From 14bc59e4aa906787da85fe04fe8ddd0d03b0e49a Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Tue, 25 Jun 2019 20:08:20 +0530
Subject: [PATCH 01/27] Added week 1 assignment via upload

---
 .../Week 1/jayakar_week1/computeCost.m        |  23 +++
 .../Week 1/jayakar_week1/computeCostMulti.m   |  24 +++
 .../Week 1/jayakar_week1/ex1.m                | 135 +++++++++++++++
 .../Week 1/jayakar_week1/ex1_multi.m          | 162 ++++++++++++++++++
 .../Week 1/jayakar_week1/ex1data1.txt         |  97 +++++++++++
 .../Week 1/jayakar_week1/ex1data2.txt         |  47 +++++
 .../Week 1/jayakar_week1/featureNormalize.m   |  42 +++++
 .../Week 1/jayakar_week1/gradientDescent.m    |  31 ++++
 .../jayakar_week1/gradientDescentMulti.m      |  44 +++++
 .../Week 1/jayakar_week1/normalEqn.m          |  23 +++
 .../Week 1/jayakar_week1/plotData.m           |  27 +++
 .../Week 1/jayakar_week1/warmUpExercise.m     |  21 +++
 12 files changed, 676 insertions(+)
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/computeCost.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/computeCostMulti.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/ex1.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/ex1_multi.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/ex1data1.txt
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/ex1data2.txt
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/featureNormalize.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/gradientDescent.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/gradientDescentMulti.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/normalEqn.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/plotData.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week1/warmUpExercise.m

