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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 (
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
)
type Dgelser interface {
Dgels(trans blas.Transpose, m, n, nrhs int, a []float64, lda int, b []float64, ldb int, work []float64, lwork int) bool
}
func DgelsTest(t *testing.T, impl Dgelser) {
rnd := rand.New(rand.NewSource(1))
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
for _, test := range []struct {
m, n, nrhs, lda, ldb int
}{
{3, 4, 5, 0, 0},
{3, 5, 4, 0, 0},
{4, 3, 5, 0, 0},
{4, 5, 3, 0, 0},
{5, 3, 4, 0, 0},
{5, 4, 3, 0, 0},
{3, 4, 5, 10, 20},
{3, 5, 4, 10, 20},
{4, 3, 5, 10, 20},
{4, 5, 3, 10, 20},
{5, 3, 4, 10, 20},
{5, 4, 3, 10, 20},
{3, 4, 5, 20, 10},
{3, 5, 4, 20, 10},
{4, 3, 5, 20, 10},
{4, 5, 3, 20, 10},
{5, 3, 4, 20, 10},
{5, 4, 3, 20, 10},
{200, 300, 400, 0, 0},
{200, 400, 300, 0, 0},
{300, 200, 400, 0, 0},
{300, 400, 200, 0, 0},
{400, 200, 300, 0, 0},
{400, 300, 200, 0, 0},
{200, 300, 400, 500, 600},
{200, 400, 300, 500, 600},
{300, 200, 400, 500, 600},
{300, 400, 200, 500, 600},
{400, 200, 300, 500, 600},
{400, 300, 200, 500, 600},
{200, 300, 400, 600, 500},
{200, 400, 300, 600, 500},
{300, 200, 400, 600, 500},
{300, 400, 200, 600, 500},
{400, 200, 300, 600, 500},
{400, 300, 200, 600, 500},
} {
m := test.m
n := test.n
nrhs := test.nrhs
lda := test.lda
if lda == 0 {
lda = n
}
a := make([]float64, m*lda)
for i := range a {
a[i] = rnd.Float64()
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
// Size of b is the same trans or no trans, because the number of rows
// has to be the max of (m,n).
mb := max(m, n)
nb := nrhs
ldb := test.ldb
if ldb == 0 {
ldb = nb
}
b := make([]float64, mb*ldb)
for i := range b {
b[i] = rnd.Float64()
}
bCopy := make([]float64, len(b))
copy(bCopy, b)
// Find optimal work length.
work := make([]float64, 1)
impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, -1)
// Perform linear solve
work = make([]float64, int(work[0]))
lwork := len(work)
for i := range work {
work[i] = rnd.Float64()
}
impl.Dgels(trans, m, n, nrhs, a, lda, b, ldb, work, lwork)
// Check that the answer is correct by comparing to the normal equations.
aMat := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, len(aCopy)),
}
copy(aMat.Data, aCopy)
szAta := n
if trans == blas.Trans {
szAta = m
}
aTA := blas64.General{
Rows: szAta,
Cols: szAta,
Stride: szAta,
Data: make([]float64, szAta*szAta),
}
// Compute Aᵀ * A if notrans and A * Aᵀ otherwise.
if trans == blas.NoTrans {
blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, aMat, 0, aTA)
} else {
blas64.Gemm(blas.NoTrans, blas.Trans, 1, aMat, aMat, 0, aTA)
}
// Multiply by X.
X := blas64.General{
Rows: szAta,
Cols: nrhs,
Stride: ldb,
Data: b,
}
ans := blas64.General{
Rows: aTA.Rows,
Cols: X.Cols,
Stride: X.Cols,
Data: make([]float64, aTA.Rows*X.Cols),
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aTA, X, 0, ans)
B := blas64.General{
Rows: szAta,
Cols: nrhs,
Stride: ldb,
Data: make([]float64, len(bCopy)),
}
copy(B.Data, bCopy)
var ans2 blas64.General
if trans == blas.NoTrans {
ans2 = blas64.General{
Rows: aMat.Cols,
Cols: B.Cols,
Stride: B.Cols,
Data: make([]float64, aMat.Cols*B.Cols),
}
} else {
ans2 = blas64.General{
Rows: aMat.Rows,
Cols: B.Cols,
Stride: B.Cols,
Data: make([]float64, aMat.Rows*B.Cols),
}
}
// Compute Aᵀ B if Trans or A * B otherwise
if trans == blas.NoTrans {
blas64.Gemm(blas.Trans, blas.NoTrans, 1, aMat, B, 0, ans2)
} else {
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, B, 0, ans2)
}
if !floats.EqualApprox(ans.Data, ans2.Data, 1e-12) {
t.Errorf("Normal equations not satisfied")
}
}
}
}
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