github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/testlapack/dhseqr.go (about)

     1  // Copyright ©2016 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package testlapack
     6  
     7  import (
     8  	"fmt"
     9  	"math"
    10  	"testing"
    11  
    12  	"github.com/jingcheng-WU/gonum/blas"
    13  	"github.com/jingcheng-WU/gonum/blas/blas64"
    14  	"github.com/jingcheng-WU/gonum/floats"
    15  	"github.com/jingcheng-WU/gonum/lapack"
    16  )
    17  
    18  type Dhseqrer interface {
    19  	Dhseqr(job lapack.SchurJob, compz lapack.SchurComp, n, ilo, ihi int, h []float64, ldh int, wr, wi []float64,
    20  		z []float64, ldz int, work []float64, lwork int) int
    21  }
    22  
    23  type dhseqrTest struct {
    24  	n   int
    25  	ilo int
    26  	ihi int
    27  	h   []float64
    28  	tol float64
    29  
    30  	evWant []complex128
    31  }
    32  
    33  func DhseqrTest(t *testing.T, impl Dhseqrer) {
    34  	for i, tc := range dhseqrTests {
    35  		for _, job := range []lapack.SchurJob{lapack.EigenvaluesOnly, lapack.EigenvaluesAndSchur} {
    36  			for _, wantz := range []bool{false, true} {
    37  				for _, extra := range []int{0, 11} {
    38  					testDhseqr(t, impl, i, tc, job, wantz, extra, true)
    39  					testDhseqr(t, impl, i, tc, job, wantz, extra, false)
    40  				}
    41  			}
    42  		}
    43  	}
    44  }
    45  
    46  func testDhseqr(t *testing.T, impl Dhseqrer, i int, test dhseqrTest, job lapack.SchurJob, wantz bool, extra int, optwork bool) {
    47  	const tol = 1e-14
    48  	evTol := test.tol
    49  	if evTol == 0 {
    50  		evTol = tol
    51  	}
    52  
    53  	n := test.n
    54  	ihi := test.ihi
    55  	ilo := test.ilo
    56  	h := zeros(n, n, n+extra)
    57  	copyGeneral(h, blas64.General{Rows: n, Cols: n, Stride: max(1, n), Data: test.h})
    58  	hCopy := cloneGeneral(h)
    59  
    60  	compz := lapack.SchurNone
    61  	z := blas64.General{Stride: max(1, n)}
    62  	if wantz {
    63  		// First, let Dhseqr initialize Z to the identity matrix.
    64  		compz = lapack.SchurHess
    65  		z = nanGeneral(n, n, n+extra)
    66  	}
    67  
    68  	wr := nanSlice(n)
    69  	wi := nanSlice(n)
    70  
    71  	work := nanSlice(max(1, n))
    72  	if optwork {
    73  		impl.Dhseqr(job, lapack.SchurHess, n, ilo, ihi, h.Data, h.Stride, wr, wi, z.Data, z.Stride, work, -1)
    74  		work = nanSlice(int(work[0]))
    75  	}
    76  
    77  	unconverged := impl.Dhseqr(job, compz, n, ilo, ihi, h.Data, h.Stride, wr, wi, z.Data, z.Stride, work, len(work))
    78  	prefix := fmt.Sprintf("Case %v: job=%c, compz=%c, n=%v, ilo=%v, ihi=%v, extra=%v, optwk=%v",
    79  		i, job, compz, n, ilo, ihi, extra, optwork)
    80  	if unconverged > 0 {
    81  		t.Logf("%v: Dhseqr did not compute all eigenvalues. unconverged=%v", prefix, unconverged)
    82  		if unconverged <= ilo {
    83  			t.Fatalf("%v: 0 < unconverged <= ilo", prefix)
    84  		}
    85  	}
    86  
    87  	// Check that wr and wi have been assigned completely.
    88  	if floats.HasNaN(wr) {
    89  		t.Errorf("%v: wr has NaN elements", prefix)
    90  	}
    91  	if floats.HasNaN(wi) {
    92  		t.Errorf("%v: wi has NaN elements", prefix)
    93  	}
    94  
    95  	// Check that complex eigenvalues are stored in consecutive elements as
    96  	// complex conjugate pairs.
    97  	for i := 0; i < n; {
    98  		if unconverged > 0 && i == ilo {
    99  			// Skip the unconverged eigenvalues.
   100  			i = unconverged
   101  			continue
   102  		}
   103  		if wi[i] == 0 {
   104  			// Real eigenvalue.