diff --git a/Programming Assignment/Week 1/jayakar_week1/computeCost.m b/Programming Assignment/Week 1/jayakar_week1/computeCost.m
new file mode 100644
index 0000000..67babf2
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/computeCost.m	
@@ -0,0 +1,23 @@
+function J = computeCost(X, y, theta)
+%COMPUTECOST Compute cost for linear regression
+%   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
+%   parameter for linear regression to fit the data points in X and y
+
+% Initialize some useful values
+m = length(y);
+h=zeros(m); % number of training examples
+h=X*theta;
+% You need to return the following variables correctly 
+J = 0;
+for i=1:m,J=J+((h(i)-y(i))^2);,end;
+J=(J/(2*m));
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta
+%               You should set J to the cost.
+
+
+
+
+
+% =========================================================================
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/computeCostMulti.m b/Programming Assignment/Week 1/jayakar_week1/computeCostMulti.m
new file mode 100644
index 0000000..b2aec95
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/computeCostMulti.m	
@@ -0,0 +1,24 @@
+function J = computeCostMulti(X, y, theta)
+%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
+%   J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
+%   parameter for linear regression to fit the data points in X and y
+
+% Initialize some useful values
+m = length(y);
+h=zeros(m); % number of training examples
+h=X*theta;
+% You need to return the following variables correctly 
+J = 0;
+for i=1:m,J=J+((h(i)-y(i))^2);,end;
+J=(J/(2*m));
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta
+%               You should set J to the cost.
+
+
+
+
+
+% =========================================================================
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/ex1.m b/Programming Assignment/Week 1/jayakar_week1/ex1.m
new file mode 100644
index 0000000..ad6a4aa
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/ex1.m	
@@ -0,0 +1,135 @@
+%% Machine Learning Online Class - Exercise 1: Linear Regression
+
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the
+%  linear exercise. You will need to complete the following functions
+%  in this exericse:
+%
+%     warmUpExercise.m
+%     plotData.m
+%     gradientDescent.m
+%     computeCost.m
+%     gradientDescentMulti.m
+%     computeCostMulti.m
+%     featureNormalize.m
+%     normalEqn.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+% x refers to the population size in 10,000s
+% y refers to the profit in $10,000s
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% ==================== Part 1: Basic Function ====================
+% Complete warmUpExercise.m
+fprintf('Running warmUpExercise ... \n');
+fprintf('5x5 Identity Matrix: \n');
+warmUpExercise()
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ======================= Part 2: Plotting =======================
+fprintf('Plotting Data ...\n')
+data = load('ex1data1.txt');
+X = data(:, 1); y = data(:, 2);
+m = length(y); % number of training examples
+
+% Plot Data
+% Note: You have to complete the code in plotData.m
+plotData(X, y);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% =================== Part 3: Cost and Gradient descent ===================
+
+X = [ones(m, 1), data(:,1)]; % Add a column of ones to x
+theta = zeros(2, 1); % initialize fitting parameters
+
+% Some gradient descent settings
+iterations = 1500;
+alpha = 0.01;
+
+fprintf('\nTesting the cost function ...\n')
+% compute and display initial cost
+J = computeCost(X, y, theta);
+fprintf('With theta = [0 ; 0]\nCost computed = %f\n', J);
+fprintf('Expected cost value (approx) 32.07\n');
+
+% further testing of the cost function
+J = computeCost(X, y, [-1 ; 2]);
+fprintf('\nWith theta = [-1 ; 2]\nCost computed = %f\n', J);
+fprintf('Expected cost value (approx) 54.24\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+fprintf('\nRunning Gradient Descent ...\n')
+% run gradient descent
+theta = gradientDescent(X, y, theta, alpha, iterations);
+
+% print theta to screen
+fprintf('Theta found by gradient descent:\n');
+fprintf('%f\n', theta);
+fprintf('Expected theta values (approx)\n');
+fprintf(' -3.6303\n  1.1664\n\n');
+
+% Plot the linear fit
+hold on; % keep previous plot visible
+plot(X(:,2), X*theta, '-')
+legend('Training data', 'Linear regression')
+hold off % don't overlay any more plots on this figure
+
+% Predict values for population sizes of 35,000 and 70,000
+predict1 = [1, 3.5] *theta;
+fprintf('For population = 35,000, we predict a profit of %f\n',...
+    predict1*10000);
+predict2 = [1, 7] * theta;
+fprintf('For population = 70,000, we predict a profit of %f\n',...
+    predict2*10000);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ============= Part 4: Visualizing J(theta_0, theta_1) =============
+fprintf('Visualizing J(theta_0, theta_1) ...\n')
+
+% Grid over which we will calculate J
+theta0_vals = linspace(-10, 10, 100);
+theta1_vals = linspace(-1, 4, 100);
+
+% initialize J_vals to a matrix of 0's
+J_vals = zeros(length(theta0_vals), length(theta1_vals));
+
+% Fill out J_vals
+for i = 1:length(theta0_vals)
+    for j = 1:length(theta1_vals)
+	  t = [theta0_vals(i); theta1_vals(j)];
+	  J_vals(i,j) = computeCost(X, y, t);
+    end
+end
+
+
+% Because of the way meshgrids work in the surf command, we need to
+% transpose J_vals before calling surf, or else the axes will be flipped
+J_vals = J_vals';
+% Surface plot
+figure;
+surf(theta0_vals, theta1_vals, J_vals)
+xlabel('\theta_0'); ylabel('\theta_1');
+
+% Contour plot
+figure;
+% Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
+contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
+xlabel('\theta_0'); ylabel('\theta_1');
+hold on;
+plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);
diff --git a/Programming Assignment/Week 1/jayakar_week1/ex1_multi.m b/Programming Assignment/Week 1/jayakar_week1/ex1_multi.m
new file mode 100644
index 0000000..cfb2a20
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/ex1_multi.m	
@@ -0,0 +1,162 @@
+%% Machine Learning Online Class
+%  Exercise 1: Linear regression with multiple variables
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the
+%  linear regression exercise. 
+%
+%  You will need to complete the following functions in this 
+%  exericse:
+%
+%     warmUpExercise.m
+%     plotData.m
+%     gradientDescent.m
+%     computeCost.m
+%     gradientDescentMulti.m
+%     computeCostMulti.m
+%     featureNormalize.m
+%     normalEqn.m
+%
+%  For this part of the exercise, you will need to change some
+%  parts of the code below for various experiments (e.g., changing
+%  learning rates).
+%
+
+%% Initialization
+
+%% ================ Part 1: Feature Normalization ================
+
+%% Clear and Close Figures
+clear ; close all; clc
+
+fprintf('Loading data ...\n');
+
+%% Load Data
+data = load('ex1data2.txt');
+X = data(:, 1:2);
+y = data(:, 3);
+m = length(y);
+
+% Print out some data points
+fprintf('First 10 examples from the dataset: \n');
+fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+% Scale features and set them to zero mean
+fprintf('Normalizing Features ...\n');
+
+[X mu sigma] = featureNormalize(X);
+
+% Add intercept term to X
+X = [ones(m, 1) X];
+
+
+%% ================ Part 2: Gradient Descent ================
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: We have provided you with the following starter
+%               code that runs gradient descent with a particular
+%               learning rate (alpha). 
+%
+%               Your task is to first make sure that your functions - 
+%               computeCost and gradientDescent already work with 
+%               this starter code and support multiple variables.
+%
+%               After that, try running gradient descent with 
+%               different values of alpha and see which one gives
+%               you the best result.
+%
+%               Finally, you should complete the code at the end
+%               to predict the price of a 1650 sq-ft, 3 br house.
+%
+% Hint: By using the 'hold on' command, you can plot multiple
+%       graphs on the same figure.
+%
+% Hint: At prediction, make sure you do the same feature normalization.
+%
+
+fprintf('Running gradient descent ...\n');
+
+% Choose some alpha value
+alpha = 0.01;
+num_iters = 400;
+% Init Theta and Run Gradient Descent 
+theta = zeros(3, 1);
+[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);
+alpha=0.3;
+[theta, J1] = gradientDescentMulti(X, y, theta, alpha, num_iters);
+alpha=0.1;
+[theta, J2] = gradientDescentMulti(X, y, theta, alpha, num_iters);
+alpha=0.03;
+[theta, J3] = gradientDescentMulti(X, y, theta, alpha, num_iters);
+% Plot the convergence graph
+figure;
+plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
+xlabel('Number of iterations');
+ylabel('Cost J');
+% Display gradient descent's result
+fprintf('Theta computed from gradient descent: \n');
+fprintf(' %f \n', theta);
+fprintf('\n');
+
+% Estimate the price of a 1650 sq-ft, 3 br house
+% ====================== YOUR CODE HERE ======================
+% Recall that the first column of X is all-ones. Thus, it does
+% not need to be normalized.
+price = 0; % You should change this
+pogo=([1650,3]-mu)./sigma;
+price=([1,pogo])*theta;
+% ============================================================
+
+fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
+         '(using gradient descent):\n $%f\n'], price);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ================ Part 3: Normal Equations ================
+
+fprintf('Solving with normal equations...\n');
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: The following code computes the closed form 
+%               solution for linear regression using the normal
+%               equations. You should complete the code in 
+%               normalEqn.m
+%
+%               After doing so, you should complete this code 
+%               to predict the price of a 1650 sq-ft, 3 br house.
+%
+
+%% Load Data
+data = csvread('ex1data2.txt');
+X = data(:, 1:2);
+y = data(:, 3);
+m = length(y);
+
+% Add intercept term to X
+X = [ones(m, 1) X];
+
+% Calculate the parameters from the normal equation
+theta = normalEqn(X, y);
+
+% Display normal equation's result
+fprintf('Theta computed from the normal equations: \n');
+fprintf(' %f \n', theta);
+fprintf('\n');
+
+
+% Estimate the price of a 1650 sq-ft, 3 br house
+% ====================== YOUR CODE HERE ======================
+price = 0; % You should change this
+price =[1,1650,3]*theta;
+
+% ============================================================
+
+fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
+         '(using normal equations):\n $%f\n'], price);
+
diff --git a/Programming Assignment/Week 1/jayakar_week1/ex1data1.txt b/Programming Assignment/Week 1/jayakar_week1/ex1data1.txt
new file mode 100644
index 0000000..0f88ccb
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/ex1data1.txt	
@@ -0,0 +1,97 @@
+6.1101,17.592
+5.5277,9.1302
+8.5186,13.662
+7.0032,11.854
+5.8598,6.8233
+8.3829,11.886
+7.4764,4.3483
+8.5781,12
+6.4862,6.5987
+5.0546,3.8166
+5.7107,3.2522
+14.164,15.505
+5.734,3.1551
+8.4084,7.2258
+5.6407,0.71618
+5.3794,3.5129
+6.3654,5.3048
+5.1301,0.56077
+6.4296,3.6518
+7.0708,5.3893
+6.1891,3.1386
+20.27,21.767
+5.4901,4.263
+6.3261,5.1875
+5.5649,3.0825
+18.945,22.638
+12.828,13.501
+10.957,7.0467
+13.176,14.692
+22.203,24.147
+5.2524,-1.22
+6.5894,5.9966
+9.2482,12.134
+5.8918,1.8495
+8.2111,6.5426
+7.9334,4.5623
+8.0959,4.1164
+5.6063,3.3928
+12.836,10.117
+6.3534,5.4974
+5.4069,0.55657
+6.8825,3.9115
+11.708,5.3854
+5.7737,2.4406
+7.8247,6.7318
+7.0931,1.0463
+5.0702,5.1337
+5.8014,1.844
+11.7,8.0043
+5.5416,1.0179
+7.5402,6.7504
+5.3077,1.8396
+7.4239,4.2885
+7.6031,4.9981
+6.3328,1.4233
+6.3589,-1.4211
+6.2742,2.4756
+5.6397,4.6042
+9.3102,3.9624
+9.4536,5.4141
+8.8254,5.1694
+5.1793,-0.74279
+21.279,17.929
+14.908,12.054
+18.959,17.054
+7.2182,4.8852
+8.2951,5.7442
+10.236,7.7754
+5.4994,1.0173
+20.341,20.992
+10.136,6.6799
+7.3345,4.0259
+6.0062,1.2784
+7.2259,3.3411
+5.0269,-2.6807
+6.5479,0.29678
+7.5386,3.8845
+5.0365,5.7014
+10.274,6.7526
+5.1077,2.0576
+5.7292,0.47953
+5.1884,0.20421
+6.3557,0.67861
+9.7687,7.5435
+6.5159,5.3436
+8.5172,4.2415
+9.1802,6.7981
+6.002,0.92695
+5.5204,0.152
+5.0594,2.8214
+5.7077,1.8451
+7.6366,4.2959
+5.8707,7.2029
+5.3054,1.9869
+8.2934,0.14454
+13.394,9.0551
+5.4369,0.61705
diff --git a/Programming Assignment/Week 1/jayakar_week1/ex1data2.txt b/Programming Assignment/Week 1/jayakar_week1/ex1data2.txt
new file mode 100644
index 0000000..79e9a80
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/ex1data2.txt	
@@ -0,0 +1,47 @@
+2104,3,399900
+1600,3,329900
+2400,3,369000
+1416,2,232000
+3000,4,539900
+1985,4,299900
+1534,3,314900
+1427,3,198999
+1380,3,212000
+1494,3,242500
+1940,4,239999
+2000,3,347000
+1890,3,329999
+4478,5,699900
+1268,3,259900
+2300,4,449900
+1320,2,299900
+1236,3,199900
+2609,4,499998
+3031,4,599000
+1767,3,252900
+1888,2,255000
+1604,3,242900
+1962,4,259900
+3890,3,573900
+1100,3,249900
+1458,3,464500
+2526,3,469000
+2200,3,475000
+2637,3,299900
+1839,2,349900
+1000,1,169900
+2040,4,314900
+3137,3,579900
+1811,4,285900
+1437,3,249900
+1239,3,229900
+2132,4,345000
+4215,4,549000
+2162,4,287000
+1664,2,368500
+2238,3,329900
+2567,4,314000
+1200,3,299000
+852,2,179900
+1852,4,299900
+1203,3,239500
diff --git a/Programming Assignment/Week 1/jayakar_week1/featureNormalize.m b/Programming Assignment/Week 1/jayakar_week1/featureNormalize.m
new file mode 100644
index 0000000..49660a5
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/featureNormalize.m	
@@ -0,0 +1,42 @@
+function [X_norm, mu, sigma] = featureNormalize(X)
+%FEATURENORMALIZE Normalizes the features in X 
+%   FEATURENORMALIZE(X) returns a normalized version of X where
+%   the mean value of each feature is 0 and the standard deviation
+%   is 1. This is often a good preprocessing step to do when
+%   working with learning algorithms.
+
+% You need to set these values correctly
+X_norm = X;
+mu = zeros(1, size(X, 2));
+sigma = zeros(1, size(X, 2));
+mu=mean(X_norm);
+X_norm=X_norm-mu;
+sigma=std(X_norm);
+X_norm=X_norm./sigma;
+% ====================== YOUR CODE HERE ======================
+% Instructions: First, for each feature dimension, compute the mean
+%               of the feature and subtract it from the dataset,
+%               storing the mean value in mu. Next, compute the 
+%               standard deviation of each feature and divide
+%               each feature by it's standard deviation, storing
+%               the standard deviation in sigma. 
+%
+%               Note that X is a matrix where each column is a 
+%               feature and each row is an example. You need 
+%               to perform the normalization separately for 
+%               each feature. 
+%
+% Hint: You might find the 'mean' and 'std' functions useful.
+%       
+
+
+
+
+
+
+
+
+
+% ============================================================
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/gradientDescent.m b/Programming Assignment/Week 1/jayakar_week1/gradientDescent.m
new file mode 100644
index 0000000..f4c81a7
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/gradientDescent.m	
@@ -0,0 +1,31 @@
+function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
+%GRADIENTDESCENT Performs gradient descent to learn theta
+%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
+%   taking num_iters gradient steps with learning rate alpha
+
+% Initialize some useful values
+m = length(y); % number of training examples
+J_history = zeros(num_iters, 1);
+h=zeros(m);
+delta=zeros(size(X,2));
+for iter = 1:num_iters
+  h=X*theta;
+  t=theta;
+  delta=(X'*(h-y));
+  theta=t-((alpha/m)*delta);
+  if(theta==t)
+    break;
+  end;
+    % ====================== YOUR CODE HERE ======================
+    % Instructions: Perform a single gradient step on the parameter vector
+    %               theta. 
+    %
+    % Hint: While debugging, it can be useful to print out the values
+    %       of the cost function (computeCost) and gradient here.
+    % ============================================================
+
+    % Save the cost J in every iteration    
+    J_history(iter) = computeCost(X, y, theta);
+end
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/gradientDescentMulti.m b/Programming Assignment/Week 1/jayakar_week1/gradientDescentMulti.m
new file mode 100644
index 0000000..489e34b
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/gradientDescentMulti.m	
@@ -0,0 +1,44 @@
+function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
+%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
+%   theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
+%   taking num_iters gradient steps with learning rate alpha
+
+% Initialize some useful values
+m = length(y); % number of training examples
+J_history = zeros(num_iters, 1);
+h=zeros(m);
+delta=zeros(size(X,2));
+for iter = 1:num_iters
+  h=X*theta;
+  t=theta;
+  delta=(X'*(h-y));
+  theta=t-((alpha/m)*delta);
+  if(theta==t)
+    break;
+  end;
+    % ====================== YOUR CODE HERE ======================
+    % Instructions: Perform a single gradient step on the parameter vector
+    %               theta. 
+    %
+    % Hint: While debugging, it can be useful to print out the values
+    %       of the cost function (computeCostMulti) and gradient here.
+    %
+
+
+
+
+
+
+
+
+
+
+
+    % ============================================================
+
+    % Save the cost J in every iteration    
+    J_history(iter) = computeCostMulti(X, y, theta);
+
+end
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/normalEqn.m b/Programming Assignment/Week 1/jayakar_week1/normalEqn.m
new file mode 100644
index 0000000..a3186f4
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/normalEqn.m	
@@ -0,0 +1,23 @@
+function [theta] = normalEqn(X, y)
+%NORMALEQN Computes the closed-form solution to linear regression 
+%   NORMALEQN(X,y) computes the closed-form solution to linear 
+%   regression using the normal equations.
+
+theta = zeros(size(X, 2), 1);
+theta=pinv(X'*X)*X'*y;
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the code to compute the closed form solution
+%               to linear regression and put the result in theta.
+%
+
+% ---------------------- Sample Solution ----------------------
+
+
+
+
+% -------------------------------------------------------------
+
+
+% ============================================================
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/plotData.m b/Programming Assignment/Week 1/jayakar_week1/plotData.m
new file mode 100644
index 0000000..a223398
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/plotData.m	
@@ -0,0 +1,27 @@
+function plotData(x, y)
+%PLOTDATA Plots the data points x and y into a new figure 
+%   PLOTDATA(x,y) plots the data points and gives the figure axes labels of
+%   population and profit.
+
+figure; % open a new figure window
+plot(x, y, 'rx', 'MarkerSize', 10);
+ylabel('Profit in $10,000s');
+xlabel('Population of City in 10,000s');
+% ====================== YOUR CODE HERE ======================
+% Instructions: Plot the training data into a figure using the 
+%               "figure" and "plot" commands. Set the axes labels using
+%               the "xlabel" and "ylabel" commands. Assume the 
+%               population and revenue data have been passed in
+%               as the x and y arguments of this function.
+%
+% Hint: You can use the 'rx' option with plot to have the markers
+%       appear as red crosses. Furthermore, you can make the
+%       markers larger by using plot(..., 'rx', 'MarkerSize', 10);
+
+
+
+
+
+% ============================================================
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week1/warmUpExercise.m b/Programming Assignment/Week 1/jayakar_week1/warmUpExercise.m
new file mode 100644
index 0000000..cbd295f
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week1/warmUpExercise.m	
@@ -0,0 +1,21 @@
+function A = warmUpExercise()
+%WARMUPEXERCISE Example function in octave
+%   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix
+
+A = eye(5);
+% ============= YOUR CODE HERE ==============
+% Instructions: Return the 5x5 identity matrix 
+%               In octave, we return values by defining which variables
+%               represent the return values (at the top of the file)
+%               and then set them accordingly. 
+
+
+
+
+
+
+
+% ===========================================
+
+
+end

