--- /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/lapack"
+)
+
+type Dggsvp3er interface {
+ Dlanger
+ Dggsvp3(jobU, jobV, jobQ lapack.GSVDJob, m, p, n int, a []float64, lda int, b []float64, ldb int, tola, tolb float64, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, iwork []int, tau, work []float64, lwork int) (k, l int)
+}
+
+func Dggsvp3Test(t *testing.T, impl Dggsvp3er) {
+ rnd := rand.New(rand.NewSource(1))
+ for cas, test := range []struct {
+ m, p, n, lda, ldb, ldu, ldv, ldq int
+ }{
+ {m: 3, p: 3, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0},
+ {m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10},
+ {m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10},
+ {m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
+ {m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
+ {m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20},
+ {m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10},
+ {m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10},
+ {m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20},
+ {m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20},
+ } {
+ m := test.m
+ p := test.p
+ n := test.n
+ 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 := randomGeneral(m, n, lda, rnd)
+ aCopy := cloneGeneral(a)
+ b := randomGeneral(p, n, ldb, 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
+
+ u := nanGeneral(m, m, ldu)
+ v := nanGeneral(p, p, ldv)
+ q := nanGeneral(n, n, ldq)
+
+ iwork := make([]int, n)
+ tau := make([]float64, n)
+
+ work := []float64{0}
+ impl.Dggsvp3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
+ m, p, n,
+ a.Data, a.Stride,
+ b.Data, b.Stride,
+ tola, tolb,
+ u.Data, u.Stride,
+ v.Data, v.Stride,
+ q.Data, q.Stride,
+ iwork, tau,
+ work, -1)
+
+ lwork := int(work[0])
+ work = make([]float64, lwork)
+
+ k, l := impl.Dggsvp3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
+ m, p, n,
+ a.Data, a.Stride,
+ b.Data, b.Stride,
+ tola, tolb,
+ u.Data, u.Stride,
+ v.Data, v.Stride,
+ q.Data, q.Stride,
+ iwork, tau,
+ work, lwork)
+
+ // 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)
+ }
+
+ zeroA, zeroB := constructGSVPresults(n, p, m, k, l, a, b)
+
+ // Check U^T*A*Q = [ 0 RA ].
+ 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)
+
+ if !equalApproxGeneral(uAns, zeroA, 1e-14) {
+ t.Errorf("test %d: U^T*A*Q != [ 0 RA ]\nU^T*A*Q:\n%+v\n[ 0 RA ]:\n%+v",
+ cas, uAns, zeroA)
+ }
+
+ // Check V^T*B*Q = [ 0 RB ].
+ 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)
+
+ if !equalApproxGeneral(vAns, zeroB, 1e-14) {
+ t.Errorf("test %d: V^T*B*Q != [ 0 RB ]\nV^T*B*Q:\n%+v\n[ 0 RB ]:\n%+v",
+ cas, vAns, zeroB)
+ }
+ }
+}
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