lapack/gonum: add Dgetc2 (#1655)

lapack/testlapack/dgetc2.go

@@ -0,0 +1,98 @@
+// Copyright ©2021 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"
+	"math"
+	"testing"
+
+	"golang.org/x/exp/rand"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dgetc2er interface {
+	Dgetc2(n int, a []float64, lda int, ipiv, jpiv []int) (k int)
+}
+
+func Dgetc2Test(t *testing.T, impl Dgetc2er) {
+	const tol = 1e-12
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20} {
+		for _, lda := range []int{n, n + 5} {
+			dgetc2Test(t, impl, rnd, n, lda, tol)
+		}
+	}
+}
+
+func dgetc2Test(t *testing.T, impl Dgetc2er, rnd *rand.Rand, n, lda int, tol float64) {
+	name := fmt.Sprintf("n=%v,lda=%v", n, lda)
+	if lda == 0 {
+		lda = 1
+	}
+	// Generate a random general matrix A.
+	a := randomGeneral(n, n, lda, rnd)
+	// ipiv and jpiv are outputs.
+	ipiv := make([]int, n)
+	jpiv := make([]int, n)
+	for i := 0; i < n; i++ {
+		ipiv[i], jpiv[i] = -1, -1 // Set to non-indices.
+	}
+	// Copy to store output (LU decomposition).
+	lu := cloneGeneral(a)
+	k := impl.Dgetc2(n, lu.Data, lu.Stride, ipiv, jpiv)
+	if k >= 0 {
+		t.Logf("%v: matrix was perturbed at %d", name, k)
+	}
+
+	// Verify all indices are set.
+	for i := 0; i < n; i++ {
+		if ipiv[i] < 0 {
+			t.Errorf("%v: ipiv[%d] is negative", name, i)
+		}
+		if jpiv[i] < 0 {
+			t.Errorf("%v: jpiv[%d] is negative", name, i)
+		}
+	}
+	bi := blas64.Implementation()
+	// Construct L and U triangular matrices from Dgetc2 output.
+	L := zeros(n, n, lda)
+	U := zeros(n, n, lda)
+	for i := 0; i < n; i++ {
+		for j := 0; j < n; j++ {
+			idx := i*lda + j
+			if j >= i { // On upper triangle and setting of L's unit diagonal elements.
+				U.Data[idx] = lu.Data[idx]
+				if j == i {
+					L.Data[idx] = 1.0
+				}
+			} else if i > j { // On diagonal or lower triangle.
+				L.Data[idx] = lu.Data[idx]
+			}
+		}
+	}
+	work := zeros(n, n, lda)
+	bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, L.Data, L.Stride, U.Data, U.Stride, 0, work.Data, work.Stride)
+
+	// Apply Permutations P and Q to L*U.
+	for i := n - 1; i >= 0; i-- {
+		ipv, jpv := ipiv[i], jpiv[i]
+		if ipv != i {
+			bi.Dswap(n, work.Data[i*lda:], 1, work.Data[ipv*lda:], 1)
+		}
+		if jpv != i {
+			bi.Dswap(n, work.Data[i:], work.Stride, work.Data[jpv:], work.Stride)
+		}
+	}
+
+	// A should be reconstructed by now.
+	for i := range work.Data {
+		if math.Abs(work.Data[i]-a.Data[i]) > tol {
+			t.Errorf("%v: matrix %d idx not equal after reconstruction. got %g, expected %g", name, i, work.Data[i], a.Data[i])
+		}
+	}
+}