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// Copyright ©2023 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/floats"
"gonum.org/v1/gonum/lapack"
)
type Dptconer interface {
Dptcon(n int, d, e []float64, anorm float64, work []float64) (rcond float64)
Dpttrf(n int, d, e []float64) (ok bool)
Dpttrs(n, nrhs int, d, e []float64, b []float64, ldb int)
}
func DptconTest(t *testing.T, impl Dptconer) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20, 50, 51, 52, 53, 54, 100} {
dptconTest(t, impl, rnd, n)
}
}
func dptconTest(t *testing.T, impl Dptconer, rnd *rand.Rand, n int) {
const tol = 1e-15
name := fmt.Sprintf("n=%v", n)
// Generate a random diagonally dominant symmetric tridiagonal matrix A.
d, e := newRandomSymTridiag(n, rnd)
aNorm := dlanst(lapack.MaxColumnSum, n, d, e)
// Compute the Cholesky factorization of A.
ok := impl.Dpttrf(n, d, e)
if !ok {
t.Errorf("%v: bad test matrix, Dpttrf failed", name)
return
}
// Compute the reciprocal of the condition number of A.
dCopy := make([]float64, len(d))
copy(dCopy, d)
eCopy := make([]float64, len(e))
copy(eCopy, e)
work := make([]float64, 3*n)
rcondGot := impl.Dptcon(n, d, e, aNorm, work)
// Check that Dptcon didn't modify d and e.
if !floats.Equal(d, dCopy) {
t.Errorf("%v: unexpected modification of d", name)
}
if !floats.Equal(e, eCopy) {
t.Errorf("%v: unexpected modification of e", name)
}
// Compute the norm of A⁻¹.
aInv, lda := make([]float64, n*n), max(1, n)
for i := 0; i < n; i++ {
aInv[i*lda+i] = 1
}
impl.Dpttrs(n, n, d, e, aInv, lda)
aInvNorm := dlange(lapack.MaxColumnSum, n, n, aInv, lda)
rcondWant := 1.0
if aNorm > 0 && aInvNorm > 0 {
rcondWant = 1 / aNorm / aInvNorm
}
diff := math.Abs(rcondGot - rcondWant)
if diff > tol {
t.Errorf("%v: unexpected value of rcond. got=%v, want=%v (diff=%v)", name, rcondGot, rcondWant, diff)
}
}
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