lapack/{gonum,testlapack}: add Dlangb and its test

lapack/testlapack/dlangb.go

@@ -0,0 +1,109 @@
+// 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/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dlangber interface {
+	Dlangb(norm lapack.MatrixNorm, n, kl, ku int, ab []float64, ldab int, work []float64) float64
+}
+
+func DlangbTest(t *testing.T, impl Dlangber) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxRowSum, lapack.MaxColumnSum, lapack.Frobenius} {
+		t.Run(normToString(norm), func(t *testing.T) {
+			for _, n := range []int{0, 1, 2, 3, 4, 5, 10} {
+				for _, kl := range []int{0, 1, 2, 3, 4, 5, 10} {
+					for _, ku := range []int{0, 1, 2, 3, 4, 5, 10} {
+						for _, ldab := range []int{kl + ku + 1, kl + ku + 1 + 7} {
+							for iter := 0; iter < 10; iter++ {
+								dlangbTest(t, impl, rnd, norm, n, kl, ku, ldab)
+							}
+						}
+					}
+				}
+			}
+		})
+	}
+}
+
+func dlangbTest(t *testing.T, impl Dlangber, rnd *rand.Rand, norm lapack.MatrixNorm, n, kl, ku, ldab int) {
+	const tol = 1e-14
+
+	name := fmt.Sprintf("n=%v,kl=%v,ku=%v,ldab=%v", n, kl, ku, ldab)
+
+	// Generate a random band matrix.
+	ab := randomSlice(n*ldab, rnd)
+	// Sometimes put a NaN into the matrix.
+	if n > 0 && rnd.Float64() < 0.5 {
+		i := rnd.Intn(n)
+		ab[i*ldab+kl] = math.NaN()
+	}
+	abCopy := make([]float64, len(ab))
+	copy(abCopy, ab)
+
+	// Deal with zero-sized matrices early.
+	if n == 0 {
+		got := impl.Dlangb(norm, n, kl, ku, nil, ldab, nil)
+		if got != 0 {
+			t.Errorf("%v: unexpected result for zero-sized matrix with nil input", name)
+		}
+		got = impl.Dlangb(norm, n, kl, ku, ab, ldab, nil)
+		if !floats.Same(ab, abCopy) {
+			t.Errorf("%v: unexpected modification in dl", name)
+		}
+		if got != 0 {
+			t.Errorf("%v: unexpected result for zero-sized matrix with non-nil input", name)
+		}
+		return
+	}
+
+	// Generate a dense representation of the matrix and compute the wanted result.
+	a := zeros(n, n, n)
+	for i := 0; i < n; i++ {
+		for j := max(0, i-kl); j < min(i+ku+1, n); j++ {
+			a.Data[i*a.Stride+j] = ab[i*ldab+j-i+kl]
+		}
+	}
+
+	var work []float64
+	if norm == lapack.MaxColumnSum {
+		work = make([]float64, n)
+	}
+	got := impl.Dlangb(norm, n, kl, ku, ab, ldab, work)
+
+	if !floats.Same(ab, abCopy) {
+		t.Errorf("%v: unexpected modification in ab", name)
+	}
+
+	want := dlange(norm, n, n, a.Data, a.Stride)
+
+	if math.IsNaN(want) {
+		if !math.IsNaN(got) {
+			t.Errorf("%v: unexpected result with NaN element; got %v, want %v", name, got, want)
+		}
+		return
+	}
+
+	if norm == lapack.MaxAbs {
+		if got != want {
+			t.Errorf("%v: unexpected result; got %v, want %v", name, got, want)
+		}
+		return
+	}
+	diff := math.Abs(got - want)
+	if diff > tol {
+		t.Errorf("%v: unexpected result; got %v, want %v, diff=%v", name, got, want, diff)
+	}
+}