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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / testlapack / dhseqr.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 testlapack

import (
        "fmt"
        "math"
        "testing"

        "gonum.org/v1/gonum/blas"
        "gonum.org/v1/gonum/blas/blas64"
        "gonum.org/v1/gonum/floats"
        "gonum.org/v1/gonum/lapack"
)

type Dhseqrer interface {
        Dhseqr(job lapack.EVJob, compz lapack.EVComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64,
                z []float64, ldz int, work []float64, lwork int) int
}

type dhseqrTest struct {
        n   int
        ilo int
        ihi int
        h   []float64
        tol float64

        evWant []complex128
}

func DhseqrTest(t *testing.T, impl Dhseqrer) {
        for i, tc := range dhseqrTests {
                for _, job := range []lapack.EVJob{lapack.EigenvaluesOnly, lapack.EigenvaluesAndSchur} {
                        for _, wantz := range []bool{false, true} {
                                for _, extra := range []int{0, 11} {
                                        testDhseqr(t, impl, i, tc, job, wantz, extra, true)
                                        testDhseqr(t, impl, i, tc, job, wantz, extra, false)
                                }
                        }
                }
        }
}

func testDhseqr(t *testing.T, impl Dhseqrer, i int, test dhseqrTest, job lapack.EVJob, wantz bool, extra int, optwork bool) {
        const tol = 1e-14
        evTol := test.tol
        if evTol == 0 {
                evTol = tol
        }

        n := test.n
        ihi := test.ihi
        ilo := test.ilo
        h := zeros(n, n, n+extra)
        copyGeneral(h, blas64.General{Rows: n, Cols: n, Stride: max(1, n), Data: test.h})
        hCopy := cloneGeneral(h)

        var compz lapack.EVComp = lapack.None
        z := blas64.General{Stride: max(1, n)}
        if wantz {
                // First, let Dhseqr initialize Z to the identity matrix.
                compz = lapack.HessEV
                z = nanGeneral(n, n, n+extra)
        }

        wr := nanSlice(n)
        wi := nanSlice(n)

        work := nanSlice(max(1, n))
        if optwork {
                impl.Dhseqr(job, lapack.HessEV, n, ilo, ihi, nil, h.Stride, nil, nil, nil, z.Stride, work, -1)
                work = nanSlice(int(work[0]))
        }

        unconverged := impl.Dhseqr(job, compz, n, ilo, ihi, h.Data, h.Stride, wr, wi, z.Data, z.Stride, work, len(work))
        prefix := fmt.Sprintf("Case %v: job=%v, compz=%v, n=%v, ilo=%v, ihi=%v, extra=%v, optwk=%v",
                i, job, compz, n, ilo, ihi, extra, optwork)
        if unconverged > 0 {
                t.Logf("%v: Dhseqr did not compute all eigenvalues. unconverged=%v", prefix, unconverged)
                if unconverged <= ilo {
                        t.Fatalf("%v: 0 < unconverged <= ilo", prefix)
                }
        }

        // Check that wr and wi have been assigned completely.
        if floats.HasNaN(wr) {
                t.Errorf("%v: wr has NaN elements", prefix)
        }
        if floats.HasNaN(wi) {
                t.Errorf("%v: wi has NaN elements", prefix)
        }

        // Check that complex eigenvalues are stored in consecutive elements as
        // complex conjugate pairs.
        for i := 0; i < n; {
                if unconverged > 0 && i == ilo {
                        // Skip the unconverged eigenvalues.
                        i = unconverged
                        continue
                }
                if wi[i] == 0 {
                        // Real eigenvalue.
                        i++
                        continue
                }
                // Complex conjugate pair.
                if wr[i] != wr[i+1] {
                        t.Errorf("%v: conjugate pair has real parts unequal", prefix)
                }
                if wi[i] < 0 {
                        t.Errorf("%v: first in conjugate pair has negative imaginary part", prefix)
                }
                if wi[i+1] != -wi[i] {
                        t.Errorf("%v: complex pair is not conjugate", prefix)
                }
                i += 2
        }

        // Check that H contains the Schur form T.
        if job == lapack.EigenvaluesAndSchur {
                for i := 0; i < n; {
                        if unconverged > 0 && i == ilo {
                                // Skip the unconverged eigenvalues.
                                i = unconverged
                                continue
                        }
                        if wi[i] == 0 {
                                // Real eigenvalue.
                                if wr[i] != h.Data[i*h.Stride+i] {
                                        t.Errorf("%v: T not in Schur form (real eigenvalue not on diagonal)", prefix)
                                }
                                i++
                                continue
                        }
                        // Complex conjugate pair.
                        im := math.Sqrt(math.Abs(h.Data[(i+1)*h.Stride+i])) * math.Sqrt(math.Abs(h.Data[i*h.Stride+i+1]))
                        if wr[i] != h.Data[i*h.Stride+i] || wr[i] != h.Data[(i+1)*h.Stride+i+1] ||
                                math.Abs(wi[i]-im) > tol {
                                t.Errorf("%v: conjugate pair and 2×2 diagonal block don't correspond", prefix)
                        }
                        i += 2
                }
        }

