#!/usr/bin/env python

# ----------------------------------------------------------------
# John Kerl
# kerl.john.r@gmail.com
# 2006-06-04
# ----------------------------------------------------------------
# This software is released under the terms of the GNU GPL.
# Please see LICENSE.txt in the same directory as this file.
# ================================================================

from __future__ import division # 1/2 = 0.5, not 0.
# Import the cmath module rather than the math module so that exp et al. may
# take complex arguments.
from cmath import *
import sys

# ----------------------------------------------------------------
def f(z):
	return exp(1j*z)/((z-1j)**2)

# ----------------------------------------------------------------
def pathz(t):
	return t * (1+0j)

# ----------------------------------------------------------------
# Mesh over path
tlo = -40.0
thi =  40.0
nt  = 10000
tabulate = 0

# Start of numerical approximation to the integral
sum = 0.0
t   = tlo
dt  = (thi - tlo) / nt
for it in range(0, nt):
	t1 = t
	t2 = t + dt

	z  = pathz(t1)
	dz = pathz(t2) - z

	w = f(z)
	sum += w * dz

	if tabulate:
		print ">> t = %8.4f/2pi z = %8.4f +%8.4fi dz = %8.4f +%8.4fi w = %8.4f +%8.4fi sum = %8.4f +%8.4fi" % \
			(t/2/pi, z.real, z.imag, dz.real, dz.imag, w.real, w.imag, sum.real, sum.imag)

	t += dt

print "%11.7f +%11.7fi" % (sum.real, sum.imag)