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 // Copyright ©2015 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/floats" "gonum.org/v1/gonum/lapack" ) type Dgeconer interface { 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) { 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) 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 } // 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) } } }