        // Check that all the found eigenvalues are really eigenvalues.
        foundEV := make([]bool, len(test.evWant))
        for i := 0; i < n; {
                if unconverged > 0 && i == ilo {
                        // Skip the unconverged eigenvalues.
                        i = unconverged
                        continue
                }
                ev := complex(wr[i], wi[i])
                // Use problem-specific tolerance for testing eigenvalues.
                found, index := containsComplex(test.evWant, ev, evTol)
                if !found {
                        t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
                } else {
                        foundEV[index] = true
                }
                i++
        }
        if unconverged == 0 {
                // Check that all eigenvalues have been found.
                // This simple check assumes that all eigenvalues are
                // sufficiently separated from each other at least by evTol.
                for i := range foundEV {
                        if !foundEV[i] {
                                t.Errorf("%v: %vth eigenvalue not found", prefix, i)
                        }
                }
        }

        if !wantz {
                return
        }

        // Z must be orthogonal.
        if !isOrthonormal(z) {
                t.Errorf("%v: Z is not orthogonal", prefix)
        }

        if job == lapack.EigenvaluesAndSchur {
                tz := zeros(n, n, n)
                blas64.Gemm(blas.NoTrans, blas.Trans, 1, h, z, 0, tz)
                ztz := zeros(n, n, n)
                blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, z, tz, 0, ztz)
                if !equalApproxGeneral(ztz, hCopy, evTol) {
                        t.Errorf("%v: H != Z T Z^T", prefix)
                }
        }

        // Restore H.
        copyGeneral(h, hCopy)
        // Call Dhseqr again with the identity matrix given explicitly in Q.
        q := eye(n, n+extra)
        impl.Dhseqr(job, lapack.OriginalEV, n, ilo, ihi, h.Data, h.Stride, wr, wi, q.Data, q.Stride, work, len(work))
        if !equalApproxGeneral(z, q, 0) {
                t.Errorf("%v: Z and Q are not equal", prefix)
        }
}

