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228 lines
6.8 KiB
Go
228 lines
6.8 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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"math/rand"
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"testing"
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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type Dlaexcer interface {
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Dlaexc(wantq bool, n int, t []float64, ldt int, q []float64, ldq int, j1, n1, n2 int, work []float64) bool
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}
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func DlaexcTest(t *testing.T, impl Dlaexcer) {
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rnd := rand.New(rand.NewSource(1))
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for _, wantq := range []bool{true, false} {
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for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
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for _, extra := range []int{0, 1, 11} {
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for cas := 0; cas < 100; cas++ {
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j1 := rnd.Intn(n)
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n1 := min(rnd.Intn(3), n-j1)
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n2 := min(rnd.Intn(3), n-j1-n1)
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testDlaexc(t, impl, wantq, n, j1, n1, n2, extra, rnd)
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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 testDlaexc(t *testing.T, impl Dlaexcer, wantq bool, n, j1, n1, n2, extra int, rnd *rand.Rand) {
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const tol = 1e-14
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tmat := randomGeneral(n, n, n+extra, rnd)
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// Zero out the lower triangle.
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for i := 1; i < n; i++ {
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for j := 0; j < i; j++ {
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tmat.Data[i*tmat.Stride+j] = 0
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}
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}
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// Make any 2x2 diagonal block to be in Schur canonical form.
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if n1 == 2 {
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// Diagonal elements equal.
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tmat.Data[(j1+1)*tmat.Stride+j1+1] = tmat.Data[j1*tmat.Stride+j1]
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// Off-diagonal elements of opposite sign.
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c := rnd.NormFloat64()
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if math.Signbit(c) == math.Signbit(tmat.Data[j1*tmat.Stride+j1+1]) {
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c *= -1
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}
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tmat.Data[(j1+1)*tmat.Stride+j1] = c
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}
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if n2 == 2 {
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// Diagonal elements equal.
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tmat.Data[(j1+n1+1)*tmat.Stride+j1+n1+1] = tmat.Data[(j1+n1)*tmat.Stride+j1+n1]
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// Off-diagonal elements of opposite sign.
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c := rnd.NormFloat64()
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if math.Signbit(c) == math.Signbit(tmat.Data[(j1+n1)*tmat.Stride+j1+n1+1]) {
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c *= -1
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}
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tmat.Data[(j1+n1+1)*tmat.Stride+j1+n1] = c
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}
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tmatCopy := cloneGeneral(tmat)
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var q, qCopy blas64.General
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if wantq {
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q = eye(n, n+extra)
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qCopy = cloneGeneral(q)
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}
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work := nanSlice(n)
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ok := impl.Dlaexc(wantq, n, tmat.Data, tmat.Stride, q.Data, q.Stride, j1, n1, n2, work)
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prefix := fmt.Sprintf("Case n=%v, j1=%v, n1=%v, n2=%v, wantq=%v, extra=%v", n, j1, n1, n2, wantq, extra)
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if !generalOutsideAllNaN(tmat) {
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t.Errorf("%v: out-of-range write to T", prefix)
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}
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if wantq && !generalOutsideAllNaN(q) {
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t.Errorf("%v: out-of-range write to Q", prefix)
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}
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if !ok {
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if n1 == 1 && n2 == 1 {
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t.Errorf("%v: unexpected failure", prefix)
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} else {
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t.Logf("%v: Dlaexc returned false", prefix)
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}
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}
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if !ok || n1 == 0 || n2 == 0 || j1+n1 >= n {
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// Check that T is not modified.
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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if tmat.Data[i*tmat.Stride+j] != tmatCopy.Data[i*tmatCopy.Stride+j] {
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t.Errorf("%v: ok == false but T[%v,%v] modified", prefix, i, j)
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}
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}
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}
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if !wantq {
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return
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}
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// Check that Q is not modified.
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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if q.Data[i*q.Stride+j] != qCopy.Data[i*qCopy.Stride+j] {
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t.Errorf("%v: ok == false but Q[%v,%v] modified", prefix, i, j)
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}
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}
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}
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return
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}
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// Check that T is not modified outside of rows and columns [j1:j1+n1+n2].
