lapack/testlapack: rewrite test for Dgecon from table-based to randomized
MODIFY
lapack/testlapack/dgecon.go
lapack/testlapack/dgecon.go
package testlapack
import (
+ "fmt"
"testing"
+ "golang.org/x/exp/rand"
+
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dgeconer interface {
- Dlanger
- Dgetrfer
Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
+
+ Dgetrier
+ Dlanger
}
func DgeconTest(t *testing.T, impl Dgeconer) {
- for _, test := range []struct {
- m int
- n int
- a []float64
- condOne float64
- condInf float64
- }{
- {
- a: []float64{
- 8, 1, 6,
- 3, 5, 7,
- 4, 9, 2,
- },
- m: 3,
- n: 3,
- condOne: 3.0 / 16,
- condInf: 3.0 / 16,
- },
- {
- a: []float64{
- 2, 9, 3, 2,
- 10, 9, 9, 3,
- 1, 1, 5, 2,
- 8, 4, 10, 2,
- },
- m: 4,
- n: 4,
- condOne: 0.024740155174938,
- condInf: 0.012034465570035,
- },
- // Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
- {
- a: []float64{
- 2.9995576045549965, -2.0898894566158663, 3.965560740124006,
- -2.0898894566158663, 1.9634729526261008, -2.8681002706874104,
- 3.965560740124006, -2.8681002706874104, 5.502416670471008,
- },
- m: 3,
- n: 3,
- condOne: 0.024054837369015203,
- condInf: 0.024054837369015203,
- },
- } {
- m := test.m
- n := test.n
- lda := n
- a := make([]float64, len(test.a))
- copy(a, test.a)
- ipiv := make([]int, min(m, n))
-
- // Find the norms of the original matrix.
- work := make([]float64, 4*n)
- oneNorm := impl.Dlange(lapack.MaxColumnSum, m, n, a, lda, work)
- infNorm := impl.Dlange(lapack.MaxRowSum, m, n, a, lda, work)
-
- // Compute LU factorization of a.
- impl.Dgetrf(m, n, a, lda, ipiv)
-
- // Compute the condition number
+ rnd := rand.New(rand.NewSource(1))
+ for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 50} {
+ for _, lda := range []int{max(1, n), n + 3} {
+ dgeconTest(t, impl, rnd, n, lda)
+ }
+ }
+}
+
+func dgeconTest(t *testing.T, impl Dgeconer, rnd *rand.Rand, n, lda int) {
+ const ratioThresh = 10
+
+ // Generate a random square matrix A with elements uniformly in [-1,1).
+ a := make([]float64, max(0, (n-1)*lda+n))
+ for i := range a {
+ a[i] = 2*rnd.Float64() - 1
+ }
+
+ // Allocate work slices.
iwork := make([]int, n)
- condOne := impl.Dgecon(lapack.MaxColumnSum, n, a, lda, oneNorm, work, iwork)
- condInf := impl.Dgecon(lapack.MaxRowSum, n, a, lda, infNorm, work, iwork)
-
- // Error if not the same order, otherwise log the difference.
- if !floats.EqualWithinAbsOrRel(condOne, test.condOne, 1e0, 1e0) {
- t.Errorf("One norm mismatch. Want %v, got %v.", test.condOne, condOne)
- } else if !floats.EqualWithinAbsOrRel(condOne, test.condOne, 1e-14, 1e-14) {
- t.Logf("Dgecon one norm mismatch. Want %v, got %v.", test.condOne, condOne)
+ work := make([]float64, max(1, 4*n))
+
+ // Compute the LU factorization of A.
+ aFac := make([]float64, len(a))
+ copy(aFac, a)
+ ipiv := make([]int, n)
+ ok := impl.Dgetrf(n, n, aFac, lda, ipiv)
+ if !ok {
+ t.Fatalf("n=%v,lda=%v: bad matrix, Dgetrf failed", n, lda)
+ }
+ aFacCopy := make([]float64, len(aFac))
+ copy(aFacCopy, aFac)
+
+ // Compute the inverse A^{-1} from the LU factorization.
+ aInv := make([]float64, len(aFac))
+ copy(aInv, aFac)
+ ok = impl.Dgetri(n, aInv, lda, ipiv, work, len(work))
+ if !ok {
+ t.Fatalf("n=%v,lda=%v: bad matrix, Dgetri failed", n, lda)
+ }
+
+ for _, norm := range []lapack.MatrixNorm{lapack.MaxColumnSum, lapack.MaxRowSum} {
+ name := fmt.Sprintf("norm%v,n=%v,lda=%v", string(norm), n, lda)
+
+ // Compute the norm of A and A^{-1}.
+ aNorm := impl.Dlange(norm, n, n, a, lda, work)
+ aInvNorm := impl.Dlange(norm, n, n, aInv, lda, work)
+
+ // Compute a good estimate of the condition number
+ // rcondWant := 1/(norm(A) * norm(inv(A)))
+ rcondWant := 1.0
+ if aNorm > 0 && aInvNorm > 0 {
+ rcondWant = 1 / aNorm / aInvNorm
}
- if !floats.EqualWithinAbsOrRel(condInf, test.condInf, 1e0, 1e0) {
- t.Errorf("One norm mismatch. Want %v, got %v.", test.condInf, condInf)
- } else if !floats.EqualWithinAbsOrRel(condInf, test.condInf, 1e-14, 1e-14) {
- t.Logf("Dgecon one norm mismatch. Want %v, got %v.", test.condInf, condInf)
+
+ // Compute an estimate of rcond using the LU factorization and Dgecon.
+ rcondGot := impl.Dgecon(norm, n, aFac, lda, aNorm, work, iwork)
+ if !floats.Equal(aFac, aFacCopy) {
+ t.Errorf("%v: unexpected modification of aFac", name)
+ }
+
+ ratio := rCondTestRatio(rcondGot, rcondWant)
+ if ratio >= ratioThresh {
+ t.Errorf("%v: unexpected value of rcond; got=%v, want=%v (ratio=%v)",
+ name, rcondGot, rcondWant, ratio)
}
}
}

lapack/testlapack: rewrite test for Dgecon from table-based to randomized