var dhseqrTests = []dhseqrTest{
        {
                n:   0,
                ilo: 0,
                ihi: -1,
        },
        {
                n:      1,
                ilo:    0,
                ihi:    0,
                h:      []float64{0},
                evWant: []complex128{0},
        },
        {
                n:      1,
                ilo:    0,
                ihi:    0,
                h:      []float64{7.09965484086874e-1},
                evWant: []complex128{7.09965484086874e-1},
        },
        {
                n:      2,
                ilo:    0,
                ihi:    1,
                h:      []float64{0, 0, 0, 0},
                evWant: []complex128{0},
        },
        {
                n:   2,
                ilo: 0,
                ihi: 1,
                h: []float64{
                        1, 0,
                        0, 1,
                },
                evWant: []complex128{1},
        },
        {
                n:   2,
                ilo: 0,
                ihi: 1,
                h: []float64{
                        0, -1,
                        1, 0,
                },
                evWant: []complex128{1i, -1i},
        },
        {
                n:   2,
                ilo: 0,
                ihi: 1,
                h: []float64{
                        6.25219991450918e-1, 8.17510791994361e-1,
                        3.31218891622294e-1, 1.24103744878131e-1,
                },
                evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
        },
        {
                n:   4,
                ilo: 1,
                ihi: 2,
                h: []float64{
                        1, 0, 0, 0,
                        0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
                        0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
                        0, 0, 0, 2,
                },
                evWant: []complex128{1, 2, 9.52203547663447e-1, -2.02879811334398e-1},
        },
        {
                n:   2,
                ilo: 0,
                ihi: 1,
                h: []float64{
                        -1.1219562276608, 6.85473513349362e-1,
                        -8.19951061145131e-1, 1.93728523178888e-1,
                },
                evWant: []complex128{
                        -4.64113852240958e-1 + 3.59580510817350e-1i,
                        -4.64113852240958e-1 - 3.59580510817350e-1i,
                },
        },
        {
                n:   5,
                ilo: 0,
                ihi: 4,
                h: []float64{
                        9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
                        -1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
                        0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
                        0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
                        0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
                },
                evWant: []complex128{
                        2.94393309555622,
                        4.97029793606701e-1 + 3.63041654992384e-1i,
                        4.97029793606701e-1 - 3.63041654992384e-1i,
                        -1.74079119166145e-1 + 2.01570009462092e-1i,
                        -1.74079119166145e-1 - 2.01570009462092e-1i,
                },
        },
        {
                // BFW62A matrix from MatrixMarket, balanced and factorized into
                // upper Hessenberg form in Octave.
                // Eigenvalues computed by eig function in Octave.
                // Dhseqr considers this matrix small (n <= 75).
                n:   62,
                ilo: 0,
                ihi: 61,
                tol: 1e-12,
                h: []float64{
                        0.7610708, -0.71474042262732, -1.03373461417302e-17, 8.218284875369092e-18, -4.39003777724509e-18, -7.633870714681998e-18, -9.951525116511751e-18, -6.538760279193677e-18, -1.656240811786753e-18, -4.915424973452908e-18, -7.590492820502813e-18, -4.532592864746854e-18, 1.137360639223451e-18, -2.088794138001457e-18, 4.330727699351238e-18, 4.88172964159538e-18, -6.438459345602974e-18, 7.414402965763168e-18, 8.592387304092668e-19, 2.905505475188102e-18, -5.210204793418634e-18, 2.377023457149656e-18, -1.958364175388968e-18, -8.746122759061733e-20, 1.839015672758814e-18, 3.097454207400904e-18, 1.545856657360309e-18, 1.713923049773744e-21, 1.333951071201153e-18, -1.256151066318485e-18, 5.489655201308922e-19, -2.191335276195054e-18, 3.211054779957158e-18, -4.585099368362507e-19, 4.064807180521144e-18, -3.621561583390336e-18, 4.638803832189033e-19, 1.306132013406548e-18, 7.71710094138792e-19, 2.320760977517361e-18, -6.538298612520761e-19, -3.498839827985687e-18, 2.699116500378558e-18, -1.653627855476782e-18, 7.006984532830204e-19, -2.829108657299736e-18, -5.260772120044258e-18, 1.014346572590618e-18, -1.751563831849658e-18, -1.850186018112724e-19, 2.870415308417256e-18, -8.423700664162806e-19, 3.498345394735042e-19, 1.448350507022323e-18, -3.119800500343431e-18, 4.170966784863917e-18, -4.413795207992463e-19, -2.550853151356032e-18, 2.058575286932081e-18, 1.11609155804576e-18, -2.819648393130598e-18, -2.691434041700446e-19,
                        -0.71474042262732, 1.938395745278447, -1.179041092366627, 2.994496337305918e-17, -1.886890458028042e-17, -1.696051150581149e-17, -1.066654178739982e-17, -6.29828959344471e-18, -3.017613522337327e-18, -6.087774183044001e-18, -1.623722797471356e-17, -1.609066043798334e-17, 1.1222991062801e-17, -1.199415856132727e-17, 3.254808477409891e-17, 3.032574771313234e-17, -2.950307698970009e-17, 3.390164991463985e-17, 3.580652213399182e-17, -1.363239170451582e-17, 5.318959619432346e-19, -2.094826370136215e-17, 2.503105756608372e-17, 1.02172885473953e-17, 2.072365201436764e-17, 5.419721687057681e-17, 2.946627912791419e-17, -1.348815353957071e-17, -6.109538294302727e-18, 8.919596400140564e-19, -4.965011212156456e-18, -8.892555328798407e-18, -8.533370652960768e-18, 2.670935841220357e-17, 6.294143735482237e-17, -6.631964574578866e-17, 1.610888675267686e-17, -1.914212496162892e-17, 7.491989417296875e-17, 2.433601037912241e-17, -3.471972221532949e-17, 1.239231453972595e-18, 8.477927675716922e-17, 1.832368873558869e-17, -3.15614722379294e-17, -3.481308523858143e-17, 8.753655535825511e-17, -2.311094913977048e-17, -1.97736043621337e-17, -4.591312368362259e-18, -4.090767028097941e-17, 9.630744841167777e-17, 6.376373378245906e-17, 3.517117740157962e-18, -4.504796150838874e-17, 7.517908631343054e-17, 5.08947280115584e-17, -1.382149857389238e-17, -2.198919507523352e-18, 7.280187019637593e-18, -4.195544216643798e-17, -1.69351463438629e-16,
