 1.5132498974070285e-01, 1.4790300421921079e-01, 1.3809371553328023e-01, 1.2316720474285285e-01, 1.0493731687783339e-01, 8.5401153510804823e-02, 6.6386134961517171e-02, 4.9288724246681882e-02, 3.4949960453868167e-02, 2.3666975130344652e-02, 1.5303805411902717e-02, 9.4487851093380676e-03, 5.5696401904272858e-03, 3.1340302956109622e-03, 1.6832545363270029e-03, 8.6279569789330843e-04, 4.2200152760283493e-04, 1.9692436368292282e-04, 8.7657861198914500e-05, 3.7214305501073257e-05, 1.5065139508846480e-05, 5.8142267442915587e-06, 2.1388110362272039e-06, 7.4974774628062337e-07, 2.5038904484412268e-07, 7.9645691304111948e-08, 2.4123461087320678e-08, 6.9554442384546823e-09, 1.9084879833147422e-09, 4.9819378483709125e-10, 1.2368298646403665e-10, 2.9192823809511808e-11, 6.5484943121277863e-12, 1.3955439320917938e-12, 2.8243097014577004e-13, 5.4258798698008971e-14, 9.8907988394494626e-15, 1.7100226833829111e-15, 2.8027154496363443e-16, 4.3526236743179514e-17, 6.4017277272147784e-18, 8.9122322093114715e-19, 1.1737567188678477e-19, 1.4615728740382834e-20, 1.7196934641222891e-21, 1.9107136033126365e-22, 2.0034006172471768e-23, 1.9809275961773415e-24, 1.8458039741402227e-25, 1.6195422525877890e-26, 1.3370496163293642e-27, 1.0377543674300410e-28, 7.5658951790722304e-30, 5.1767166839129889e-31, 3.3209946083724174e-32, 1.9956009474900652e-33, 1.1220768467833071e-34, 5.8971855560501346e-36, 2.8936578029605094e-37, 1.3240736407971940e-38, 5.6428177886700861e-40, 2.2368010157343200e-41, 8.2357837374304705e-43, 2.8125213532676820e-44, 8.8947358191690260e-46, 2.6008368230936308e-47, 7.0192904730947679e-49, 1.7453732998154445e-50, 3.9908716881614503e-52, 8.3743579179261028e-54, 1.6091856250751163e-55, 2.8251413443094276e-57, 4.5206307708839604e-59, 6.5759615285599325e-61, 8.6720569345151135e-63, 1.0337280935884043e-64, 1.1102986726619406e-66, 1.0709039437896534e-68, 9.2417798747589595e-71, 7.1080340648382430e-73, 4.8516529695481360e-75, 2.9253709118548054e-77, 1.5504440487214177e-79, 7.1838069610206879e-82, 2.8926565116618279e-84, 1.0056653752640396e-86, 2.9971587600601123e-89, 7.5966487579367170e-92, 1.6231768954981774e-94, 2.8951564896303124e-97, 4.2633269887655389e-100, 5.1189805080467357e-103, 4.9410774014014167e-106, 3.7723274691873339e-109, 2.2355880918528976e-112, 1.0061133084529732e-115, 3.3506484324551954e-119, 8.0053233705919762e-123, 1.3214094652141891e-126, 1.4382941114934084e-130, 9.7310398950542353e-135, 3.7894855074137878e-139, 7.6575370428605554e-144, 6.9363023753259492e-149, 2.2601442864626069e-154, 1.8432377040276421e-160, 1.8797130400856443e-167, 4.0474005560499094e-176},
		},
		{
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5.0074481042562811e-112, 2.7680773700442792e-115, 1.1608863141459933e-118, 3.5986937020445443e-122, 7.9930519467022852e-126, 1.2247428452374434e-129, 1.2353061004428027e-133, 7.7287684331971630e-138, 2.7763562197121041e-142, 5.1593581306426363e-147, 4.2810879764792902e-152, 1.2712817065467470e-157, 9.3801386072360495e-164, 8.5565157993831952e-171, 1.6118004761490936e-179},
		},
		{
			n: 220,
