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// Copyright ©2015 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 functions
import (
"math"
"testing"
"gonum.org/v1/gonum/diff/fd"
"gonum.org/v1/gonum/floats"
)
func TestMinimalSurface(t *testing.T) {
t.Parallel()
for _, size := range [][2]int{
{20, 30},
{30, 30},
{50, 40},
} {
f := NewMinimalSurface(size[0], size[1])
x0 := f.InitX()
grad := make([]float64, len(x0))
f.Grad(grad, x0)
fdGrad := fd.Gradient(nil, f.Func, x0, &fd.Settings{Formula: fd.Central})
// Test that the numerical and analytical gradients agree.
dist := floats.Distance(grad, fdGrad, math.Inf(1))
if dist > 1e-9 {
t.Errorf("grid %v x %v: numerical and analytical gradient do not match. |fdGrad - grad|_∞ = %v",
size[0], size[1], dist)
}
// Test that the gradient at the minimum is small enough.
// In some sense this test is not completely correct because ExactX
// returns the exact solution to the continuous problem projected on the
// grid, not the exact solution to the discrete problem which we are
// solving. This is the reason why a relatively loose tolerance 1e-4
// must be used.
xSol := f.ExactX()
f.Grad(grad, xSol)
norm := floats.Norm(grad, math.Inf(1))
if norm > 1e-4 {
t.Errorf("grid %v x %v: gradient at the minimum not small enough. |grad|_∞ = %v",
size[0], size[1], norm)
}
}
}
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