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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 Dgetf2er interface {
Dgetf2(m, n int, a []float64, lda int, ipiv []int) bool
}
func Dgetf2Test(t *testing.T, impl Dgetf2er) {
rnd := rand.New(rand.NewSource(1))
for _, test := range []struct {
m, n, lda int
}{
{10, 10, 0},
{10, 5, 0},
{10, 5, 0},
{10, 10, 20},
{5, 10, 20},
{10, 5, 20},
} {
m := test.m
n := test.n
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)
mn := min(m, n)
ipiv := make([]int, mn)
for i := range ipiv {
ipiv[i] = rnd.Int()
}
ok := impl.Dgetf2(m, n, a, lda, ipiv)
checkPLU(t, ok, m, n, lda, ipiv, a, aCopy, 1e-14, true)
}
// Test with singular matrices (random matrices are almost surely non-singular).
for _, test := range []struct {
m, n, lda int
a []float64
}{
{
m: 2,
n: 2,
lda: 2,
a: []float64{
1, 0,
0, 0,
},
},
{
m: 2,
n: 2,
lda: 2,
a: []float64{
1, 5,
2, 10,
},
},
{
m: 3,
n: 3,
lda: 3,
// row 3 = row1 + 2 * row2
a: []float64{
1, 5, 7,
2, 10, -3,
5, 25, 1,
},
},
{
m: 3,
n: 4,
lda: 4,
// row 3 = row1 + 2 * row2
a: []float64{
1, 5, 7, 9,
2, 10, -3, 11,
5, 25, 1, 31,
},
},
} {
if impl.Dgetf2(test.m, test.n, test.a, test.lda, make([]int, min(test.m, test.n))) {
t.Log("Returned ok with singular matrix.")
}
}
}
// checkPLU checks that the PLU factorization contained in factorize matches
// the original matrix contained in original.
func checkPLU(t *testing.T, ok bool, m, n, lda int, ipiv []int, factorized, original []float64, tol float64, print bool) {
var hasZeroDiagonal bool
for i := 0; i < min(m, n); i++ {
if factorized[i*lda+i] == 0 {
hasZeroDiagonal = true
break
}
}
if hasZeroDiagonal && ok {
t.Error("Has a zero diagonal but returned ok")
}
if !hasZeroDiagonal && !ok {
t.Error("Non-zero diagonal but returned !ok")
}
// Check that the LU decomposition is correct.
mn := min(m, n)
l := make([]float64, m*mn)
ldl := mn
u := make([]float64, mn*n)
ldu := n
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
v := factorized[i*lda+j]
switch {
case i == j:
l[i*ldl+i] = 1
u[i*ldu+i] = v
case i > j:
l[i*ldl+j] = v
case i < j:
u[i*ldu+j] = v
}
}
}
LU := blas64.General{
Rows: m,
Cols: n,
Stride: n,
Data: make([]float64, m*n),
}
U := blas64.General{
Rows: mn,
Cols: n,
Stride: ldu,
Data: u,
}
L := blas64.General{
Rows: m,
Cols: mn,
Stride: ldl,
Data: l,
}
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, U, 0, LU)
p := make([]float64, m*m)
ldp := m
for i := 0; i < m; i++ {
p[i*ldp+i] = 1
}
for i := len(ipiv) - 1; i >= 0; i-- {
v := ipiv[i]
blas64.Swap(blas64.Vector{N: m, Inc: 1, Data: p[i*ldp:]},
blas64.Vector{N: m, Inc: 1, Data: p[v*ldp:]})
}
P := blas64.General{
Rows: m,
Cols: m,
Stride: m,
Data: p,
}
aComp := blas64.General{
Rows: m,
Cols: n,
Stride: lda,
Data: make([]float64, m*lda),
}
copy(aComp.Data, factorized)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, P, LU, 0, aComp)
if !floats.EqualApprox(aComp.Data, original, tol) {
if print {
t.Errorf("PLU multiplication does not match original matrix.\nWant: %v\nGot: %v", original, aComp.Data)
return
}
t.Error("PLU multiplication does not match original matrix.")
}
}
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