BesselJ-0.2.0.0: tests/Main.hs
module Main where
import Approx ( assertAreClose )
import Data.Complex ( Complex(..), conjugate )
import Test.Tasty ( defaultMain, testGroup )
import Test.Tasty.HUnit ( testCase )
import Math.BesselJ ( BesselResult(..), besselJ )
import Math.AngerJ ( AngerResult(..), angerJ )
import Math.WeberE ( WeberResult(..), weberE )
import Math.AngerWeber ( AngerWeberResult(..), angerWeber )
aResult :: AngerResult -> Complex Double
aResult (AngerResult r _ _) = r
bResult :: BesselResult -> Complex Double
bResult (BesselResult r _ _) = r
wResult :: WeberResult -> Complex Double
wResult (WeberResult r _ _) = r
awResult :: AngerWeberResult -> Complex Double
awResult (AngerWeberResult r _ _) = r
main :: IO ()
main = defaultMain $
testGroup "Tests"
[
testCase "nu = 1+2i -- z = 3+4i" $ do
my <- bResult <$> besselJ (1 :+ 2) (3 :+ 4) 1e-5 5000
let wolfram = 0.31925 :+ (-0.66956)
assertAreClose "" 1e-5 my wolfram,
-- testCase "Relation Bessel-J" $ do
-- let nu = 0.5 :+ 2
-- z = 3 :+ 4
-- y = 2 * sin (nu * pi) / (pi * z)
-- x1 <- bResult <$> jnu (nu-1) z
-- x2 <- bResult <$> jnu (-nu) z
-- x3 <- bResult <$> jnu (1-nu) z
-- x4 <- bResult <$> jnu nu z
-- assertAreClose "" 1e-3 (x1*x2 + x3*x4) y
testCase "recurrence relation" $ do
let nu = 0.5 :+ 2
z = 3 :+ 4
x1 <- bResult <$> besselJ nu z 1e-8 10000
x2 <- bResult <$> besselJ (nu+1) z 1e-8 10000
x3 <- bResult <$> besselJ (nu+2) z 1e-8 10000
let y = 2*(nu+1)/z * x2 - x3
assertAreClose "" 1e-8 x1 y,
testCase "elementary equality" $ do
let z = 3 :+ 4
s = sqrt(2 / pi / z) * sin z
x <- bResult <$> besselJ 0.5 z 1e-5 5000
assertAreClose "" 1e-10 x s,
testCase "remove square root" $ do
let z = 2 :+ 1
nu = (-0.3) :+ 1
x <- bResult <$> besselJ nu (sqrt (z*z)) 1e-5 5000
y <- bResult <$> besselJ nu z 1e-5 5000
assertAreClose "" 1e-7 x (z**(-nu) * (z*z)**(nu/2) * y),
testCase "remove square root --- integer nu" $ do
let z = 2 :+ 1
nu = -4
x <- bResult <$> besselJ nu (sqrt (z*z)) 1e-5 5000
y <- bResult <$> besselJ nu z 1e-5 5000
assertAreClose "" 1e-7 x (z**(-nu) * (z*z)**(nu/2) * y),
testCase "remove minus sign" $ do
let z = 2 :+ 1
nu = (-0.3) :+ 1
x <- bResult <$> besselJ nu (-z) 1e-5 5000
y <- bResult <$> besselJ nu z 1e-5 5000
assertAreClose "" 1e-7 x ((-z)**nu * z**(-nu) * y),
testCase "conjugate" $ do
let z = 2 :+ 5
nu = 0.3 :+ (-1)
x <- bResult <$> besselJ (conjugate nu) (conjugate z) 1e-5 5000
y <- bResult <$> besselJ nu z 1e-5 5000
assertAreClose "" 1e-7 x (conjugate y),
testCase "conjugate --- integer nu" $ do
let z = 2 :+ 5
nu = 7
x <- bResult <$> besselJ nu (conjugate z) 1e-5 5000
y <- bResult <$> besselJ nu z 1e-5 5000
assertAreClose "" 1e-7 x (conjugate y),
-- Anger --------
testCase "Anger at z = 0" $ do
let nu = (-2.3) :+ 1
y = sin(pi*nu) / (pi*nu)
x <- aResult <$> angerJ nu 0 1e-5 5000
assertAreClose "" 1e-8 x y,
testCase "Anger is Bessel when nu is integer" $ do
let z = 2 :+ 6
nu = 10
x <- aResult <$> angerJ nu z 1e-5 5000
y <- bResult <$> besselJ nu z 1e-5 5000
assertAreClose "" 1e-8 x y,
testCase "Anger - remove minus sign" $ do
let z = 2 :+ 1
nu = (-0.3) :+ 1
x <- aResult <$> angerJ nu (-z) 1e-5 5000
y <- aResult <$> angerJ (-nu) z 1e-5 5000
assertAreClose "" 1e-8 x y,
testCase "Anger - recurrence relation" $ do
let z = (-2) :+ 1
nu = (-0.3) :+ 1
x1 <- aResult <$> angerJ (nu-1) z 1e-5 5000
x2 <- aResult <$> angerJ (nu+1) z 1e-5 5000
y <- aResult <$> angerJ nu z 1e-5 5000
let x = x1 + x2
y' = 2*nu/z * y - 2*sin(pi*nu)/(pi*z)
assertAreClose "" 1e-8 x y',
-- Weber --------
testCase "Weber at z = 0" $ do
let nu = (-2.3) :+ 1
y = (1 - cos(pi*nu)) / (pi*nu)
x <- wResult <$> weberE nu 0 1e-5 5000
assertAreClose "" 1e-7 x y,
testCase "Weber - remove minus sign" $ do
let z = 2 :+ 1
nu = (-0.3) :+ 1
x <- wResult <$> weberE nu (-z) 1e-5 5000
y <- wResult <$> weberE (-nu) z 1e-5 5000
assertAreClose "" 1e-7 x (-y),
testCase "Weber - recurrence relation" $ do
let z = (-2) :+ 1
nu = (-0.3) :+ 1
x1 <- wResult <$> weberE (nu-1) z 1e-5 5000
x2 <- wResult <$> weberE (nu+1) z 1e-5 5000
y <- wResult <$> weberE nu z 1e-5 5000
let x = x1 + x2
y' = 2*nu/z * y - 2*(1-cos(pi*nu))/(pi*z)
assertAreClose "" 1e-7 x y',
-- Relations between Anger and Weber --------
testCase "Relation 1 between Anger and Weber" $ do
let z = (-7) :+ 6
nu = (-3.3) :+ 9
w1 <- wResult <$> weberE nu z 1e-5 5000
w2 <- wResult <$> weberE (-nu) z 1e-5 5000
a <- aResult <$> angerJ nu z 1e-5 5000
assertAreClose "" 1e-7 (sin(pi*nu)*a) (cos(pi*nu)*w1 - w2),
testCase "Relation 2 between Anger and Weber" $ do
let z = (-7) :+ 6
nu = (-3.3) :+ 9
a1 <- aResult <$> angerJ nu z 1e-5 5000
a2 <- aResult <$> angerJ (-nu) z 1e-5 5000
w <- wResult <$> weberE nu z 1e-5 5000
assertAreClose "" 1e-7 (sin(pi*nu)*w) (a2 - cos(pi*nu)*a1),
-- Anger-Weber --------
testCase "A value of Anger-Weber" $ do
let z = 2.5 :+ 0.5
nu = 1.0 / 3.0
wolfram = 0.102015 :+ (-0.0162118)
aw <- awResult <$> angerWeber nu z 1e-6 5000
assertAreClose "" 1e-5 aw wolfram
]