Repository: gonum/gonum
Pull request #1753 (2021-11-20 23:24:26)

A+C: add Evgeny Savinov
Adding myself to contributors list after [comment](https://github.com/gonum/gonum/pull/1752#pullrequestreview-811860127)

kortschak: For #1752. Approved when that is approved.

Patch:
diff --git a/AUTHORS b/AUTHORS
index a93544d9..9cde70c8 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -35,6 +35,7 @@ Egon Elbre <egonelbre@gmail.com>
 Ekaterina Efimova <katerina.efimova@gmail.com>
 Ethan Burns <burns.ethan@gmail.com>
 Evert Lammerts <evert.lammerts@gmail.com>
+Evgeny Savinov <notime.sea@gmail.com>
 Fabian Wickborn <fabian@wickborn.net>
 Facundo Gaich <facugaich@gmail.com>
 Fazlul Shahriar <fshahriar@gmail.com>
diff --git a/CONTRIBUTORS b/CONTRIBUTORS
index 9fc7d7ed..7f3af241 100644
--- a/CONTRIBUTORS
+++ b/CONTRIBUTORS
@@ -43,6 +43,7 @@ Egon Elbre <egonelbre@gmail.com>
 Ekaterina Efimova <katerina.efimova@gmail.com>
 Ethan Burns <burns.ethan@gmail.com>
 Evert Lammerts <evert.lammerts@gmail.com>
+Evgeny Savinov <notime.sea@gmail.com>
 Fabian Wickborn <fabian@wickborn.net>
 Facundo Gaich <facugaich@gmail.com>
 Fazlul Shahriar <fshahriar@gmail.com>
diff --git a/integrate/quad/hermite.go b/integrate/quad/hermite.go
index 9fd9ead2..88ff4697 100644
--- a/integrate/quad/hermite.go
+++ b/integrate/quad/hermite.go
@@ -273,7 +273,7 @@ func (h Hermite) hermiteInitialGuess(i, n int) float64 {
 	}
 
 	// Use Gatteschi guesses in the second half where x is nearer to sqrt(n+0.5)
-	i = i + 1 - m
+	i = m - (i + 1)
 	var ar float64
 	if i < len(airyRtsExact) {
 		ar = airyRtsExact[i]


Test patch:
diff --git a/integrate/quad/hermite_test.go b/integrate/quad/hermite_test.go
index c76ac4e0..be200c06 100644
--- a/integrate/quad/hermite_test.go
+++ b/integrate/quad/hermite_test.go
@@ -63,6 +63,12 @@ func TestHermite(t *testing.T) {
 			ev:  math.SqrtPi * math.Exp(4),
 			tol: 1e-12,
 		},
+		{
+			n:   1000,
+			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) {
@@ -76,65 +82,80 @@ func TestHermiteLocations(t *testing.T) {
 	// 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
+		n   int
+		x   []float64
+		w   []float64
+		tol 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:   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},
+			tol: 1e-14,
 		},
 		{
-			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:   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},
+			tol: 1e-14,
 		},
 		{
-			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, 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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, 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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, 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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},
+			tol: 1e-13,
 		},
 	} {
 		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) {
+		if !floats.EqualApprox(x, test.x, test.tol) {
 			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) {
+		if !floats.EqualApprox(weight, test.w, test.tol) {
 			t.Errorf("n = %v, w mismatch", test.n)
 			//t.Errorf("w mismatch. Want %v, got %v", test.w, weight)
 		}