			x: []float64{-2.0325189139629405e+01, -1.9817257977795947e+01, -1.9399516717870224e+01, -1.9028866794578029e+01, -1.8688834225534919e+01, -1.8370926385157830e+01, -1.8070047892967271e+01, -1.7782841268044042e+01, -1.7506947669788651e+01, -1.7240630469775191e+01, -1.6982564625621777e+01, -1.6731710220470223e+01, -1.6487232253468321e+01, -1.6248447477010238e+01, -1.6014787864496149e+01, -1.5785774736307584e+01, -1.5560999958339213e+01, -1.5340111975060188e+01, -1.5122805233008011e+01, -1.4908812035694833e+01, -1.4697896176804390e+01, -1.4489847896889446e+01, -1.4284479840564213e+01, -1.4081623780688842e+01, -1.3881127938034011e+01, -1.3682854768615876e+01, -1.3486679122200039e+01, -1.3292486698232523e+01, -1.3100172742223814e+01, -1.2909640938118768e+01, -1.2720802461619986e+01, -1.2533575166624548e+01, -1.2347882882470566e+01, -1.2163654803990811e+01, -1.1980824959739557e+01, -1.1799331746419007e+01, -1.1619117519647554e+01, -1.1440128232906956e+01, -1.1262313117871999e+01, 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1.5122805233008011e+01, 1.5340111975060188e+01, 1.5560999958339213e+01, 1.5785774736307584e+01, 1.6014787864496149e+01, 1.6248447477010238e+01, 1.6487232253468321e+01, 1.6731710220470223e+01, 1.6982564625621777e+01, 1.7240630469775191e+01, 1.7506947669788651e+01, 1.7782841268044042e+01, 1.8070047892967271e+01, 1.8370926385157830e+01, 1.8688834225534919e+01, 1.9028866794578029e+01, 1.9399516717870224e+01, 1.9817257977795947e+01, 2.0325189139629405e+01},
			w: []float64{2.2761605731502931e-180, 1.2490844229282551e-171, 1.4077080884426324e-164, 1.9558070725961945e-158, 6.7396164617778564e-153, 8.3007451278928549e-148, 4.5605427168506885e-143, 1.2952107195320918e-138, 2.1106922482765282e-134, 2.1325182525295938e-130, 1.4176541142180510e-126, 6.4990818384221324e-123, 2.1340663816447175e-119, 5.1782994410611593e-116, 9.5303885471678039e-113, 1.3600769560707746e-109, 1.5337501625076215e-106, 1.3892626373123839e-103, 1.0252931948997944e-100, 6.2430026550428978e-98, 3.1713496923820005e-95, 1.3573663268548106e-92, 4.9385791079870452e-90, 1.5396613562557895e-87, 4.1428768007295419e-85, 9.6845718261332366e-83, 1.9785969337019459e-80, 3.5522955000635345e-78, 5.6327088700629997e-76, 7.9248469784581938e-74, 9.9353884108905009e-72, 1.1143371044053519e-69, 1.1222249771693660e-67, 1.0182568638449594e-65, 8.3508496445242703e-64, 6.2085535684767686e-62, 4.1960840622737107e-60, 2.5847807937901128e-58, 1.4547608917709417e-56, 7.4980265458380947e-55, 3.5467498009174184e-53, 1.5428702374218767e-51, 6.1841637682672203e-50, 2.2881100073201874e-48, 7.8282784948541621e-47, 2.4806114249059706e-45, 7.2916745732054914e-44, 1.9911806078855746e-42, 5.0584298583405264e-41, 1.1970700137586669e-39, 2.6422337190194530e-38, 5.4462015155980312e-37, 1.0495069994748297e-35, 1.8928725655710039e-34, 3.1985659419085236e-33, 5.0689745622498271e-32, 7.5410079936029980e-31, 1.0540919389712685e-29, 1.3856239612378123e-28, 1.7143191474654609e-27, 1.9978524188114189e-26, 2.1947842513043781e-25, 2.2745432296820405e-24, 2.2252271383645215e-23, 2.0564749726923156e-22, 1.7964719327802204e-21, 1.4843379300503135e-20, 1.1606915413845120e-19, 8.5944540731309027e-19, 6.0293824390549243e-18, 4.0096487904356170e-17, 2.5289217277543671e-16, 1.5134484435681475e-15, 8.5980922774659504e-15, 4.6390554602844329e-14, 2.3781148094626393e-13, 1.1587426167580950e-12, 5.3685841373417416e-12, 2.3659835874748833e-11, 9.9219381603477156e-11, 3.9606009206879336e-10, 1.5053791970450186e-09, 5.4498580894419877e-09, 1.8797800781026250e-08, 6.1792198822459984e-08, 1.9363392840773747e-07, 5.7857719375034532e-07, 1.6488403637671232e-06, 4.4826356596959815e-06, 1.1628419918195159e-05, 2.8789242845201347e-05, 6.8037279449589797e-05, 1.5351500720814013e-04, 3.3076323494923371e-04, 6.8063888690970183e-04, 1.3378748383672085e-03, 2.5123201954271616e-03, 4.5076732111920138e-03, 7.7285957578851656e-03, 1.2663915587278220e-02, 1.9833481075447929e-02, 2.9691593353631068e-02, 