tanveer-sayyed

import matplotlib.pyplot as plt
import numpy as np
from numpy import array
from sklearn.decomposition import PCA

D = array([[1, 1],[2, 2],[3, 3],[4, 4],[5, 5], # Matrix D has all the 
           [6, 6],[7, 7],[8, 8],[9, 9]])       # points on line x = y
# Adding noise:
E = np.zeros(np.shape(D))
E = D + np.random.rand(np.shape(D)[0], np.shape(D)[1])

tanveer-sayyed

A = np.array([[1, 4], [2, 3]])
lambdas, eigenVectors = np.linalg.eig(A)
eigenVectors = Scaling_Eigen_Vectors(eigenVectors= eigenVectors)
print('lambdas: \n', lambdas)
Λ = np.around(np.linalg.inv(eigenVectors).dot(A).dot(eigenVectors),
              decimals= 8)
print('diagonalized lambdas (Λ): \n', Λ)
# power of matrix = 20
print('With factorization: \n', eigenVectors.dot(Λ**20).dot(np.linalg.inv(eigenVectors)))
print('Without factorization: \n', M .dot(M).dot(M).dot(M).dot(M).dot(M).

tanveer-sayyed

F = np.array([[1,1],[1,0]])
print('F^1: \n', F)
print('F^2: \n', F.dot(F))
print('F^3: \n', F.dot(F).dot(F))
print('F^4: \n', F.dot(F).dot(F).dot(F))
print('F^5: \n', F.dot(F).dot(F).dot(F).dot(F))

lambdas, eigenVectors = np.linalg.eig(F)
eigenVectors = Scaling_Eigen_Vectors(eigenVectors= eigenVectors)
print('lambdas of F^1: \n', lambdas)

tanveer-sayyed

A = np.array([[1, 4], [2, 3]])
print('A: \n', A)
lambdas, eigenVectors = np.linalg.eig(A)
eigenVectors = Scaling_Eigen_Vectors(eigenVectors= eigenVectors)
print('lambdas: \n', lambdas)
print('eigenvectors: \n', eigenVectors)
Plot_All(A, eigenVectors)

Output:
A:

tanveer-sayyed

def Plot_All(A, eigenvectors):
    plt.figure(figsize=(12,3))
    plt.subplot(1,3,1)
    V = [np.array([[0, 0]]), [eigenVectors]] # padded [0,0] just to get the pink colour
    for i in range(len(V)):
        for j in range(len(V[i])):
            plt.quiver(*([0],[0]), V[i][j][0], V[i][j][1], angles='xy', scale_units='xy', scale=1, color=plt.cm.Paired((i+3)/10.))
    plt.grid(b=True, which='major', linestyle= ':')
    plt.xticks(np.arange(-5, 5 + 1, 1))
    plt.yticks(np.arange(-5, 5 + 1, 1))

tanveer-sayyed

Q = np.array([[0, -1], [1, 0]]) # All REAL numbers
print('Asymmetry check: \n', Q == -np.transpose(Q) )
lambdas, eigenVectors = np.linalg.eig(Q)
eigenVectors = Scaling_Eigen_Vectors(eigenVectors= eigenVectors)
print('lambdas: \n', lambdas)
print('eigenvectors: \n', eigenVectors)


Output:
Asymmetry check: 

tanveer-sayyed

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
@author: tanveer
"""

import pandas as pd
import numpy as np
import random
from sklearn.datasets import load_iris

tanveer-sayyed

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
@author: tanveer
"""

"""On Spyder editor hit F5. On jupyter-notebook paste in a single cell and press ctrl+Enter. Run atleast 15 times."""
threshold = 0.70 # TRY thresholds -> {0.72, 0.73, 0.74, 0.75}

import time

tanveer-sayyed

valueCounts = {}
def CountAll():
    global all_columns, nanCounts, valueCounts
    all_columns = list(df)
    nanCounts = df.isnull().sum()
    for x in all_columns:
        valueCounts[x] = df[x].value_counts()

"""Random but proportional replacement(RBPR) of numeric"""
def Fill_NaNs_Numeric(col):

tanveer-sayyed

valueCounts = {}
def CountAll():
    global all_columns, nanCounts, valueCounts
    all_columns = list(df)
    nanCounts = df.isnull().sum()
    for x in all_columns:
        valueCounts[x] = df[x].value_counts()        
"""-------------------------------------------------------------------------"""

def Fill_NaNs_Catigorical(col):