                        0, -1.179041092366627, 1.770797890903813, 0.9251612011433773, 0.003661446613681521, -0.005110479724841567, 0.0005014497289028411, 0.00268637752732762, -0.003137790817099964, 0.0001251340392028716, 0.005236816389348038, -0.007596537304410319, -0.003216883293048434, 0.002836879838039065, 0.006069520262676079, 0.002668518333518884, 0.009131523505676264, 0.004626632495050776, 0.00181579510454105, 0.001123900611304629, 0.001677485377614088, 0.00363754391761903, -0.0007470406844762735, 0.002833257933303097, -0.0002375815340930377, -0.002849024657372476, -0.0002629124003065383, -0.0009435052243060314, -0.001501677820905836, 0.0007867717317979819, -0.003255814847476796, 0.0001229596171032013, 0.001899497807037465, 0.001586135347885108, -0.002155598204409179, -0.004095921626627291, -0.004749259183184092, -0.0003901939289968589, -0.00126397970751315, 0.001155644134671306, 0.000291837164140963, -0.0008540793573406925, 0.0005498493646965147, -0.000512747881346778, 0.001308619245804509, -0.001057469234737898, 8.364932352209563e-05, -0.0004759538737373512, 0.0002832407173157385, -2.502295625364179e-05, -0.001116422235449543, 0.0008744887175767913, -0.001577030646119032, 0.0006630051771088335, 0.0008174386956312274, 0.0005885600522543514, -0.000529324123745168, 0.0006462360717703873, -0.0005292503950906053, -0.0008409757119361148, 0.001179292096398777, -7.042243897656571e-05,
                        0, 0, 0.9256234889252499, 2.188661152704918, -1.116554836905615, -0.02243454666837822, 0.001818477623431723, 0.01031345522542573, -0.02255181751639313, 0.01064389372187288, 0.02644236613167033, -0.03711341885334873, -0.01368507023909662, 0.005876976997280983, 0.04065670610764593, 0.01666467627475975, 0.04720670725274503, 0.02074371568474985, 0.02492606640786733, -0.0007477579555839802, 0.008780018993769038, 0.02228545976823896, -0.001309713708470288, 0.02515283874752867, -0.002695437114195642, -0.03058898397162627, -0.004721936411831751, -0.01112709820777293, 0.005156744291122814, 0.001266520229863774, -0.0173310067274492, 0.006032177243961209, 0.01546906824241716, 0.004122912475005991, -0.01457685983271352, -0.02472315268907353, -0.0146012575743626, 0.01613627552485761, -0.03570849487210562, 0.009634392591632741, 0.01396210133689555, -0.01085301942984549, 0.02308071799914048, -0.01534806641683973, 0.007461896675297811, 0.001678793578211992, -0.004550709803423801, -0.003543952787451961, 0.01328644094056202, 0.01722933205866279, -0.01604068924890588, 0.01061524273934986, -0.01948663408394128, 0.02488657490054273, 0.002560204204893632, -0.007049942019567433, -0.005861737475764968, 0.007063905438215945, -0.01302170441839208, -0.01452116548010346, 0.008856002952171451, 0.003352799875293177,
                        0, 0, 0, -1.131565669446545, 3.458875937128813, -2.92300025604371, 0.0004977656856497978, 0.006279968970473544, 0.0775979532222543, -0.07809248806636047, -0.04323656216106807, 0.05001022064587737, 0.003864067108285046, 0.04141643188583877, -0.1284617838883834, -0.04493800214431209, -0.07456343090218126, -0.01563872481200422, -0.1339020629421785, 0.04186908269102881, -0.01575262227867954, -0.05122401589211525, -0.01356095585891559, -0.1061570482803366, 0.01819813598371521, 0.1481253462698246, 0.02550194602547843, 0.04637287461870648, -0.07444378895306285, 0.01361958240422481, 0.04035022896181466, -0.04232248915252568, -0.06075940528348658, 0.027263798939883, 0.03953143432541723, 0.06518841156851282, -0.03410646432627348, -0.1414076406563496, 0.2323217246349602, -0.03415439789233707, -0.1031903658536844, 0.06725801721048928, -0.1560521418148311, 0.1014900809050588, -0.02098771321982528, -0.03982159107235207, 0.03695361299827822, 0.01067293209294729, -0.09426629859219736, -0.1345822610538289, 0.09362330513280395, -0.05670709861587474, 0.1059566486421828, -0.1760916487632087, 0.003702764511325265, 0.07422105386227762, 0.02742567045198715, -0.03734725575689604, 0.08146131944298318, 0.09081980084945049, -0.03823012624212198, -0.02882941691361127,
                        0, 0, 0, 0, -2.935177932025793, 5.590160898106907, -2.264162462726681, -0.02411424982833118, -0.1133643811701465, 0.1104837624251364, 0.05106708784671347, -0.03981053811687705, -0.02554107703230142, -0.06918772930550876, 0.1627330379332113, 0.0515325563326872, 0.0562468014393183, 0.0339155492439978, 0.1634368483167388, -0.06785129040640099, 0.04039982620620088, 0.04044710731973533, 0.0285518510842595, 0.1485759249940305, -0.0304537251951914, -0.2009213484930713, -0.05273834253818357, -0.03107458918212595, 0.09792748883617711, -0.0337039884304953, -0.06657284881035327, 0.04914327832710783, 0.07368372187446774, -0.0404082088678178, -0.04421178865717079, -0.0709487906769288, 0.048430647567918, 0.1864479159285081, -0.3079556699470428, 0.01491993158702447, 0.1333753802314968, -0.09591074161204663, 0.1894696359177905, -0.1319027537070656, 0.03081270942006841, 0.04847952392626505, -0.04816809266890478, -0.0008101823853040729, 0.1149477702272877, 0.1970244006374306, -0.1184305631819092, 0.07656633356645355, -0.140928669738484, 0.2423845347140408, -0.01430733985161339, -0.0967298709856266, -0.03791764167457073, 0.04501910433428818, -0.09499757971636948, -0.1139200858550714, 0.04630019674988028, 0.03975991363586522,
