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