import matplotlib.pyplot as plt
import numpy as np
#import pandas as pd
from array import *

#vectors x1 and x2 drawn independently from Gaussian distribution with zero mean
#and unit variance

row = np.arange(0,1,0.001)

#CREATE AN ARRAY FOR EACH COMPONENT

for i in row:
	A = np.random.normal(loc=0.0, scale=1.0, size=100)
	x1 = np.array([A])

for i in row:
	B = np.random.normal(loc=0.0, scale=1.0, size=100)
	x2 = np.array([B])

#print x2.shape
	
for i in row:
	C = A + B
	x3 = np.array([C])

#print x3.shape

array = np.array([[x1], [x2], [x3]])
#print array
#print array.shape

#CALCULATE COVARIANCE

#matrix = np.asmatrix(array)
#print matrix

#matrix has to be square to calculate covar
#totalcovar = np.cov(matrix)
#print '\n', "the complete covariance matrix is:", '\n', totalcovar


#find covariance matrix between each dimension

covar_x1_x2 = np.cov(x1, x2)
covar_x1_x3 = np.cov(x1, x3)
covar_x2_x3 = np.cov(x2, x3)

print '\n',"covariances for x1 & x2 are:", '\n',covar_x1_x2
print '\n',"covariances for x1 & x3 are:", '\n',covar_x1_x3
print '\n',"covariances for x2 & x3 are:", '\n',covar_x2_x3

#check that covar is an array:
#print "covar shape =", covar_x1_x2.shape

#FIND EIGEN VALUES AND EIGEN VECTORS

evalx1x2, evecx1x2 = np.linalg.eig(covar_x1_x2)
evalx1x3, evecx1x3 = np.linalg.eig(covar_x1_x3)
evalx2x3, evecx2x3 = np.linalg.eig(covar_x2_x3)

print '\n',"eigen values for x1 & x2 are:", '\n',evalx1x2
print '\n',"eigen vectors for x1 & x2 are:", '\n',evecx1x2
print '\n',"eigen values for x1 & x3 are:", '\n',evalx1x3
print '\n',"eigen vectors for x1 & x3 are:", '\n',evecx1x3
print '\n',"eigen values for x2 & x3 are:", '\n',evalx2x3
print '\n',"eigen vectors for x2 & x3 are:", '\n',evecx2x3

#CREATE A FEATURE VECTOR FROM 3D EIGEN VECTORS

#sort eigen vectors by eigen value
#right now I have an array for each eigen value and eigen vector for each component
#columns in evecxx correspond to i in eval.

#sort dimension x1,x2

index = evalx1x2.argsort()
evalx1x2 = evalx1x2[index]
evecx1x2 = evecx1x2[:,index]

print '\n',"sorted eigen values & vectors for x1,x2:"
print '\n', evalx1x2
print '\n', evecx1x2

#sort dimesion x1, x3

index = evalx1x3.argsort()
evalx1x2 = evalx1x3[index]
evecx1x2 = evecx1x3[:,index]

print '\n',"sorted eigen values & vectors for x1,x3:"
print '\n', evalx1x3
print '\n', evecx1x3

#sort dimension x2, x3

index = evalx2x3.argsort()
evalx1x2 = evalx2x3[index]
evecx1x2 = evecx2x3[:,index]

print '\n',"sorted eigen values & vectors for x2,x3:"
print '\n', evalx2x3
print '\n', evecx2x3

#select highest values as PC F

print '\n',"Here are my Feature Vectors:"

PC1 = np.delete(evecx1x2, 1, 1)
print '\n', PC1

PC2 = np.delete(evecx1x3, 1, 1)
print '\n', PC2

PC3 = np.delete(evecx2x3, 1, 1)
print '\n', PC3

#RECONSTRUCT DATA

#FinalData =  RowFeatureVector x RowDataAdjust
#RowFeatureVector = matrix of eigen vectors transposed
#RowDataAdjust = mean-adjusted data transposed

RowFeatVec1 = PC1.transpose
RowFeatVec2 = PC2.transpose
RowFeatVec3 = PC3.transpose

#print PC1.shape

#RowDataAdjust1 = x1.transpose
#RowDataAdjust2 = x2.transpose
#RowDataAdjust3 = x3.transpose

print "this runs"

FinalData1 = np.multiply(PC1, x1)
FinalData2 = np.multiply(PC2, x2)
FinalData3 = np.multiply(PC3, x3)

print '\n',"Final Data 1, 2 & 3:"
print '\n', FinalData1, '\n', FinalData2, '\n', FinalData3

#PLOT

plt.plot(FinalData1, 'r--') 
plt.show()

#write output to a txt and csv file
#location = "/Users/eroyall/Documents/Modules/vectorsgen.txt"
#location2= "/Users/eroyall/Documents/Modules/vectorsgen.csv"
#np.savetxt(location, vector, fmt='%2.5f', delimiter=' ')
#np.savetxt(location2, vector, fmt='%2.5f', delimiter=' ')