   105  			i++
   106  			continue
   107  		}
   108  		// Complex conjugate pair.
   109  		if wr[i] != wr[i+1] {
   110  			t.Errorf("%v: conjugate pair has real parts unequal", prefix)
   111  		}
   112  		if wi[i] < 0 {
   113  			t.Errorf("%v: first in conjugate pair has negative imaginary part", prefix)
   114  		}
   115  		if wi[i+1] != -wi[i] {
   116  			t.Errorf("%v: complex pair is not conjugate", prefix)
   117  		}
   118  		i += 2
   119  	}
   120  
   121  	// Check that H contains the Schur form T.
   122  	if job == lapack.EigenvaluesAndSchur {
   123  		for i := 0; i < n; {
   124  			if unconverged > 0 && i == ilo {
   125  				// Skip the unconverged eigenvalues.
   126  				i = unconverged
   127  				continue
   128  			}
   129  			if wi[i] == 0 {
   130  				// Real eigenvalue.
   131  				if wr[i] != h.Data[i*h.Stride+i] {
   132  					t.Errorf("%v: T not in Schur form (real eigenvalue not on diagonal)", prefix)
   133  				}
   134  				i++
   135  				continue
   136  			}
   137  			// Complex conjugate pair.
   138  			im := math.Sqrt(math.Abs(h.Data[(i+1)*h.Stride+i])) * math.Sqrt(math.Abs(h.Data[i*h.Stride+i+1]))
   139  			if wr[i] != h.Data[i*h.Stride+i] || wr[i] != h.Data[(i+1)*h.Stride+i+1] ||
   140  				math.Abs(wi[i]-im) > tol {
   141  				t.Errorf("%v: conjugate pair and 2×2 diagonal block don't correspond", prefix)
   142  			}
   143  			i += 2
   144  		}
   145  	}
   146  
   147  	// Check that all the found eigenvalues are really eigenvalues.
   148  	foundEV := make([]bool, len(test.evWant))
   149  	for i := 0; i < n; {
   150  		if unconverged > 0 && i == ilo {
   151  			// Skip the unconverged eigenvalues.
   152  			i = unconverged
   153  			continue
   154  		}
   155  		ev := complex(wr[i], wi[i])
   156  		// Use problem-specific tolerance for testing eigenvalues.
   157  		found, index := containsComplex(test.evWant, ev, evTol)
   158  		if !found {
   159  			t.Errorf("%v: unexpected eigenvalue %v", prefix, ev)
   160  		} else {
   161  			foundEV[index] = true
   162  		}
   163  		i++
   164  	}
   165  	if unconverged == 0 {
   166  		// Check that all eigenvalues have been found.
   167  		// This simple check assumes that all eigenvalues are
   168  		// sufficiently separated from each other at least by evTol.
   169  		for i := range foundEV {
   170  			if !foundEV[i] {
   171  				t.Errorf("%v: %vth eigenvalue not found", prefix, i)
   172  			}
   173  		}
   174  	}
   175  
   176  	if !wantz {
   177  		return
   178  	}
   179  
   180  	// Z must be orthogonal.
   181  	if resid := residualOrthogonal(z, false); resid > tol*float64(n) {
   182  		t.Errorf("Case %v: Z is not orthogonal; resid=%v, want<=%v", prefix, resid, tol*float64(n))
   183  	}
   184  
   185  	if job == lapack.EigenvaluesAndSchur {
   186  		tz := zeros(n, n, n)
   187  		blas64.Gemm(blas.NoTrans, blas.Trans, 1, h, z, 0, tz)
   188  		ztz := zeros(n, n, n)
   189  		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, z, tz, 0, ztz)
   190  		if !equalApproxGeneral(ztz, hCopy, evTol) {
   191  			t.Errorf("%v: H != Z T Zᵀ", prefix)
   192  		}
   193  	}
   194  
   195  	// Restore H.
   196  	copyGeneral(h, hCopy)
   197  	// Call Dhseqr again with the identity matrix given explicitly in Q.
