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737 lines
17 KiB
Go
737 lines
17 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package testlapack
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import (
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"fmt"
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"math"
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"math/cmplx"
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"strconv"
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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/floats"
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"gonum.org/v1/gonum/lapack"
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)
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type Dgeever interface {
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Dgeev(jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, n int, a []float64, lda int,
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wr, wi []float64, vl []float64, ldvl int, vr []float64, ldvr int, work []float64, lwork int) int
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}
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type dgeevTest struct {
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a blas64.General
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evWant []complex128 // If nil, the eigenvalues are not known.
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valTol float64 // Tolerance for eigenvalue checks.
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vecTol float64 // Tolerance for eigenvector checks.
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}
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func DgeevTest(t *testing.T, impl Dgeever) {
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rnd := rand.New(rand.NewSource(1))
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for i, test := range []dgeevTest{
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{
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a: A123{}.Matrix(),
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evWant: A123{}.Eigenvalues(),
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},
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dgeevTestForAntisymRandom(10, rnd),
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dgeevTestForAntisymRandom(11, rnd),
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dgeevTestForAntisymRandom(50, rnd),
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dgeevTestForAntisymRandom(51, rnd),
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dgeevTestForAntisymRandom(100, rnd),
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dgeevTestForAntisymRandom(101, rnd),
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{
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a: Circulant(2).Matrix(),
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evWant: Circulant(2).Eigenvalues(),
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},
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{
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a: Circulant(3).Matrix(),
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evWant: Circulant(3).Eigenvalues(),
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},
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{
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a: Circulant(4).Matrix(),
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evWant: Circulant(4).Eigenvalues(),
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},
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{
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a: Circulant(5).Matrix(),
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evWant: Circulant(5).Eigenvalues(),
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},
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{
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a: Circulant(10).Matrix(),
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evWant: Circulant(10).Eigenvalues(),
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},
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{
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a: Circulant(15).Matrix(),
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evWant: Circulant(15).Eigenvalues(),
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valTol: 1e-12,
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},
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{
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a: Circulant(30).Matrix(),
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evWant: Circulant(30).Eigenvalues(),
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valTol: 1e-11,
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vecTol: 1e-12,
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},
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{
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a: Circulant(50).Matrix(),
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evWant: Circulant(50).Eigenvalues(),
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valTol: 1e-11,
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vecTol: 1e-12,
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},
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{
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a: Circulant(101).Matrix(),
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evWant: Circulant(101).Eigenvalues(),
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valTol: 1e-10,
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vecTol: 1e-11,
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},
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{
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a: Circulant(150).Matrix(),
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evWant: Circulant(150).Eigenvalues(),
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valTol: 1e-9,
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vecTol: 1e-10,
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},
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{
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a: Clement(2).Matrix(),
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evWant: Clement(2).Eigenvalues(),
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},
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{
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a: Clement(3).Matrix(),
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evWant: Clement(3).Eigenvalues(),
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},
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{
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a: Clement(4).Matrix(),
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evWant: Clement(4).Eigenvalues(),
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},
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{
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a: Clement(5).Matrix(),
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evWant: Clement(5).Eigenvalues(),
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},
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{
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a: Clement(10).Matrix(),
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evWant: Clement(10).Eigenvalues(),
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},
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{
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a: Clement(15).Matrix(),
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evWant: Clement(15).Eigenvalues(),
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},
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{
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a: Clement(30).Matrix(),
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evWant: Clement(30).Eigenvalues(),
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valTol: 1e-11,
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},
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{
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a: Clement(50).Matrix(),
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evWant: Clement(50).Eigenvalues(),
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valTol: 1e-7,
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vecTol: 1e-11,
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},
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{
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a: Creation(2).Matrix(),
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evWant: Creation(2).Eigenvalues(),
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},
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{