From b9e8e4b70b038e3081c18f3492664d22b22a7eaf Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Tue, 25 Jun 2019 21:14:59 +0530
Subject: [PATCH 02/27] Delete ex1data1.txt

---
 .../Week 1/jayakar_week1/ex1data1.txt         | 97 -------------------
 1 file changed, 97 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week1/ex1data1.txt

diff --git a/Programming Assignment/Week 1/jayakar_week1/ex1data1.txt b/Programming Assignment/Week 1/jayakar_week1/ex1data1.txt
deleted file mode 100644
index 0f88ccb..0000000
--- a/Programming Assignment/Week 1/jayakar_week1/ex1data1.txt	
+++ /dev/null
@@ -1,97 +0,0 @@
-6.1101,17.592
-5.5277,9.1302
-8.5186,13.662
-7.0032,11.854
-5.8598,6.8233
-8.3829,11.886
-7.4764,4.3483
-8.5781,12
-6.4862,6.5987
-5.0546,3.8166
-5.7107,3.2522
-14.164,15.505
-5.734,3.1551
-8.4084,7.2258
-5.6407,0.71618
-5.3794,3.5129
-6.3654,5.3048
-5.1301,0.56077
-6.4296,3.6518
-7.0708,5.3893
-6.1891,3.1386
-20.27,21.767
-5.4901,4.263
-6.3261,5.1875
-5.5649,3.0825
-18.945,22.638
-12.828,13.501
-10.957,7.0467
-13.176,14.692
-22.203,24.147
-5.2524,-1.22
-6.5894,5.9966
-9.2482,12.134
-5.8918,1.8495
-8.2111,6.5426
-7.9334,4.5623
-8.0959,4.1164
-5.6063,3.3928
-12.836,10.117
-6.3534,5.4974
-5.4069,0.55657
-6.8825,3.9115
-11.708,5.3854
-5.7737,2.4406
-7.8247,6.7318
-7.0931,1.0463
-5.0702,5.1337
-5.8014,1.844
-11.7,8.0043
-5.5416,1.0179
-7.5402,6.7504
-5.3077,1.8396
-7.4239,4.2885
-7.6031,4.9981
-6.3328,1.4233
-6.3589,-1.4211
-6.2742,2.4756
-5.6397,4.6042
-9.3102,3.9624
-9.4536,5.4141
-8.8254,5.1694
-5.1793,-0.74279
-21.279,17.929
-14.908,12.054
-18.959,17.054
-7.2182,4.8852
-8.2951,5.7442
-10.236,7.7754
-5.4994,1.0173
-20.341,20.992
-10.136,6.6799
-7.3345,4.0259
-6.0062,1.2784
-7.2259,3.3411
-5.0269,-2.6807
-6.5479,0.29678
-7.5386,3.8845
-5.0365,5.7014
-10.274,6.7526
-5.1077,2.0576
-5.7292,0.47953
-5.1884,0.20421
-6.3557,0.67861
-9.7687,7.5435
-6.5159,5.3436
-8.5172,4.2415
-9.1802,6.7981
-6.002,0.92695
-5.5204,0.152
-5.0594,2.8214
-5.7077,1.8451
-7.6366,4.2959
-5.8707,7.2029
-5.3054,1.9869
-8.2934,0.14454
-13.394,9.0551
-5.4369,0.61705

From 3383f30451c5e2b667735c8eb7d8ad54cad8a164 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Tue, 25 Jun 2019 21:15:32 +0530
Subject: [PATCH 03/27] Delete ex1data2.txt

---
 .../Week 1/jayakar_week1/ex1data2.txt         | 47 -------------------
 1 file changed, 47 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week1/ex1data2.txt

diff --git a/Programming Assignment/Week 1/jayakar_week1/ex1data2.txt b/Programming Assignment/Week 1/jayakar_week1/ex1data2.txt
deleted file mode 100644
index 79e9a80..0000000
--- a/Programming Assignment/Week 1/jayakar_week1/ex1data2.txt	
+++ /dev/null
@@ -1,47 +0,0 @@
-2104,3,399900
-1600,3,329900
-2400,3,369000
-1416,2,232000
-3000,4,539900
-1985,4,299900
-1534,3,314900
-1427,3,198999
-1380,3,212000
-1494,3,242500
-1940,4,239999
-2000,3,347000
-1890,3,329999
-4478,5,699900
-1268,3,259900
-2300,4,449900
-1320,2,299900
-1236,3,199900
-2609,4,499998
-3031,4,599000
-1767,3,252900
-1888,2,255000
-1604,3,242900
-1962,4,259900
-3890,3,573900
-1100,3,249900
-1458,3,464500
-2526,3,469000
-2200,3,475000
-2637,3,299900
-1839,2,349900
-1000,1,169900
-2040,4,314900
-3137,3,579900
-1811,4,285900
-1437,3,249900
-1239,3,229900
-2132,4,345000
-4215,4,549000
-2162,4,287000
-1664,2,368500
-2238,3,329900
-2567,4,314000
-1200,3,299000
-852,2,179900
-1852,4,299900
-1203,3,239500

From 15e42b6ffff27b095787efe4e327c59223e8feea Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:45:46 +0530
Subject: [PATCH 04/27] Add files via upload

---
 costFunction.m         |  35 ++++++++++
 costFunctionReg.m      |  32 +++++++++
 ex2.m                  | 151 +++++++++++++++++++++++++++++++++++++++++
 ex2_reg.m              | 136 +++++++++++++++++++++++++++++++++++++
 mapFeature.m           |  21 ++++++
 plotData.m             |  32 +++++++++
 plotDecisionBoundary.m |  48 +++++++++++++
 predict.m              |  28 ++++++++
 sigmoid.m              |  20 ++++++
 9 files changed, 503 insertions(+)
 create mode 100644 costFunction.m
 create mode 100644 costFunctionReg.m
 create mode 100644 ex2.m
 create mode 100644 ex2_reg.m
 create mode 100644 mapFeature.m
 create mode 100644 plotData.m
 create mode 100644 plotDecisionBoundary.m
 create mode 100644 predict.m
 create mode 100644 sigmoid.m

