lapack/testlapack: test Dpbtf2 like Dpbtrf
MODIFY
lapack/gonum/dpbtf2.go
lapack/gonum/dpbtf2.go
@@ -61,7 +61,7 @@ func (Implementation) Dpbtf2(uplo blas.Uplo, n, kd int, ab []float64, ldab int)
// Quick return if possible.
if n == 0 {
- return
+ return true
}
if len(ab) < (n-1)*ldab+kd {

MODIFY
lapack/testlapack/dpbtf2.go
lapack/testlapack/dpbtf2.go
package testlapack
import (
+ "fmt"
+ "math"
"testing"
"golang.org/x/exp/rand"
@@ -13,40 +15,81 @@ import (
)
type Dpbtf2er interface {
- Dpbtf2(ul blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
- Dpotrfer
+ Dpbtf2(uplo blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool)
}
+// Dpbtf2Test tests Dpbtf2 on random symmetric positive definite band matrices
+// by checking that the Cholesky factors multiply back to the original matrix.
func Dpbtf2Test(t *testing.T, impl Dpbtf2er) {
- // Test random symmetric banded matrices against the full version.
+ // TODO(vladimir-ch): include expected-failure test case.
rnd := rand.New(rand.NewSource(1))
+ for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20} {
+ 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} {
+ dpbtf2Test(t, impl, rnd, uplo, n, kd, ldab)
+ }
+ }
+ }
+ }
+}
- for _, n := range []int{5, 10, 20} {
- for _, kb := range []int{0, 1, 3, n - 1} {
- for _, ldoff := range []int{0, 4} {
- for _, ul := range []blas.Uplo{blas.Upper, blas.Lower} {
- ldab := kb + 1 + ldoff
- band, sym := randSymBand(ul, n, kb, ldab, rnd)
+func dpbtf2Test(t *testing.T, impl Dpbtf2er, rnd *rand.Rand, uplo blas.Uplo, n, kd int, ldab int) {
+ const tol = 1e-12
- // Compute the Cholesky decomposition of the symmetric matrix.
- ok := impl.Dpotrf(ul, sym.N, sym.Data, sym.Stride)
- if !ok {
- panic("bad test: symmetric cholesky decomp failed")
+ name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,ldab=%v", string(uplo), n, kd, ldab)
+
+ // Allocate a band matrix and fill it with random numbers.
+ ab := make([]float64, n*ldab)
+ for i := range ab {
+ ab[i] = rnd.NormFloat64()
}
+ // Make sure that the matrix U or L has a sufficiently positive diagonal.
+ switch uplo {
+ case blas.Upper:
+ for i := 0; i < n; i++ {
+ ab[i*ldab] = 2 + rnd.Float64()
+ }
+ case blas.Lower:
+ for i := 0; i < n; i++ {
+ ab[i*ldab+kd] = 2 + rnd.Float64()
+ }
+ }
+ // Compute U^T*U or L*L^T. The resulting (symmetric) matrix A will be positive definite.
+ dsbmm(uplo, n, kd, ab, ldab)
- // Compute the Cholesky decomposition of the banded matrix.
- ok = impl.Dpbtf2(band.Uplo, band.N, band.K, band.Data, band.Stride)
+ // Compute the Cholesky decomposition of A.
+ abFac := make([]float64, len(ab))
+ copy(abFac, ab)
+ ok := impl.Dpbtf2(uplo, n, kd, abFac, ldab)
if !ok {
- t.Errorf("SymBand cholesky decomp failed")
+ t.Fatalf("%v: bad test matrix, Dpbtf2 failed", name)
}
- // Compare the result to the Symmetric decomposition.
- sb := symBandToSym(ul, band.Data, n, kb, ldab)
- if !equalApproxSymmetric(sym, sb, 1e-10) {
- t.Errorf("chol mismatch banded and sym. n = %v, kb = %v, ldoff = %v", n, kb, ldoff)
+ if n == 0 {
+ return
+ }
+
+ // Reconstruct an symmetric band matrix from the U^T*U or L*L^T factorization, overwriting abFac.
+ dsbmm(uplo, n, kd, abFac, ldab)
+
+ // Compute and check the max-norm distance between the reconstructed and original matrix A.
+ var diff float64
+ switch uplo {
+ case blas.Upper:
+ for i := 0; i < n; i++ {
+ for j := 0; j < min(kd+1, n-i); j++ {
+ diff = math.Max(diff, math.Abs(abFac[i*ldab+j]-ab[i*ldab+j]))
+ }
}
+ case blas.Lower:
+ for i := 0; i < n; i++ {
+ for j := max(0, kd-i); j < kd+1; j++ {
+ diff = math.Max(diff, math.Abs(abFac[i*ldab+j]-ab[i*ldab+j]))
}
}
}
+ if diff > tol {
+ t.Errorf("%v: unexpected result, diff=%v", name, diff)
}
}

lapack/testlapack: test Dpbtf2 like Dpbtrf