   198  	q := eye(n, n+extra)
   199  	impl.Dhseqr(job, lapack.SchurOrig, n, ilo, ihi, h.Data, h.Stride, wr, wi, q.Data, q.Stride, work, len(work))
   200  	if !equalApproxGeneral(z, q, 0) {
   201  		t.Errorf("%v: Z and Q are not equal", prefix)
   202  	}
   203  }
   204  
   205  var dhseqrTests = []dhseqrTest{
   206  	{
   207  		n:   0,
   208  		ilo: 0,
   209  		ihi: -1,
   210  	},
   211  	{
   212  		n:      1,
   213  		ilo:    0,
   214  		ihi:    0,
   215  		h:      []float64{0},
   216  		evWant: []complex128{0},
   217  	},
   218  	{
   219  		n:      1,
   220  		ilo:    0,
   221  		ihi:    0,
   222  		h:      []float64{7.09965484086874e-1},
   223  		evWant: []complex128{7.09965484086874e-1},
   224  	},
   225  	{
   226  		n:      2,
   227  		ilo:    0,
   228  		ihi:    1,
   229  		h:      []float64{0, 0, 0, 0},
   230  		evWant: []complex128{0},
   231  	},
   232  	{
   233  		n:   2,
   234  		ilo: 0,
   235  		ihi: 1,
   236  		h: []float64{
   237  			1, 0,
   238  			0, 1,
   239  		},
   240  		evWant: []complex128{1},
   241  	},
   242  	{
   243  		n:   2,
   244  		ilo: 0,
   245  		ihi: 1,
   246  		h: []float64{
   247  			0, -1,
   248  			1, 0,
   249  		},
   250  		evWant: []complex128{1i, -1i},
   251  	},
   252  	{
   253  		n:   2,
   254  		ilo: 0,
   255  		ihi: 1,
   256  		h: []float64{
   257  			6.25219991450918e-1, 8.17510791994361e-1,
   258  			3.31218891622294e-1, 1.24103744878131e-1,
   259  		},
   260  		evWant: []complex128{9.52203547663447e-1, -2.02879811334398e-1},
   261  	},
   262  	{
   263  		n:   4,
   264  		ilo: 1,
   265  		ihi: 2,
   266  		h: []float64{
   267  			1, 0, 0, 0,
   268  			0, 6.25219991450918e-1, 8.17510791994361e-1, 0,
   269  			0, 3.31218891622294e-1, 1.24103744878131e-1, 0,
   270  			0, 0, 0, 2,
   271  		},
   272  		evWant: []complex128{1, 2, 9.52203547663447e-1, -2.02879811334398e-1},
   273  	},
   274  	{
   275  		n:   2,
   276  		ilo: 0,
   277  		ihi: 1,
   278  		h: []float64{
   279  			-1.1219562276608, 6.85473513349362e-1,
   280  			-8.19951061145131e-1, 1.93728523178888e-1,
   281  		},
   282  		evWant: []complex128{
   283  			-4.64113852240958e-1 + 3.59580510817350e-1i,
   284  			-4.64113852240958e-1 - 3.59580510817350e-1i,
   285  		},
   286  	},
   287  	{
   288  		n:   5,
   289  		ilo: 0,
   290  		ihi: 4,
   291  		h: []float64{
   292  			9.57590178533658e-1, -5.10651295522708e-1, 9.24974510015869e-1, -1.30016306879522e-1, 2.92601986926954e-2,
   293  			-1.08084756637964, 1.77529701001213, -1.36480197632509, 2.23196371219601e-1, 1.12912853063308e-1,
   294  			0, -8.44075612174676e-1, 1.067867614486, -2.55782915176399e-1, -2.00598563137468e-1,
   295  			0, 0, -5.67097237165410e-1, 2.07205057427341e-1, 6.54998340743380e-1,
   296  			0, 0, 0, -1.89441413886041e-1, -4.18125416021786e-1,
   297  		},
   298  		evWant: []complex128{
   299  			2.94393309555622,
   300  			4.97029793606701e-1 + 3.63041654992384e-1i,
   301  			4.97029793606701e-1 - 3.63041654992384e-1i,
   302  			-1.74079119166145e-1 + 2.01570009462092e-1i,
   303  			-1.74079119166145e-1 - 2.01570009462092e-1i,
   304  		},
   305  	},
   306  	{
   307  		// BFW62A matrix from MatrixMarket, balanced and factorized into
   308  		// upper Hessenberg form in Octave.
   309  		// Eigenvalues computed by eig function in Octave.
   310  		// Dhseqr considers this matrix small (n <= 75).