diff --git a/costFunction.m b/costFunction.m
new file mode 100644
index 0000000..9f7d711
--- /dev/null
+++ b/costFunction.m
@@ -0,0 +1,35 @@
+function [J, grad] = costFunction(theta, X, y)
+%COSTFUNCTION Compute cost and gradient for logistic regression
+%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
+%   parameter for logistic regression and the gradient of the cost
+%   w.r.t. to the parameters.
+
+% Initialize some useful values
+m = length(y); % number of training examples
+% You need to return the following variables correctly 
+h=X*theta;
+h=sigmoid(h);
+J = 0;
+J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
+J=J/m;
+grad = zeros(size(theta));
+grad=(1/m)*(X'*(h-y));
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+%
+% Note: grad should have the same dimensions as theta
+%
+
+
+
+
+
+
+
+
+% =============================================================
+
+end
diff --git a/costFunctionReg.m b/costFunctionReg.m
new file mode 100644
index 0000000..86e2e21
--- /dev/null
+++ b/costFunctionReg.m
@@ -0,0 +1,32 @@
+function [J, grad] = costFunctionReg(theta, X, y, lambda)
+%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
+%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
+%   theta as the parameter for regularized logistic regression and the
+%   gradient of the cost w.r.t. to the parameters. 
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+h=X*theta;
+h=sigmoid(h);
+J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
+J=J/m;
+k=ones(1,size(theta,1));
+l=theta.^2;
+J=J+(lambda/(2*m))*(k*l);
+J=J-(lambda/(2*m))*l(1,1);
+grad=(1/m)*(X'*(h-y));
+grad=grad+(lambda/m)*theta;
+grad(1)=grad(1)-(lambda/m)*theta(1);
+% =============================================================
+
+end
diff --git a/ex2.m b/ex2.m
new file mode 100644
index 0000000..103fe11
--- /dev/null
+++ b/ex2.m
@@ -0,0 +1,151 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the logistic
+%  regression exercise. You will need to complete the following functions 
+%  in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = load('ex2data1.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+%% ==================== Part 1: Plotting ====================
+%  We start the exercise by first plotting the data to understand the 
+%  the problem we are working with.
+
+fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
+         'indicating (y = 0) examples.\n']);
+
+plotData(X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============ Part 2: Compute Cost and Gradient ============
+%  In this part of the exercise, you will implement the cost and gradient
+%  for logistic regression. You neeed to complete the code in 
+%  costFunction.m
+
+%  Setup the data matrix appropriately, and add ones for the intercept term
+[m, n] = size(X);
+
+% Add intercept term to x and X_test
+X = [ones(m, 1) X];
+
+% Initialize fitting parameters
+initial_theta = zeros(n + 1, 1);
+
+% Compute and display initial cost and gradient
+[cost, grad] = costFunction(initial_theta, X, y);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros): \n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
+
+% Compute and display cost and gradient with non-zero theta
+test_theta = [-24; 0.2; 0.2];
+[cost, grad] = costFunction(test_theta, X, y);
+
+fprintf('\nCost at test theta: %f\n', cost);
+fprintf('Expected cost (approx): 0.218\n');
+fprintf('Gradient at test theta: \n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============= Part 3: Optimizing using fminunc  =============
+%  In this exercise, you will use a built-in function (fminunc) to find the
+%  optimal parameters theta.
+
+%  Set options for fminunc
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+%  Run fminunc to obtain the optimal theta
+%  This function will return theta and the cost 
+[theta, cost] = ...
+	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
+
+% Print theta to screen
+fprintf('Cost at theta found by fminunc: %f\n', cost);
+fprintf('Expected cost (approx): 0.203\n');
+fprintf('theta: \n');
+fprintf(' %f \n', theta);
+fprintf('Expected theta (approx):\n');
+fprintf(' -25.161\n 0.206\n 0.201\n');
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============== Part 4: Predict and Accuracies ==============
+%  After learning the parameters, you'll like to use it to predict the outcomes
+%  on unseen data. In this part, you will use the logistic regression model
+%  to predict the probability that a student with score 45 on exam 1 and 
+%  score 85 on exam 2 will be admitted.
+%
+%  Furthermore, you will compute the training and test set accuracies of 
+%  our model.
+%
+%  Your task is to complete the code in predict.m
+
+%  Predict probability for a student with score 45 on exam 1 
+%  and score 85 on exam 2 
+
+prob = sigmoid([1 45 85] * theta);
+fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
+         'probability of %f\n'], prob);
+fprintf('Expected value: 0.775 +/- 0.002\n\n');
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+fprintf('Expected accuracy (approx): 89.0\n');
+fprintf('\n');
+
+
diff --git a/ex2_reg.m b/ex2_reg.m
new file mode 100644
index 0000000..f363318
--- /dev/null
+++ b/ex2_reg.m
@@ -0,0 +1,136 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the second part
+%  of the exercise which covers regularization with logistic regression.
+%
+%  You will need to complete the following functions in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the X values and the third column
+%  contains the label (y).
+
+data = load('ex2data2.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+plotData(X, y);
+
+% Put some labels
+hold on;
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+% Specified in plot order
+legend('y = 1', 'y = 0')
+hold off;
+
+
+%% =========== Part 1: Regularized Logistic Regression ============
+%  In this part, you are given a dataset with data points that are not
+%  linearly separable. However, you would still like to use logistic
+%  regression to classify the data points.
+%
+%  To do so, you introduce more features to use -- in particular, you add
+%  polynomial features to our data matrix (similar to polynomial
+%  regression).
+%
+
+% Add Polynomial Features
+
+% Note that mapFeature also adds a column of ones for us, so the intercept
+% term is handled
+X = mapFeature(X(:,1), X(:,2));
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1
+lambda = 1;
+
+% Compute and display initial cost and gradient for regularized logistic
+% regression
+[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros) - first five values only:\n');
+fprintf(' %f \n', grad(1:5));
+fprintf('Expected gradients (approx) - first five values only:\n');
+fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+% Compute and display cost and gradient
+% with all-ones theta and lambda = 10
+test_theta = ones(size(X,2),1);
+[cost, grad] = costFunctionReg(test_theta, X, y, 10);
+
+fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
+fprintf('Expected cost (approx): 3.16\n');
+fprintf('Gradient at test theta - first five values only:\n');
+fprintf(' %f \n', grad(1:5));
+fprintf('Expected gradients (approx) - first five values only:\n');
+fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============= Part 2: Regularization and Accuracies =============
+%  Optional Exercise:
+%  In this part, you will get to try different values of lambda and
+%  see how regularization affects the decision coundart
+%
+%  Try the following values of lambda (0, 1, 10, 100).
+%
+%  How does the decision boundary change when you vary lambda? How does
+%  the training set accuracy vary?
+%
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1 (you should vary this)
+lambda = 1;
+
+% Set Options
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+% Optimize
+[theta, J, exit_flag] = ...
+	fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+hold on;
+title(sprintf('lambda = %g', lambda))
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+legend('y = 1', 'y = 0', 'Decision boundary')
+hold off;
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
+
diff --git a/mapFeature.m b/mapFeature.m
new file mode 100644
index 0000000..d02a72a
--- /dev/null
+++ b/mapFeature.m
@@ -0,0 +1,21 @@
+function out = mapFeature(X1, X2)
+% MAPFEATURE Feature mapping function to polynomial features
+%
+%   MAPFEATURE(X1, X2) maps the two input features
+%   to quadratic features used in the regularization exercise.
+%
+%   Returns a new feature array with more features, comprising of 
+%   X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
+%
+%   Inputs X1, X2 must be the same size
+%
+
+degree = 6;
+out = ones(size(X1(:,1)));
+for i = 1:degree
+    for j = 0:i
+        out(:, end+1) = (X1.^(i-j)).*(X2.^j);
+    end
+end
+
+end
\ No newline at end of file
diff --git a/plotData.m b/plotData.m
new file mode 100644
index 0000000..d8e7f9d
--- /dev/null
+++ b/plotData.m
@@ -0,0 +1,32 @@
+function plotData(X, y)
+%PLOTDATA Plots the data points X and y into a new figure 
+%   PLOTDATA(x,y) plots the data points with + for the positive examples
+%   and o for the negative examples. X is assumed to be a Mx2 matrix.
+figure;
+pos = find(y==1); neg = find(y == 0);
+plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,'MarkerSize', 7);
+ hold on;
+plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
+
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Plot the positive and negative examples on a
+%               2D plot, using the option 'k+' for the positive
+%               examples and 'ko' for the negative examples.
+%
+
+
+
+
+
+
+
+
+
+% =========================================================================
+
+
+
+hold off;
+
+end
diff --git a/plotDecisionBoundary.m b/plotDecisionBoundary.m
new file mode 100644
index 0000000..cd36314
--- /dev/null
+++ b/plotDecisionBoundary.m
@@ -0,0 +1,48 @@
+function plotDecisionBoundary(theta, X, y)
+%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
+%the decision boundary defined by theta
+%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
+%   positive examples and o for the negative examples. X is assumed to be 
+%   a either 
+%   1) Mx3 matrix, where the first column is an all-ones column for the 
+%      intercept.
+%   2) MxN, N>3 matrix, where the first column is all-ones
+
+% Plot Data
+plotData(X(:,2:3), y);
+hold on
+
+if size(X, 2) <= 3
+    % Only need 2 points to define a line, so choose two endpoints
+    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
+
+    % Calculate the decision boundary line
+    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
+
+    % Plot, and adjust axes for better viewing
+    plot(plot_x, plot_y)
+    
+    % Legend, specific for the exercise
+    legend('Admitted', 'Not admitted', 'Decision Boundary')
+    axis([30, 100, 30, 100])
+else
+    % Here is the grid range
+    u = linspace(-1, 1.5, 50);
+    v = linspace(-1, 1.5, 50);
+
+    z = zeros(length(u), length(v));
+    % Evaluate z = theta*x over the grid
+    for i = 1:length(u)
+        for j = 1:length(v)
+            z(i,j) = mapFeature(u(i), v(j))*theta;
+        end
+    end
+    z = z'; % important to transpose z before calling contour
+
+    % Plot z = 0
+    % Notice you need to specify the range [0, 0]
+    contour(u, v, z, [0, 0], 'LineWidth', 2)
+end
+hold off
+
+end
diff --git a/predict.m b/predict.m
new file mode 100644
index 0000000..c85ac58
--- /dev/null
+++ b/predict.m
@@ -0,0 +1,28 @@
+function p = predict(theta, X)
+%PREDICT Predict whether the label is 0 or 1 using learned logistic 
+%regression parameters theta
+%   p = PREDICT(theta, X) computes the predictions for X using a 
+%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
+
+m = size(X, 1); % Number of training examples
+
+% You need to return the following variables correctly
+p = zeros(m, 1);
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the following code to make predictions using
+%               your learned logistic regression parameters. 
+%               You should set p to a vector of 0's and 1's
+%
+h=sigmoid(X*theta);
+for i=1:m
+  if  h(i)>=0.5
+    p(i)=1;
+  end;
+  if h(i) < 0.5
+    p(i)=0;
+   end;
+end;
+% =========================================================================
+
+
+end
diff --git a/sigmoid.m b/sigmoid.m
new file mode 100644
index 0000000..e36d8d0
--- /dev/null
+++ b/sigmoid.m
@@ -0,0 +1,20 @@
+function g = sigmoid(z)
+%SIGMOID Compute sigmoid function
+%   g = SIGMOID(z) computes the sigmoid of z.
+
+% You need to return the following variables correctly 
+g = zeros(size(z));
+z= -1*z;
+g= 1+exp(z);
+g=1./g;
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
+%               vector or scalar).
+
+
+
+
+
+% =============================================================
+
+end

From 39e93116db27bbc027a38547975a13cb4a624f1d Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:47:43 +0530
Subject: [PATCH 05/27] Delete costFunction.m

