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// Copyright ©2018 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 testblas
import (
"fmt"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
)
type Ztbsver interface {
Ztbsv(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, k int, ab []complex128, ldab int, x []complex128, incX int)
Ztbmver
}
func ZtbsvTest(t *testing.T, impl Ztbsver) {
rnd := rand.New(rand.NewSource(1))
for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans, blas.ConjTrans} {
for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
for _, n := range []int{1, 2, 3, 4, 10} {
for k := 0; k < n; k++ {
for _, ldab := range []int{k + 1, k + 1 + 10} {
for _, incX := range []int{-4, 1, 5} {
ztbsvTest(t, impl, rnd, uplo, trans, diag, n, k, ldab, incX)
}
}
}
}
}
}
}
}
// ztbsvTest tests Ztbsv by checking whether Ztbmv followed by Ztbsv
// round-trip.
func ztbsvTest(t *testing.T, impl Ztbsver, rnd *rand.Rand, uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, k, ldab, incX int) {
const tol = 1e-10
// Allocate a dense-storage triangular band matrix filled with NaNs that
// will be used as a for creating the actual triangular band matrix.
lda := max(1, n)
a := makeZGeneral(nil, n, n, lda)
// Fill the referenced triangle of A with random data within the band
// and with zeros outside.
if uplo == blas.Upper {
for i := 0; i < n; i++ {
for j := i; j < min(n, i+k+1); j++ {
re := rnd.NormFloat64()
im := rnd.NormFloat64()
a[i*lda+j] = complex(re, im)
}
for j := i + k + 1; j < n; j++ {
a[i*lda+j] = 0
}
}
} else {
for i := 0; i < n; i++ {
for j := 0; j < i-k; j++ {
a[i*lda+j] = 0
}
for j := max(0, i-k); j <= i; j++ {
re := rnd.NormFloat64()
im := rnd.NormFloat64()
a[i*lda+j] = complex(re, im)
}
}
}
if diag == blas.Unit {
// The diagonal should not be referenced by Ztbmv and Ztbsv, so
// invalidate it with NaNs.
for i := 0; i < n; i++ {
a[i*lda+i] = znan
}
}
// Create the triangular band matrix.
ab := zPackTriBand(k, ldab, uplo, n, a, lda)
abCopy := make([]complex128, len(ab))
copy(abCopy, ab)
// Generate a random complex vector x.
xtest := make([]complex128, n)
for i := range xtest {
re := rnd.NormFloat64()
im := rnd.NormFloat64()
xtest[i] = complex(re, im)
}
x := makeZVector(xtest, incX)
// Store a copy of x as the correct result that we want.
want := make([]complex128, len(x))
copy(want, x)
// Compute A*x, denoting the result by b and storing it in x.
impl.Ztbmv(uplo, trans, diag, n, k, ab, ldab, x, incX)
// Solve A*x = b, that is, x = A^{-1}*b = A^{-1}*A*x.
impl.Ztbsv(uplo, trans, diag, n, k, ab, ldab, x, incX)
// If Ztbsv is correct, A^{-1}*A = I and x contains again its original value.
name := fmt.Sprintf("uplo=%v,trans=%v,diag=%v,n=%v,k=%v,ldab=%v,incX=%v", uplo, trans, diag, n, k, ldab, incX)
if !zsame(ab, abCopy) {
t.Errorf("%v: unexpected modification of A", name)
}
if !zSameAtNonstrided(x, want, incX) {
t.Errorf("%v: unexpected modification of x\nwant %v\ngot %v", name, want, x)
}
if !zEqualApproxAtStrided(x, want, incX, tol) {
t.Errorf("%v: unexpected result\nwant %v\ngot %v", name, want, x)
}
}
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