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a: Creation(3).Matrix(),
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evWant: Creation(3).Eigenvalues(),
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},
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{
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a: Creation(4).Matrix(),
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evWant: Creation(4).Eigenvalues(),
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},
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{
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a: Creation(5).Matrix(),
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evWant: Creation(5).Eigenvalues(),
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},
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{
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a: Creation(10).Matrix(),
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evWant: Creation(10).Eigenvalues(),
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},
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{
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a: Creation(15).Matrix(),
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evWant: Creation(15).Eigenvalues(),
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},
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{
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a: Creation(30).Matrix(),
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evWant: Creation(30).Eigenvalues(),
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},
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{
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a: Creation(50).Matrix(),
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evWant: Creation(50).Eigenvalues(),
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},
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{
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a: Creation(101).Matrix(),
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evWant: Creation(101).Eigenvalues(),
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},
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{
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a: Creation(150).Matrix(),
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evWant: Creation(150).Eigenvalues(),
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},
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{
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a: Diagonal(0).Matrix(),
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evWant: Diagonal(0).Eigenvalues(),
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},
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{
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a: Diagonal(10).Matrix(),
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evWant: Diagonal(10).Eigenvalues(),
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},
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{
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a: Diagonal(50).Matrix(),
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evWant: Diagonal(50).Eigenvalues(),
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},
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{
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a: Diagonal(151).Matrix(),
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evWant: Diagonal(151).Eigenvalues(),
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},
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{
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a: Downshift(2).Matrix(),
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evWant: Downshift(2).Eigenvalues(),
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},
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{
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a: Downshift(3).Matrix(),
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evWant: Downshift(3).Eigenvalues(),
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},
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{
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a: Downshift(4).Matrix(),
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evWant: Downshift(4).Eigenvalues(),
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},
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{
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a: Downshift(5).Matrix(),
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evWant: Downshift(5).Eigenvalues(),
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},
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{
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a: Downshift(10).Matrix(),
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evWant: Downshift(10).Eigenvalues(),
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},
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{
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a: Downshift(15).Matrix(),
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evWant: Downshift(15).Eigenvalues(),
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},
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{
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a: Downshift(30).Matrix(),
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evWant: Downshift(30).Eigenvalues(),
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},
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{
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a: Downshift(50).Matrix(),
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evWant: Downshift(50).Eigenvalues(),
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},
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{
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a: Downshift(101).Matrix(),
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evWant: Downshift(101).Eigenvalues(),
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},
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{
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a: Downshift(150).Matrix(),
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evWant: Downshift(150).Eigenvalues(),
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},
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{
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a: Fibonacci(2).Matrix(),
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evWant: Fibonacci(2).Eigenvalues(),
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},
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{
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a: Fibonacci(3).Matrix(),
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evWant: Fibonacci(3).Eigenvalues(),
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},
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{
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a: Fibonacci(4).Matrix(),
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evWant: Fibonacci(4).Eigenvalues(),
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},
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{
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a: Fibonacci(5).Matrix(),
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evWant: Fibonacci(5).Eigenvalues(),
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},
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{
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a: Fibonacci(10).Matrix(),
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evWant: Fibonacci(10).Eigenvalues(),
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},
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{
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a: Fibonacci(15).Matrix(),
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evWant: Fibonacci(15).Eigenvalues(),
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},
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{
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a: Fibonacci(30).Matrix(),
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evWant: Fibonacci(30).Eigenvalues(),
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},
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{
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a: Fibonacci(50).Matrix(),
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evWant: Fibonacci(50).Eigenvalues(),
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},
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{
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a: Fibonacci(101).Matrix(),
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evWant: Fibonacci(101).Eigenvalues(),
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},
