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// Copyright ©2015 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"
"sort"
"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/floats/scalar"
)
type Dbdsqrer interface {
Dbdsqr(uplo blas.Uplo, n, ncvt, nru, ncc int, d, e, vt []float64, ldvt int, u []float64, ldu int, c []float64, ldc int, work []float64) (ok bool)
}
func DbdsqrTest(t *testing.T, impl Dbdsqrer) {
rnd := rand.New(rand.NewSource(1))
bi := blas64.Implementation()
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, test := range []struct {
n, ncvt, nru, ncc, ldvt, ldu, ldc int
}{
{5, 5, 5, 5, 0, 0, 0},
{10, 10, 10, 10, 0, 0, 0},
{10, 11, 12, 13, 0, 0, 0},
{20, 13, 12, 11, 0, 0, 0},
{5, 5, 5, 5, 6, 7, 8},
{10, 10, 10, 10, 30, 40, 50},
{10, 12, 11, 13, 30, 40, 50},
{20, 12, 13, 11, 30, 40, 50},
{130, 130, 130, 500, 900, 900, 500},
} {
for cas := 0; cas < 10; cas++ {
n := test.n
ncvt := test.ncvt
nru := test.nru
ncc := test.ncc
ldvt := test.ldvt
ldu := test.ldu
ldc := test.ldc
if ldvt == 0 {
ldvt = max(1, ncvt)
}
if ldu == 0 {
ldu = max(1, n)
}
if ldc == 0 {
ldc = max(1, ncc)
}
d := make([]float64, n)
for i := range d {
d[i] = rnd.NormFloat64()
}
e := make([]float64, n-1)
for i := range e {
e[i] = rnd.NormFloat64()
}
dCopy := make([]float64, len(d))
copy(dCopy, d)
eCopy := make([]float64, len(e))
copy(eCopy, e)
work := make([]float64, 4*(n-1))
for i := range work {
work[i] = rnd.NormFloat64()
}
// First test the decomposition of the bidiagonal matrix. Set
// pt and u equal to I with the correct size. At the result
// of Dbdsqr, p and u will contain the data of Pᵀ and Q, which
// will be used in the next step to test the multiplication
// with Q and VT.
q := make([]float64, n*n)
ldq := n
pt := make([]float64, n*n)
ldpt := n
for i := 0; i < n; i++ {
q[i*ldq+i] = 1
}
for i := 0; i < n; i++ {
pt[i*ldpt+i] = 1
}
ok := impl.Dbdsqr(uplo, n, n, n, 0, d, e, pt, ldpt, q, ldq, nil, 1, work)
isUpper := uplo == blas.Upper
errStr := fmt.Sprintf("isUpper = %v, n = %v, ncvt = %v, nru = %v, ncc = %v", isUpper, n, ncvt, nru, ncc)
if !ok {
t.Errorf("Unexpected Dbdsqr failure: %s", errStr)
}
bMat := constructBidiagonal(uplo, n, dCopy, eCopy)
sMat := constructBidiagonal(uplo, n, d, e)
tmp := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
ansMat := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, q, ldq, sMat.Data, sMat.Stride, 0, tmp.Data, tmp.Stride)
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, tmp.Data, tmp.Stride, pt, ldpt, 0, ansMat.Data, ansMat.Stride)
same := true
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
if !scalar.EqualWithinAbsOrRel(ansMat.Data[i*ansMat.Stride+j], bMat.Data[i*bMat.Stride+j], 1e-8, 1e-8) {
same = false
}
}
}
if !same {
t.Errorf("Bidiagonal mismatch. %s", errStr)
}
if !sort.IsSorted(sort.Reverse(sort.Float64Slice(d))) {
t.Errorf("D is not sorted. %s", errStr)
}
// The above computed the real P and Q. Now input data for Vᵀ,
// U, and C to check that the multiplications happen properly.
dAns := make([]float64, len(d))
copy(dAns, d)
eAns := make([]float64, len(e))
copy(eAns, e)
u := make([]float64, nru*ldu)
for i := range u {
u[i] = rnd.NormFloat64()
}
uCopy := make([]float64, len(u))
copy(uCopy, u)
vt := make([]float64, n*ldvt)
for i := range vt {
vt[i] = rnd.NormFloat64()
}
vtCopy := make([]float64, len(vt))
copy(vtCopy, vt)
c := make([]float64, n*ldc)
for i := range c {
c[i] = rnd.NormFloat64()
}
cCopy := make([]float64, len(c))
copy(cCopy, c)
// Reset input data
copy(d, dCopy)
copy(e, eCopy)
impl.Dbdsqr(uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work)
// Check result.
if !floats.EqualApprox(d, dAns, 1e-14) {
t.Errorf("D mismatch second time. %s", errStr)
}
if !floats.EqualApprox(e, eAns, 1e-14) {
t.Errorf("E mismatch second time. %s", errStr)
}
ans := make([]float64, len(vtCopy))
copy(ans, vtCopy)
ldans := ldvt
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, ncvt, n, 1, pt, ldpt, vtCopy, ldvt, 0, ans, ldans)
if !floats.EqualApprox(ans, vt, 1e-10) {
t.Errorf("Vt result mismatch. %s", errStr)
}
ans = make([]float64, len(uCopy))
copy(ans, uCopy)
ldans = ldu
bi.Dgemm(blas.NoTrans, blas.NoTrans, nru, n, n, 1, uCopy, ldu, q, ldq, 0, ans, ldans)
if !floats.EqualApprox(ans, u, 1e-10) {
t.Errorf("U result mismatch. %s", errStr)
}
ans = make([]float64, len(cCopy))
copy(ans, cCopy)
ldans = ldc
bi.Dgemm(blas.Trans, blas.NoTrans, n, ncc, n, 1, q, ldq, cCopy, ldc, 0, ans, ldans)
if !floats.EqualApprox(ans, c, 1e-10) {
t.Errorf("C result mismatch. %s", errStr)
}
}
}
}
}
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