4.2492045448586743e-02, 5.8137078835965875e-02, 7.6049788530935164e-02, 9.5118681388506904e-02, 1.1375654825578213e-01, 1.3009049092173738e-01, 1.4226074789149157e-01, 1.4876572633109977e-01, 1.4876572633109977e-01, 1.4226074789149157e-01, 1.3009049092173738e-01, 1.1375654825578213e-01, 9.5118681388506904e-02, 7.6049788530935164e-02, 5.8137078835965875e-02, 4.2492045448586743e-02, 2.9691593353631068e-02, 1.9833481075447929e-02, 1.2663915587278220e-02, 7.7285957578851656e-03, 4.5076732111920138e-03, 2.5123201954271616e-03, 1.3378748383672085e-03, 6.8063888690970183e-04, 3.3076323494923371e-04, 1.5351500720814013e-04, 6.8037279449589797e-05, 2.8789242845201347e-05, 1.1628419918195159e-05, 4.4826356596959815e-06, 1.6488403637671232e-06, 5.7857719375034532e-07, 1.9363392840773747e-07, 6.1792198822459984e-08, 1.8797800781026250e-08, 5.4498580894419877e-09, 1.5053791970450186e-09, 3.9606009206879336e-10, 9.9219381603477156e-11, 2.3659835874748833e-11, 5.3685841373417416e-12, 1.1587426167580950e-12, 2.3781148094626393e-13, 4.6390554602844329e-14, 8.5980922774659504e-15, 1.5134484435681475e-15, 2.5289217277543671e-16, 4.0096487904356170e-17, 6.0293824390549243e-18, 8.5944540731309027e-19, 1.1606915413845120e-19, 1.4843379300503135e-20, 1.7964719327802204e-21, 2.0564749726923156e-22, 2.2252271383645215e-23, 2.2745432296820405e-24, 2.1947842513043781e-25, 1.9978524188114189e-26, 1.7143191474654609e-27, 1.3856239612378123e-28, 1.0540919389712685e-29, 7.5410079936029980e-31, 5.0689745622498271e-32, 3.1985659419085236e-33, 1.8928725655710039e-34, 1.0495069994748297e-35, 5.4462015155980312e-37, 2.6422337190194530e-38, 1.1970700137586669e-39, 5.0584298583405264e-41, 1.9911806078855746e-42, 7.2916745732054914e-44, 2.4806114249059706e-45, 7.8282784948541621e-47, 2.2881100073201874e-48, 6.1841637682672203e-50, 1.5428702374218767e-51, 3.5467498009174184e-53, 7.4980265458380947e-55, 1.4547608917709417e-56, 2.5847807937901128e-58, 4.1960840622737107e-60, 6.2085535684767686e-62, 8.3508496445242703e-64, 1.0182568638449594e-65, 1.1222249771693660e-67, 1.1143371044053519e-69, 9.9353884108905009e-72, 7.9248469784581938e-74, 5.6327088700629997e-76, 3.5522955000635345e-78, 1.9785969337019459e-80, 9.6845718261332366e-83, 4.1428768007295419e-85, 1.5396613562557895e-87, 4.9385791079870452e-90, 1.3573663268548106e-92, 3.1713496923820005e-95, 6.2430026550428978e-98, 1.0252931948997944e-100, 1.3892626373123839e-103, 1.5337501625076215e-106, 1.3600769560707746e-109, 9.5303885471678039e-113, 5.1782994410611593e-116, 2.1340663816447175e-119, 6.4990818384221324e-123, 1.4176541142180510e-126, 2.1325182525295938e-130, 2.1106922482765282e-134, 1.2952107195320918e-138, 4.5605427168506885e-143, 8.3007451278928549e-148, 6.7396164617778564e-153, 1.9558070725961945e-158, 1.4077080884426324e-164, 1.2490844229282551e-171, 2.2761605731502931e-180},
		},
	} {
		h := Hermite{}
		x := make([]float64, test.n)
		weight := make([]float64, test.n)
		h.FixedLocations(x, weight, math.Inf(-1), math.Inf(1))
		if !floats.EqualApprox(x, test.x, 1e-14) {
			t.Errorf("n = %v, x mismatch", test.n)
			fmt.Println(x)
			fmt.Println()
			fmt.Println(test.x)
			//t.Errorf("x mismatch. \nWant %v\ngot %v", test.x, x)
		}
		if !floats.EqualApprox(weight, test.w, 1e-14) {
			t.Errorf("n = %v, w mismatch", test.n)
			//t.Errorf("w mismatch. Want %v, got %v", test.w, weight)
		}
	}
}

func TestHermiteInitialGuesses(t *testing.T) {
	t.Parallel()
	for _, test := range []struct {
		n    int
		want []float64
	}{
		// Evaluated from Chebfun.