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{
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a: Fibonacci(150).Matrix(),
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evWant: Fibonacci(150).Eigenvalues(),
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},
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{
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a: Gear(2).Matrix(),
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evWant: Gear(2).Eigenvalues(),
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},
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{
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a: Gear(3).Matrix(),
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evWant: Gear(3).Eigenvalues(),
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},
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{
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a: Gear(4).Matrix(),
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evWant: Gear(4).Eigenvalues(),
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valTol: 1e-7,
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},
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{
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a: Gear(5).Matrix(),
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evWant: Gear(5).Eigenvalues(),
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},
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{
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a: Gear(10).Matrix(),
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evWant: Gear(10).Eigenvalues(),
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valTol: 1e-8,
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},
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{
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a: Gear(15).Matrix(),
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evWant: Gear(15).Eigenvalues(),
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},
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{
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a: Gear(30).Matrix(),
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evWant: Gear(30).Eigenvalues(),
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valTol: 1e-8,
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},
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{
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a: Gear(50).Matrix(),
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evWant: Gear(50).Eigenvalues(),
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valTol: 1e-8,
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},
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{
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a: Gear(101).Matrix(),
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evWant: Gear(101).Eigenvalues(),
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},
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{
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a: Gear(150).Matrix(),
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evWant: Gear(150).Eigenvalues(),
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valTol: 1e-8,
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},
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{
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a: Grcar{N: 10, K: 3}.Matrix(),
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evWant: Grcar{N: 10, K: 3}.Eigenvalues(),
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},
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{
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a: Grcar{N: 10, K: 7}.Matrix(),
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evWant: Grcar{N: 10, K: 7}.Eigenvalues(),
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},
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{
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a: Grcar{N: 11, K: 7}.Matrix(),
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evWant: Grcar{N: 11, K: 7}.Eigenvalues(),
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},
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{
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a: Grcar{N: 50, K: 3}.Matrix(),
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evWant: Grcar{N: 50, K: 3}.Eigenvalues(),
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},
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{
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a: Grcar{N: 51, K: 3}.Matrix(),
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evWant: Grcar{N: 51, K: 3}.Eigenvalues(),
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},
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{
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a: Grcar{N: 50, K: 10}.Matrix(),
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evWant: Grcar{N: 50, K: 10}.Eigenvalues(),
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},
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{
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a: Grcar{N: 51, K: 10}.Matrix(),
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evWant: Grcar{N: 51, K: 10}.Eigenvalues(),
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},
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{
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a: Grcar{N: 50, K: 30}.Matrix(),
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evWant: Grcar{N: 50, K: 30}.Eigenvalues(),
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},
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{
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a: Grcar{N: 150, K: 2}.Matrix(),
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evWant: Grcar{N: 150, K: 2}.Eigenvalues(),
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},
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{
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a: Grcar{N: 150, K: 148}.Matrix(),
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evWant: Grcar{N: 150, K: 148}.Eigenvalues(),
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},
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{
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a: Hanowa{N: 6, Alpha: 17}.Matrix(),
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evWant: Hanowa{N: 6, Alpha: 17}.Eigenvalues(),
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},
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{
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a: Hanowa{N: 50, Alpha: -1}.Matrix(),
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evWant: Hanowa{N: 50, Alpha: -1}.Eigenvalues(),
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},
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{
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a: Hanowa{N: 100, Alpha: -1}.Matrix(),
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evWant: Hanowa{N: 100, Alpha: -1}.Eigenvalues(),
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},
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{
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a: Lesp(2).Matrix(),
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evWant: Lesp(2).Eigenvalues(),
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},
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{
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a: Lesp(3).Matrix(),
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evWant: Lesp(3).Eigenvalues(),
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},
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{
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a: Lesp(4).Matrix(),
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evWant: Lesp(4).Eigenvalues(),
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},
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{
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a: Lesp(5).Matrix(),
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evWant: Lesp(5).Eigenvalues(),
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},
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{
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a: Lesp(10).Matrix(),
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evWant: Lesp(10).Eigenvalues(),
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},
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{
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a: Lesp(15).Matrix(),
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evWant: Lesp(15).Eigenvalues(),
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},
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{
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a: Lesp(30).Matrix(),