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                },
                evWant: []complex128{
                        -0.01716884621227793,
                        -0.1844331609734137,
                        0.05200651487352193,
                        0.1336851109127556,
                        0.2020936631953806,
                        0.3566470363060668,
                        0.3627207699831158,
                        0.4388555152488943,
                        0.4776853636435153,
                        0.5598821450074998,
                        0.6249350549980947,
                        0.6791310689291772,
                        0.985877008147705 + 0.01929363300192029i,
                        0.985877008147705 - 0.01929363300192029i,
                        0.9908483217835712,
                        1.011990761364073,
                        1.130046345264462,
                        1.323698071765709,
                        1.348598229483672,
                        1.363190626641638 + 0.05400660173350781i,
                        1.363190626641638 - 0.05400660173350781i,
                        1.632832316477256,
                        1.646239548684271,
                        1.742738908029794,
                        1.763069014878969,
                        1.789601126186348,
                        1.945228042429256,
                        1.946373262056993,
                        1.997152389795002,
                        2.261322781594966,
                        2.286944100979884,
                        2.447712649969029,
                        2.557857506923634,
                        2.608379034892128,
                        2.653335615965549,
                        2.675270309760236,
                        2.964219802766918 + 0.01767482509567778i,
                        2.964219802766918 - 0.01767482509567778i,
                        3.014604817775139,
                        3.158289371199042,
                        3.311794215710077,
                        3.389894197376214,
                        3.553333074879877,
                        3.641274442796651,
                        3.857556223000175,
                        4.045817381029103,
                        4.330901939363569,
                        4.337313647767939,
                        4.527400487637496,
                        4.917229128467305,
                        4.985609414964091,
                        5.687686849958608,
                        5.79422309012183,
                        5.997813119506478,
                        6.732426637899077,
                        6.957609338485607,
                        7.529842664573327,
                        7.609108287806763,
                        7.761261355516287,
                        8.311941758006698,
                        9.07053741884884,
                        9.217944588000314,
                },
        },
        {
                // TOLS90 matrix from MatrixMarket, balanced and factorized into
                // upper Hessenberg form in Octave.
                // Eigenvalues computed by eig function in Octave.
                // Dhseqr considers this matrix big (n > 75).
                n:   90,
                ilo: 0,
                ihi: 89,
                tol: 1e-12,
                h: []float64{
                        0, 15.87097792952162, -0.08018778146407576, 1.923854288576926, 0.2308884192434597, 0.3394611053158814, -0.137843056509317, 0.08273319299962868, 0.09094485832017182, -0.1932984706702652, 0.1180502933247899, -0.2497600660136686, 0.05058238526630414, 0.1559958264692184, -0.1159258671363344, 0.009240657808439554, -0.07576925270220009, -0.08136563335139357, 0.03812188405626555, 0.08890970810264923, 0.03109600803532232, -0.01649595143487545, -0.03210884292964193, -0.06264912164116895, 0.02576130685189339, 0.07030469513274047, -0.03577429596420342, -0.06755584096587573, -0.01609449751643862, -0.034609250889499, -0.006417485131372289, -0.03097242984568944, 0.009636702832094541, 0.03557221482377193, 0.03197869740177413, 0.006433398911967483, -0.01135683279223704, 0.005555822920782794, 0.005082647305173025, 0.009385366191684759, 0.008128896608623586, -0.02296712755081439, -0.003777413820214802, 0.005123235117691023, -0.001849213959133196, -0.02340110883416673, 0.03713005378535863, 0.001732375396842803, -0.002750608017025007, -0.008067437745595896, 0.007330916864526544, -0.002616316716217023, -0.006297132815168344, -0.005559964495164493, -0.009996463242082429, 0.005115046921377182, 0.001491016327339477, -0.000957347151456719, 0.006745577006930539, -0.004544035710017501, -0.004411949528299773, -0.006799740101884459, 0.0005344071027975155, 0.0004690847920096184, -0.004718575501368472, -0.002540214169642457, 0.00357159293854215, -0.003314789809413553, -0.003402372051470523, 0.0006527769815598059, -0.002716170091878954, -0.001540321517093821, 0.001756589868588563, -0.001379260966541515, 2.681259838616508e-05, -0.004307760317855304, -0.001109087032949234, -0.0001659937040461595, -0.0002235436314482387, -0.00119569899683125, 0.0005623327348935116, -0.0006320070189143994, 0.001043573892153891, -0.0008750118344396425, 0.0005348270042878935, 0.0008273143853381587, -0.0006622544067919339, -0.0008492128694001077, -0.0007986665099336194, -0.0009015882205421384,