---
 costFunction.m | 35 -----------------------------------
 1 file changed, 35 deletions(-)
 delete mode 100644 costFunction.m

diff --git a/costFunction.m b/costFunction.m
deleted file mode 100644
index 9f7d711..0000000
--- a/costFunction.m
+++ /dev/null
@@ -1,35 +0,0 @@
-function [J, grad] = costFunction(theta, X, y)
-%COSTFUNCTION Compute cost and gradient for logistic regression
-%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
-%   parameter for logistic regression and the gradient of the cost
-%   w.r.t. to the parameters.
-
-% Initialize some useful values
-m = length(y); % number of training examples
-% You need to return the following variables correctly 
-h=X*theta;
-h=sigmoid(h);
-J = 0;
-J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
-J=J/m;
-grad = zeros(size(theta));
-grad=(1/m)*(X'*(h-y));
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the cost of a particular choice of theta.
-%               You should set J to the cost.
-%               Compute the partial derivatives and set grad to the partial
-%               derivatives of the cost w.r.t. each parameter in theta
-%
-% Note: grad should have the same dimensions as theta
-%
-
-
-
-
-
-
-
-
-% =============================================================
-
-end

From f90793bf01ed468afe34e48677be12214ecfff6e Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:47:54 +0530
Subject: [PATCH 06/27] Delete costFunctionReg.m

---
 costFunctionReg.m | 32 --------------------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 costFunctionReg.m

diff --git a/costFunctionReg.m b/costFunctionReg.m
deleted file mode 100644
index 86e2e21..0000000
--- a/costFunctionReg.m
+++ /dev/null
@@ -1,32 +0,0 @@
-function [J, grad] = costFunctionReg(theta, X, y, lambda)
-%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
-%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
-%   theta as the parameter for regularized logistic regression and the
-%   gradient of the cost w.r.t. to the parameters. 
-
-% Initialize some useful values
-m = length(y); % number of training examples
-
-% You need to return the following variables correctly 
-J = 0;
-grad = zeros(size(theta));
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the cost of a particular choice of theta.
-%               You should set J to the cost.
-%               Compute the partial derivatives and set grad to the partial
-%               derivatives of the cost w.r.t. each parameter in theta
-h=X*theta;
-h=sigmoid(h);
-J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
-J=J/m;
-k=ones(1,size(theta,1));
-l=theta.^2;
-J=J+(lambda/(2*m))*(k*l);
-J=J-(lambda/(2*m))*l(1,1);
-grad=(1/m)*(X'*(h-y));
-grad=grad+(lambda/m)*theta;
-grad(1)=grad(1)-(lambda/m)*theta(1);
-% =============================================================
-
-end

From d8a47c064c3ab6a34460b3a230b1149b8c94ad4e Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:48:10 +0530
Subject: [PATCH 07/27] Delete ex2.m

---
 ex2.m | 151 ----------------------------------------------------------
 1 file changed, 151 deletions(-)
 delete mode 100644 ex2.m

diff --git a/ex2.m b/ex2.m
deleted file mode 100644
index 103fe11..0000000
--- a/ex2.m
+++ /dev/null
@@ -1,151 +0,0 @@
-%% Machine Learning Online Class - Exercise 2: Logistic Regression
-%
-%  Instructions
-%  ------------
-% 
-%  This file contains code that helps you get started on the logistic
-%  regression exercise. You will need to complete the following functions 
-%  in this exericse:
-%
-%     sigmoid.m
-%     costFunction.m
-%     predict.m
-%     costFunctionReg.m
-%
-%  For this exercise, you will not need to change any code in this file,
-%  or any other files other than those mentioned above.
-%
-
-%% Initialization
-clear ; close all; clc
-
-%% Load Data
-%  The first two columns contains the exam scores and the third column
-%  contains the label.
-
-data = load('ex2data1.txt');
-X = data(:, [1, 2]); y = data(:, 3);
-
-%% ==================== Part 1: Plotting ====================
-%  We start the exercise by first plotting the data to understand the 
-%  the problem we are working with.
-
-fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
-         'indicating (y = 0) examples.\n']);
-
-plotData(X, y);
-
-% Put some labels 
-hold on;
-% Labels and Legend
-xlabel('Exam 1 score')
-ylabel('Exam 2 score')
-
-% Specified in plot order
-legend('Admitted', 'Not admitted')
-hold off;
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-
-%% ============ Part 2: Compute Cost and Gradient ============
-%  In this part of the exercise, you will implement the cost and gradient
-%  for logistic regression. You neeed to complete the code in 
-%  costFunction.m
-
-%  Setup the data matrix appropriately, and add ones for the intercept term
-[m, n] = size(X);
-
-% Add intercept term to x and X_test
-X = [ones(m, 1) X];
-
-% Initialize fitting parameters
-initial_theta = zeros(n + 1, 1);
-
-% Compute and display initial cost and gradient
-[cost, grad] = costFunction(initial_theta, X, y);
-
-fprintf('Cost at initial theta (zeros): %f\n', cost);
-fprintf('Expected cost (approx): 0.693\n');
-fprintf('Gradient at initial theta (zeros): \n');
-fprintf(' %f \n', grad);
-fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
-
-% Compute and display cost and gradient with non-zero theta
-test_theta = [-24; 0.2; 0.2];
-[cost, grad] = costFunction(test_theta, X, y);
-
-fprintf('\nCost at test theta: %f\n', cost);
-fprintf('Expected cost (approx): 0.218\n');
-fprintf('Gradient at test theta: \n');
-fprintf(' %f \n', grad);
-fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-
-%% ============= Part 3: Optimizing using fminunc  =============
-%  In this exercise, you will use a built-in function (fminunc) to find the
-%  optimal parameters theta.
-
-%  Set options for fminunc
-options = optimset('GradObj', 'on', 'MaxIter', 400);
-
-%  Run fminunc to obtain the optimal theta
-%  This function will return theta and the cost 
-[theta, cost] = ...
-	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
-
-% Print theta to screen
-fprintf('Cost at theta found by fminunc: %f\n', cost);
-fprintf('Expected cost (approx): 0.203\n');
-fprintf('theta: \n');
-fprintf(' %f \n', theta);
-fprintf('Expected theta (approx):\n');
-fprintf(' -25.161\n 0.206\n 0.201\n');
-
-% Plot Boundary
-plotDecisionBoundary(theta, X, y);
-
-% Put some labels 
-hold on;
-% Labels and Legend
-xlabel('Exam 1 score')
-ylabel('Exam 2 score')
-
-% Specified in plot order
-legend('Admitted', 'Not admitted')
-hold off;
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-%% ============== Part 4: Predict and Accuracies ==============
-%  After learning the parameters, you'll like to use it to predict the outcomes
-%  on unseen data. In this part, you will use the logistic regression model
-%  to predict the probability that a student with score 45 on exam 1 and 
-%  score 85 on exam 2 will be admitted.
-%
-%  Furthermore, you will compute the training and test set accuracies of 
-%  our model.
-%
-%  Your task is to complete the code in predict.m
-
-%  Predict probability for a student with score 45 on exam 1 
-%  and score 85 on exam 2 
-
-prob = sigmoid([1 45 85] * theta);
-fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
-         'probability of %f\n'], prob);
-fprintf('Expected value: 0.775 +/- 0.002\n\n');
-
-% Compute accuracy on our training set
-p = predict(theta, X);
-
-fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
-fprintf('Expected accuracy (approx): 89.0\n');
-fprintf('\n');
-
-

From a7476804c749c3f136094d9da8cae6ac7a0e387e Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:48:19 +0530
Subject: [PATCH 08/27] Delete ex2_reg.m

---
 ex2_reg.m | 136 ------------------------------------------------------
 1 file changed, 136 deletions(-)
 delete mode 100644 ex2_reg.m

diff --git a/ex2_reg.m b/ex2_reg.m
deleted file mode 100644
index f363318..0000000
--- a/ex2_reg.m
+++ /dev/null
@@ -1,136 +0,0 @@
-%% Machine Learning Online Class - Exercise 2: Logistic Regression
-%
-%  Instructions
-%  ------------
-%
-%  This file contains code that helps you get started on the second part
-%  of the exercise which covers regularization with logistic regression.
-%
-%  You will need to complete the following functions in this exericse:
-%
-%     sigmoid.m
-%     costFunction.m
-%     predict.m
-%     costFunctionReg.m
-%
-%  For this exercise, you will not need to change any code in this file,
-%  or any other files other than those mentioned above.
-%
-
-%% Initialization
-clear ; close all; clc
-
-%% Load Data
-%  The first two columns contains the X values and the third column
-%  contains the label (y).
-
-data = load('ex2data2.txt');
-X = data(:, [1, 2]); y = data(:, 3);
-
-plotData(X, y);
-
-% Put some labels
-hold on;
-
-% Labels and Legend
-xlabel('Microchip Test 1')
-ylabel('Microchip Test 2')
-
-% Specified in plot order
-legend('y = 1', 'y = 0')
-hold off;
-
-
-%% =========== Part 1: Regularized Logistic Regression ============
-%  In this part, you are given a dataset with data points that are not
-%  linearly separable. However, you would still like to use logistic
-%  regression to classify the data points.
-%
-%  To do so, you introduce more features to use -- in particular, you add
-%  polynomial features to our data matrix (similar to polynomial
-%  regression).
-%
-
-% Add Polynomial Features
-
-% Note that mapFeature also adds a column of ones for us, so the intercept
-% term is handled
-X = mapFeature(X(:,1), X(:,2));
-
-% Initialize fitting parameters
-initial_theta = zeros(size(X, 2), 1);
-
-% Set regularization parameter lambda to 1
-lambda = 1;
-
-% Compute and display initial cost and gradient for regularized logistic
-% regression
-[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
-
-fprintf('Cost at initial theta (zeros): %f\n', cost);
-fprintf('Expected cost (approx): 0.693\n');
-fprintf('Gradient at initial theta (zeros) - first five values only:\n');
-fprintf(' %f \n', grad(1:5));
-fprintf('Expected gradients (approx) - first five values only:\n');
-fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-% Compute and display cost and gradient
-% with all-ones theta and lambda = 10
-test_theta = ones(size(X,2),1);
-[cost, grad] = costFunctionReg(test_theta, X, y, 10);
-
-fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
-fprintf('Expected cost (approx): 3.16\n');
-fprintf('Gradient at test theta - first five values only:\n');
-fprintf(' %f \n', grad(1:5));
-fprintf('Expected gradients (approx) - first five values only:\n');
-fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-%% ============= Part 2: Regularization and Accuracies =============
-%  Optional Exercise:
-%  In this part, you will get to try different values of lambda and
-%  see how regularization affects the decision coundart
-%
-%  Try the following values of lambda (0, 1, 10, 100).
-%
-%  How does the decision boundary change when you vary lambda? How does
-%  the training set accuracy vary?
-%
-
-% Initialize fitting parameters
-initial_theta = zeros(size(X, 2), 1);
-
-% Set regularization parameter lambda to 1 (you should vary this)
-lambda = 1;
-
-% Set Options
-options = optimset('GradObj', 'on', 'MaxIter', 400);
-
-% Optimize
-[theta, J, exit_flag] = ...
-	fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
-
-% Plot Boundary
-plotDecisionBoundary(theta, X, y);
-hold on;
-title(sprintf('lambda = %g', lambda))
-
-% Labels and Legend
-xlabel('Microchip Test 1')
-ylabel('Microchip Test 2')
-
-legend('y = 1', 'y = 0', 'Decision boundary')
-hold off;
-
-% Compute accuracy on our training set
-p = predict(theta, X);
-
-fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
-fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
-