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evWant: Lesp(30).Eigenvalues(),
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},
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{
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a: Lesp(50).Matrix(),
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evWant: Lesp(50).Eigenvalues(),
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valTol: 1e-12,
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vecTol: 1e-12,
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},
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{
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a: Lesp(101).Matrix(),
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evWant: Lesp(101).Eigenvalues(),
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valTol: 1e-12,
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vecTol: 1e-12,
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},
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{
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a: Lesp(150).Matrix(),
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evWant: Lesp(150).Eigenvalues(),
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valTol: 1e-12,
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vecTol: 1e-12,
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},
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{
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a: Rutis{}.Matrix(),
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evWant: Rutis{}.Eigenvalues(),
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},
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{
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a: Tris{N: 74, X: 1, Y: -2, Z: 1}.Matrix(),
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evWant: Tris{N: 74, X: 1, Y: -2, Z: 1}.Eigenvalues(),
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},
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{
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a: Tris{N: 74, X: 1, Y: 2, Z: -3}.Matrix(),
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evWant: Tris{N: 74, X: 1, Y: 2, Z: -3}.Eigenvalues(),
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},
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{
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a: Tris{N: 75, X: 1, Y: 2, Z: -3}.Matrix(),
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evWant: Tris{N: 75, X: 1, Y: 2, Z: -3}.Eigenvalues(),
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},
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{
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a: Wilk4{}.Matrix(),
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evWant: Wilk4{}.Eigenvalues(),
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},
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{
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a: Wilk12{}.Matrix(),
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evWant: Wilk12{}.Eigenvalues(),
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valTol: 1e-7,
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},
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{
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a: Wilk20(0).Matrix(),
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evWant: Wilk20(0).Eigenvalues(),
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},
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{
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a: Wilk20(1e-10).Matrix(),
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evWant: Wilk20(1e-10).Eigenvalues(),
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valTol: 1e-12,
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vecTol: 1e-12,
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},
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{
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a: Zero(1).Matrix(),
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evWant: Zero(1).Eigenvalues(),
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},
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{
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a: Zero(10).Matrix(),
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evWant: Zero(10).Eigenvalues(),
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},
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{
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a: Zero(50).Matrix(),
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evWant: Zero(50).Eigenvalues(),
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},
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{
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a: Zero(100).Matrix(),
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evWant: Zero(100).Eigenvalues(),
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},
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} {
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for _, jobvl := range []lapack.LeftEVJob{lapack.ComputeLeftEV, lapack.None} {
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for _, jobvr := range []lapack.RightEVJob{lapack.ComputeRightEV, lapack.None} {
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for _, extra := range []int{0, 11} {
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for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} {
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testDgeev(t, impl, strconv.Itoa(i), test, jobvl, jobvr, extra, wl)
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}
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}
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}
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}
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}
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for _, n := range []int{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 50, 51, 100, 101} {
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for _, jobvl := range []lapack.LeftEVJob{lapack.ComputeLeftEV, lapack.None} {
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for _, jobvr := range []lapack.RightEVJob{lapack.ComputeRightEV, lapack.None} {
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for cas := 0; cas < 10; cas++ {
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// Create a block diagonal matrix with
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// random eigenvalues of random multiplicity.
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ev := make([]complex128, n)
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tmat := zeros(n, n, n)
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for i := 0; i < n; {
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re := rnd.NormFloat64()
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if i == n-1 || rnd.Float64() < 0.5 {
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// Real eigenvalue.
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nb := rnd.Intn(min(4, n-i)) + 1
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for k := 0; k < nb; k++ {
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tmat.Data[i*tmat.Stride+i] = re
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ev[i] = complex(re, 0)
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i++
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}
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continue
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}
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// Complex eigenvalue.
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im := rnd.NormFloat64()
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nb := rnd.Intn(min(4, (n-i)/2)) + 1
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for k := 0; k < nb; k++ {
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// 2×2 block for the complex eigenvalue.
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tmat.Data[i*tmat.Stride+i] = re
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tmat.Data[(i+1)*tmat.Stride+i+1] = re
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tmat.Data[(i+1)*tmat.Stride+i] = -im
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tmat.Data[i*tmat.Stride+i+1] = im
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ev[i] = complex(re, im)
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ev[i+1] = complex(re, -im)
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i += 2
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}
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}
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// Compute A = Q T Q^T where Q is an
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// orthogonal matrix.