   311  		n:   62,
   312  		ilo: 0,
   313  		ihi: 61,
   314  		tol: 1e-12,
   315  		h: []float64{
   316  			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,
   317  			-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,
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   367  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.4817927293509213, 1.408851322535897, -0.7676055176021872, -0.04505523423060897, 0.01813562786331449, 0.03138728238085502, 0.0007373169379419269, 0.001847667170281647, -0.01640431370966648, 0.04696818974656805, -0.004393748298759055, -0.02848496648956977,
   368  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.7883892138973269, 1.746055173045302, 0.4846783430365095, -0.0003922243062844435, 0.01186867835550373, 0.01648380387048428, -0.03174672656471393, -0.03627511739090696, -0.004853687188112606, -0.06885884936290802, -0.004917829299265958,
   369  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5208363315616994, 2.037277859382022, 0.5232085356010402, 0.07175407188317283, -0.07019064479939288, -0.02385694223436976, -0.00819063541887864, 0.07192359009199149, -0.06656167507443485, -0.04927759893361527,
   370  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.5819314677010843, 2.130167978098713, 0.5667361680393177, -0.01053764587057425, 0.01592751856907668, -0.01111604356574088, -0.004404610058468247, 0.03850545663289814, 0.04729794670040405,
   371  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.6488904808178829, 1.974426530381294, -0.2820471741701222, 0.02456494941736511, 0.03486280653024869, -0.01809831529884736, 0.08408521068644187, -0.006474401058818371,
   372  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.3312307167387429, 1.235934836863219, -0.2452582871525679, 0.01878427096720662, 0.04975840840483642, 0.05672553943361373, 0.01742942062643791,
   373  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.2654365696129733, 2.208256891929066, 0.3360201888498769, 0.06660725081463706, -0.01286437627536736, -0.002070231898763094,
   374  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.3639062481633207, 2.248588741393716, -0.1889980205327704, 0.05688507493685012, -0.04579504315826421,
   375  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.1624755988486198, 1.590085647221482, 0.1168533202179821, 0.005293082667091636,
   376  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.173908380119132, 1.450043378319349, 0.02765965035599782,
   377  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02984095753646376, 1.759629990218614,
   378  		},
   379  		evWant: []complex128{
   380  			-0.01716884621227793,
   381  			-0.1844331609734137,
   382  			0.05200651487352193,
   383  			0.1336851109127556,
   384  			0.2020936631953806,
   385  			0.3566470363060668,
   386  			0.3627207699831158,
   387  			0.4388555152488943,
   388  			0.4776853636435153,
   389  			0.5598821450074998,
   390  			0.6249350549980947,
   391  			0.6791310689291772,
   392  			0.985877008147705 + 0.01929363300192029i,
   393  			0.985877008147705 - 0.01929363300192029i,
   394  			0.9908483217835712,
   395  			1.011990761364073,
   396  			1.130046345264462,
   397  			1.323698071765709,
   398  			1.348598229483672,
   399  			1.363190626641638 + 0.05400660173350781i,
   400  			1.363190626641638 - 0.05400660173350781i,
   401  			1.632832316477256,
   402  			1.646239548684271,
   403  			1.742738908029794,
   404  			1.763069014878969,
   405  			1.789601126186348,
   406  			1.945228042429256,
   407  			1.946373262056993,
   408  			1.997152389795002,
   409  			2.261322781594966,
   410  			2.286944100979884,
   411  			2.447712649969029,
   412  			2.557857506923634,
   413  			2.608379034892128,
   414  			2.653335615965549,
   415  			2.675270309760236,
   416  			2.964219802766918 + 0.01767482509567778i,
   417  			2.964219802766918 - 0.01767482509567778i,
   418  			3.014604817775139,
   419  			3.158289371199042,
   420  			3.311794215710077,
   421  			3.389894197376214,
   422  			3.553333074879877,
   423  			3.641274442796651,
   424  			3.857556223000175,
   425  			4.045817381029103,
   426  			4.330901939363569,
   427  			4.337313647767939,
   428  			4.527400487637496,
   429  			4.917229128467305,
   430  			4.985609414964091,
   431  			5.687686849958608,
   432  			5.79422309012183,
   433  			5.997813119506478,
   434  			6.732426637899077,
   435  			6.957609338485607,
   436  			7.529842664573327,
   437  			7.609108287806763,
   438  			7.761261355516287,
   439  			8.311941758006698,
   440  			9.07053741884884,
   441  			9.217944588000314,
   442  		},
   443  	},
   444  	{
   445  		// TOLS90 matrix from MatrixMarket, balanced and factorized into
   446  		// upper Hessenberg form in Octave.
