--- /dev/null
+// Copyright ©2017 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 (
+ "testing"
+
+ "golang.org/x/exp/rand"
+
+ "gonum.org/v1/gonum/blas"
+ "gonum.org/v1/gonum/blas/blas64"
+ "gonum.org/v1/gonum/floats"
+ "gonum.org/v1/gonum/lapack"
+)
+
+type Dtgsjaer interface {
+ Dlanger
+ Dtgsja(jobU, jobV, jobQ lapack.GSVDJob, m, p, n, k, l int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64) (cycles int, ok bool)
+}
+
+func DtgsjaTest(t *testing.T, impl Dtgsjaer) {
+ rnd := rand.New(rand.NewSource(1))
+ for cas, test := range []struct {
+ m, p, n, k, l, lda, ldb, ldu, ldv, ldq int
+
+ ok bool
+ }{
+ {m: 5, p: 5, n: 5, k: 2, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 5, p: 5, n: 5, k: 4, l: 1, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 5, p: 5, n: 10, k: 2, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 5, p: 5, n: 10, k: 4, l: 1, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 5, p: 5, n: 10, k: 4, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 10, p: 5, n: 5, k: 2, l: 2, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 10, p: 5, n: 5, k: 4, l: 1, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 10, p: 10, n: 10, k: 5, l: 3, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 10, p: 10, n: 10, k: 6, l: 4, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
+ {m: 5, p: 5, n: 5, k: 2, l: 2, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
+ {m: 5, p: 5, n: 5, k: 4, l: 1, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
+ {m: 5, p: 5, n: 10, k: 2, l: 2, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+ {m: 5, p: 5, n: 10, k: 4, l: 1, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+ {m: 5, p: 5, n: 10, k: 4, l: 2, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
+ {m: 10, p: 5, n: 5, k: 2, l: 2, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
+ {m: 10, p: 5, n: 5, k: 4, l: 1, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
+ {m: 10, p: 10, n: 10, k: 5, l: 3, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
+ {m: 10, p: 10, n: 10, k: 6, l: 4, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
+ } {
+ m := test.m
+ p := test.p
+ n := test.n
+ k := test.k
+ l := test.l
+ lda := test.lda
+ if lda == 0 {
+ lda = n
+ }
+ ldb := test.ldb
+ if ldb == 0 {
+ ldb = n
+ }
+ ldu := test.ldu
+ if ldu == 0 {
+ ldu = m
+ }
+ ldv := test.ldv
+ if ldv == 0 {
+ ldv = p
+ }
+ ldq := test.ldq
+ if ldq == 0 {
+ ldq = n
+ }
+
+ a := blockedUpperTriGeneral(m, n, k, l, lda, true, rnd)
+ aCopy := cloneGeneral(a)
+ b := blockedUpperTriGeneral(p, n, k, l, ldb, false, rnd)
+ bCopy := cloneGeneral(b)
+
+ tola := float64(max(m, n)) * impl.Dlange(lapack.NormFrob, m, n, a.Data, a.Stride, nil) * dlamchE
+ tolb := float64(max(p, n)) * impl.Dlange(lapack.NormFrob, p, n, b.Data, b.Stride, nil) * dlamchE
+
+ alpha := make([]float64, n)
+ beta := make([]float64, n)
+
+ work := make([]float64, 2*n)
+
+ u := nanGeneral(m, m, ldu)
+ v := nanGeneral(p, p, ldv)
+ q := nanGeneral(n, n, ldq)
+
+ _, ok := impl.Dtgsja(lapack.GSVDUnit, lapack.GSVDUnit, lapack.GSVDUnit,
+ m, p, n, k, l,
+ a.Data, a.Stride,
+ b.Data, b.Stride,
+ tola, tolb,
+ alpha, beta,
+ u.Data, u.Stride,
+ v.Data, v.Stride,
+ q.Data, q.Stride,
+ work)
+
+ if !ok {
+ if test.ok {
+ t.Errorf("test %d unexpectedly did not converge", cas)
+ }
+ continue
+ }
+
+ // Check orthogonality of U, V and Q.
+ if !isOrthonormal(u) {
+ t.Errorf("test %d: U is not orthogonal\n%+v", cas, u)
+ }
+ if !isOrthonormal(v) {
+ t.Errorf("test %d: V is not orthogonal\n%+v", cas, v)
+ }
+ if !isOrthonormal(q) {
+ t.Errorf("test %d: Q is not orthogonal\n%+v", cas, q)
+ }
+
+ // Check C^2 + S^2 = I.
+ var elements []float64
+ if m-k-l >= 0 {
+ elements = alpha[k : k+l]
+ } else {
+ elements = alpha[k:m]
+ }
+ for i := range elements {
+ i += k
+ d := alpha[i]*alpha[i] + beta[i]*beta[i]
+ if !floats.EqualWithinAbsOrRel(d, 1, 1e-14, 1e-14) {
+ t.Errorf("test %d: alpha_%d^2 + beta_%d^2 != 1: got: %v", cas, i, i, d)
+ }
+ }
+
+ zeroR, d1, d2 := constructGSVDresults(n, p, m, k, l, a, b, alpha, beta)
+
+ // Check U^T*A*Q = D1*[ 0 R ].
+ uTmp := nanGeneral(m, n, n)
+ blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, aCopy, 0, uTmp)
+ uAns := nanGeneral(m, n, n)
+ blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uTmp, q, 0, uAns)
+
+ d10r := nanGeneral(m, n, n)
+ blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d1, zeroR, 0, d10r)
+
+ if !equalApproxGeneral(uAns, d10r, 1e-14) {
+ t.Errorf("test %d: U^T*A*Q != D1*[ 0 R ]\nU^T*A*Q:\n%+v\nD1*[ 0 R ]:\n%+v",
+ cas, uAns, d10r)
+ }
+
+ // Check V^T*B*Q = D2*[ 0 R ].
+ vTmp := nanGeneral(p, n, n)
+ blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, bCopy, 0, vTmp)
+ vAns := nanGeneral(p, n, n)
+ blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vTmp, q, 0, vAns)
+
+ d20r := nanGeneral(p, n, n)
+ blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d2, zeroR, 0, d20r)
+
+ if !equalApproxGeneral(vAns, d20r, 1e-14) {
+ t.Errorf("test %d: V^T*B*Q != D2*[ 0 R ]\nV^T*B*Q:\n%+v\nD2*[ 0 R ]:\n%+v",
+ cas, vAns, d20r)
+ }
+ }
+}
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