--- /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)
+ }
+}
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