   447  		// Eigenvalues computed by eig function in Octave.
   448  		// Dhseqr considers this matrix big (n > 75).
   449  		n:   90,
   450  		ilo: 0,
   451  		ihi: 89,
   452  		tol: 1e-12,
   453  		h: []float64{
   454  			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,
   455  			-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,
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   538  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   539  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   540  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   541  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   542  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   543  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   544  		},
   545  		evWant: []complex128{
   546  			-0.2513649571095319 + 26.5196181977274i,
   547  			-0.2513649571095319 - 26.5196181977274i,
   548  			-0.3323427794627154 + 14.12147023570828i,
   549  			-0.3323427794627154 - 14.12147023570828i,
   550  			-0.3885760957072044 + 34.01549575140551i,
   551  			-0.3885760957072044 - 34.01549575140551i,
   552  			-0.4938394681672298 + 19.28755724237434i,
   553  			-0.4938394681672298 - 19.28755724237434i,
   554  			-0.5354723308245726 + 44.07811563049843i,
   555  			-0.5354723308245726 - 44.07811563049843i,
   556  			-0.8831210193505878 + 40.64617136580856i,
   557  			-0.8831210193505878 - 40.64617136580856i,
   558  			-1.063691744877652 + 54.90113796777709i,
   559  			-1.063691744877652 - 54.90113796777709i,
   560  			-1.270999250073418 + 55.92169849615225i,
   561  			-1.270999250073418 - 55.92169849615225i,
   562  			-1.641962795944021 + 124.0727533257146i,
   563  			-1.641962795944021 - 124.0727533257146i,
   564  			-1.866212165366329 + 67.51198073484791i,
   565  			-1.866212165366329 - 67.51198073484791i,
   566  			-2.66562659457705 + 102.4818444744388i,
   567  			-2.66562659457705 - 102.4818444744388i,
   568  			-2.677285588970379 + 109.3976583973073i,
   569  			-2.677285588970379 - 109.3976583973073i,
   570  			-3.592328373007462 + 116.2450441105874i,
   571  			-3.592328373007462 - 116.2450441105874i,
   572  			-3.658587455178502 + 105.6223525143237i,
   573  			-3.658587455178502 - 105.6223525143237i,
   574  			-3.738335632746128 + 95.41374995650723i,
   575  			-3.738335632746128 - 95.41374995650723i,
   576  			-4.05659124602542 + 85.08673687146815i,
   577  			-4.05659124602542 - 85.08673687146815i,
   578  			-11.7967401639067 + 0.03421683561959875i,
   579  			-11.7967401639067 - 0.03421683561959875i,
   580  			-12.06591356324058 + 0.03010079020722811i,
   581  			-12.06591356324058 - 0.03010079020722811i,
   582  			-12.08354870692898,
   583  			-12.09435136773809 + 0.0007639916648241464i,
   584  			-12.09435136773809 - 0.0007639916648241464i,
   585  			-12.09785209014901 + 0.02991559300476182i,
   586  			-12.09785209014901 - 0.02991559300476182i,
   587  			-12.09806212746318,
   588  			-12.09850417485291,
   589  			-12.09864274565634,
   590  			-12.10160612637007 + 0.004700099158908263i,
   591  			-12.10160612637007 - 0.004700099158908263i,
   592  			-12.16873692768957 + 0.02446545858852495i,
   593  			-12.16873692768957 - 0.02446545858852495i,
   594  			-12.23495190373921 + 0.1453184367031505i,
   595  			-12.23495190373921 - 0.1453184367031505i,
   596  			-13.54778407074696 + 141.1839768257274i,
   597  			-13.54778407074696 - 141.1839768257274i,
   598  			-15.38790969472481 + 114.0584849752244i,
   599  			-15.38790969472481 - 114.0584849752244i,
   600  			-23.60369882806601 + 0.2464158068361128i,
   601  			-23.60369882806601 - 0.2464158068361128i,
   602  			-24.04314341198735 + 0.3315626206724418i,
   603  			-24.04314341198735 - 0.3315626206724418i,
   604  			-24.12753399862331 + 0.1634093642552133i,
   605  			-24.12753399862331 - 0.1634093642552133i,
   606  			-24.18103712080912,
   607  			-24.18908889661277,
   608  			-24.19357072143492,