		{
			n:    215,
			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},
		},
		{
			n:    216,
			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},
		},
	} {
		got := make([]float64, test.n/2+test.n%2)
		for i := range got {
			got[i] = Hermite{}.hermiteInitialGuess(i, test.n)
		}
		if !floats.EqualApprox(got, test.want, 1e-14) {
			t.Errorf("n = %v, hermite initial guesses mismatch", test.n)
		}
	}
}

func TestHermiteLocationsAsy0(t *testing.T) {
	t.Parallel()
	for _, test := range []struct {
		n int
		x []float64
		w []float64
	}{
		// Evaluated from Chebfun.
		{
			n: 215,
			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},
			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},
		},
		{
			n: 216,
			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},
			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},
		},
	} {
		n := test.n
		x := make([]float64, n/2+n%2)
		w := make([]float64, n/2+n%2)
		for i := range x {
			x[i], w[i] = Hermite{}.locationsAsy0(i, n)
		}
		if !floats.EqualApprox(x, test.x, 1e-13) {
			t.Errorf("n = %v, x mismatch", n)
			fmt.Println(x[107])
			fmt.Println(test.x[107])
		}
		if !floats.EqualApprox(w, test.w, 1e-13) {
			t.Errorf("n = %v, w mismatch", n)
		}
	}
}

func TestHermiteAsyAiry(t *testing.T) {
	t.Parallel()
	for _, test := range []struct {
		n     int
		theta []float64
		val   []float64
		dval  []float64
	}{
		{
			n:     215,
			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},
			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},
			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},
		},
		{
			n:     215,
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			theta: []float64{1.5671686105755023e+00, 1.5599127961684220e+00, 1.5526558355346407e+00, 1.5453969634495357e+00, 1.5381354130756992e+00, 1.5308704153127000e+00, 1.5236011981417006e+00, 1.5163269859634152e+00, 1.5090469989278730e+00, 1.5017604522544048e+00, 1.4944665555402459e+00, 1.4871645120560699e+00, 1.4798535180267400e+00, 1.4725327618954691e+00, 1.4652014235695219e+00, 1.4578586736455008e+00, 1.4505036726121565e+00, 1.4431355700285682e+00, 1.4357535036754083e+00, 1.4283565986768869e+00, 1.4209439665908115e+00, 1.4135147044640579e+00, 1.4060678938505511e+00, 1.3986025997886760e+00, 1.3911178697348172e+00, 1.3836127324494960e+00, 1.3760861968323106e+00, 1.3685372507016056e+00, 1.3609648595144777e+00, 1.3533679650223920e+00, 1.3457454838572851e+00, 1.3380963060426339e+00, 1.3304192934234869e+00, 1.3227132780089634e+00, 1.3149770602201478e+00, 1.3072094070356892e+00, 1.2994090500267301e+00, 1.2915746832720101e+00, 1.2837049611431546e+00, 1.2757984959492026e+00, 1.2678538554283829e+00, 1.2598695600739727e+00, 1.2518440802797628e+00, 1.2437758332892002e+00, 1.2356631799306261e+00, 1.2275044211192108e+00, 1.2192977941041021e+00, 1.2110414684370108e+00, 1.2027335416358120e+00, 1.1943720345138122e+00, 1.1859548861419755e+00, 1.1774799484076148e+00, 1.1689449801287550e+00, 1.1603476406784692e+00, 1.1516854830678944e+00, 1.1429559464302423e+00, 1.1341563478407819e+00, 1.1252838733993509e+00, 1.1163355684922343e+00, 1.1073083271390356e+00, 1.0981988803171721e+00, 1.0890037831415225e+00, 1.0797194007591668e+00, 1.0703418927985888e+00, 1.0608671961885900e+00, 1.0512910061337959e+00, 1.0416087550001036e+00, 