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for i := 0; i < n; i++ {
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if j1 <= i && i < j1+n1+n2 {
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continue
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}
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for j := 0; j < n; j++ {
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if j1 <= j && j < j1+n1+n2 {
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continue
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}
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diff := tmat.Data[i*tmat.Stride+j] - tmatCopy.Data[i*tmatCopy.Stride+j]
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if diff != 0 {
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t.Errorf("%v: unexpected modification of T[%v,%v]", prefix, i, j)
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}
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}
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}
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if n1 == 1 {
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// 1×1 blocks are swapped exactly.
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got := tmat.Data[(j1+n2)*tmat.Stride+j1+n2]
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want := tmatCopy.Data[j1*tmatCopy.Stride+j1]
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if want != got {
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t.Errorf("%v: unexpected value of T[%v,%v]. Want %v, got %v", prefix, j1+n2, j1+n2, want, got)
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}
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} else {
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// Check that the swapped 2×2 block is in Schur canonical form.
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// The n1×n1 block is now located at T[j1+n2,j1+n2].
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a, b, c, d := extract2x2Block(tmat.Data[(j1+n2)*tmat.Stride+j1+n2:], tmat.Stride)
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if !isSchurCanonical(a, b, c, d) {
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t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, j1+n2, j1+n2)
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}
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ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
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// Check that the swapped 2×2 block has the same eigenvalues.
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// The n1×n1 block was originally located at T[j1,j1].
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a, b, c, d = extract2x2Block(tmatCopy.Data[j1*tmatCopy.Stride+j1:], tmatCopy.Stride)
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ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
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if cmplx.Abs(ev1Got-ev1Want) > tol {
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t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
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prefix, j1+n2, j1+n2, ev1Want, ev1Got)
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}
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if cmplx.Abs(ev2Got-ev2Want) > tol {
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t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
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prefix, j1+n2, j1+n2, ev2Want, ev2Got)
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}
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}
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if n2 == 1 {
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// 1×1 blocks are swapped exactly.
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got := tmat.Data[j1*tmat.Stride+j1]
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want := tmatCopy.Data[(j1+n1)*tmatCopy.Stride+j1+n1]
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if want != got {
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t.Errorf("%v: unexpected value of T[%v,%v]. Want %v, got %v", prefix, j1, j1, want, got)
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}
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} else {
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// Check that the swapped 2×2 block is in Schur canonical form.
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// The n2×n2 block is now located at T[j1,j1].
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a, b, c, d := extract2x2Block(tmat.Data[j1*tmat.Stride+j1:], tmat.Stride)
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if !isSchurCanonical(a, b, c, d) {
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t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, j1, j1)
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}
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ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
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// Check that the swapped 2×2 block has the same eigenvalues.
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// The n2×n2 block was originally located at T[j1+n1,j1+n1].
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a, b, c, d = extract2x2Block(tmatCopy.Data[(j1+n1)*tmatCopy.Stride+j1+n1:], tmatCopy.Stride)
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ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
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if cmplx.Abs(ev1Got-ev1Want) > tol {
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t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
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prefix, j1, j1, ev1Want, ev1Got)
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}
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if cmplx.Abs(ev2Got-ev2Want) > tol {
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t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
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prefix, j1, j1, ev2Want, ev2Got)
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}
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}
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if !wantq {
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return
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}
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if !isOrthonormal(q) {
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t.Errorf("%v: Q is not orthogonal", prefix)
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}
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// Check that Q is unchanged outside of columns [j1:j1+n1+n2].
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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if j1 <= j && j < j1+n1+n2 {
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continue
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}
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diff := q.Data[i*q.Stride+j] - qCopy.Data[i*qCopy.Stride+j]
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if diff != 0 {
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t.Errorf("%v: unexpected modification of Q[%v,%v]", prefix, i, j)
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}
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}
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}
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// Check that Q^T TOrig Q == T.
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tq := eye(n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmatCopy, q, 0, tq)
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qtq := eye(n, n)
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tq, 0, qtq)
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for i := 0; i < n; i++ {
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for j := 0; j < n; j++ {
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diff := qtq.Data[i*qtq.Stride+j] - tmat.Data[i*tmat.Stride+j]
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if math.Abs(diff) > tol {
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t.Errorf("%v: unexpected value of T[%v,%v]", prefix, i, j)
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}
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}
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}
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}
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