                        -12.61872336344661, -0.7232497785660141, 7.609159226285555, 0.3870426982100038, 5.924856640096555, 0.6102682886559223, -0.1693535996869482, -1.919018099340693, -0.2138609560373459, 0.8042623392399718, 0.8674124147325857, 1.331963567449537, -1.782290696158441, -0.8346237530841022, -1.552156412468403, -0.6151273144224881, -0.7391936693539152, 0.9311934770410842, 0.6166024938842418, -1.54644771695033, -1.776481997993627, -0.934164018650274, 1.955449870926906, -2.082936149197492, -0.222464503236819, 0.1331142802435182, -0.7633944660137448, -0.8176194198678164, 0.2746498608375185, -0.1119720547510174, -0.3046093297897633, 0.093708523663493, -0.1254384253653835, -0.3826156782538976, 0.9720657328245648, 0.4435611080311743, -0.002705519800257373, 0.4068502033494004, 0.8228026417475635, 1.898141183528268, -2.19419418629088, -2.26250233043472, 1.169369389476936, -2.320900757809857, 1.963641620262248, -0.9292511308866737, 1.20566753941007, -3.909359844030778, -1.745106869690986, -0.1674293744185332, 1.824325508201922, -0.611032518780414, -0.8172751651339325, -0.379367811436249, -1.118039132172379, -2.1156899896767, 0.6317312221182597, 1.675601832555065, -0.1958681401344015, 3.202902011360347, 0.2083144054490269, 1.651454396883902, -1.879950006164014, 1.114962429097019, -3.728120039552464, 2.115800549383747, 1.993994934513307, 1.036800346894651, 2.843012388647532, 2.665528597975866, -0.08443708961414848, -1.658265513220315, 2.825691629937317, 1.163068598831327, 1.032612155987785, -0.3464359914213002, -0.7374155713124153, -0.009825846309687306, -1.878310233217088, 1.038183449333641, 0.8683442149070821, 0.2096953654957043, 1.097533010763627, -1.40566207568186, 1.539718090250373, -0.3057191046244732, 0.9596910019319377, 0.4410690813618931, -0.01734977865916698, -0.7028527205475527,
                        0, -21.14096588949502, -11.77071611766029, 91.38817973790069, 24.01994594814793, 7.139034668143506, -7.77684013545977, 11.8189112903465, 4.350214240774185, -13.41161300072837, 0.8429515510200203, -0.1960485971162483, -1.892239827255886, -2.481138864200454, -4.993335484535367, -1.462743953230215, -1.649744938703439, -3.306123402194819, 0.6299802354863298, 0.006312776908129815, 0.7029217322720615, 0.1969979096896496, 0.6484394805159026, 0.4612739081461551, 1.218623710778157, 1.937283920899595, -4.274393204137636, -1.417028232311232, 1.761975679896983, -1.207846701077455, -2.947009378633724, -1.111456928119195, 2.001483835367479, -0.3273985739357373, 1.27142153234808, 2.470518283440578, -0.497592748085565, -1.01776837453108, 0.1736631347448449, 0.2170284795451557, -1.102797734602059, -0.8983239378242805, 0.8376082516437703, -1.015605628895311, 1.888662040615523, -1.813946159105028, 3.745871277192266, -1.691058864813766, 0.5544744103796291, -0.95962769863539, 1.495178118153111, 0.1369976805376806, -3.134133785033962, -1.134766199832475, -2.142472928604951, 0.4360359463007911, 1.080773790484485, 0.9136687613609559, 1.421868877932455, -0.4939788885367615, 0.01579620756278606, -0.4041188740514539, -0.3370957888349073, 0.4032844546374829, -1.281049156842126, 1.334866305935072, -0.4288161314791398, -0.4076960827986253, 0.8975402184760907, 0.008483305617251051, -0.02300021991545602, -0.4779200297205075, 0.8640559542693361, 0.6740166979504152, 1.271173988705413, -0.125268363712917, -0.02783785192682384, -0.7952831181002197, -0.1834134462936435, -0.3033906534395994, -0.1842466257842833, 0.3294577790658342, 0.4265858101126394, -1.050551059782219, 0.5557053448408287, -0.07549099980078718, 0.4485085972651929, 0.604772326452039, 0.02668915155289681, -0.35958437456048,
                        0, 0, -71.67241414253803, -12.6925239065222, -58.51026881403752, -9.923972440030834, -18.08337737101079, 23.73437311293314, 10.42624729020936, -7.39628437264571, 6.93334510855383, -16.20186028661058, 19.09098951338167, 7.231158491837533, 25.86051183536314, 4.692849852643402, 13.50562601772541, -23.8959783279092, 10.46795736800158, 26.42552249365325, 25.55147405605497, 30.98455252329583, -38.26426057779729, 41.72459242758727, 14.01187370572939, -9.227025126956866, 17.69341876066779, 17.7058942448478, -13.2182156659012, 3.273277215940703, 7.82096407961303, -6.540134857551783, 5.302726399754003, 21.6168229759513, -35.45773268931614, -39.5771763658349, 16.91907564224343, 16.55810765769962, 10.84170890675409, 4.539182245882841, 5.966139065523301, 10.43624249585104, -6.306944364017387, 25.11309378553394, -23.98463112536712, -3.253554932408899, -26.20327820737005, 34.95346757431584, -22.06848426488626, 0.3787905650745691, 12.79793983153946, -15.15662916810503, 30.10820985389998, 17.18239253486946, 26.44238280127885, -17.53916820777098, -21.59984930800645, -20.89069843604591, -10.62614963929214, -4.16861219455282, -15.8281632392319, -15.45413424684084, 7.28126264287692, -17.30978445489622, 25.83878482866339, -18.20409699627451, 1.341279973912325, 6.060701390094514, -0.9930555858249585, -0.4770067839263625, -8.050723322366107, 15.00633993006825, -10.12301020599794, -15.02267685265745, -28.87546819977945, -4.887384695963816, 3.812851132430744, 19.10682316350844, 7.478580657962908, -7.486104775378393, 8.24517564743228, -7.51905558097683, -6.644004835040043, 16.04319982377311, -12.24015636297471, -0.4152718733052826, -15.37260980717165, -14.36579932723399, -1.30513875795791, 5.356894027365968,
                        0, 0, 0, 88.73441744471468, -9.667604704172753, -22.84943872004879, 5.044285909895449, -2.76004875036668, 0.3050715430090338, 2.281066203460998, -3.081685045157843, 5.563173468318147, 1.196920824152984, 0.7508125732458136, 3.261490552895722, -0.1915889730517104, 2.178042983750966, -5.719722606964433, -0.808717831824074, 3.567750315780947, 4.405620166473985, 8.068713509838501, -3.974147763943233, 4.024558504483837, 1.343369353638846, -1.554164148226279, 1.397410693322202, 1.549071510171349, -0.6861822032616559, -0.03144220974090741, -1.503375319686877, -1.213563509509453, 1.485658175240746, 1.102628808733887, -2.836353822887371, -2.651198571403894, 1.944770277514162, 1.800720538730825, 2.925044559436877, 2.489394773406274, -3.99962439548742, -1.365153890760246, 1.729186611640552, 0.90732580595284, 0.02970965138899272, -9.802670261550649, -3.377885239589956, 3.311681996737421, -2.102890043550365, -2.752571666784161, 7.725320034635699, -0.8099349955071451, 0.5680350525364315, 2.461090824551101, 1.671002962178604, -4.651796111745832, -3.019627268376409, -1.456848301794733, 0.6765376227892419, -2.208873565004413, -2.755468168868538, -2.723938546851782, 1.844529360647301, -1.962817053181678, 2.77164872022158, -0.6312645341808628, 0.9959732581947718, -0.01141276076056162, -1.047045912982139, 0.9659655272370172, -1.069371622104567, -0.564318267120407, -0.9606489624515147, -0.3731646049074267, -0.4361324066751411, -1.228953081985217, 2.112718903093324, 3.774673462225595, 2.038526286226191, -2.037134562294253, -0.6272498215703869, -0.9130826952549337, -0.5356753186936942, 1.739354952287502, -2.607676632661601, 1.167128690015535, -3.643945638175477, -2.247788469333459, 0.4447578257714688, 0.8814188227164721,