1.0318155888237164e+00, 1.0219063411101317e+00, 1.0118755035330074e+00, 1.0017171930750695e+00, 9.9142511507162645e-01, 9.8099252151840288e-01, 9.7041216388519547e-01, 9.5967623952979786e-01, 9.4877633062585665e-01, 9.3770333429470865e-01, 9.2644738235305046e-01, 9.1499774873988793e-01, 9.0334274224692235e-01, 8.9146958161860457e-01, 8.7936424937397950e-01, 8.6701131978084423e-01, 8.5439375521282512e-01, 8.4149266354281749e-01, 8.2828700713198744e-01, 8.1475325116200825e-01, 8.0086493523862246e-01, 7.8659214693830359e-01, 7.7190086863415974e-01, 7.5675215854165734e-01, 7.4110111194290051e-01, 7.2489552655247935e-01, 7.0807416302356885e-01, 6.9056444104412407e-01, 6.7227933193754241e-01, 6.5311307983969791e-01, 6.3293516775593595e-01, 6.1158156935716357e-01, 5.8884164425859431e-01, 5.6443772421506910e-01, 5.3799175946275157e-01, 5.0896747562778555e-01, 4.7656205323872197e-01, 4.3948124005672007e-01, 3.9539840620540745e-01, 3.3931369540774287e-01, 2.5576413755369809e-01},
			val:   []float64{-2.1420664007171084e-13, 5.3170379037842784e-14, -3.4734236933038639e-15, 2.3242110868118431e-13, 3.7943143720204046e-14, -5.7160511614569708e-14, 2.1177269961331864e-13, -3.4948583926844979e-14, 1.7369271883827313e-13, 3.5623756291990570e-13, 6.5520118362261941e-14, 1.1255590127344777e-13, 9.4867994932892441e-14, -6.1601712969494469e-14, 4.7023788875015558e-14, -1.4272998866826663e-13, -2.6605445153274162e-14, -2.5223571223200907e-13, -1.3724084095111965e-13, -7.0111736669803626e-14, 5.7347666545680944e-14, -5.0924962889888544e-14, -5.2683776576685045e-15, -2.1544335394504838e-13, 4.0230445264824984e-15, 6.9175538975130938e-15, -1.1339463388095042e-13, -3.9896959286779273e-14, -8.8360560296236634e-14, -1.0474371284611670e-13, 1.2687327963040444e-14, -1.7782734520430910e-13, 2.0086781777635686e-13, -7.5400883703521135e-14, 1.2278140016266356e-13, -1.1244970732922019e-13, 1.6072100253117342e-14, 5.2340169298568757e-15, 1.1013085876614924e-13, -9.6621831158318670e-15, -1.8366177977891496e-13, 1.0601073284832238e-14, -1.3784763212103856e-13, -1.5863525424166753e-13, -1.6638681463670250e-13, 8.6360908147481066e-14, -7.8672683965135368e-14, 6.8378486764803313e-14, 9.0534733729868808e-14, 6.6505185887739604e-15, 3.3141885340142080e-15, -2.0537396911778824e-13, 7.3393589371575821e-14, 9.8483281662822096e-14, -2.3812738806298458e-13, 6.5975425886450090e-15, 8.7013139463913052e-14, 7.5278742714453987e-14, -1.0708940266003440e-13, 2.0958580081069137e-13, -1.5480716019053119e-14, 4.8469624575186930e-15, -6.1362291991375536e-14, -3.5942923464396180e-14, -7.6176865685553763e-14, 1.0095757892256693e-13, -4.2683956504767779e-14, -4.8938621882647329e-14, 1.6489272569372713e-15, -1.1390338364880240e-13, 2.1513601964632049e-14, -1.0152923724696736e-14, -3.9597826958407387e-14, -8.5123156147931521e-14, -6.5276802085245163e-14, 6.3966825794140229e-14, -2.8207572680644779e-14, -5.9767990455898208e-15, -1.1189271498293956e-13, -4.5600777141900301e-14, 1.5226732724861721e-14, 3.9473540473700922e-14, -5.6017378761616795e-15, -2.4079255903843183e-14, -3.1139558336514997e-14, -5.6034014603771978e-14, 6.9309294575728887e-14, -3.7871955014469560e-14, 4.2988763678275364e-14, 1.0661412180664073e-14, 6.2069599395465107e-14, -4.8913422170368503e-14, 3.3884911719768557e-14, 2.8191908465098299e-15, 2.1228960171536080e-14, -5.6191478942893769e-14, -1.4786950368470112e-14, -2.1665036441200809e-14, 1.4936420829725019e-14, -1.1615745673091571e-13, 1.4661728300981146e-13, -3.6088669931521093e-13, 1.1825080499589470e-12, -4.7300739521811106e-12, 2.5459387908526307e-11, -2.2842779135337983e-10, 5.3230524570865730e-09, 1.8504694403187737e-14},
