mirror of
https://github.com/gonum/gonum.git
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105 lines
3.5 KiB
Go
105 lines
3.5 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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"golang.org/x/exp/rand"
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)
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// Testing EllipticF (and EllipticRF) using the addition theorems from http://dlmf.nist.gov/19.11.i
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func TestEllipticF(t *testing.T) {
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const tol = 1.0e-14
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rnd := rand.New(rand.NewSource(1))
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// The following EllipticF(pi/3,m), m=0.1(0.1)0.9 was computed in Maxima 5.38.0 using Bigfloat arithmetic.
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vF := [...]float64{
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1.0631390181954904767742338285104637431858016483079,
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1.0803778062523490005579242592072579594037132891908,
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1.0991352230920430074586978843452269008747645822123,
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1.1196949183404746257742176145632376703505764745654,
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1.1424290580457772555013955266260457822322036529624,
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1.1678400583161860445148860686430780757517286094732,
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1.1966306515644649360767197589467723191317720122309,
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1.2298294422249382706933871574135731278765534034979,
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1.2690359140762658660446752406901433173504503955036,
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}
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phi := math.Pi / 3
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for m := 1; m <= 9; m++ {
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mf := float64(m) / 10
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delta := math.Abs(EllipticF(phi, mf) - vF[m-1])
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if delta > tol {
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t.Fatalf("EllipticF(pi/3,m) test fail for m=%v", mf)
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}
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}
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for test := 0; test < 100; test++ {
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alpha := rnd.Float64() * math.Pi / 4
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beta := rnd.Float64() * math.Pi / 4
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for mi := 0; mi < 9999; mi++ {
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m := float64(mi) / 10000
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Fa := EllipticF(alpha, m)
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Fb := EllipticF(beta, m)
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sina, cosa := math.Sincos(alpha)
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sinb, cosb := math.Sincos(beta)
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tan := (sina*math.Sqrt(1-m*sinb*sinb) + sinb*math.Sqrt(1-m*sina*sina)) / (cosa + cosb)
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gamma := 2 * math.Atan(tan)
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Fg := EllipticF(gamma, m)
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delta := math.Abs(Fa + Fb - Fg)
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if delta > tol {
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t.Fatalf("EllipticF test fail for m=%v, alpha=%v, beta=%v", m, alpha, beta)
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}
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}
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}
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}
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// Testing EllipticE (and EllipticRF, EllipticRD) using the addition theorems from http://dlmf.nist.gov/19.11.i
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func TestEllipticE(t *testing.T) {
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const tol = 1.0e-14
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rnd := rand.New(rand.NewSource(1))
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// The following EllipticE(pi/3,m), m=0.1(0.1)0.9 was computed in Maxima 5.38.0 using Bigfloat arithmetic.
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vE := [...]float64{
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1.0316510822817691068014397636905610074934300946730,
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1.0156973658341766636288643556414001451527597364432,
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9.9929636467826398814855428365155224243586391115108e-1,
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9.8240033979859736941287149003648737502960015189033e-1,
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9.6495145764299257550956863602992167490195750321518e-1,
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9.4687829659158090935158610908054896203271861698355e-1,
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9.2809053417715769009517654522979827392794124845027e-1,
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9.0847044378047233264777277954768245721857017157916e-1,
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8.8785835036531301307661603341327881634688308777383e-1,
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}
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phi := math.Pi / 3
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for m := 1; m <= 9; m++ {
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mf := float64(m) / 10
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delta := math.Abs(EllipticE(phi, mf) - vE[m-1])
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if delta > tol {
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t.Fatalf("EllipticE(pi/3,m) test fail for m=%v", mf)
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}
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}
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for test := 0; test < 100; test++ {
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alpha := rnd.Float64() * math.Pi / 4
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beta := rnd.Float64() * math.Pi / 4
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for mi := 0; mi < 9999; mi++ {
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m := float64(mi) / 10000
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Ea := EllipticE(alpha, m)
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Eb := EllipticE(beta, m)
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sina, cosa := math.Sincos(alpha)
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sinb, cosb := math.Sincos(beta)
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tan := (sina*math.Sqrt(1-m*sinb*sinb) + sinb*math.Sqrt(1-m*sina*sina)) / (cosa + cosb)
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gamma := 2 * math.Atan(tan)
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Eg := EllipticE(gamma, m)
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delta := math.Abs(Ea + Eb - Eg - m*sina*sinb*math.Sin(gamma))
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if delta > tol {
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t.Fatalf("EllipticE test fail for m=%v, alpha=%v, beta=%v", m, alpha, beta)
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}
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}
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}
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}
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