lapack/gonum: add Dpotri

lapack/testlapack/dpotri.go

@@ -0,0 +1,108 @@
+// Copyright ©2019 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"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dpotrier interface {
+	Dpotri(uplo blas.Uplo, n int, a []float64, lda int) bool
+
+	Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool
+}
+
+func DpotriTest(t *testing.T, impl Dpotrier) {
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		name := "Upper"
+		if uplo == blas.Lower {
+			name = "Lower"
+		}
+		t.Run(name, func(t *testing.T) {
+			// Include small and large sizes to make sure that both
+			// unblocked and blocked paths are taken.
+			ns := []int{0, 1, 2, 3, 4, 5, 10, 25, 31, 32, 33, 63, 64, 65, 127, 128, 129}
+			const tol = 1e-12
+
+			bi := blas64.Implementation()
+			rnd := rand.New(rand.NewSource(1))
+			for _, n := range ns {
+				for _, lda := range []int{max(1, n), n + 11} {
+					prefix := fmt.Sprintf("n=%v,lda=%v", n, lda)
+
+					// Generate a random diagonal matrix D with positive entries.
+					d := make([]float64, n)
+					Dlatm1(d, 3, 10000, false, 2, rnd)
+
+					// Construct a positive definite matrix A as
+					//  A = U * D * U^T
+					// where U is a random orthogonal matrix.
+					a := make([]float64, n*lda)
+					Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n))
+					// Create a copy of A.
+					aCopy := make([]float64, len(a))
+					copy(aCopy, a)
+					// Compute the Cholesky factorization of A.
+					ok := impl.Dpotrf(uplo, n, a, lda)
+					if !ok {
+						t.Fatalf("%v: unexpected Cholesky failure", prefix)
+					}
+
+					// Compute the inverse inv(A).
+					ok = impl.Dpotri(uplo, n, a, lda)
+					if !ok {
+						t.Errorf("%v: unexpected failure", prefix)
+						continue
+					}
+
+					// Check that the triangle of A opposite to uplo has not been modified.
+					if uplo == blas.Upper && !sameLowerTri(n, aCopy, lda, a, lda) {
+						t.Errorf("%v: unexpected modification in lower triangle", prefix)
+						continue
+					}
+					if uplo == blas.Lower && !sameUpperTri(n, aCopy, lda, a, lda) {
+						t.Errorf("%v: unexpected modification in upper triangle", prefix)
+						continue
+					}
+
+					// Change notation for the sake of clarity.
+					ainv := a
+					ldainv := lda
+
+					// Expand ainv into a full dense matrix so that we can call Dsymm below.
+					if uplo == blas.Upper {
+						for i := 1; i < n; i++ {
+							for j := 0; j < i; j++ {
+								ainv[i*ldainv+j] = ainv[j*ldainv+i]
+							}
+						}
+					} else {
+						for i := 0; i < n-1; i++ {
+							for j := i + 1; j < n; j++ {
+								ainv[i*ldainv+j] = ainv[j*ldainv+i]
+							}
+						}
+					}
+
+					// Compute A*inv(A) and store the result into want.
+					ldwant := max(1, n)
+					want := make([]float64, n*ldwant)
+					bi.Dsymm(blas.Left, uplo, n, n, 1, aCopy, lda, ainv, ldainv, 0, want, ldwant)
+
+					// Check that want is the identity matrix.
+					if !isIdentity(n, want, ldwant, tol) {
+						t.Errorf("%v: A * inv(A) != I", prefix)
+					}
+				}
+			}
+		})
+	}
+}