#!/usr/bin/python -Wall

# ================================================================
# John Kerl
# kerl.john.r@gmail.com
# 2007-06-26
#
# Numerical complex integration.
#
# ----------------------------------------------------------------
# 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.
from math     import *
from cmath    import * # For complex-valued sqrt, exp, etc.
from kerlutil import * # For ztrange and numint

# ----------------------------------------------------------------
def f(z):
	return sqrt(z) / (1 + z**2)

# ----------------------------------------------------------------
N = 10000
R = 0.001
print "Inner loop:"
print numint(f, ztrange(R, 0, 2*pi,  N))
print

print "Along real axis, above branch cut:"
for R in [40, 60, 80, 100, 200, 300, 1000]:
	print "R = %8.3f" % (R),
	print numint(f, frange(0.0+0j, R+0j, N*10))
print

R = 10000
print "Outer loop:"
print numint(f, ztrange(R, 0, 2*pi,  N*10))