#!/usr/bin/env python
#----------------------------------------------------------------------
#	stdnorml.py
#	
#	This program outputs a table showing areas under the standard
#	Normal Distribution from  0  to  z > 0  in increments of 0.01.
#
#		execute using:  $ python ./stdnorml.py
#
#	programmer: ALLAN CRUSE
#	written on: 22 FEB 2011
#----------------------------------------------------------------------

import math

def phi( z ):
	root_2pi = math.sqrt( 2.0 * 3.141592653589793 )
	den = root_2pi * math.exp( z * z / 2.0 )
	return	1.0 / den

def area( z ):
	# returns area under graph of  y = phi()  from 0 to z 
	# computed using the Trapezoid Rule with 400 rectangles
	areasum = 0.0
	delta_x = z / 400.0
	x0 = 0.0
	x1 = delta_x
	for i in range( 400 ):
		phi_0 = phi( x0 )
		phi_1 = phi( x1 )
		areasum += (phi_0 + phi_1) * delta_x / 2.0
		x0 += delta_x
		x1 += delta_x
	return	areasum	

print		
print
print "          ",
print "Table of areas under the standard normal curve from 0 to z "
print
print
print "   z    ",
for col in range( 10 ):
	print "  %d   " % col,
print

z = 0.0
delta_z = 0.01
for row in range( 40 ):
	print " %1.2f: " % z,
	for col in range( 10 ):
		val = area( z )
		z += delta_z
		print "%1.4f" % val,
	print
	if ( (row % 5) == 4 ):
		 print  
print