   609  			-24.19567681157636,
   610  			-24.20660003986661,
   611  			-24.228086198612 + 0.0220672004906673i,
   612  			-24.228086198612 - 0.0220672004906673i,
   613  			-24.30677145425284 + 0.1813999700804981i,
   614  			-24.30677145425284 - 0.1813999700804981i,
   615  			-25.23862373866253 + 0.8733279005402655i,
   616  			-25.23862373866253 - 0.8733279005402655i,
   617  			-29.42427841595277 + 1.666886570068163i,
   618  			-29.42427841595277 - 1.666886570068163i,
   619  			-33.94959271558832,
   620  			-35.51958918286584,
   621  			-36.20666045708104 + 0.1660921702962803i,
   622  			-36.20666045708104 - 0.1660921702962803i,
   623  			-36.25710351845593 + 0.01052251476620707i,
   624  			-36.25710351845593 - 0.01052251476620707i,
   625  			-36.28714605125749,
   626  			-36.29431583135849,
   627  			-36.29711199023137,
   628  			-36.31304183793699,
   629  			-36.32232768169418,
   630  			-36.37871120972082 + 0.1557647672076243i,
   631  			-36.37871120972082 - 0.1557647672076243i,
   632  			-36.47694233727385 + 0.3738707259908102i,
   633  			-36.47694233727385 - 0.3738707259908102i,
   634  			-36.66483183150206,
   635  			-37.75937189360096,
   636  		},
   637  	},
   638  	{
   639  		// TUB100 matrix from MatrixMarket, balanced and factorized into
   640  		// upper Hessenberg form in Octave, and embedded into a 104×104
   641  		// diagonal matrix to test with ilo != 0 and ihi != n-1.
   642  		// Eigenvalues computed by eig function in Octave.
   643  		// Dhseqr considers this matrix big (n > 75).
   644  		n:   104,
   645  		ilo: 2,
   646  		ihi: 101,
   647  		tol: 1e-10,
   648  		h: []float64{
   649  			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,
   650  			0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   651  			0, 0, -1063.761, -960.3970563202379, -0.0006079108185996773, -0.009201940691316367, 0.002442836240270196, 0.01550988534551903, -0.005482455008401117, -0.02216870959395947, 0.009747347615349792, 0.02941831540681939, -0.01530136178573213, -0.03750794345694437, 0.02225359194453896, 0.046705617938318, -0.0307619752542162, -0.05730825585675074, 0.04103856105936231, 0.06965250072575992, -0.05335624663776811, -0.08412633500439758, 0.06805680196063389, 0.1011811513254484, -0.08555957035531082, -0.1213434441393789, 0.106369291926541, 0.1452243676184516, -0.1310809449650698, 0.1735240650736495, 0.1603769717276725, 0.2070245946752049, -0.195009056622052, 0.2465616197175694, 0.2357520481176992, 0.2929587463757468, -0.2833105069304027, 0.3469005841220431, 0.3381503031304328, 0.4087132445918312, -0.4002236126054999, 0.4780213717840138, 0.4685650013761221, 0.5532750093152425, -0.5407842250274101, 0.6312148133425258, 0.6125866029330725, 0.7064838330293224, -0.6776224584955323, 0.7717672671130079, 0.728093737707456, 0.4477228711606641, -1.832801684441419, 1.950252997191289, 0.804390452586547, 0.4832557718849113, 0.3060066166102118, 0.2756451553030591, 0.1719798268352208, 0.1844690914416081, 0.1028522851629666, 0.1338501876768783, 0.05922545829023376, 0.1041210893998114, 0.0294781768570502, 0.08738772703908808, 0.008665658061761334, 0.07957418017688388, -0.005841802748350547, 0.07832978350913038, -0.01561691241238414, 0.08229737118429636, -0.02164114160477788, 0.09076446627208183, -0.02452178964005379, -0.1034535010713481, 0.02461324557496748, 0.1203839900069163, -0.02209524508102444, 0.1417838483570761, -0.01702626635186736, 0.1680394493064578, 0.009377435518891378, -0.1996795871970759, -0.0009558646643977288, 0.2373933824702814, -0.01416583764558031, 0.2820880046959302, 0.03057782300299389, -0.3349961435755344, 0.05073634798692103, -0.3978562481735693, -0.0755607412701291, -0.4732063781751494, 0.1066126139010085, -0.5648764073871733, 0.1465759215609417, 0.67885880956596, 0.2001993093624898, -0.8249735752515708, 0.2762967421832379, -7.383366696690373, 0, 0,
