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lapack: imported lapack as a subtree
This commit is contained in:
Brendan Tracey
173
lapack/testlapack/dggsvd3.go
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173
lapack/testlapack/dggsvd3.go
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// Copyright ©2017 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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"math/rand"
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"testing"
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"github.com/gonum/blas"
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"github.com/gonum/blas/blas64"
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"github.com/gonum/floats"
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"github.com/gonum/lapack"
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)
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type Dggsvd3er interface {
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Dggsvd3(jobU, jobV, jobQ lapack.GSVDJob, m, n, p int, a []float64, lda int, b []float64, ldb int, alpha, beta, u []float64, ldu int, v []float64, ldv int, q []float64, ldq int, work []float64, lwork int, iwork []int) (k, l int, ok bool)
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}
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func Dggsvd3Test(t *testing.T, impl Dggsvd3er) {
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rnd := rand.New(rand.NewSource(1))
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for cas, test := range []struct {
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m, p, n, lda, ldb, ldu, ldv, ldq int
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ok bool
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}{
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{m: 3, p: 3, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 5, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 5, p: 5, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 10, p: 5, n: 5, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 10, p: 10, n: 10, lda: 0, ldb: 0, ldu: 0, ldv: 0, ldq: 0, ok: true},
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{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
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{m: 5, p: 5, n: 5, lda: 10, ldb: 10, ldu: 10, ldv: 10, ldq: 10, ok: true},
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{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
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{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
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{m: 5, p: 5, n: 10, lda: 20, ldb: 20, ldu: 10, ldv: 10, ldq: 20, ok: true},
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{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
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{m: 10, p: 5, n: 5, lda: 10, ldb: 10, ldu: 20, ldv: 10, ldq: 10, ok: true},
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{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
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{m: 10, p: 10, n: 10, lda: 20, ldb: 20, ldu: 20, ldv: 20, ldq: 20, ok: true},
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} {
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m := test.m
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p := test.p
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n := test.n
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lda := test.lda
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if lda == 0 {
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lda = n
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}
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ldb := test.ldb
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if ldb == 0 {
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ldb = n
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}
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ldu := test.ldu
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if ldu == 0 {
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ldu = m
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}
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ldv := test.ldv
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if ldv == 0 {
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ldv = p
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}
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ldq := test.ldq
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if ldq == 0 {
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ldq = n
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}
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a := randomGeneral(m, n, lda, rnd)
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aCopy := cloneGeneral(a)
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b := randomGeneral(p, n, ldb, rnd)
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bCopy := cloneGeneral(b)
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alpha := make([]float64, n)
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beta := make([]float64, n)
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u := nanGeneral(m, m, ldu)
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v := nanGeneral(p, p, ldv)
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q := nanGeneral(n, n, ldq)
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iwork := make([]int, n)
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work := []float64{0}
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impl.Dggsvd3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
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m, n, p,
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a.Data, a.Stride,
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b.Data, b.Stride,
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alpha, beta,
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u.Data, u.Stride,
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v.Data, v.Stride,
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q.Data, q.Stride,
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work, -1, iwork)
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lwork := int(work[0])
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work = make([]float64, lwork)
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k, l, ok := impl.Dggsvd3(lapack.GSVDU, lapack.GSVDV, lapack.GSVDQ,
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m, n, p,
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a.Data, a.Stride,
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b.Data, b.Stride,
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alpha, beta,
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u.Data, u.Stride,
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v.Data, v.Stride,
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q.Data, q.Stride,
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work, lwork, iwork)
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if !ok {
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if test.ok {
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t.Errorf("test %d unexpectedly did not converge", cas)
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}
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continue
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}
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// Check orthogonality of U, V and Q.
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if !isOrthonormal(u) {
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t.Errorf("test %d: U is not orthogonal\n%+v", cas, u)
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}
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if !isOrthonormal(v) {
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t.Errorf("test %d: V is not orthogonal\n%+v", cas, v)
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}
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if !isOrthonormal(q) {
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t.Errorf("test %d: Q is not orthogonal\n%+v", cas, q)
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}
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// Check C^2 + S^2 = I.
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var elements []float64
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if m-k-l >= 0 {
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elements = alpha[k : k+l]
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} else {
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elements = alpha[k:m]
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}
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for i := range elements {
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i += k
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d := alpha[i]*alpha[i] + beta[i]*beta[i]
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if !floats.EqualWithinAbsOrRel(d, 1, 1e-14, 1e-14) {
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t.Errorf("test %d: alpha_%d^2 + beta_%d^2 != 1: got: %v", cas, i, i, d)
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}
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}
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zeroR, d1, d2 := constructGSVDresults(n, p, m, k, l, a, b, alpha, beta)
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// Check U^T*A*Q = D1*[ 0 R ].
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uTmp := nanGeneral(m, n, n)
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, u, aCopy, 0, uTmp)
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uAns := nanGeneral(m, n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, uTmp, q, 0, uAns)
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d10r := nanGeneral(m, n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d1, zeroR, 0, d10r)
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if !equalApproxGeneral(uAns, d10r, 1e-14) {
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t.Errorf("test %d: U^T*A*Q != D1*[ 0 R ]\nU^T*A*Q:\n%+v\nD1*[ 0 R ]:\n%+v",
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cas, uAns, d10r)
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}
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// Check V^T*B*Q = D2*[ 0 R ].
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vTmp := nanGeneral(p, n, n)
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blas64.Gemm(blas.Trans, blas.NoTrans, 1, v, bCopy, 0, vTmp)
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vAns := nanGeneral(p, n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vTmp, q, 0, vAns)
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d20r := nanGeneral(p, n, n)
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blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d2, zeroR, 0, d20r)
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if !equalApproxGeneral(vAns, d20r, 1e-14) {
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t.Errorf("test %d: V^T*B*Q != D2*[ 0 R ]\nV^T*B*Q:\n%+v\nD2*[ 0 R ]:\n%+v",
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cas, vAns, d20r)
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}
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}
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}
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