                        0, 0, 0, 0, 35.22951028609684, -22.61691132174376, 97.10536643650998, -3.714742139430975, 10.06500336745724, -16.35785983037913, 8.78437693523264, 1.985132974393485, -1.609800726068471, 10.55631691645605, 9.224290477011534, 4.722637143581605, 4.125150731568718, -5.396683914299057, 6.364591301561367, 8.24526687743292, 4.911724566872895, 6.542687463438916, -9.348997687795265, 14.18011100433374, 5.720905431367072, -1.582673805208176, 3.789638114574857, 6.440267872588953, -4.901278147004489, 0.421175984045115, 3.797008789173352, 0.2579925025997163, -1.093437933585557, -1.126991905684307, -4.4057666178694, -6.4297958780832, 4.918610437583255, 4.893900733343752, 7.627382484342153, 6.943539836193181, -10.22700285291435, -5.21717606135954, 5.635670539663245, -0.61979670671329, 1.025327494294112, -29.98298952616265, -10.87852244502099, 6.724183768213139, -5.415447368170939, -9.131548344141406, 25.08685243604318, -0.5163094225162969, 5.436141320006754, 5.254969244047728, 5.189340308692745, -14.05566775803058, -3.790558233978546, -2.867451571946585, -2.265074057881479, -13.27098968249704, -6.419573660857155, -2.44809433119093, 5.262803237338727, -6.396156300345669, 12.9332727436708, -2.828158861124294, 6.494893307712784, -4.900718840392307, -12.17623988734707, 2.132680032576169, -4.239391092443586, -4.723934051879516, -6.984654958110764, -2.787156581230434, 4.744573069448925, -7.311973630803457, 14.86842763617212, 11.70461213488476, 10.92665646005423, -8.812367256417245, -1.725823238463376, -0.599065820210566, -2.268141253505947, 2.588966312561057, -7.560432899806777, 4.711500915754516, -11.63409451724343, -3.784667325499409, 0.9845255581998278, 2.917504056968942,
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                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.831745814038495, -20.41725582289098, -1.583013759260222, -0.02098081085371714, -0.03289988933600374, -0.006011309758863401, 0.03459650459981792, 0.01348477813223562, -0.02336540423557105, -0.003969872715414671, -0.05998169351462899, 0.05263821645435009, -0.0144354245014559, -0.005674777729486418, -0.03142277004383006,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.562800616132969, -36.13433050173559, 0.2585654510438173, -0.02913169721040965, 0.002592481347938085, 0.004329834978588065, 0.06325089767860387, 0.01951445115945309, -0.03070674283592272, -0.02183384192678349, 0.009849968434859515, -0.02891816499635688, 0.002667591177598971, -0.02361460878909238,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.2286035973327459, -15.02261004686781, 5.184122379409034, -0.0264079721355016, -0.007786216137000334, -0.008663526410932022, -0.005309693290799501, -0.006680538291880966, 0.001397532516833339, -0.01528554327177548, -0.01182046150296639, 0.005955666147884051, 0.003523919303238692,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.214570242697843, -21.4621144179193, -1.555874989179182, -0.001447535808513384, 0.03124103143611023, 0.01560612912433155, 0.01254222023040845, -0.0006565581414721336, -0.005837445535672976, 0.003328905310192099, -0.003109407401498421, -0.001359993487917328,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1.575215080762542, -36.12196181704586, -0.009581763987488548, 0.02181190823948241, 0.004249343259232833, 0.008866640947567769, -0.008827428692463307, 0.0111903702615688, -0.008259743446844802, 0.005994103918828306, 0.02884522108807095,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.02332478841374811, -20.31760288431249, 5.902175782312199, 0.01411291075117598, -0.0401626029282366, -0.04333034577745157, 0.006563645334078613, -0.02686027801335236, 1.82653938945055e-05, -0.009451944888619017,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.843446424852287, -17.22694391469142, 4.615021811975704, 0.03880112444568462, 0.01156878860697344, -0.02011735633875036, 0.007254465185871957, 0.006976302646061595, 0.01061407563995378,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4.636349195088934, -35.03142250661902, 0.03540637402307944, 0.006380325215592348, -0.01715112535803765, -0.005381045082520479, -0.02796704437114206, -0.01837431744975316,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03325953074641371, -17.29072432858197, 5.995094557622266, -0.004356649575832386, 0.01324648360020382, -0.002576747161993423, -0.0164552533090047,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5.976772821535572, -18.99788030681546, 0.01396461545715264, -0.007601183590626498, 0.005853929901760483, 0.0201199907208218,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.002983340164191267, -20.0342372815637, -5.741448414658583, -0.01215113512395332, -0.00662723431795657,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5.752040939724589, -16.25515722920224, -0.00713497387655803, -0.004958024634924642,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0004916632598946193, -12.09805746213948, 0.000198676020167099,
                        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0001765653829615133, -12.09823117436413,
                },
                evWant: []complex128{
                        -0.2513649571095319 + 26.5196181977274i,
                        -0.2513649571095319 - 26.5196181977274i,
                        -0.3323427794627154 + 14.12147023570828i,
                        -0.3323427794627154 - 14.12147023570828i,
                        -0.3885760957072044 + 34.01549575140551i,
                        -0.3885760957072044 - 34.01549575140551i,
