Add Laplacian and CrossLaplacian difference functions (#154)

* Add Laplacian and CrossLaplacian difference functions

* use usesOrigin

diff/fd/crosslaplacian_test.go

@@ -0,0 +1,111 @@
+// Copyright ©2017 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 fd
+
+import (
+	"testing"
+
+	"gonum.org/v1/gonum/floats"
+	"gonum.org/v1/gonum/mat"
+)
+
+type CrossLaplacianTester interface {
+	Func(x, y []float64) float64
+	CrossLaplacian(x, y []float64) float64
+}
+
+type WrapperCL struct {
+	Tester HessianTester
+}
+
+func (WrapperCL) constructZ(x, y []float64) []float64 {
+	z := make([]float64, len(x)+len(y))
+	copy(z, x)
+	copy(z[len(x):], y)
+	return z
+}
+
+func (w WrapperCL) Func(x, y []float64) float64 {
+	z := w.constructZ(x, y)
+	return w.Tester.Func(z)
+}
+
+func (w WrapperCL) CrossLaplacian(x, y []float64) float64 {
+	z := w.constructZ(x, y)
+	hess := mat.NewSymDense(len(z), nil)
+	w.Tester.Hess(hess, z)
+	// The CrossLaplacian is the trace of the off-diagonal block of the Hessian.
+	var l float64
+	for i := 0; i < len(x); i++ {
+		l += hess.At(i, i+len(x))
+	}
+	return l
+}
+
+func TestCrossLaplacian(t *testing.T) {
+	for cas, test := range []struct {
+		l        CrossLaplacianTester
+		x, y     []float64
+		settings *Settings
+		tol      float64
+	}{
+		{
+			l:   WrapperCL{Watson{}},
+			x:   []float64{0.2, 0.3},
+			y:   []float64{0.1, 0.4},
+			tol: 1e-3,
+		},
+		{
+			l:   WrapperCL{Watson{}},
+			x:   []float64{2, 3, 1},
+			y:   []float64{1, 4, 1},
+			tol: 1e-3,
+		},
+		{
+			l:   WrapperCL{ConstFunc(6)},
+			x:   []float64{2, -3, 1},
+			y:   []float64{1, 4, -5},
+			tol: 1e-6,
+		},
+		{
+			l:   WrapperCL{LinearFunc{w: []float64{10, 6, -1, 5}, c: 5}},
+			x:   []float64{3, 1},
+			y:   []float64{8, 6},
+			tol: 1e-6,
+		},
+		{
+			l: WrapperCL{QuadFunc{
+				a: mat.NewSymDense(4, []float64{
+					10, 2, 1, 9,
+					2, 5, -3, 4,
+					1, -3, 6, 2,
+					9, 4, 2, -14,
+				}),
+				b: mat.NewVecDense(4, []float64{3, -2, -1, 4}),
+				c: 5,
+			}},
+			x:   []float64{-1.6, -3},
+			y:   []float64{1.8, 3.4},
+			tol: 1e-6,
+		},
+	} {
+		got := CrossLaplacian(test.l.Func, test.x, test.y, test.settings)
+		want := test.l.CrossLaplacian(test.x, test.y)
+		if !floats.EqualWithinAbsOrRel(got, want, test.tol, test.tol) {
+			t.Errorf("Cas %d: CrossLaplacian mismatch serial. got %v, want %v", cas, got, want)
+		}
+
+		// Test that concurrency works.
+		settings := test.settings
+		if settings == nil {
+			settings = &Settings{}
+		}
+		settings.Concurrent = true
+		got2 := CrossLaplacian(test.l.Func, test.x, test.y, settings)
+		if !floats.EqualWithinAbsOrRel(got, got2, 1e-6, 1e-6) {
+			t.Errorf("Cas %d: Laplacian mismatch. got %v, want %v", cas, got2, got)
+		}
+	}
+}