blob: f4d58d435da59c6afe9588de4569d31d0e677ca4 [file] [log] [blame]
 // 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) { 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) { 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) } } }