func TestMinimalSurface(t *testing.T) {
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)
}
}
}
func testDerivParam(t *testing.T, d derivParamTester) {
// Tests that the derivative matches for a number of different quantiles
// along the distribution.
nTest := 10
quantiles := make([]float64, nTest)
floats.Span(quantiles, 0.1, 0.9)
deriv := make([]float64, d.NumParameters())
fdDeriv := make([]float64, d.NumParameters())
initParams := d.parameters(nil)
init := make([]float64, d.NumParameters())
for i, v := range initParams {
init[i] = v.Value
}
for _, v := range quantiles {
d.setParameters(initParams)
x := d.Quantile(v)
d.DLogProbDParam(x, deriv)
f := func(p []float64) float64 {
params := d.parameters(nil)
for i, v := range p {
params[i].Value = v
}
d.setParameters(params)
return d.LogProb(x)
}
fd.Gradient(fdDeriv, f, init, nil)
if !floats.EqualApprox(deriv, fdDeriv, 1e-6) {
t.Fatal("Derivative mismatch. Want", fdDeriv, ", got", deriv, ".")
}
}
}
// testFunction checks that the function can evaluate itself (and its gradient)
// correctly.
func testFunction(f function, ftests []funcTest, t *testing.T) {
// Make a copy of tests because we may append to the slice.
tests := make([]funcTest, len(ftests))
copy(tests, ftests)
// Get information about the function.
fMinima, isMinimumer := f.(minimumer)
fGradient, isGradient := f.(gradient)
// If the function is a Minimumer, append its minima to the tests.
if isMinimumer {
for _, minimum := range fMinima.Minima() {
// Allocate gradient only if the function can evaluate it.
var grad []float64
if isGradient {
grad = make([]float64, len(minimum.X))
}
tests = append(tests, funcTest{
X: minimum.X,
F: minimum.F,
Gradient: grad,
})
}
}
for i, test := range tests {
F := f.Func(test.X)
// Check that the function value is as expected.
if math.Abs(F-test.F) > defaultTol {
t.Errorf("Test #%d: function value given by Func is incorrect. Want: %v, Got: %v",
i, test.F, F)
}
if test.Gradient == nil {
continue
}
// Evaluate the finite difference gradient.
fdGrad := fd.Gradient(nil, f.Func, test.X, nil)
// Check that the finite difference and expected gradients match.
if !floats.EqualApprox(fdGrad, test.Gradient, defaultFDGradTol) {
dist := floats.Distance(fdGrad, test.Gradient, math.Inf(1))
t.Errorf("Test #%d: numerical and expected gradients do not match. |fdGrad - WantGrad|_∞ = %v",
i, dist)
}
// If the function is a Gradient, check that it computes the gradient correctly.
if isGradient {
grad := make([]float64, len(test.Gradient))
fGradient.Grad(grad, test.X)
if !floats.EqualApprox(grad, test.Gradient, defaultGradTol) {
dist := floats.Distance(grad, test.Gradient, math.Inf(1))
t.Errorf("Test #%d: gradient given by Grad is incorrect. |grad - WantGrad|_∞ = %v",
i, dist)
}
}
}
}
