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f9d0eed525
* Added an implementation of 2 associate complete elliptic integrals B(m),D(m). * Added tests for the implemented integrals. B(m) and D(m) can be expressed via K(m) and E(m), but with cancellation problems.
53 lines
1.5 KiB
Go
53 lines
1.5 KiB
Go
// Copyright ©2017 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 mathext
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import (
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"math"
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"testing"
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)
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// TestCompleteKE checks if the Legendre's relation for m=0.0001(0.0001)0.9999
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// is satisfied with accuracy 1e-14.
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func TestCompleteKE(t *testing.T) {
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const tol = 1.0e-14
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for m := 1; m <= 9999; m++ {
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mf := float64(m) / 10000
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mp := 1 - mf
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K, Kp := CompleteK(mf), CompleteK(mp)
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E, Ep := CompleteE(mf), CompleteE(mp)
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legendre := math.Abs(E*Kp + Ep*K - K*Kp - math.Pi/2)
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if legendre > tol {
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t.Fatalf("legendre > tol: m=%v, legendre=%v, tol=%v", mf, legendre, tol)
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}
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}
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}
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// TestCompleteBD checks if the relations between two associate elliptic integrals B(m), D(m)
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// and more common Legendre's elliptic integrals K(m), E(m) are satisfied with accuracy 1e-14
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// for m=0.0001(0.0001)0.9999.
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//
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// K(m) and E(m) can be computed without cancellation problems as following:
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// K(m) = B(m) + D(m),
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// E(m) = B(m) + (1-m)D(m).
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func TestCompleteBD(t *testing.T) {
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const tol = 1.0e-14
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for m := 1; m <= 9999; m++ {
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mf := float64(m) / 10000
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B, D := CompleteB(mf), CompleteD(mf)
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K, E := CompleteK(mf), CompleteE(mf)
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difference1 := math.Abs(K - (B + D))
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difference2 := math.Abs(E - (B + (1-mf)*D))
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if difference1 > tol {
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t.Fatalf("difference1 > tol: m=%v, difference1=%v, tol=%v", mf, difference1, tol)
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}
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if difference2 > tol {
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t.Fatalf("difference2 > tol: m=%v, difference2=%v, tol=%v", mf, difference2, tol)
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}
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}
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}
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