module Main where
import Approx ( approx )
import Data.Complex ( Complex(..) )
import Math.JacobiTheta
( jtheta1
, jtheta2
, jtheta3
, jtheta4
, jtheta1'
, jtheta2'
, jtheta3'
, jtheta4'
, jtheta1Dash
, jtheta1Dash0
, jthetaAB
, jthetaAB' )
import Test.Tasty (defaultMain, testGroup)
import Test.Tasty.HUnit (assertEqual, testCase)
i_ :: Complex Double
i_ = 0.0 :+ 1.0
q :: Complex Double
q = exp (-pi)
q' :: Complex Double
q' = exp (-pi/10)
q'' :: Complex Double
q'' = exp (i_ * pi * tau)
where
tau = 2.0 :+ 2.0
main :: IO ()
main = defaultMain $
testGroup "Tests"
[ testCase "a jtheta1 value" $ do
let expected = 1.1816128551455719 :+ 0.59589712760417439
obtained = jtheta1 (1 :+ 1) q
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "another jtheta1 value" $ do
let expected = 1.75929905417707 :+ 0.0
obtained = jtheta1 2 q'
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "yet another jtheta1 value" $ do
let expected = 0.539843563932874 :+ 0.26400643871132
obtained = jtheta1 (1 :+ 1) q''
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "a jtheta2 value" $ do
let expected = 0.74328632006610539 :+ (-0.904159309718008)
obtained = jtheta2 (1 :+ 1) q
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "a jtheta3 value" $ do
let expected = 0.86456184935441778 :+ (-0.28488586703507289)
obtained = jtheta3 (1 :+ 1) q
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "a jtheta4 value" $ do
let expected = 1.1351891564632007 :+ 0.28517396444192509
obtained = jtheta4 (1 :+ 1) q
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "a jtheta3 value with a negative q" $ do
let expected = (-23.82995222123) :+ (-12.77832967427)
obtained = jtheta3 (1 :+ 1) (-0.730402691048646)
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "a jtheta1Dash value" $ do
let expected = 0.81117649363854416 :+ (-0.89452803853474627)
obtained = jtheta1Dash (1 :+ 1) q
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "Jacobi identity with the nome" $ do
let q''' = 0.556 :+ 0.283
theta2 = jtheta2 0 q'''
theta3 = jtheta3 0 q'''
theta4 = jtheta4 0 q'''
expected = theta3**4
obtained = theta2**4 + theta4**4
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "Jacobi identity with tau" $ do
let tau = 5.55 :+ 0.23
theta2 = jtheta2' 0 tau
theta3 = jtheta3' 0 tau
theta4 = jtheta4' 0 tau
expected = theta3**4
obtained = theta2**4 + theta4**4
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "Edge case" $ do
let tau = 0.7792256 :+ 1.0e-7
q'''' = exp(i_ * pi * tau)
obtained = jtheta2 0 q''''
expected = 27.746815969548447 :+ 31.241216782108797
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "jtheta1Dash at 0" $ do
let q''' = 0.556 :+ 0.283
expected = jtheta1Dash0 q'''
obtained = jtheta1Dash 0 q'''
assertEqual ""
(approx 10 obtained)
(approx 10 expected),
testCase "jtheta1 is minus jthetaAB with a=b=0.5" $ do
let tau = 5.55 :+ 0.23
z = 0.2 :+ 0.3
mtheta1 = - jtheta1' z tau
thetaAB = jthetaAB' 0.5 0.5 z tau
assertEqual ""
(approx 10 mtheta1)
(approx 10 thetaAB),
testCase "A formula involving some jthetaAB at z=0" $ do
let q''' = 0.556 :+ 0.283
expected = (jthetaAB (1/6) 0.5 0 q''')**3
obtained =
(jthetaAB (1/6) (1/6) 0 q''')**3 + (jthetaAB (1/6) (5/6) 0 q''')**3
assertEqual ""
(approx 10 obtained)
(approx 10 expected)
]