lapack: imported lapack as a subtree

lapack/testlapack/dgebak.go

@@ -0,0 +1,110 @@
+// Copyright ©2016 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/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/lapack"
+)
+
+type Dgebaker interface {
+	Dgebak(job lapack.Job, side lapack.EVSide, n, ilo, ihi int, scale []float64, m int, v []float64, ldv int)
+}
+
+func DgebakTest(t *testing.T, impl Dgebaker) {
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, job := range []lapack.Job{lapack.None, lapack.Permute, lapack.Scale, lapack.PermuteScale} {
+		for _, side := range []lapack.EVSide{lapack.LeftEV, lapack.RightEV} {
+			for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
+				for _, extra := range []int{0, 11} {
+					for cas := 0; cas < 100; cas++ {
+						m := rnd.Intn(n + 1)
+						v := randomGeneral(n, m, m+extra, rnd)
+						var ilo, ihi int
+						if v.Rows > 0 {
+							ihi = rnd.Intn(n)
+							ilo = rnd.Intn(ihi + 1)
+						} else {
+							ihi = -1
+						}
+						testDgebak(t, impl, job, side, ilo, ihi, v, rnd)
+					}
+				}
+			}
+		}
+	}
+}
+
+func testDgebak(t *testing.T, impl Dgebaker, job lapack.Job, side lapack.EVSide, ilo, ihi int, v blas64.General, rnd *rand.Rand) {
+	const tol = 1e-15
+	n := v.Rows
+	m := v.Cols
+	extra := v.Stride - v.Cols
+
+	// Create D and D^{-1} by generating random scales between ilo and ihi.
+	d := eye(n, n)
+	dinv := eye(n, n)
+	scale := nanSlice(n)
+	if job == lapack.Scale || job == lapack.PermuteScale {
+		if ilo == ihi {
+			scale[ilo] = 1
+		} else {
+			for i := ilo; i <= ihi; i++ {
+				scale[i] = 2 * rnd.Float64()
+				d.Data[i*d.Stride+i] = scale[i]
+				dinv.Data[i*dinv.Stride+i] = 1 / scale[i]
+			}
+		}
+	}
+
+	// Create P by generating random column swaps.
+	p := eye(n, n)
+	if job == lapack.Permute || job == lapack.PermuteScale {
+		// Make up some random permutations.
+		for i := n - 1; i > ihi; i-- {
+			scale[i] = float64(rnd.Intn(i + 1))
+			blas64.Swap(n,
+				blas64.Vector{p.Stride, p.Data[i:]},
+				blas64.Vector{p.Stride, p.Data[int(scale[i]):]})
+		}
+		for i := 0; i < ilo; i++ {
+			scale[i] = float64(i + rnd.Intn(ihi-i+1))
+			blas64.Swap(n,
+				blas64.Vector{p.Stride, p.Data[i:]},
+				blas64.Vector{p.Stride, p.Data[int(scale[i]):]})
+		}
+	}
+
+	got := cloneGeneral(v)
+	impl.Dgebak(job, side, n, ilo, ihi, scale, m, got.Data, got.Stride)
+
+	prefix := fmt.Sprintf("Case job=%v, side=%v, n=%v, ilo=%v, ihi=%v, m=%v, extra=%v",
+		job, side, n, ilo, ihi, m, extra)
+
+	if !generalOutsideAllNaN(got) {
+		t.Errorf("%v: out-of-range write to V\n%v", prefix, got.Data)
+	}
+
+	// Compute D*V or D^{-1}*V and store into dv.
+	dv := zeros(n, m, m)
+	if side == lapack.RightEV {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, d, v, 0, dv)
+	} else {
+		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, dinv, v, 0, dv)
+	}
+	// Compute P*D*V or P*D^{-1}*V and store into want.
+	want := zeros(n, m, m)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, p, dv, 0, want)
+
+	if !equalApproxGeneral(want, got, tol) {
+		t.Errorf("%v: unexpected value of V", prefix)
+	}
+}