			dval:  []float64{-2.9427800603424888e+01, 2.9427025985916128e+01, -2.9425476404186732e+01, 2.9423151164251305e+01, -2.9420049223750453e+01, 2.9416169190288219e+01, -2.9411509319206210e+01, 2.9406067510787015e+01, -2.9399841306877356e+01, 2.9392827886918813e+01, -2.9385024063373031e+01, 2.9376426276524445e+01, -2.9367030588643043e+01, 2.9356832677485624e+01, -2.9345827829112846e+01, 2.9334010929995465e+01, -2.9321376458381234e+01, 2.9307918474890485e+01, -2.9293630612304742e+01, 2.9278506064510257e+01, -2.9262537574553480e+01, 2.9245717421762187e+01, -2.9228037407881235e+01, 2.9209488842167364e+01, -2.9190062525382206e+01, 2.9169748732617215e+01, -2.9148537194877896e+01, 2.9126417079348521e+01, -2.9103376968250736e+01, 2.9079404836201938e+01, -2.9054488025970500e+01, 2.9028613222515034e+01, -2.9001766425185131e+01, 2.8973932917948375e+01, -2.8945097237496743e+01, 2.8915243139070423e+01, -2.8884353559822181e+01, 2.8852410579527444e+01, -2.8819395378426645e+01, 2.8785288191964142e+01, -2.8750068262165122e+01, 2.8713713785364636e+01, -2.8676201855972852e+01, 2.8637508405928578e+01, -2.8597608139454227e+01, 2.8556474462684314e+01, -2.8514079407692350e+01, 2.8470393550387161e+01, -2.8425385921689987e+01, 2.8379023911335462e+01, -2.8331273163562233e+01, 2.8282097463870926e+01, -2.8231458615927728e+01, 2.8179316307577018e+01, -2.8125627964795974e+01, 2.8070348592274335e+01, -2.8013430599129794e+01, 2.7954823608071287e+01, -2.7894474246092045e+01, 2.7832325914509109e+01, -2.7768318535855656e+01, 2.7702388274772812e+01, -2.7634467229625294e+01, 2.7564483091071331e+01, -2.7492358763234883e+01, 2.7418011942441158e+01, -2.7341354647661582e+01, 2.7262292695845463e+01, -2.7180725114157763e+01, 2.7096543479754128e+01, -2.7009631176051940e+01, 2.6919862552432292e+01, -2.6827101971847430e+01, 2.6731202727801641e+01, -2.6632005808479885e+01, 2.6529338481236724e+01, -2.6423012664989066e+01, 2.6312823050968632e+01, -2.6198544923370196e+01, 2.6079931620126928e+01, -2.5956711559610671e+01, 2.5828584740479652e+01, -2.5695218597789530e+01, 2.5556243066913513e+01, -2.5411244665072843e+01, 2.5259759344501834e+01, -2.5101263795907666e+01, 2.4935164777812918e+01, -2.4760785904536036e+01, 2.4577351124782325e+01, -2.4383963836127013e+01, 2.4179580164228856e+01, -2.3962974319142369e+01, 2.3732693009181720e+01, -2.3486994450695558e+01, 2.3223765221219963e+01, -2.2940404454626893e+01, 2.2633658531160954e+01, -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},
		},
	} {
		got := make([]float64, len(test.theta))
		gotD := make([]float64, len(test.theta))
		for i := range got {
			got[i], gotD[i] = Hermite{}.hermpolyAsyAiry(i, test.n, test.theta[i])
		}
		if !floats.EqualApprox(test.val, got, 1e-12) {
			t.Errorf("n = %v, hermpolyAsyAiry mismatch", test.n)
		}
		if !floats.EqualApprox(test.dval, gotD, 1e-12) {
			t.Errorf("n = %v, hermpolyAsyAiry deriv mismatch", test.n)
		}
	}
}