From 735b8e8235452e5a9a4fc9b13132610af3d5c5f5 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:48:30 +0530
Subject: [PATCH 09/27] Delete mapFeature.m

---
 mapFeature.m | 21 ---------------------
 1 file changed, 21 deletions(-)
 delete mode 100644 mapFeature.m

diff --git a/mapFeature.m b/mapFeature.m
deleted file mode 100644
index d02a72a..0000000
--- a/mapFeature.m
+++ /dev/null
@@ -1,21 +0,0 @@
-function out = mapFeature(X1, X2)
-% MAPFEATURE Feature mapping function to polynomial features
-%
-%   MAPFEATURE(X1, X2) maps the two input features
-%   to quadratic features used in the regularization exercise.
-%
-%   Returns a new feature array with more features, comprising of 
-%   X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
-%
-%   Inputs X1, X2 must be the same size
-%
-
-degree = 6;
-out = ones(size(X1(:,1)));
-for i = 1:degree
-    for j = 0:i
-        out(:, end+1) = (X1.^(i-j)).*(X2.^j);
-    end
-end
-
-end
\ No newline at end of file

From 68430037ed996dd6eb800901f2a7459bc0f204a0 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:48:39 +0530
Subject: [PATCH 10/27] Delete plotData.m

---
 plotData.m | 32 --------------------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 plotData.m

diff --git a/plotData.m b/plotData.m
deleted file mode 100644
index d8e7f9d..0000000
--- a/plotData.m
+++ /dev/null
@@ -1,32 +0,0 @@
-function plotData(X, y)
-%PLOTDATA Plots the data points X and y into a new figure 
-%   PLOTDATA(x,y) plots the data points with + for the positive examples
-%   and o for the negative examples. X is assumed to be a Mx2 matrix.
-figure;
-pos = find(y==1); neg = find(y == 0);
-plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,'MarkerSize', 7);
- hold on;
-plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
-
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Plot the positive and negative examples on a
-%               2D plot, using the option 'k+' for the positive
-%               examples and 'ko' for the negative examples.
-%
-
-
-
-
-
-
-
-
-
-% =========================================================================
-
-
-
-hold off;
-
-end

From e0f746ed029f03d2e0e34942d30b7414882d65b0 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:48:51 +0530
Subject: [PATCH 11/27] Delete plotDecisionBoundary.m

---
 plotDecisionBoundary.m | 48 ------------------------------------------
 1 file changed, 48 deletions(-)
 delete mode 100644 plotDecisionBoundary.m

diff --git a/plotDecisionBoundary.m b/plotDecisionBoundary.m
deleted file mode 100644
index cd36314..0000000
--- a/plotDecisionBoundary.m
+++ /dev/null
@@ -1,48 +0,0 @@
-function plotDecisionBoundary(theta, X, y)
-%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
-%the decision boundary defined by theta
-%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
-%   positive examples and o for the negative examples. X is assumed to be 
-%   a either 
-%   1) Mx3 matrix, where the first column is an all-ones column for the 
-%      intercept.
-%   2) MxN, N>3 matrix, where the first column is all-ones
-
-% Plot Data
-plotData(X(:,2:3), y);
-hold on
-
-if size(X, 2) <= 3
-    % Only need 2 points to define a line, so choose two endpoints
-    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
-
-    % Calculate the decision boundary line
-    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
-
-    % Plot, and adjust axes for better viewing
-    plot(plot_x, plot_y)
-    
-    % Legend, specific for the exercise
-    legend('Admitted', 'Not admitted', 'Decision Boundary')
-    axis([30, 100, 30, 100])
-else
-    % Here is the grid range
-    u = linspace(-1, 1.5, 50);
-    v = linspace(-1, 1.5, 50);
-
-    z = zeros(length(u), length(v));
-    % Evaluate z = theta*x over the grid
-    for i = 1:length(u)
-        for j = 1:length(v)
-            z(i,j) = mapFeature(u(i), v(j))*theta;
-        end
-    end
-    z = z'; % important to transpose z before calling contour
-
-    % Plot z = 0
-    % Notice you need to specify the range [0, 0]
-    contour(u, v, z, [0, 0], 'LineWidth', 2)
-end
-hold off
-
-end

From c6d6e668292fb9c522ff20267541d87c9d5ad239 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:49:01 +0530
Subject: [PATCH 12/27] Delete predict.m

---
 predict.m | 28 ----------------------------
 1 file changed, 28 deletions(-)
 delete mode 100644 predict.m

diff --git a/predict.m b/predict.m
deleted file mode 100644
index c85ac58..0000000
--- a/predict.m
+++ /dev/null
@@ -1,28 +0,0 @@
-function p = predict(theta, X)
-%PREDICT Predict whether the label is 0 or 1 using learned logistic 
-%regression parameters theta
-%   p = PREDICT(theta, X) computes the predictions for X using a 
-%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
-
-m = size(X, 1); % Number of training examples
-
-% You need to return the following variables correctly
-p = zeros(m, 1);
-% ====================== YOUR CODE HERE ======================
-% Instructions: Complete the following code to make predictions using
-%               your learned logistic regression parameters. 
-%               You should set p to a vector of 0's and 1's
-%
-h=sigmoid(X*theta);
-for i=1:m
-  if  h(i)>=0.5
-    p(i)=1;
-  end;
-  if h(i) < 0.5
-    p(i)=0;
-   end;
-end;
-% =========================================================================
-
-
-end

From ac157f30d1eb3ea4c6ba1a89e64ce4fefa76b691 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:49:13 +0530
Subject: [PATCH 13/27] Delete sigmoid.m

---
 sigmoid.m | 20 --------------------
 1 file changed, 20 deletions(-)
 delete mode 100644 sigmoid.m

diff --git a/sigmoid.m b/sigmoid.m
deleted file mode 100644
index e36d8d0..0000000
--- a/sigmoid.m
+++ /dev/null
@@ -1,20 +0,0 @@
-function g = sigmoid(z)
-%SIGMOID Compute sigmoid function
-%   g = SIGMOID(z) computes the sigmoid of z.
-
-% You need to return the following variables correctly 
-g = zeros(size(z));
-z= -1*z;
-g= 1+exp(z);
-g=1./g;
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
-%               vector or scalar).
-
-
-
-
-
-% =============================================================
-
-end

From f1b7cc2ab788b7faaae88178e07164bae9a57ab8 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:50:12 +0530
Subject: [PATCH 14/27] Create Jayakar_week2

---
 Programming Assignment/Week_2/Jayakar_week2 | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 Programming Assignment/Week_2/Jayakar_week2

diff --git a/Programming Assignment/Week_2/Jayakar_week2 b/Programming Assignment/Week_2/Jayakar_week2
new file mode 100644
index 0000000..8b13789
--- /dev/null
+++ b/Programming Assignment/Week_2/Jayakar_week2	
@@ -0,0 +1 @@
+

From 5f0b9e7c3a1bb4b61840565e5ac711d6d04aaa86 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:50:28 +0530
Subject: [PATCH 15/27] Delete Jayakar_week2

---
 Programming Assignment/Week_2/Jayakar_week2 | 1 -
 1 file changed, 1 deletion(-)
 delete mode 100644 Programming Assignment/Week_2/Jayakar_week2

diff --git a/Programming Assignment/Week_2/Jayakar_week2 b/Programming Assignment/Week_2/Jayakar_week2
deleted file mode 100644
index 8b13789..0000000
--- a/Programming Assignment/Week_2/Jayakar_week2	
+++ /dev/null
@@ -1 +0,0 @@
-

From 01c398a5462b8b1b1c1ce200b8af1b1a26e6722c Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:56:13 +0530
Subject: [PATCH 16/27] Add files via upload

