Add Laplacian and CrossLaplacian difference functions (#154)

* Add Laplacian and CrossLaplacian difference functions

* use usesOrigin

diff/fd/laplacian_test.go

@@ -0,0 +1,44 @@
+// 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"
+)
+
+func TestLaplacian(t *testing.T) {
+	for cas, test := range hessianTestCases {
+		// Modify the test cases where the forumla is set.
+		settings := test.settings
+		if settings != nil && !settings.Formula.isZero() {
+			settings.Formula = Forward2nd
+		}
+
+		n := len(test.x)
+		got := Laplacian(test.h.Func, test.x, test.settings)
+		hess := mat.NewSymDense(n, nil)
+		test.h.Hess(hess, test.x)
+		var want float64
+		for i := 0; i < n; i++ {
+			want += hess.At(i, i)
+		}
+		if !floats.EqualWithinAbsOrRel(got, want, test.tol, test.tol) {
+			t.Errorf("Cas %d: Laplacian mismatch. got %v, want %v", cas, got, want)
+		}
+
+		// Test that concurrency works.
+		if settings == nil {
+			settings = &Settings{}
+		}
+		settings.Concurrent = true
+		got2 := Laplacian(test.h.Func, test.x, settings)
+		if !floats.EqualWithinAbsOrRel(got, got2, 1e-5, 1e-5) {
+			t.Errorf("Cas %d: Laplacian mismatch. got %v, want %v", cas, got2, got)
+		}
+	}
+}