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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 Dgesver interface {
Dgesv(n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int) bool
Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) bool
}
func DgesvTest(t *testing.T, impl Dgesver) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 50, 100} {
for _, nrhs := range []int{0, 1, 2, 5} {
for _, lda := range []int{max(1, n), n + 5} {
for _, ldb := range []int{max(1, nrhs), nrhs + 5} {
dgesvTest(t, impl, rnd, n, nrhs, lda, ldb)
}
}
}
}
}
func dgesvTest(t *testing.T, impl Dgesver, rnd *rand.Rand, n, nrhs, lda, ldb int) {
const tol = 1e-15
name := fmt.Sprintf("n=%v,nrhs=%v,lda=%v,ldb=%v", n, nrhs, lda, ldb)
// Create a random system matrix A and the solution X.
a := randomGeneral(n, n, lda, rnd)
xWant := randomGeneral(n, nrhs, ldb, rnd)
// Compute the right hand side matrix B = A*X.
b := zeros(n, nrhs, ldb)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, a, xWant, 0, b)
// Allocate a slice for row pivots and fill it with invalid indices.
ipiv := make([]int, n)
for i := range ipiv {
ipiv[i] = -1
}
// Call Dgesv to solve A*X = B.
lu := cloneGeneral(a)
xGot := cloneGeneral(b)
ok := impl.Dgesv(n, nrhs, lu.Data, lu.Stride, ipiv, xGot.Data, xGot.Stride)
if !ok {
t.Errorf("%v: unexpected failure in Dgesv", name)
return
}
if n == 0 || nrhs == 0 {
return
}
// Check that all elements of ipiv have been set.
ipivSet := true
for _, ipv := range ipiv {
if ipv == -1 {
ipivSet = false
break
}
}
if !ipivSet {
t.Fatalf("%v: not all elements of ipiv set", name)
return
}
// Compute the reciprocal of the condition number of A from its LU
// decomposition before it's overwritten further below.
aInv := cloneGeneral(lu)
impl.Dgetri(n, aInv.Data, aInv.Stride, ipiv, make([]float64, n), n)
ainvnorm := dlange(lapack.MaxColumnSum, n, n, aInv.Data, aInv.Stride)
anorm := dlange(lapack.MaxColumnSum, n, n, a.Data, a.Stride)
rcond := 1 / anorm / ainvnorm
// Reconstruct matrix A from factors and compute residual.
//
// Extract L and U from lu.
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]
}
}
// Compute L*U.
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, l, u, 0, lu)
// Apply P to L*U.
for i := n - 1; i >= 0; i-- {
ip := ipiv[i]
if ip == i {
continue
}
row1 := blas64.Vector{N: n, Data: lu.Data[i*lu.Stride:], Inc: 1}
row2 := blas64.Vector{N: n, Data: lu.Data[ip*lu.Stride:], Inc: 1}
blas64.Swap(row1, row2)
}
// Compute P*L*U - A.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
lu.Data[i*lu.Stride+j] -= a.Data[i*a.Stride+j]
}
}
// Compute the residual |P*L*U - A|.
resid := dlange(lapack.MaxColumnSum, n, n, lu.Data, lu.Stride)
resid /= float64(n) * anorm
if resid > tol || math.IsNaN(resid) {
t.Errorf("%v: residual |P*L*U - A| is too large, got %v, want <= %v", name, resid, tol)
}
// Compute residual of the computed solution.
//
// Compute B - A*X.
blas64.Gemm(blas.NoTrans, blas.NoTrans, -1, a, xGot, 1, b)
// Compute the maximum over the number of right hand sides of |B - A*X| / (|A| * |X|).
resid = 0
for j := 0; j < nrhs; j++ {
bnorm := blas64.Asum(blas64.Vector{N: n, Data: b.Data[j:], Inc: b.Stride})
xnorm := blas64.Asum(blas64.Vector{N: n, Data: xGot.Data[j:], Inc: xGot.Stride})
resid = math.Max(resid, bnorm/anorm/xnorm)
}
if resid > tol || math.IsNaN(resid) {
t.Errorf("%v: residual |B - A*X| is too large, got %v, want <= %v", name, resid, tol)
}
// Compare the computed solution with the generated exact solution.
//
// Compute X - XWANT.
for i := 0; i < n; i++ {
for j := 0; j < nrhs; j++ {
xGot.Data[i*xGot.Stride+j] -= xWant.Data[i*xWant.Stride+j]
}
}
// Compute the maximum of |X - XWANT|/|XWANT| over all the vectors X and XWANT.
resid = 0
for j := 0; j < nrhs; j++ {
xnorm := dlange(lapack.MaxAbs, n, 1, xWant.Data[j:], xWant.Stride)
diff := dlange(lapack.MaxAbs, n, 1, xGot.Data[j:], xGot.Stride)
resid = math.Max(resid, diff/xnorm*rcond)
}
if resid > tol || math.IsNaN(resid) {
t.Errorf("%v: residual |X-XWANT| is too large, got %v, want <= %v", name, resid, tol)
}
}
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