---
 .../Week 1/jayakar_week2/costFunction.m       |  35 ++++
 .../Week 1/jayakar_week2/costFunctionReg.m    |  32 ++++
 .../Week 1/jayakar_week2/ex2.m                | 151 ++++++++++++++++++
 .../Week 1/jayakar_week2/ex2_reg.m            | 136 ++++++++++++++++
 .../Week 1/jayakar_week2/mapFeature.m         |  21 +++
 .../Week 1/jayakar_week2/plotData.m           |  32 ++++
 .../jayakar_week2/plotDecisionBoundary.m      |  48 ++++++
 .../Week 1/jayakar_week2/predict.m            |  28 ++++
 .../Week 1/jayakar_week2/sigmoid.m            |  20 +++
 9 files changed, 503 insertions(+)
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/costFunction.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/ex2.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/ex2_reg.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/mapFeature.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/plotData.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/predict.m
 create mode 100644 Programming Assignment/Week 1/jayakar_week2/sigmoid.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/costFunction.m b/Programming Assignment/Week 1/jayakar_week2/costFunction.m
new file mode 100644
index 0000000..9f7d711
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/costFunction.m	
@@ -0,0 +1,35 @@
+function [J, grad] = costFunction(theta, X, y)
+%COSTFUNCTION Compute cost and gradient for logistic regression
+%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
+%   parameter for logistic regression and the gradient of the cost
+%   w.r.t. to the parameters.
+
+% Initialize some useful values
+m = length(y); % number of training examples
+% You need to return the following variables correctly 
+h=X*theta;
+h=sigmoid(h);
+J = 0;
+J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
+J=J/m;
+grad = zeros(size(theta));
+grad=(1/m)*(X'*(h-y));
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+%
+% Note: grad should have the same dimensions as theta
+%
+
+
+
+
+
+
+
+
+% =============================================================
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m b/Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m
new file mode 100644
index 0000000..86e2e21
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m	
@@ -0,0 +1,32 @@
+function [J, grad] = costFunctionReg(theta, X, y, lambda)
+%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
+%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
+%   theta as the parameter for regularized logistic regression and the
+%   gradient of the cost w.r.t. to the parameters. 
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+h=X*theta;
+h=sigmoid(h);
+J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
+J=J/m;
+k=ones(1,size(theta,1));
+l=theta.^2;
+J=J+(lambda/(2*m))*(k*l);
+J=J-(lambda/(2*m))*l(1,1);
+grad=(1/m)*(X'*(h-y));
+grad=grad+(lambda/m)*theta;
+grad(1)=grad(1)-(lambda/m)*theta(1);
+% =============================================================
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week2/ex2.m b/Programming Assignment/Week 1/jayakar_week2/ex2.m
new file mode 100644
index 0000000..103fe11
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/ex2.m	
@@ -0,0 +1,151 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the logistic
+%  regression exercise. You will need to complete the following functions 
+%  in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = load('ex2data1.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+%% ==================== Part 1: Plotting ====================
+%  We start the exercise by first plotting the data to understand the 
+%  the problem we are working with.
+
+fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
+         'indicating (y = 0) examples.\n']);
+
+plotData(X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============ Part 2: Compute Cost and Gradient ============
+%  In this part of the exercise, you will implement the cost and gradient
+%  for logistic regression. You neeed to complete the code in 
+%  costFunction.m
+
+%  Setup the data matrix appropriately, and add ones for the intercept term
+[m, n] = size(X);
+
+% Add intercept term to x and X_test
+X = [ones(m, 1) X];
+
+% Initialize fitting parameters
+initial_theta = zeros(n + 1, 1);
+
+% Compute and display initial cost and gradient
+[cost, grad] = costFunction(initial_theta, X, y);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros): \n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
+
+% Compute and display cost and gradient with non-zero theta
+test_theta = [-24; 0.2; 0.2];
+[cost, grad] = costFunction(test_theta, X, y);
+
+fprintf('\nCost at test theta: %f\n', cost);
+fprintf('Expected cost (approx): 0.218\n');
+fprintf('Gradient at test theta: \n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============= Part 3: Optimizing using fminunc  =============
+%  In this exercise, you will use a built-in function (fminunc) to find the
+%  optimal parameters theta.
+
+%  Set options for fminunc
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+%  Run fminunc to obtain the optimal theta
+%  This function will return theta and the cost 
+[theta, cost] = ...
+	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
+
+% Print theta to screen
+fprintf('Cost at theta found by fminunc: %f\n', cost);
+fprintf('Expected cost (approx): 0.203\n');
+fprintf('theta: \n');
+fprintf(' %f \n', theta);
+fprintf('Expected theta (approx):\n');
+fprintf(' -25.161\n 0.206\n 0.201\n');
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============== Part 4: Predict and Accuracies ==============
+%  After learning the parameters, you'll like to use it to predict the outcomes
+%  on unseen data. In this part, you will use the logistic regression model
+%  to predict the probability that a student with score 45 on exam 1 and 
+%  score 85 on exam 2 will be admitted.
+%
+%  Furthermore, you will compute the training and test set accuracies of 
+%  our model.
+%
+%  Your task is to complete the code in predict.m
+
+%  Predict probability for a student with score 45 on exam 1 
+%  and score 85 on exam 2 
+
+prob = sigmoid([1 45 85] * theta);
+fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
+         'probability of %f\n'], prob);
+fprintf('Expected value: 0.775 +/- 0.002\n\n');
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+fprintf('Expected accuracy (approx): 89.0\n');
+fprintf('\n');
+
+
diff --git a/Programming Assignment/Week 1/jayakar_week2/ex2_reg.m b/Programming Assignment/Week 1/jayakar_week2/ex2_reg.m
new file mode 100644
index 0000000..f363318
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/ex2_reg.m	
@@ -0,0 +1,136 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the second part
+%  of the exercise which covers regularization with logistic regression.
+%
+%  You will need to complete the following functions in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the X values and the third column
+%  contains the label (y).
+
+data = load('ex2data2.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+plotData(X, y);
+
+% Put some labels
+hold on;
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+% Specified in plot order
+legend('y = 1', 'y = 0')
+hold off;
+
+
+%% =========== Part 1: Regularized Logistic Regression ============
+%  In this part, you are given a dataset with data points that are not
+%  linearly separable. However, you would still like to use logistic
+%  regression to classify the data points.
+%
+%  To do so, you introduce more features to use -- in particular, you add
+%  polynomial features to our data matrix (similar to polynomial
+%  regression).
+%
+
+% Add Polynomial Features
+
+% Note that mapFeature also adds a column of ones for us, so the intercept
+% term is handled
+X = mapFeature(X(:,1), X(:,2));
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1
+lambda = 1;
+
+% Compute and display initial cost and gradient for regularized logistic
+% regression
+[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros) - first five values only:\n');
+fprintf(' %f \n', grad(1:5));
+fprintf('Expected gradients (approx) - first five values only:\n');
+fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+% Compute and display cost and gradient
+% with all-ones theta and lambda = 10
+test_theta = ones(size(X,2),1);
+[cost, grad] = costFunctionReg(test_theta, X, y, 10);
+
+fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
+fprintf('Expected cost (approx): 3.16\n');
+fprintf('Gradient at test theta - first five values only:\n');
+fprintf(' %f \n', grad(1:5));
+fprintf('Expected gradients (approx) - first five values only:\n');
+fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============= Part 2: Regularization and Accuracies =============
+%  Optional Exercise:
+%  In this part, you will get to try different values of lambda and
+%  see how regularization affects the decision coundart
+%
+%  Try the following values of lambda (0, 1, 10, 100).
+%
+%  How does the decision boundary change when you vary lambda? How does
+%  the training set accuracy vary?
+%
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1 (you should vary this)
+lambda = 1;
+
+% Set Options
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+% Optimize
+[theta, J, exit_flag] = ...
+	fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+hold on;
+title(sprintf('lambda = %g', lambda))
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+legend('y = 1', 'y = 0', 'Decision boundary')
+hold off;
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
+
diff --git a/Programming Assignment/Week 1/jayakar_week2/mapFeature.m b/Programming Assignment/Week 1/jayakar_week2/mapFeature.m
new file mode 100644
index 0000000..d02a72a
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/mapFeature.m	
@@ -0,0 +1,21 @@
+function out = mapFeature(X1, X2)
+% MAPFEATURE Feature mapping function to polynomial features
+%
+%   MAPFEATURE(X1, X2) maps the two input features
+%   to quadratic features used in the regularization exercise.
+%
+%   Returns a new feature array with more features, comprising of 
+%   X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
+%
+%   Inputs X1, X2 must be the same size
+%
+
+degree = 6;
+out = ones(size(X1(:,1)));
+for i = 1:degree
+    for j = 0:i
+        out(:, end+1) = (X1.^(i-j)).*(X2.^j);
+    end
+end
+
+end
\ No newline at end of file
diff --git a/Programming Assignment/Week 1/jayakar_week2/plotData.m b/Programming Assignment/Week 1/jayakar_week2/plotData.m
new file mode 100644
index 0000000..d8e7f9d
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/plotData.m	
@@ -0,0 +1,32 @@
+function plotData(X, y)
+%PLOTDATA Plots the data points X and y into a new figure 
+%   PLOTDATA(x,y) plots the data points with + for the positive examples
+%   and o for the negative examples. X is assumed to be a Mx2 matrix.
+figure;
+pos = find(y==1); neg = find(y == 0);
+plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,'MarkerSize', 7);
+ hold on;
+plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
+
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Plot the positive and negative examples on a
+%               2D plot, using the option 'k+' for the positive
+%               examples and 'ko' for the negative examples.
+%
+
+
+
+
+
+
+
+
+
+% =========================================================================
+
+
+
+hold off;
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m b/Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m
new file mode 100644
index 0000000..cd36314
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m	
@@ -0,0 +1,48 @@
+function plotDecisionBoundary(theta, X, y)
+%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
+%the decision boundary defined by theta
+%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
+%   positive examples and o for the negative examples. X is assumed to be 
+%   a either 
+%   1) Mx3 matrix, where the first column is an all-ones column for the 
+%      intercept.
+%   2) MxN, N>3 matrix, where the first column is all-ones
+
+% Plot Data
+plotData(X(:,2:3), y);
+hold on
+
+if size(X, 2) <= 3
+    % Only need 2 points to define a line, so choose two endpoints
+    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
+
+    % Calculate the decision boundary line
+    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
+
+    % Plot, and adjust axes for better viewing
+    plot(plot_x, plot_y)
+    
+    % Legend, specific for the exercise
+    legend('Admitted', 'Not admitted', 'Decision Boundary')
+    axis([30, 100, 30, 100])
+else
+    % Here is the grid range
+    u = linspace(-1, 1.5, 50);
+    v = linspace(-1, 1.5, 50);
+
+    z = zeros(length(u), length(v));
+    % Evaluate z = theta*x over the grid
+    for i = 1:length(u)
+        for j = 1:length(v)
+            z(i,j) = mapFeature(u(i), v(j))*theta;
+        end
+    end
+    z = z'; % important to transpose z before calling contour
+
+    % Plot z = 0
+    % Notice you need to specify the range [0, 0]
+    contour(u, v, z, [0, 0], 'LineWidth', 2)
+end
+hold off
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week2/predict.m b/Programming Assignment/Week 1/jayakar_week2/predict.m
new file mode 100644
index 0000000..c85ac58
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/predict.m	
@@ -0,0 +1,28 @@
+function p = predict(theta, X)
+%PREDICT Predict whether the label is 0 or 1 using learned logistic 
+%regression parameters theta
+%   p = PREDICT(theta, X) computes the predictions for X using a 
+%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
+
+m = size(X, 1); % Number of training examples
+
+% You need to return the following variables correctly
+p = zeros(m, 1);
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the following code to make predictions using
+%               your learned logistic regression parameters. 
+%               You should set p to a vector of 0's and 1's
+%
+h=sigmoid(X*theta);
+for i=1:m
+  if  h(i)>=0.5
+    p(i)=1;
+  end;
+  if h(i) < 0.5
+    p(i)=0;
+   end;
+end;
+% =========================================================================
+
+
+end
diff --git a/Programming Assignment/Week 1/jayakar_week2/sigmoid.m b/Programming Assignment/Week 1/jayakar_week2/sigmoid.m
new file mode 100644
index 0000000..e36d8d0
--- /dev/null
+++ b/Programming Assignment/Week 1/jayakar_week2/sigmoid.m	
@@ -0,0 +1,20 @@
+function g = sigmoid(z)
+%SIGMOID Compute sigmoid function
+%   g = SIGMOID(z) computes the sigmoid of z.
+
+% You need to return the following variables correctly 
+g = zeros(size(z));
+z= -1*z;
+g= 1+exp(z);
+g=1./g;
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
+%               vector or scalar).
+
+
+
+
+
+% =============================================================
+
+end

