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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"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
type Dpttrser interface {
Dpttrs(n, nrhs int, d, e []float64, b []float64, ldb int)
Dpttrfer
}
func DpttrsTest(t *testing.T, impl Dpttrser) {
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20, 50, 51, 52, 53, 54, 100} {
for _, nrhs := range []int{0, 1, 2, 3, 4, 5, 10, 20, 50} {
for _, ldb := range []int{max(1, nrhs), nrhs + 3} {
dpttrsTest(t, impl, rnd, n, nrhs, ldb)
}
}
}
}
func dpttrsTest(t *testing.T, impl Dpttrser, rnd *rand.Rand, n, nrhs, ldb 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)
// Make a copy of d and e to hold the factorization.
dFac := make([]float64, len(d))
copy(dFac, d)
eFac := make([]float64, len(e))
copy(eFac, e)
// Compute the Cholesky factorization of A.
ok := impl.Dpttrf(n, dFac, eFac)
if !ok {
t.Errorf("%v: bad test matrix, Dpttrf failed", name)
return
}
// Generate a random solution matrix X.
xWant := randomGeneral(n, nrhs, ldb, rnd)
// Compute the right-hand side.
b := zeros(n, nrhs, ldb)
dstmm(n, nrhs, d, e, xWant.Data, xWant.Stride, b.Data, b.Stride)
// Solve A*X=B.
impl.Dpttrs(n, nrhs, dFac, eFac, b.Data, b.Stride)
resid := dpttrsResidual(b, xWant)
if resid > tol {
t.Errorf("%v: unexpected solution: |diff| = %v, want <= %v", name, resid, tol)
}
}
// dstmm computes the matrix-matrix product
//
// C = A*B
//
// where A is an m×m symmetric tridiagonal matrix represented by the diagonal d
// and subdiagonal e, and B and C are m×n matrices.
func dstmm(m, n int, d, e []float64, b []float64, ldb int, c []float64, ldc int) {
if m == 0 || n == 0 {
return
}
if m == 1 {
d0 := d[0]
for j, b0j := range b[:n] {
c[j] = d0 * b0j
}
return
}
for j := 0; j < n; j++ {
c[j] = d[0]*b[j] + e[0]*b[ldb+j]
}
for i := 1; i < m-1; i++ {
for j := 0; j < n; j++ {
c[i*ldc+j] = e[i-1]*b[(i-1)*ldb+j] + d[i]*b[i*ldb+j] + e[i]*b[(i+1)*ldb+j]
}
}
for j := 0; j < n; j++ {
c[(m-1)*ldc+j] = e[m-2]*b[(m-2)*ldb+j] + d[m-1]*b[(m-1)*ldb+j]
}
}
// dpttrsResidual returns |XGOT - XWANT|_1 / n.
func dpttrsResidual(xGot, xWant blas64.General) float64 {
n, nrhs := xGot.Rows, xGot.Cols
d := zeros(n, nrhs, nrhs)
for i := 0; i < n; i++ {
for j := 0; j < nrhs; j++ {
d.Data[i*d.Stride+j] = xGot.Data[i*xGot.Stride+j] - xWant.Data[i*xWant.Stride+j]
}
}
return dlange(lapack.MaxColumnSum, n, nrhs, d.Data, d.Stride) / float64(n)
}
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