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   739  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454.2888780517075, -959.8060141768642, 502.6209139189659, -0.1963783784418207, -1.07681015710693, 0.2118129088940946, -1.30957289263114, 0.2416506844030767, 1.594926385284288, 0.2987764905571196, -1.958528602633205, -1.89790052548914, -19.45550897611078, 0, 0,
   740  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454.6150435510897, -959.7057073918052, -504.2207918385922, 0.08191276561459389, 1.744978959223401, -0.01623102385292412, 2.044325279439126, 0.139362395300141, 2.428380353063932, -0.2989187527977135, 20.97397716279267, 4.596081079911148, 0, 0,
   741  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -453.9030102952942, -959.5514771839804, -502.0302313735755, -0.1509069873047727, 1.509921737993699, -0.1866506960156188, -1.853460072170985, -0.2470701568585754, 2.284756111156089, 3.070922511010462, 23.1773864785971, 0, 0,
   742  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -454.393273204417, -959.4263564611852, 504.2962075579032, 0.005942404933789297, 2.446660862635643, 0.1147302269971472, 2.888007099445928, -0.2794135351323237, 24.93107187619451, 6.291448555715359, 0, 0,
   743  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 453.4308183834945, -959.2306762470356, 501.2467662460859, 0.1030197566665109, 2.15672544959436, 0.1707450834055513, -2.672257869508826, -4.548465509453017, -27.68489865384783, 0, 0,
   744  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 454.1521964870133, -959.071043583621, 504.4663679395445, 0.09038098396525029, 3.453184686592636, -0.2556696326547585, 29.74790742438, 8.418178566025752, 0, 0,
   745  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 452.828604749646, -958.8118098643598, -500.1677840008083, 0.05562336274628601, -3.140588015388957, -6.465358070370396, -33.25328104675387, 0, 0,
   746  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -453.8814454933349, -958.5973523296369, -504.7879798529249, 0.2240186812962395, -35.739305932474, -11.17424401632893, 0, 0,
   747  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -452.0207842240151, -958.2280932680816, 498.6099988306628, -9.061273073482408, -40.32955903922403, 0, 0,
   748  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 453.5608878051024, -957.9144120234951, 542.7656821084641, 14.91304502929086, 0, 0,
   749  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 450.8656330991661, -969.8578951037719, 452.1887612775597, 0, 0,
   750  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 787.8967774818433, -898.9789215779133, 0, 0,
   751  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0,
   752  			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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,
   753  		},
   754  		evWant: []complex128{
   755  			1,
   756  			2,
   757  			-0.8238783640171078 + 1.579766228862017i,
   758  			-0.8238783640171078 - 1.579766228862017i,
   759  			-3.922907917607387 + 1.654540870297146i,
   760  			-3.922907917607387 - 1.654540870297146i,
   761  			-10.04176861796659 + 1.651471031280953i,
   762  			-10.04176861796659 - 1.651471031280953i,
   763  			-19.90533512613429 + 1.64196864045227i,
   764  			-19.90533512613429 - 1.64196864045227i,
   765  			-33.60610872827028 + 1.635560741682501i,
   766  			-33.60610872827028 - 1.635560741682501i,
   767  			-51.10943733404228 + 1.631805014774364i,
   768  			-51.10943733404228 - 1.631805014774364i,
   769  			-72.34919707090897 + 1.629522740505929i,
   770  			-72.34919707090897 - 1.629522740505929i,
   771  			-97.24021794530901 + 1.628064860261413i,
   772  			-97.24021794530901 - 1.628064860261413i,
   773  			-125.6811625494976 + 1.627074041605065i,
   774  			-125.6811625494976 - 1.627074041605065i,
   775  			-157.5556174346503 + 1.626392967840776i,
   776  			-157.5556174346503 - 1.626392967840776i,
   777  			-192.732837945876 + 1.625893674037654i,
   778  			-192.732837945876 - 1.625893674037654i,
   779  			-231.0684238575969 + 1.625523897559938i,
   780  			-231.0684238575969 - 1.625523897559938i,
