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// Copyright ©2021 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"
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
type Dgetc2er interface {
Dgetc2(n int, a []float64, lda int, ipiv, jpiv []int) (k int)
}
func Dgetc2Test(t *testing.T, impl Dgetc2er) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20} {
for _, lda := range []int{n, n + 5} {
dgetc2Test(t, impl, rnd, n, lda, false)
dgetc2Test(t, impl, rnd, n, lda, true)
}
}
}
func dgetc2Test(t *testing.T, impl Dgetc2er, rnd *rand.Rand, n, lda int, perturb bool) {
const tol = 1e-14
name := fmt.Sprintf("n=%v,lda=%v,perturb=%v", n, lda, perturb)
// Generate a random lower-triangular matrix with unit diagonal.
l := randomGeneral(n, n, max(1, n), rnd)
for i := 0; i < n; i++ {
l.Data[i*l.Stride+i] = 1
for j := i + 1; j < n; j++ {
l.Data[i*l.Stride+j] = 0
}
}
// Generate a random upper-triangular matrix.
u := randomGeneral(n, n, max(1, n), rnd)
for i := 0; i < n; i++ {
for j := 0; j < i; j++ {
u.Data[i*u.Stride+j] = 0
}
}
if perturb && n > 0 {
// Make U singular by randomly placing a zero on the diagonal.
i := rnd.Intn(n)
u.Data[i*u.Stride+i] = 0
}
// Construct A = L*U.
a := zeros(n, n, max(1, lda))
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, l, u, 0, a)
// Allocate slices for pivots and pre-fill them with invalid indices.
ipiv := make([]int, n)
jpiv := make([]int, n)
for i := 0; i < n; i++ {
ipiv[i] = -1
jpiv[i] = -1
}
// Call Dgetc2 to compute the LU decomposition.
lu := cloneGeneral(a)
k := impl.Dgetc2(n, lu.Data, lu.Stride, ipiv, jpiv)
if n == 0 {
return
}
if perturb && k < 0 {
t.Errorf("%v: expected matrix perturbation", name)
}
// Verify all indices have been set.
for i := 0; i < n; i++ {
if ipiv[i] < 0 {
t.Errorf("%v: ipiv[%d] is not set", name, i)
}
if jpiv[i] < 0 {
t.Errorf("%v: jpiv[%d] is not set", name, i)
}
}
// Construct L and U matrices from Dgetc2 output.
l = zeros(n, n, n)
u = zeros(n, n, n)
for i := 0; i < n; i++ {
for j := 0; j < i; j++ {
l.Data[i*l.Stride+j] = lu.Data[i*lu.Stride+j]
}
l.Data[i*l.Stride+i] = 1
for j := i; j < n; j++ {
u.Data[i*u.Stride+j] = lu.Data[i*lu.Stride+j]
}
}
diff := zeros(n, n, n)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, l, u, 0, diff)
// Apply permutation matrices P and Q to L*U.
for i := n - 1; i >= 0; i-- {
ipv := ipiv[i]
if ipv != i {
row1 := blas64.Vector{N: n, Data: diff.Data[i*diff.Stride:], Inc: 1}
row2 := blas64.Vector{N: n, Data: diff.Data[ipv*diff.Stride:], Inc: 1}
blas64.Swap(row1, row2)
}
jpv := jpiv[i]
if jpv != i {
col1 := blas64.Vector{N: n, Data: diff.Data[i:], Inc: diff.Stride}
col2 := blas64.Vector{N: n, Data: diff.Data[jpv:], Inc: diff.Stride}
blas64.Swap(col1, col2)
}
}
// Compute the residual |P*L*U*Q - A| and check that it is small.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
diff.Data[i*diff.Stride+j] -= a.Data[i*a.Stride+j]
}
}
resid := dlange(lapack.MaxColumnSum, n, n, diff.Data, diff.Stride)
if resid > tol || math.IsNaN(resid) {
t.Errorf("%v: unexpected result; resid=%v, want<=%v", name, resid, tol)
}
}
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