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// Copyright ©2019 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 Dlansber interface {
Dlansb(norm lapack.MatrixNorm, uplo blas.Uplo, n, kd int, ab []float64, ldab int, work []float64) float64
}
func DlansbTest(t *testing.T, impl Dlansber) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 10} {
for _, kd := range []int{0, (n + 1) / 4, (3*n - 1) / 4, (5*n + 1) / 4} {
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, ldab := range []int{kd + 1, kd + 1 + 7} {
dlansbTest(t, impl, rnd, uplo, n, kd, ldab)
}
}
}
}
}
func dlansbTest(t *testing.T, impl Dlansber, rnd *rand.Rand, uplo blas.Uplo, n, kd int, ldab int) {
const tol = 1e-15
// Generate a random symmetric band matrix and compute all its norms.
ab := make([]float64, max(0, (n-1)*ldab+kd+1))
rowsum := make([]float64, n)
colsum := make([]float64, n)
var frobWant, maxabsWant float64
if uplo == blas.Upper {
for i := 0; i < n; i++ {
for jb := 0; jb < min(n-i, kd+1); jb++ {
aij := 2*rnd.Float64() - 1
ab[i*ldab+jb] = aij
j := jb + i
colsum[j] += math.Abs(aij)
rowsum[i] += math.Abs(aij)
maxabsWant = math.Max(maxabsWant, math.Abs(aij))
frobWant += aij * aij
if i != j {
// Take into account the symmetric elements.
colsum[i] += math.Abs(aij)
rowsum[j] += math.Abs(aij)
frobWant += aij * aij
}
}
}
} else {
for i := 0; i < n; i++ {
for jb := max(0, kd-i); jb < kd+1; jb++ {
aij := 2*rnd.Float64() - 1
ab[i*ldab+jb] = aij
j := jb - kd + i
colsum[j] += math.Abs(aij)
rowsum[i] += math.Abs(aij)
maxabsWant = math.Max(maxabsWant, math.Abs(aij))
frobWant += aij * aij
if i != j {
// Take into account the symmetric elements.
colsum[i] += math.Abs(aij)
rowsum[j] += math.Abs(aij)
frobWant += aij * aij
}
}
}
}
frobWant = math.Sqrt(frobWant)
var maxcolsumWant, maxrowsumWant float64
if n > 0 {
maxcolsumWant = floats.Max(colsum)
maxrowsumWant = floats.Max(rowsum)
}
abCopy := make([]float64, len(ab))
copy(abCopy, ab)
work := make([]float64, n)
var maxcolsumGot, maxrowsumGot float64
for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxColumnSum, lapack.MaxRowSum, lapack.Frobenius} {
name := fmt.Sprintf("norm=%v,uplo=%v,n=%v,kd=%v,ldab=%v", string(norm), string(uplo), n, kd, ldab)
normGot := impl.Dlansb(norm, uplo, n, kd, ab, ldab, work)
if !floats.Equal(ab, abCopy) {
t.Fatalf("%v: unexpected modification of ab", name)
}
if norm == lapack.MaxAbs {
// MaxAbs norm involves no 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
maxcolsumGot = normGot
case lapack.MaxRowSum:
normWant = maxrowsumWant
maxrowsumGot = normGot
case lapack.Frobenius:
normWant = frobWant
}
if math.Abs(normGot-normWant) > tol*float64(n) {
t.Errorf("%v: unexpected result; got %v, want %v", name, normGot, normWant)
}
}
// MaxColSum and MaxRowSum norms should be exactly equal because the
// matrix is symmetric.
if maxcolsumGot != maxrowsumGot {
name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,ldab=%v", string(uplo), n, kd, ldab)
t.Errorf("%v: unexpected mismatch between MaxColSum and MaxRowSum norms of A; MaxColSum %v, MaxRowSum %v", name, maxcolsumGot, maxrowsumGot)
}
}
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