# HW 32
#
# The integrate.quad function cannot handle
# the improper integrals from Problems 1 and 
# 3 from HW 29.  It can do the second problem.

import numpy as np
from scipy import integrate

def hw29p2(x):
    return np.exp(-x**2)

def hw30p1(x,r):
    return np.exp(-r*x)

def hw30p2(x,m,n):
    return np.sin(m*x)*np.cos(n*x)

def hw30p3(x,r):
    return np.exp(-r*x)*np.cos(2*x)

# HW 29, P2
s1 = integrate.quad(hw29p2,0,np.inf)
exact = np.sqrt(np.pi)/2
re = (s1[0]-exact)/exact
print('HW 29, p2 =',s1,re)

# Hw 30, P1
r = 0.3
s2 = integrate.quad(lambda x: hw30p1(x,r),0,2)
print('HW 30, p1 = ',s2)

# HW 30, P2
m = 0.5
n = 1.4
s3 = integrate.quad(lambda x: hw30p2(x,m,n),0,2)
print('HW 30, p2',s3)
      
# HW 30, P3
I = []
r = []
print('r   I')
for i in range(11):
    rval = i/10
    r.append(rval)
    temp = integrate.quad(lambda x: hw30p3(x,rval),0,1)
    I.append(temp[0])
    print(rval,temp[0])


# HW 29, p2 = (0.8862269254527579, 7.101318390915439e-09) 0.0
# HW 30, p1 =  (1.5039612130199118, 1.6697323668378858e-14)
# HW 30, p2 (-0.21047164888710243, 5.512197086338426e-15)
# r   I
# 0.0 0.45464871341284085
# 0.1 0.44468508597054823
# 0.2 0.43492128134880575
# 0.3 0.4253630687826127
# 0.4 0.4160147145847368
# 0.5 0.4068791632915984
# 0.6 0.3979582001736366
# 0.7 0.3892525969149162
# 0.8 0.3807622420968074
# 0.9 0.37248625796640916
# 1.0 0.3644231048305502