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q := randomOrthogonal(n, rnd)
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tq := zeros(n, n, n)
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blas64.Gemm(blas.NoTrans, blas.Trans, 1, tmat, q, 0, tq)
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a := zeros(n, n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, tq, 0, a)
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test := dgeevTest{
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a: a,
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evWant: ev,
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valTol: 1e-12,
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vecTol: 1e-7,
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}
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testDgeev(t, impl, "random", test, jobvl, jobvr, 0, optimumWork)
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}
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}
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}
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}
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}
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|
||
func testDgeev(t *testing.T, impl Dgeever, tc string, test dgeevTest, jobvl lapack.LeftEVJob, jobvr lapack.RightEVJob, extra int, wl worklen) {
|
||
const defaultTol = 1e-12
|
||
valTol := test.valTol
|
||
if valTol == 0 {
|
||
valTol = defaultTol
|
||
}
|
||
vecTol := test.vecTol
|
||
if vecTol == 0 {
|
||
vecTol = defaultTol
|
||
}
|
||
|
||
a := cloneGeneral(test.a)
|
||
n := a.Rows
|
||
|
||
var vl blas64.General
|
||
if jobvl == lapack.ComputeLeftEV {
|
||
vl = nanGeneral(n, n, n)
|
||
}
|
||
|
||
var vr blas64.General
|
||
if jobvr == lapack.ComputeRightEV {
|
||
vr = nanGeneral(n, n, n)
|
||
}
|
||
|
||
wr := make([]float64, n)
|
||
wi := make([]float64, n)
|
||
|
||
var lwork int
|
||
switch wl {
|
||
case minimumWork:
|
||
if jobvl == lapack.ComputeLeftEV || jobvr == lapack.ComputeRightEV {
|
||
lwork = max(1, 4*n)
|
||
} else {
|
||
lwork = max(1, 3*n)
|
||
}
|
||
case mediumWork:
|
||
work := make([]float64, 1)
|
||
impl.Dgeev(jobvl, jobvr, n, nil, 1, nil, nil, nil, 1, nil, 1, work, -1)
|
||
if jobvl == lapack.ComputeLeftEV || jobvr == lapack.ComputeRightEV {
|
||
lwork = (int(work[0]) + 4*n) / 2
|
||
} else {
|
||
lwork = (int(work[0]) + 3*n) / 2
|
||
}
|
||
lwork = max(1, lwork)
|
||
case optimumWork:
|
||
work := make([]float64, 1)
|
||
impl.Dgeev(jobvl, jobvr, n, nil, 1, nil, nil, nil, 1, nil, 1, work, -1)
|
||
lwork = int(work[0])
|
||
}
|
||
work := make([]float64, lwork)
|
||
|
||
first := impl.Dgeev(jobvl, jobvr, n, a.Data, a.Stride, wr, wi,
|
||
vl.Data, vl.Stride, vr.Data, vr.Stride, work, len(work))
|
||
|
||
prefix := fmt.Sprintf("Case #%v: n=%v, jobvl=%v, jobvr=%v, extra=%v, work=%v",
|
||
tc, n, jobvl, jobvr, extra, wl)
|
||
|
||
if !generalOutsideAllNaN(vl) {
|
||
t.Errorf("%v: out-of-range write to VL", prefix)
|
||
}
|
||
if !generalOutsideAllNaN(vr) {
|
||
t.Errorf("%v: out-of-range write to VR", prefix)
|
||
}
|
||
|
||
if first > 0 {
|
||
t.Logf("%v: all eigenvalues haven't been computed, first=%v", prefix, first)
|
||
}
|
||
|
||
// Check that conjugate pair eigevalues are ordered correctly.
|
||
for i := first; i < n; {
|
||
if wi[i] == 0 {
|
||
i++
|
||
continue
|
||
}
|
||
if wr[i] != wr[i+1] {
|
||
t.Errorf("%v: real parts of %vth conjugate pair not equal", prefix, i)
|
||
}
|
||
if wi[i] < 0 || wi[i+1] > 0 {
|
||
t.Errorf("%v: unexpected ordering of %vth conjugate pair", prefix, i)
|
||
}
|
||
i += 2
|
||
}
|
||
|
||
// Check the computed eigenvalues against provided known eigenvalues.
|
||
if test.evWant != nil {
|
||
used := make([]bool, n)
|
||
for i := first; i < n; i++ {
|
||
evGot := complex(wr[i], wi[i])
|
||
idx := -1
|
||
for k, evWant := range test.evWant {
|
||
if !used[k] && cmplx.Abs(evWant-evGot) < valTol {
|
||
idx = k
|
||
used[k] = true
|
||
break
|
||
}
|
||
}
|
||
if idx == -1 {
|
||
t.Errorf("%v: unexpected eigenvalue %v", prefix, evGot)
|
||
}
|
||
}
|
||
}
|
||
|
||
if first > 0 || (jobvl == lapack.None && jobvr == lapack.None) {
|
||
// No eigenvectors have been computed.
