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// 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 mathext
import (
"math"
"testing"
)
// TestCompleteKE checks if the Legendre's relation for m=0.0001(0.0001)0.9999
// is satisfied with accuracy 1e-14.
func TestCompleteKE(t *testing.T) {
t.Parallel()
const tol = 1.0e-14
for m := 1; m <= 9999; m++ {
mf := float64(m) / 10000
mp := 1 - mf
K, Kp := CompleteK(mf), CompleteK(mp)
E, Ep := CompleteE(mf), CompleteE(mp)
legendre := math.Abs(E*Kp + Ep*K - K*Kp - math.Pi/2)
if legendre > tol {
t.Fatalf("legendre > tol: m=%v, legendre=%v, tol=%v", mf, legendre, tol)
}
}
}
// TestCompleteBD checks if the relations between two associate elliptic integrals B(m), D(m)
// and more common Legendre's elliptic integrals K(m), E(m) are satisfied with accuracy 1e-14
// for m=0.0001(0.0001)0.9999.
//
// K(m) and E(m) can be computed without cancellation problems as following:
//
// K(m) = B(m) + D(m),
// E(m) = B(m) + (1-m)D(m).
func TestCompleteBD(t *testing.T) {
t.Parallel()
const tol = 1.0e-14
for m := 1; m <= 9999; m++ {
mf := float64(m) / 10000
B, D := CompleteB(mf), CompleteD(mf)
K, E := CompleteK(mf), CompleteE(mf)
difference1 := math.Abs(K - (B + D))
difference2 := math.Abs(E - (B + (1-mf)*D))
if difference1 > tol {
t.Fatalf("difference1 > tol: m=%v, difference1=%v, tol=%v", mf, difference1, tol)
}
if difference2 > tol {
t.Fatalf("difference2 > tol: m=%v, difference2=%v, tol=%v", mf, difference2, tol)
}
}
}
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