lapack: imported lapack as a subtree

lapack/testlapack/dpocon.go

@@ -0,0 +1,157 @@
+// 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 (
+	"log"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/floats"
+	"github.com/gonum/lapack"
+)
+
+type Dpoconer interface {
+	Dpotrfer
+	Dgeconer
+	Dlansy(norm lapack.MatrixNorm, uplo blas.Uplo, n int, a []float64, lda int, work []float64) float64
+	Dpocon(uplo blas.Uplo, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64
+}
+
+func DpoconTest(t *testing.T, impl Dpoconer) {
+	for _, test := range []struct {
+		a    []float64
+		n    int
+		cond float64
+		uplo blas.Uplo
+	}{
+		{
+			a: []float64{
+				89, 59, 77,
+				0, 107, 59,
+				0, 0, 89,
+			},
+			uplo: blas.Upper,
+			n:    3,
+			cond: 0.050052137643379,
+		},
+		{
+			a: []float64{
+				89, 0, 0,
+				59, 107, 0,
+				77, 59, 89,
+			},
+			uplo: blas.Lower,
+			n:    3,
+			cond: 0.050052137643379,
+		},
+		// Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
+		{
+			a: []float64{
+				2.9995576045549965, -2.0898894566158663, 3.965560740124006,
+				0, 1.9634729526261008, -2.8681002706874104,
+				0, 0, 5.502416670471008,
+			},
+			uplo: blas.Upper,
+			n:    3,
+			cond: 0.024054837369015203,
+		},
+	} {
+		n := test.n
+		a := make([]float64, len(test.a))
+		copy(a, test.a)
+		lda := n
+		uplo := test.uplo
+		work := make([]float64, 3*n)
+		anorm := impl.Dlansy(lapack.MaxColumnSum, uplo, n, a, lda, work)
+		// Compute cholesky decomposition
+		ok := impl.Dpotrf(uplo, n, a, lda)
+		if !ok {
+			t.Errorf("Bad test, matrix not positive definite")
+			continue
+		}
+		iwork := make([]int, n)
+		cond := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
+		// Error if not the same order, otherwise log the difference.
+		if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e0, 1e0) {
+			t.Errorf("Cond mismatch. Want %v, got %v.", test.cond, cond)
+		} else if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e-14, 1e-14) {
+			log.Printf("Dpocon cond mismatch. Want %v, got %v.", test.cond, cond)
+		}
+	}
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	// Randomized tests compared against Dgecon.
+	for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+		for _, test := range []struct {
+			n, lda int
+		}{
+			{3, 0},
+			{3, 5},
+		} {
+			for trial := 0; trial < 100; trial++ {
+				n := test.n
+				lda := test.lda
+				if lda == 0 {
+					lda = n
+				}
+				a := make([]float64, n*lda)
+				for i := range a {
+					a[i] = rnd.NormFloat64()
+				}
+
+				// Multiply a by itself to make it symmetric positive definite.
+				aCopy := make([]float64, len(a))
+				copy(aCopy, a)
+				bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, aCopy, lda, aCopy, lda, 0, a, lda)
+
+				aDat := make([]float64, len(aCopy))
+				copy(aDat, a)
+
+				aDense := make([]float64, len(a))
+				if uplo == blas.Upper {
+					for i := 0; i < n; i++ {
+						for j := i; j < n; j++ {
+							v := a[i*lda+j]
+							aDense[i*lda+j] = v
+							aDense[j*lda+i] = v
+						}
+					}
+				} else {
+					for i := 0; i < n; i++ {
+						for j := 0; j <= i; j++ {
+							v := a[i*lda+j]
+							aDense[i*lda+j] = v
+							aDense[j*lda+i] = v
+						}
+					}
+				}
+				work := make([]float64, 4*n)
+				iwork := make([]int, n)
+
+				anorm := impl.Dlansy(lapack.MaxColumnSum, uplo, n, a, lda, work)
+				ok := impl.Dpotrf(uplo, n, a, lda)
+				if !ok {
+					t.Errorf("Bad test, matrix not positive definite")
+					continue
+				}
+				got := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
+
+				denseNorm := impl.Dlange(lapack.MaxColumnSum, n, n, aDense, lda, work)
+				ipiv := make([]int, n)
+				impl.Dgetrf(n, n, aDense, lda, ipiv)
+				want := impl.Dgecon(lapack.MaxColumnSum, n, aDense, lda, denseNorm, work, iwork)
+				// Error if not the same order, otherwise log the difference.
+				if !floats.EqualWithinAbsOrRel(want, got, 1e0, 1e0) {
+					t.Errorf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
+				} else if !floats.EqualWithinAbsOrRel(want, got, 1e-14, 1e-14) {
+					log.Printf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
+				}
+			}
+		}
+	}
+}