lapack: imported lapack as a subtree

lapack/testlapack/dgetri.go

@@ -0,0 +1,89 @@
+// 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 (
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+)
+
+type Dgetrier interface {
+	Dgetrfer
+	Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) bool
+}
+
+func DgetriTest(t *testing.T, impl Dgetrier) {
+	rnd := rand.New(rand.NewSource(1))
+	bi := blas64.Implementation()
+	for _, test := range []struct {
+		n, lda int
+	}{
+		{5, 0},
+		{5, 8},
+		{45, 0},
+		{45, 50},
+		{65, 0},
+		{65, 70},
+		{150, 0},
+		{150, 250},
+	} {
+		n := test.n
+		lda := test.lda
+		if lda == 0 {
+			lda = n
+		}
+		// Generate a random well conditioned matrix
+		perm := rnd.Perm(n)
+		a := make([]float64, n*lda)
+		for i := 0; i < n; i++ {
+			a[i*lda+perm[i]] = 1
+		}
+		for i := range a {
+			a[i] += 0.01 * rnd.Float64()
+		}
+		aCopy := make([]float64, len(a))
+		copy(aCopy, a)
+		ipiv := make([]int, n)
+		// Compute LU decomposition.
+		impl.Dgetrf(n, n, a, lda, ipiv)
+		// Compute inverse.
+		work := make([]float64, 1)
+		impl.Dgetri(n, a, lda, ipiv, work, -1)
+		work = make([]float64, int(work[0]))
+		lwork := len(work)
+
+		ok := impl.Dgetri(n, a, lda, ipiv, work, lwork)
+		if !ok {
+			t.Errorf("Unexpected singular matrix.")
+		}
+
+		// Check that A(inv) * A = I.
+		ans := make([]float64, len(a))
+		bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, aCopy, lda, a, lda, 0, ans, lda)
+		isEye := true
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if i == j {
+					// This tolerance is so high because computing matrix inverses
+					// is very unstable.
+					if math.Abs(ans[i*lda+j]-1) > 5e-2 {
+						isEye = false
+					}
+				} else {
+					if math.Abs(ans[i*lda+j]) > 5e-2 {
+						isEye = false
+					}
+				}
+			}
+		}
+		if !isEye {
+			t.Errorf("Inv(A) * A != I. n = %v, lda = %v", n, lda)
+		}
+	}
+}