+++ /dev/null
-// Copyright ©2016 The Gonum Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package testlapack
-
-import (
- "fmt"
- "math/cmplx"
- "testing"
-
- "golang.org/x/exp/rand"
-
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/blas/blas64"
- "gonum.org/v1/gonum/lapack"
-)
-
-type Dtrexcer interface {
- Dtrexc(compq lapack.EVComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
-}
-
-func DtrexcTest(t *testing.T, impl Dtrexcer) {
- rnd := rand.New(rand.NewSource(1))
-
- for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
- for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
- for _, extra := range []int{0, 1, 11} {
- for cas := 0; cas < 100; cas++ {
- tmat := randomSchurCanonical(n, n+extra, rnd)
- ifst := rnd.Intn(n)
- ilst := rnd.Intn(n)
- testDtrexc(t, impl, compq, tmat, ifst, ilst, extra, rnd)
- }
- }
- }
- }
-
- for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
- for _, extra := range []int{0, 1, 11} {
- tmat := randomSchurCanonical(0, extra, rnd)
- testDtrexc(t, impl, compq, tmat, 0, 0, extra, rnd)
- }
- }
-}
-
-func testDtrexc(t *testing.T, impl Dtrexcer, compq lapack.EVComp, tmat blas64.General, ifst, ilst, extra int, rnd *rand.Rand) {
- const tol = 1e-13
-
- n := tmat.Rows
- fstSize, fstFirst := schurBlockSize(tmat, ifst)
- lstSize, lstFirst := schurBlockSize(tmat, ilst)
-
- tmatCopy := cloneGeneral(tmat)
-
- var wantq bool
- var q, qCopy blas64.General
- if compq == lapack.UpdateSchur {
- wantq = true
- q = eye(n, n+extra)
- qCopy = cloneGeneral(q)
- }
-
- work := nanSlice(n)
-
- ifstGot, ilstGot, ok := impl.Dtrexc(compq, n, tmat.Data, tmat.Stride, q.Data, q.Stride, ifst, ilst, work)
-
- prefix := fmt.Sprintf("Case compq=%v, n=%v, ifst=%v, nbf=%v, ilst=%v, nbl=%v, extra=%v",
- compq, n, ifst, fstSize, ilst, lstSize, extra)
-
- if !generalOutsideAllNaN(tmat) {
- t.Errorf("%v: out-of-range write to T", prefix)
- }
- if wantq && !generalOutsideAllNaN(q) {
- t.Errorf("%v: out-of-range write to Q", prefix)
- }
-
- if !ok {
- t.Logf("%v: Dtrexc returned ok=false", prefix)
- }
-
- // Check that the index of the first block was correctly updated (if
- // necessary).
- ifstWant := ifst
- if !fstFirst {
- ifstWant = ifst - 1
- }
- if ifstWant != ifstGot {
- t.Errorf("%v: unexpected ifst index. Want %v, got %v ", prefix, ifstWant, ifstGot)
- }
-
- // Check that the index of the last block is as expected when ok=true.
- // When ok=false, we don't know at which block the algorithm failed, so
- // we don't check.
- ilstWant := ilst
- if !lstFirst {
- ilstWant--
- }
- if ok {
- if ifstWant < ilstWant {
- // If the blocks are swapped backwards, these
- // adjustments are not necessary, the first row of the
- // last block will end up at ifst.
- switch {
- case fstSize == 2 && lstSize == 1:
- ilstWant--
- case fstSize == 1 && lstSize == 2:
- ilstWant++
- }
- }
- if ilstWant != ilstGot {
- t.Errorf("%v: unexpected ilst index. Want %v, got %v", prefix, ilstWant, ilstGot)
- }
- }
-
- if n <= 1 || ifstGot == ilstGot {
- // Too small matrix or no swapping.
- // Check that T was not modified.
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- if tmat.Data[i*tmat.Stride+j] != tmatCopy.Data[i*tmatCopy.Stride+j] {
- t.Errorf("%v: unexpected modification at T[%v,%v]", prefix, i, j)
- }
- }
- }
- if !wantq {
- return
- }
- // Check that Q was not modified.
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- if q.Data[i*q.Stride+j] != qCopy.Data[i*qCopy.Stride+j] {
- t.Errorf("%v: unexpected modification at Q[%v,%v]", prefix, i, j)
- }
- }
- }
- return
- }
-
- if !isSchurCanonicalGeneral(tmat) {
- t.Errorf("%v: T is not in Schur canonical form", prefix)
- }
-
- // Check that T was not modified except above the second subdiagonal in
- // rows and columns [modMin,modMax].
- modMin := min(ifstGot, ilstGot)
- modMax := max(ifstGot, ilstGot) + fstSize
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- if modMin <= i && i < modMax && j+1 >= i {
- continue
- }
- if modMin <= j && j < modMax && j+1 >= i {
- continue
- }
- diff := tmat.Data[i*tmat.Stride+j] - tmatCopy.Data[i*tmatCopy.Stride+j]
- if diff != 0 {
- t.Errorf("%v: unexpected modification at T[%v,%v]", prefix, i, j)
- }
- }
- }
-
- // Check that the block at ifstGot was delivered to ilstGot correctly.
- if fstSize == 1 {
- // 1×1 blocks are swapped exactly.
- got := tmat.Data[ilstGot*tmat.Stride+ilstGot]
- want := tmatCopy.Data[ifstGot*tmatCopy.Stride+ifstGot]
- if want != got {
- t.Errorf("%v: unexpected 1×1 block at T[%v,%v]. Want %v, got %v",
- prefix, want, got, ilstGot, ilstGot)
- }
- } else {
- // Check that the swapped 2×2 block is in Schur canonical form.
- a, b, c, d := extract2x2Block(tmat.Data[ilstGot*tmat.Stride+ilstGot:], tmat.Stride)
- if !isSchurCanonical(a, b, c, d) {
- t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, ilstGot, ilstGot)
- }
- ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
-
- // Check that the swapped 2×2 block has the same eigenvalues.
- // The block was originally located at T[ifstGot,ifstGot].
- a, b, c, d = extract2x2Block(tmatCopy.Data[ifstGot*tmatCopy.Stride+ifstGot:], tmatCopy.Stride)
- ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
- if cmplx.Abs(ev1Got-ev1Want) > tol {
- t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
- prefix, ilstGot, ilstGot, ev1Want, ev1Got)
- }
- if cmplx.Abs(ev2Got-ev2Want) > tol {
- t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
- prefix, ilstGot, ilstGot, ev2Want, ev2Got)
- }
- }
-
- if !wantq {
- return
- }
-
- if !isOrthonormal(q) {
- t.Errorf("%v: Q is not orthogonal", prefix)
- }
- // Check that Q is unchanged outside of columns [modMin,modMax].
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- if modMin <= j && j < modMax {
- continue
- }
- if q.Data[i*q.Stride+j]-qCopy.Data[i*qCopy.Stride+j] != 0 {
- t.Errorf("%v: unexpected modification of Q[%v,%v]", prefix, i, j)
- }
- }
- }
- // Check that Q^T TOrig Q == T.
- tq := eye(n, n)
- blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmatCopy, q, 0, tq)
- qtq := eye(n, n)
- blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tq, 0, qtq)
- if !equalApproxGeneral(qtq, tmat, tol) {
- t.Errorf("%v: Q^T (initial T) Q and (final T) are not equal", prefix)
- }
-}
OSDN Git Service