|
||
return
|
||
}
|
||
|
||
// Check that the columns of VL and VR are eigenvectors that correspond
|
||
// to the computed eigenvalues.
|
||
for k := 0; k < n; {
|
||
if wi[k] == 0 {
|
||
if jobvl == lapack.ComputeLeftEV {
|
||
ev := columnOf(vl, k)
|
||
if !isLeftEigenvectorOf(test.a, ev, nil, complex(wr[k], 0), vecTol) {
|
||
t.Errorf("%v: VL[:,%v] is not left real eigenvector",
|
||
prefix, k)
|
||
}
|
||
|
||
norm := floats.Norm(ev, 2)
|
||
if math.Abs(norm-1) >= defaultTol {
|
||
t.Errorf("%v: norm of left real eigenvector %v not equal to 1: got %v",
|
||
prefix, k, norm)
|
||
}
|
||
}
|
||
if jobvr == lapack.ComputeRightEV {
|
||
ev := columnOf(vr, k)
|
||
if !isRightEigenvectorOf(test.a, ev, nil, complex(wr[k], 0), vecTol) {
|
||
t.Errorf("%v: VR[:,%v] is not right real eigenvector",
|
||
prefix, k)
|
||
}
|
||
|
||
norm := floats.Norm(ev, 2)
|
||
if math.Abs(norm-1) >= defaultTol {
|
||
t.Errorf("%v: norm of right real eigenvector %v not equal to 1: got %v",
|
||
prefix, k, norm)
|
||
}
|
||
}
|
||
k++
|
||
} else {
|
||
if jobvl == lapack.ComputeLeftEV {
|
||
evre := columnOf(vl, k)
|
||
evim := columnOf(vl, k+1)
|
||
if !isLeftEigenvectorOf(test.a, evre, evim, complex(wr[k], wi[k]), vecTol) {
|
||
t.Errorf("%v: VL[:,%v:%v] is not left complex eigenvector",
|
||
prefix, k, k+1)
|
||
}
|
||
floats.Scale(-1, evim)
|
||
if !isLeftEigenvectorOf(test.a, evre, evim, complex(wr[k+1], wi[k+1]), vecTol) {
|
||
t.Errorf("%v: VL[:,%v:%v] is not left complex eigenvector",
|
||
prefix, k, k+1)
|
||
}
|
||
|
||
norm := math.Hypot(floats.Norm(evre, 2), floats.Norm(evim, 2))
|
||
if math.Abs(norm-1) > defaultTol {
|
||
t.Errorf("%v: norm of left complex eigenvector %v not equal to 1: got %v",
|
||
prefix, k, norm)
|
||
}
|
||
}
|
||
if jobvr == lapack.ComputeRightEV {
|
||
evre := columnOf(vr, k)
|
||
evim := columnOf(vr, k+1)
|
||
if !isRightEigenvectorOf(test.a, evre, evim, complex(wr[k], wi[k]), vecTol) {
|
||
t.Errorf("%v: VR[:,%v:%v] is not right complex eigenvector",
|
||
prefix, k, k+1)
|
||
}
|
||
floats.Scale(-1, evim)
|
||
if !isRightEigenvectorOf(test.a, evre, evim, complex(wr[k+1], wi[k+1]), vecTol) {
|
||
t.Errorf("%v: VR[:,%v:%v] is not right complex eigenvector",
|
||
prefix, k, k+1)
|
||
}
|
||
|
||
norm := math.Hypot(floats.Norm(evre, 2), floats.Norm(evim, 2))
|
||
if math.Abs(norm-1) > defaultTol {
|
||
t.Errorf("%v: norm of right complex eigenvector %v not equal to 1: got %v",
|
||
prefix, k, norm)
|
||
}
|
||
}
|
||
// We don't test whether the largest component is real
|
||
// because checking it is flaky due to rounding errors.
|
||
|
||
k += 2
|
||
}
|
||
}
|
||
}
|
||
|
||
func dgeevTestForAntisymRandom(n int, rnd *rand.Rand) dgeevTest {
|
||
a := NewAntisymRandom(n, rnd)
|
||
return dgeevTest{
|
||
a: a.Matrix(),
|
||
evWant: a.Eigenvalues(),
|
||
}
|
||
}
|