   781  			-272.404932676379 + 1.625248463045784i,
   782  			-272.404932676379 - 1.625248463045784i,
   783  			-316.5725618120467 + 1.625029322230836i,
   784  			-316.5725618120467 - 1.625029322230836i,
   785  			-363.3898435346347 + 1.624863705104029i,
   786  			-363.3898435346347 - 1.624863705104029i,
   787  			-412.6644183160402 + 1.624734783685709i,
   788  			-412.6644183160402 - 1.624734783685709i,
   789  			-464.1938275598905 + 1.624629407600858i,
   790  			-464.1938275598905 - 1.624629407600858i,
   791  			-517.7663337295413 + 1.624555040627727i,
   792  			-517.7663337295413 - 1.624555040627727i,
   793  			-573.1617958392867 + 1.62448889134649i,
   794  			-573.1617958392867 - 1.62448889134649i,
   795  			-630.1525854166166 + 1.624445355378192i,
   796  			-630.1525854166166 - 1.624445355378192i,
   797  			-688.5045249303587 + 1.624414401302088i,
   798  			-688.5045249303587 - 1.624414401302088i,
   799  			-747.9778126976437 + 1.624396390555459i,
   800  			-747.9778126976437 - 1.624396390555459i,
   801  			-808.3280706224909 + 1.62438480760184i,
   802  			-808.3280706224909 - 1.62438480760184i,
   803  			-869.3072903249724 + 1.624387678902335i,
   804  			-869.3072903249724 - 1.624387678902335i,
   805  			-930.6648831979091 + 1.624396130880259i,
   806  			-930.6648831979091 - 1.624396130880259i,
   807  			-992.1487134378474 + 1.624417808682915i,
   808  			-992.1487134378474 - 1.624417808682915i,
   809  			-1053.506114553354 + 1.624453056189826i,
   810  			-1053.506114553354 - 1.624453056189826i,
   811  			-1114.484928198698 + 1.62449544649428i,
   812  			-1114.484928198698 - 1.62449544649428i,
   813  			-1174.834554234014 + 1.624553207269019i,
   814  			-1174.834554234014 - 1.624553207269019i,
   815  			-1234.306981514973 + 1.624623553438826i,
   816  			-1234.306981514973 - 1.624623553438826i,
   817  			-1292.657768972259 + 1.624709216827242i,
   818  			-1292.657768972259 - 1.624709216827242i,
   819  			-1349.647106741638 + 1.624814444572517i,
   820  			-1349.647106741638 - 1.624814444572517i,
   821  			-1405.040739357668 + 1.624951632752096i,
   822  			-1405.040739357668 - 1.624951632752096i,
   823  			-1458.610953350783 + 1.625104547041682i,
   824  			-1458.610953350783 - 1.625104547041682i,
   825  			-1510.137508646807 + 1.625304666073007i,
   826  			-1510.137508646807 - 1.625304666073007i,
   827  			-1559.408520122221 + 1.625548293255404i,
   828  			-1559.408520122221 - 1.625548293255404i,
   829  			-1606.221305250554 + 1.625851986073836i,
   830  			-1606.221305250554 - 1.625851986073836i,
   831  			-1650.383201531125 + 1.62624202844641i,
   832  			-1650.383201531125 - 1.62624202844641i,
   833  			-1691.712315735984 + 1.6267345498979i,
   834  			-1691.712315735984 - 1.6267345498979i,
   835  			-1730.038177420971 + 1.627388968656263i,
   836  			-1730.038177420971 - 1.627388968656263i,
   837  			-1765.20230058066 + 1.628268412022146i,
   838  			-1765.20230058066 - 1.628268412022146i,
   839  			-1797.05860162894 + 1.629473972633416i,
   840  			-1797.05860162894 - 1.629473972633416i,
   841  			-1825.473493639258 + 1.631220665229006i,
   842  			-1825.473493639258 - 1.631220665229006i,
   843  			-1850.32542664842 + 1.633834593918563i,
   844  			-1850.32542664842 - 1.633834593918563i,
   845  			-1871.503056018116 + 1.637993570641514i,
   846  			-1871.503056018116 - 1.637993570641514i,
   847  			-1888.90026514681 + 1.64508855982818i,
   848  			-1888.90026514681 - 1.64508855982818i,
   849  			-1902.402515327158 + 1.658179541614067i,
   850  			-1902.402515327158 - 1.658179541614067i,
   851  			-1911.858940404498 + 1.682209391409579i,
   852  			-1911.858940404498 - 1.682209391409579i,
   853  			-1916.92602113601 + 1.761877988650816i,
   854  			-1916.92602113601 - 1.761877988650816i,
   855  			-1930.484166851586 + 1.202676762393897i,
   856  			-1930.484166851586 - 1.202676762393897i,
   857  			3,
   858  			4,
   859  		},
   860  	},
   861  }