func expensive(v float64) float64 {
for i := 0; i < 100; i++ {
v = math.J0(v)
}
return v
}
/*
Test evaluation of interpolation at x
EDGE CASES:
- test for linear extrapolation outside data bounds
*/
func TestSplineOuts(t *testing.T) {
//Data represents Bessel function of 1st kind
xs := Arange(0, 20, 500)
ys := Arange(0, 20, 500)
PPmap(math.J1, ys)
bvd := MakeBiVariateData(xs, ys)
spl := CubicSpline(bvd)
for i, _ := range xs {
yi := ys[i]
xi := xs[i]
if !areSimilar(yi, spl.F(xi)) {
t.Error("Spline does not conform to yi = f(xi) rule")
}
if !areSimilar(spl.coeffs[i], spl.DF(xi)*(20.0/500.0)) {
t.Error("Spline does not conform to Di*h = df(xi) rule")
}
}
//Check integration over (0, 20) with closed-form answer
relError := relativeError(1.0-math.J0(20.0), spl.Integral(0.0, 20.0))
if relError > 1E-5 {
t.Error("Spline did not integrate accurately enough. Error:", relError)
}
}
func TestFindRoot1(t *testing.T) {
out, conv := FindRoot(math.J0, 0.0, 4.0)
if !conv {
t.Error("FindRoot failed to converge.")
} else {
if math.Abs(out-2.4048255576957727) > 1E-14 {
t.Error("FindRoot didn't compute the right value.")
t.Error("Expected:", 2.4048255576957727)
t.Error("Got:", out)
t.Error("Evaluates to:", math.J0(out))
}
}
}
// float32 version of math.J0
func J0(x float32) float32 {
return float32(math.J0(float64(x)))
}