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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"
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dlantrer interface {
Dlanger
Dlantr(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, m, n int, a []float64, lda int, work []float64) float64
}
func DlantrTest(t *testing.T, impl Dlantrer) {
rnd := rand.New(rand.NewSource(1))
for _, m := range []int{0, 1, 2, 3, 4, 5, 10} {
for _, n := range []int{0, 1, 2, 3, 4, 5, 10} {
for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
if uplo == blas.Upper && m > n {
continue
}
if uplo == blas.Lower && n > m {
continue
}
for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
for _, lda := range []int{max(1, n), n + 3} {
dlantrTest(t, impl, rnd, uplo, diag, m, n, lda)
}
}
}
}
}
}
func dlantrTest(t *testing.T, impl Dlantrer, rnd *rand.Rand, uplo blas.Uplo, diag blas.Diag, m, n, lda int) {
const tol = 1e-14
// Generate a random triangular matrix. If the matrix has unit diagonal,
// don't set the diagonal elements to 1.
a := make([]float64, max(0, (m-1)*lda+n))
for i := range a {
a[i] = rnd.NormFloat64()
}
rowsum := make([]float64, m)
colsum := make([]float64, n)
var frobWant, maxabsWant float64
if diag == blas.Unit {
// Account for the unit diagonal.
for i := 0; i < min(m, n); i++ {
rowsum[i] = 1
colsum[i] = 1
}
frobWant = float64(min(m, n))
if min(m, n) > 0 {
maxabsWant = 1
}
}
if uplo == blas.Upper {
for i := 0; i < min(m, n); i++ {
start := i
if diag == blas.Unit {
start = i + 1
}
for j := start; j < n; j++ {
aij := 2*rnd.Float64() - 1
a[i*lda+j] = aij
rowsum[i] += math.Abs(aij)
colsum[j] += math.Abs(aij)
maxabsWant = math.Max(maxabsWant, math.Abs(aij))
frobWant += aij * aij
}
}
} else {
for i := 0; i < m; i++ {
end := i
if diag == blas.Unit {
end = i - 1
}
for j := 0; j <= min(end, n-1); j++ {
aij := 2*rnd.Float64() - 1
a[i*lda+j] = aij
rowsum[i] += math.Abs(aij)
colsum[j] += math.Abs(aij)
maxabsWant = math.Max(maxabsWant, math.Abs(aij))
frobWant += aij * aij
}
}
}
frobWant = math.Sqrt(frobWant)
var maxcolsumWant, maxrowsumWant float64
if n > 0 {
maxcolsumWant = floats.Max(colsum)
}
if m > 0 {
maxrowsumWant = floats.Max(rowsum)
}
aCopy := make([]float64, len(a))
copy(aCopy, a)
for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxColumnSum, lapack.MaxRowSum, lapack.Frobenius} {
name := fmt.Sprintf("norm=%v,uplo=%v,diag=%v,m=%v,n=%v,lda=%v", string(norm), string(uplo), string(diag), m, n, lda)
var work []float64
if norm == lapack.MaxColumnSum {
work = make([]float64, n)
}
normGot := impl.Dlantr(norm, uplo, diag, m, n, a, lda, work)
if !floats.Equal(a, aCopy) {
t.Fatalf("%v: unexpected modification of a", name)
}
if norm == lapack.MaxAbs {
// MaxAbs norm involves no floating-point computation,
// so we expect exact equality here.
if normGot != maxabsWant {
t.Errorf("%v: unexpected result; got %v, want %v", name, normGot, maxabsWant)
}
continue
}
var normWant float64
switch norm {
case lapack.MaxColumnSum:
normWant = maxcolsumWant
case lapack.MaxRowSum:
normWant = maxrowsumWant
case lapack.Frobenius:
normWant = frobWant
}
if math.Abs(normGot-normWant) >= tol {
t.Errorf("%v: unexpected result; got %v, want %v", name, normGot, normWant)
}
}
}
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