                        -0.4938394681672298 + 19.28755724237434i,
                        -0.4938394681672298 - 19.28755724237434i,
                        -0.5354723308245726 + 44.07811563049843i,
                        -0.5354723308245726 - 44.07811563049843i,
                        -0.8831210193505878 + 40.64617136580856i,
                        -0.8831210193505878 - 40.64617136580856i,
                        -1.063691744877652 + 54.90113796777709i,
                        -1.063691744877652 - 54.90113796777709i,
                        -1.270999250073418 + 55.92169849615225i,
                        -1.270999250073418 - 55.92169849615225i,
                        -1.641962795944021 + 124.0727533257146i,
                        -1.641962795944021 - 124.0727533257146i,
                        -1.866212165366329 + 67.51198073484791i,
                        -1.866212165366329 - 67.51198073484791i,
                        -2.66562659457705 + 102.4818444744388i,
                        -2.66562659457705 - 102.4818444744388i,
                        -2.677285588970379 + 109.3976583973073i,
                        -2.677285588970379 - 109.3976583973073i,
                        -3.592328373007462 + 116.2450441105874i,
                        -3.592328373007462 - 116.2450441105874i,
                        -3.658587455178502 + 105.6223525143237i,
                        -3.658587455178502 - 105.6223525143237i,
                        -3.738335632746128 + 95.41374995650723i,
                        -3.738335632746128 - 95.41374995650723i,
                        -4.05659124602542 + 85.08673687146815i,
                        -4.05659124602542 - 85.08673687146815i,
                        -11.7967401639067 + 0.03421683561959875i,
                        -11.7967401639067 - 0.03421683561959875i,
                        -12.06591356324058 + 0.03010079020722811i,
                        -12.06591356324058 - 0.03010079020722811i,
                        -12.08354870692898,
                        -12.09435136773809 + 0.0007639916648241464i,
                        -12.09435136773809 - 0.0007639916648241464i,
                        -12.09785209014901 + 0.02991559300476182i,
                        -12.09785209014901 - 0.02991559300476182i,
                        -12.09806212746318,
                        -12.09850417485291,
                        -12.09864274565634,
                        -12.10160612637007 + 0.004700099158908263i,
                        -12.10160612637007 - 0.004700099158908263i,
                        -12.16873692768957 + 0.02446545858852495i,
                        -12.16873692768957 - 0.02446545858852495i,
                        -12.23495190373921 + 0.1453184367031505i,
                        -12.23495190373921 - 0.1453184367031505i,
                        -13.54778407074696 + 141.1839768257274i,
                        -13.54778407074696 - 141.1839768257274i,
                        -15.38790969472481 + 114.0584849752244i,
                        -15.38790969472481 - 114.0584849752244i,
                        -23.60369882806601 + 0.2464158068361128i,
                        -23.60369882806601 - 0.2464158068361128i,
                        -24.04314341198735 + 0.3315626206724418i,
                        -24.04314341198735 - 0.3315626206724418i,
                        -24.12753399862331 + 0.1634093642552133i,
                        -24.12753399862331 - 0.1634093642552133i,
                        -24.18103712080912,
                        -24.18908889661277,
                        -24.19357072143492,
                        -24.19567681157636,
                        -24.20660003986661,
                        -24.228086198612 + 0.0220672004906673i,
                        -24.228086198612 - 0.0220672004906673i,
                        -24.30677145425284 + 0.1813999700804981i,
                        -24.30677145425284 - 0.1813999700804981i,
                        -25.23862373866253 + 0.8733279005402655i,
                        -25.23862373866253 - 0.8733279005402655i,
                        -29.42427841595277 + 1.666886570068163i,
                        -29.42427841595277 - 1.666886570068163i,
                        -33.94959271558832,
                        -35.51958918286584,
                        -36.20666045708104 + 0.1660921702962803i,
                        -36.20666045708104 - 0.1660921702962803i,
                        -36.25710351845593 + 0.01052251476620707i,
                        -36.25710351845593 - 0.01052251476620707i,
                        -36.28714605125749,
                        -36.29431583135849,
                        -36.29711199023137,
                        -36.31304183793699,
                        -36.32232768169418,
                        -36.37871120972082 + 0.1557647672076243i,
                        -36.37871120972082 - 0.1557647672076243i,
                        -36.47694233727385 + 0.3738707259908102i,
                        -36.47694233727385 - 0.3738707259908102i,
                        -36.66483183150206,
                        -37.75937189360096,
                },
        },
        {
                // TUB100 matrix from MatrixMarket, balanced and factorized into
                // upper Hessenberg form in Octave, and embedded into a 104×104
                // diagonal matrix to test with ilo != 0 and ihi != n-1.
                // Eigenvalues computed by eig function in Octave.
                // Dhseqr considers this matrix big (n > 75).
                n:   104,
                ilo: 2,
                ihi: 101,
                tol: 1e-10,
                h: []float64{
                        1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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                        -1930.484166851586 + 1.202676762393897i,
                        -1930.484166851586 - 1.202676762393897i,
                        3,
                        4,
                },
        },
}