# -*- coding: utf-8 -*-

"""

Spyder Editor

This is a temporary script file.

"""

import sympy as sy

import numpy as np

from matplotlib import pyplot as plt

from sympy import fourier_series,pi,cos,sin

from sympy.abc import x,t

from sympy import Piecewise,And,plot

print("1:Fourier Series of a function in an interval")

print("2:Fourier Series of a piecewise function")#to be added

n=int(input("Enter your Choice"))

if n==1:

expr1=input("Enter the function to find fourier series")

expr1=sy.factor(expr1)

try1=int(input("Enter 1 to enter interval in terms of pi or it's multiples,Otherwise enter 0"))

if try1==1:

interval1=int(input("Enter the multiple of pi that you want,Eg:2 represents 2*pi"))

interval2=int(input("Enter the multiple of pi that you want,Eg:2 represents 2*pi"))

interval1=interval1*pi

interval2=interval2*pi

else:

interval1=float(input("Enter the Starting point of the interval"))

interval2=float(input("Enter the Ending point of the interval"))

s = fourier_series(expr1, (x,interval1,interval2 ))

truncval=int(input("enter the number of terms desired in the fourier series"))

v=s.truncate(truncval)

print("FOURIER SERIES OF THE ENTERED FUNCTION\n\n\n")

print(v)

x1=[i for i in np.arange(interval1,interval2,0.02)]

y1=[(v.evalf(subs={x:j})) for j in np.arange(interval1,interval2,0.02)]

x2=[i for i in np.arange(interval1,interval2,0.0001)]

y2=[(expr1.evalf(subs={x:j})) for j in np.arange(interval1,interval2,0.0001)]

plt.plot(x1,y1,'red',label="GRAPH OF FOURIER SERIES")

plt.plot(x2,y2,'green',label="ORIGINAL GRAPH OF THE FUNCTION")

print("#PLOT IN GREEN SHOWS THE ACTUAL GRAPH OF THE FUNCTION")

print("#PLOT IN RED SHOWS THE GRAPH OF THE FOURIER SERIES")

plt.legend(loc="best")

plt.title('Harmonic Analysis')

plt.show()

elif n==2:

print("Enter all functions as functions of 't' ie. f(t)")

fval1=input("Enter the Value of the piecewise function in the first interval")

fval1=sy.factor(fval1)

fval2=input("Enter the Value of the piecewise function in the second interval")

fval2=sy.factor(fval2)

try1=int(input("Enter 1 to enter limits in terms of pi,Else enter 0"))

if try1==0:

fval1_lowerlimit=float(input("Enter the lower limit for the first interval"))

fval1_upperlimit=float(input("Enter the upper limit for the first interval"))

fval2_lowerlimit=float(input("Enter the lower limit for the second interval"))

fval2_upperlimit=float(input("Enter the upper limit for the second interval"))

elif try1==1:

fval1_lowerlimit=float(input("Enter the lower limit for the first interval in terms of multiples of pi,Eg:2 represents 2*pi"))

fval1_upperlimit=float(input("Enter the upper limit for the first interval in terms of multiples of pi,Eg:2 represents 2*pi"))

fval2_lowerlimit=float(input("Enter the lower limit for the second interval in terms of multiples of pi,Eg:2 represents 2*pi"))

fval2_upperlimit=float(input("Enter the upper limit for the second interval in terms of multiples of pi,Eg:2 represents 2*pi"))

fval1_lowerlimit=fval1_lowerlimit*pi

fval1_upperlimit=fval1_upperlimit*pi

fval2_lowerlimit=fval2_lowerlimit*pi

fval2_upperlimit=fval2_upperlimit*pi

truncval1=int(input("Enter the number of terms desired in the fourier series"))

p=Piecewise((fval1,And(fval1_lowerlimit<t, t <fval1_upperlimit)),(fval2, And(t >fval2_lowerlimit,t<fval2_upperlimit)))

fs = fourier_series(p, (t,fval1_lowerlimit,fval2_upperlimit)).truncate(truncval1)

print("FOURIER SERIES OF THE ENTERED FUNCTION\n\n\n")

print(fs)

x1=[i for i in np.arange(fval1_lowerlimit,fval2_upperlimit,0.02)]

y1=[(fs.evalf(subs={t:j})) for j in np.arange(fval1_lowerlimit,fval2_upperlimit,0.02)]

x2=[i for i in np.arange(fval1_lowerlimit,fval2_upperlimit,0.0001)]

y2=[(p.evalf(subs={t:j})) for j in np.arange(fval1_lowerlimit,fval2_upperlimit,0.0001)]

plt.plot(x1,y1,'red',label="GRAPH OF FOURIER SERIES")

plt.plot(x2,y2,'green',label="ORIGINAL GRAPH OF THE FUNCTION")

print("\n\n#PLOT IN GREEN SHOWS THE ACTUAL GRAPH OF THE FUNCTION")

print("\n\n#PLOT IN RED SHOWS THE GRAPH OF THE FOURIER SERIES")

plt.legend(loc="best")

plt.title('Harmonic Analysis')

plt.show()