mirror of
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117 lines
3.6 KiB
Go
117 lines
3.6 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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"testing"
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"golang.org/x/exp/rand"
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)
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type Dlanv2er interface {
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Dlanv2(a, b, c, d float64) (aa, bb, cc, dd float64, rt1r, rt1i, rt2r, rt2i float64, cs, sn float64)
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}
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func Dlanv2Test(t *testing.T, impl Dlanv2er) {
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rnd := rand.New(rand.NewSource(1))
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t.Run("UpperTriangular", func(t *testing.T) {
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for i := 0; i < 10; i++ {
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a := rnd.NormFloat64()
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b := rnd.NormFloat64()
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d := rnd.NormFloat64()
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dlanv2Test(t, impl, a, b, 0, d)
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}
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})
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t.Run("LowerTriangular", func(t *testing.T) {
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for i := 0; i < 10; i++ {
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a := rnd.NormFloat64()
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c := rnd.NormFloat64()
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d := rnd.NormFloat64()
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dlanv2Test(t, impl, a, 0, c, d)
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}
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})
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t.Run("StandardSchur", func(t *testing.T) {
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for i := 0; i < 10; i++ {
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a := rnd.NormFloat64()
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b := rnd.NormFloat64()
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c := rnd.NormFloat64()
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if math.Signbit(b) == math.Signbit(c) {
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c = -c
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}
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dlanv2Test(t, impl, a, b, c, a)
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}
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})
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t.Run("General", func(t *testing.T) {
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for i := 0; i < 100; i++ {
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a := rnd.NormFloat64()
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b := rnd.NormFloat64()
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c := rnd.NormFloat64()
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d := rnd.NormFloat64()
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dlanv2Test(t, impl, a, b, c, d)
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}
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// https://github.com/Reference-LAPACK/lapack/issues/263
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dlanv2Test(t, impl, 0, 1, -1, math.Nextafter(0, 1))
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})
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}
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func dlanv2Test(t *testing.T, impl Dlanv2er, a, b, c, d float64) {
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aa, bb, cc, dd, rt1r, rt1i, rt2r, rt2i, cs, sn := impl.Dlanv2(a, b, c, d)
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mat := fmt.Sprintf("[%v %v; %v %v]", a, b, c, d)
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if cc == 0 {
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// The eigenvalues are real, so check that the imaginary parts
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// are zero.
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if rt1i != 0 || rt2i != 0 {
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t.Errorf("Unexpected complex eigenvalues for %v", mat)
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}
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} else {
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// The eigenvalues are complex, so check that documented
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// conditions hold.
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if aa != dd {
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t.Errorf("Diagonal elements not equal for %v: got [%v %v]", mat, aa, dd)
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}
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if bb*cc >= 0 {
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t.Errorf("Non-diagonal elements have the same sign for %v: got [%v %v]", mat, bb, cc)
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} else {
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// Compute the absolute value of the imaginary part.
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im := math.Sqrt(-bb * cc)
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// Check that ±im is close to one of the returned
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// imaginary parts.
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if math.Abs(rt1i-im) > 1e-14 && math.Abs(rt1i+im) > 1e-14 {
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t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt1i, im, -im)
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}
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if math.Abs(rt2i-im) > 1e-14 && math.Abs(rt2i+im) > 1e-14 {
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t.Errorf("Unexpected imaginary part of eigenvalue for %v: got %v, want %v or %v", mat, rt2i, im, -im)
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}
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}
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}
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// Check that the returned real parts are consistent.
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if rt1r != aa && rt1r != dd {
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t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt1r, aa, dd)
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}
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if rt2r != aa && rt2r != dd {
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t.Errorf("Unexpected real part of eigenvalue for %v: got %v, want %v or %v", mat, rt2r, aa, dd)
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}
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// Check that the columns of the orthogonal matrix have unit norm.
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if math.Abs(math.Hypot(cs, sn)-1) > 1e-14 {
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t.Errorf("Unexpected unitary matrix for %v: got cs %v, sn %v", mat, cs, sn)
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}
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// Re-compute the original matrix [a b; c d] from its factorization.
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gota := cs*(aa*cs-bb*sn) - sn*(cc*cs-dd*sn)
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gotb := cs*(aa*sn+bb*cs) - sn*(cc*sn+dd*cs)
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gotc := sn*(aa*cs-bb*sn) + cs*(cc*cs-dd*sn)
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gotd := sn*(aa*sn+bb*cs) + cs*(cc*sn+dd*cs)
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if math.Abs(gota-a) > 1e-14 ||
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math.Abs(gotb-b) > 1e-14 ||
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math.Abs(gotc-c) > 1e-14 ||
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math.Abs(gotd-d) > 1e-14 {
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t.Errorf("Unexpected factorization: got [%v %v; %v %v], want [%v %v; %v %v]", gota, gotb, gotc, gotd, a, b, c, d)
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}
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}
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