 #!/usr/bin/env python
# A. Pletzer Tue Mar 20 11:42:05 EST 2001

"""
Gauss Integration
"""


_ngmax = 12
_ngmin = 1


_nodes  =(
(0.,),
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)

_weights=(
(2.,),
(1.,
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(0.05566856711621584,
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)

_nodesLog  =(
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(0.1120088061669761,
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(0.06389079308732544,
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(0.04144848019938324,
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(0.02913447215197205,
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(0.02163400584411693,
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_weightsLog=(
(-1.,),
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(-0.5134045522323634,
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def sum(a):
	return reduce(lambda x, y: x+y, a)

def mult(a, b):
	return map(lambda x, y: x*y, a, b)

# make global 
xmin, xmax, =0., 1.
dx = xmax - xmin

def gauss(xmin, xmax, funct, ng=10):
	"""
	Gauss quadature (weight function = 1.0):
	xmin, xmax: boundaries of integration domain
	funct: integrand function
	ng: Gauss integration order
	"""
	ng = max((min((ng, _ngmax)), _ngmin))
	ns = _nodes[ng-1]
	ws = _weights[ng-1];
	dx = xmax - xmin
	x = map(lambda y: (dx*y + xmin + xmax)/2., ns)
	return 0.5*dx*sum(mult(funct(x), ws))

def gaussLog(xmin, xmax, funct, ng=10):
	"""
	Gauss quadature with Log singularity at x=xmin:
	xmin, xmax: boundaries of integration domain
	funct: integrand function
	ng: Gauss integration order
	"""
	ng = max((min((ng, _ngmax)), _ngmin))
	ns = _nodesLog[ng-1]
	ws = _weightsLog[ng-1];
	dx = xmax - xmin
	x = map(lambda y: (dx*y + xmin), ns)
	return dx*sum(mult(funct(x), ws))


####

if __name__ == '__main__':

	from math import *


	def f2(x):
		return map(lambda y: y**2, x)
	def f3(x):
		return map(lambda y: y**4, x)
	def f4(x):
		return map(lambda y: cos(2.*pi*(y-0.128726465)), x)
	def f5(x):
		return map(lambda y: 2.*cos(2.*pi*(y-0.128726465))**2, x)

	print '-'*80
	print 'Gauss (weight function = 1)'
	print '-'*80

	# simple tests
	print 'gauss(0., 1., f3, 1)=', gauss(0., 1., f3, 1)
	print 'gauss(0., 1., f3, 2)=', gauss(0., 1., f3, 2)
	print 'gauss(0., 1., f4, 3)=', gauss(0., 1., f3, 3)
	print 'gauss(0., 1., f3   )=', gauss(0., 1., f3   )

	# convergence test 
	ng = range(_ngmin, _ngmax+1)

	print """\n
	Integrate[Cos[2.*Pi*(x-0.128726465)], {x, 0, 1}]
	\n"""

	error = []
	for n in ng:
		error.append(gauss(0., 10.0, f4, n))
	print '    n = ', '%8d'*len(ng)    % tuple(ng)
	print 'error = ','%8.0e'*len(error) % tuple(error) 
		
	print """\n
	Integrate[2.*Cos[2.*Pi*(x-0.128726465)]^2, {x, 0, 1}]
	\n"""

	error = []
	for n in ng:
		error.append(gauss(0., 1.0, f5, n)-1.0)
	print '    n = ', '%8d'*len(ng)    % tuple(ng)
	print 'error = ','%8.0e'*len(error) % tuple(error) 


	print '-'*80
	print 'Gauss with Log singularity at left boundary'
	print '-'*80

	a, b = 0., 1.

	print """\n
	Integrate[Log[x]*x^2, {x, 0, 1}]
	\n"""

	exact = -1./9.
	error = []
	for n in ng:
		error.append(gaussLog(a, b, f2, n) - exact)
	print '    n = ', '%8d'*len(ng)    % tuple(ng)
	print 'error = ','%8.0e'*len(error) % tuple(error) 

	print """\n
	Integrate[Log[x]*2.*Cos[2.*Pi*(x-0.128726465)]^2, {x, 0, 1}]
	\n"""

	exact = -1.242002481967963
	error = []
	for n in ng:
		error.append(gaussLog(a, b, f5, n) - exact)
	print '    n = ', '%8d'*len(ng)    % tuple(ng)
	print 'error = ','%8.0e'*len(error) % tuple(error) 