From d9188afae6d00ced49051b3aff294aff747e9e85 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 00:57:52 +0530
Subject: [PATCH 17/27] Add files via upload

---
 .../Week_2/jayakar_week2/costFunction.m       |  35 ++++
 .../Week_2/jayakar_week2/costFunctionReg.m    |  32 ++++
 .../Week_2/jayakar_week2/ex2.m                | 151 ++++++++++++++++++
 .../Week_2/jayakar_week2/ex2_reg.m            | 136 ++++++++++++++++
 .../Week_2/jayakar_week2/mapFeature.m         |  21 +++
 .../Week_2/jayakar_week2/plotData.m           |  32 ++++
 .../jayakar_week2/plotDecisionBoundary.m      |  48 ++++++
 .../Week_2/jayakar_week2/predict.m            |  28 ++++
 .../Week_2/jayakar_week2/sigmoid.m            |  20 +++
 9 files changed, 503 insertions(+)
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/costFunction.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/costFunctionReg.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/ex2.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/ex2_reg.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/mapFeature.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/plotData.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/plotDecisionBoundary.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/predict.m
 create mode 100644 Programming Assignment/Week_2/jayakar_week2/sigmoid.m

diff --git a/Programming Assignment/Week_2/jayakar_week2/costFunction.m b/Programming Assignment/Week_2/jayakar_week2/costFunction.m
new file mode 100644
index 0000000..9f7d711
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/costFunction.m	
@@ -0,0 +1,35 @@
+function [J, grad] = costFunction(theta, X, y)
+%COSTFUNCTION Compute cost and gradient for logistic regression
+%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
+%   parameter for logistic regression and the gradient of the cost
+%   w.r.t. to the parameters.
+
+% Initialize some useful values
+m = length(y); % number of training examples
+% You need to return the following variables correctly 
+h=X*theta;
+h=sigmoid(h);
+J = 0;
+J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
+J=J/m;
+grad = zeros(size(theta));
+grad=(1/m)*(X'*(h-y));
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+%
+% Note: grad should have the same dimensions as theta
+%
+
+
+
+
+
+
+
+
+% =============================================================
+
+end
diff --git a/Programming Assignment/Week_2/jayakar_week2/costFunctionReg.m b/Programming Assignment/Week_2/jayakar_week2/costFunctionReg.m
new file mode 100644
index 0000000..86e2e21
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/costFunctionReg.m	
@@ -0,0 +1,32 @@
+function [J, grad] = costFunctionReg(theta, X, y, lambda)
+%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
+%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
+%   theta as the parameter for regularized logistic regression and the
+%   gradient of the cost w.r.t. to the parameters. 
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+h=X*theta;
+h=sigmoid(h);
+J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
+J=J/m;
+k=ones(1,size(theta,1));
+l=theta.^2;
+J=J+(lambda/(2*m))*(k*l);
+J=J-(lambda/(2*m))*l(1,1);
+grad=(1/m)*(X'*(h-y));
+grad=grad+(lambda/m)*theta;
+grad(1)=grad(1)-(lambda/m)*theta(1);
+% =============================================================
+
+end
diff --git a/Programming Assignment/Week_2/jayakar_week2/ex2.m b/Programming Assignment/Week_2/jayakar_week2/ex2.m
new file mode 100644
index 0000000..103fe11
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/ex2.m	
@@ -0,0 +1,151 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the logistic
+%  regression exercise. You will need to complete the following functions 
+%  in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = load('ex2data1.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+%% ==================== Part 1: Plotting ====================
+%  We start the exercise by first plotting the data to understand the 
+%  the problem we are working with.
+
+fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
+         'indicating (y = 0) examples.\n']);
+
+plotData(X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============ Part 2: Compute Cost and Gradient ============
+%  In this part of the exercise, you will implement the cost and gradient
+%  for logistic regression. You neeed to complete the code in 
+%  costFunction.m
+
+%  Setup the data matrix appropriately, and add ones for the intercept term
+[m, n] = size(X);
+
+% Add intercept term to x and X_test
+X = [ones(m, 1) X];
+
+% Initialize fitting parameters
+initial_theta = zeros(n + 1, 1);
+
+% Compute and display initial cost and gradient
+[cost, grad] = costFunction(initial_theta, X, y);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros): \n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
+
+% Compute and display cost and gradient with non-zero theta
+test_theta = [-24; 0.2; 0.2];
+[cost, grad] = costFunction(test_theta, X, y);
+
+fprintf('\nCost at test theta: %f\n', cost);
+fprintf('Expected cost (approx): 0.218\n');
+fprintf('Gradient at test theta: \n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% ============= Part 3: Optimizing using fminunc  =============
+%  In this exercise, you will use a built-in function (fminunc) to find the
+%  optimal parameters theta.
+
+%  Set options for fminunc
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+%  Run fminunc to obtain the optimal theta
+%  This function will return theta and the cost 
+[theta, cost] = ...
+	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
+
+% Print theta to screen
+fprintf('Cost at theta found by fminunc: %f\n', cost);
+fprintf('Expected cost (approx): 0.203\n');
+fprintf('theta: \n');
+fprintf(' %f \n', theta);
+fprintf('Expected theta (approx):\n');
+fprintf(' -25.161\n 0.206\n 0.201\n');
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+
+% Put some labels 
+hold on;
+% Labels and Legend
+xlabel('Exam 1 score')
+ylabel('Exam 2 score')
+
+% Specified in plot order
+legend('Admitted', 'Not admitted')
+hold off;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============== Part 4: Predict and Accuracies ==============
+%  After learning the parameters, you'll like to use it to predict the outcomes
+%  on unseen data. In this part, you will use the logistic regression model
+%  to predict the probability that a student with score 45 on exam 1 and 
+%  score 85 on exam 2 will be admitted.
+%
+%  Furthermore, you will compute the training and test set accuracies of 
+%  our model.
+%
+%  Your task is to complete the code in predict.m
+
+%  Predict probability for a student with score 45 on exam 1 
+%  and score 85 on exam 2 
+
+prob = sigmoid([1 45 85] * theta);
+fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
+         'probability of %f\n'], prob);
+fprintf('Expected value: 0.775 +/- 0.002\n\n');
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+fprintf('Expected accuracy (approx): 89.0\n');
+fprintf('\n');
+
+
diff --git a/Programming Assignment/Week_2/jayakar_week2/ex2_reg.m b/Programming Assignment/Week_2/jayakar_week2/ex2_reg.m
new file mode 100644
index 0000000..f363318
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/ex2_reg.m	
@@ -0,0 +1,136 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the second part
+%  of the exercise which covers regularization with logistic regression.
+%
+%  You will need to complete the following functions in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the X values and the third column
+%  contains the label (y).
+
+data = load('ex2data2.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+plotData(X, y);
+
+% Put some labels
+hold on;
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+% Specified in plot order
+legend('y = 1', 'y = 0')
+hold off;
+
+
+%% =========== Part 1: Regularized Logistic Regression ============
+%  In this part, you are given a dataset with data points that are not
+%  linearly separable. However, you would still like to use logistic
+%  regression to classify the data points.
+%
+%  To do so, you introduce more features to use -- in particular, you add
+%  polynomial features to our data matrix (similar to polynomial
+%  regression).
+%
+
+% Add Polynomial Features
+
+% Note that mapFeature also adds a column of ones for us, so the intercept
+% term is handled
+X = mapFeature(X(:,1), X(:,2));
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1
+lambda = 1;
+
+% Compute and display initial cost and gradient for regularized logistic
+% regression
+[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Expected cost (approx): 0.693\n');
+fprintf('Gradient at initial theta (zeros) - first five values only:\n');
+fprintf(' %f \n', grad(1:5));
+fprintf('Expected gradients (approx) - first five values only:\n');
+fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+% Compute and display cost and gradient
+% with all-ones theta and lambda = 10
+test_theta = ones(size(X,2),1);
+[cost, grad] = costFunctionReg(test_theta, X, y, 10);
+
+fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
+fprintf('Expected cost (approx): 3.16\n');
+fprintf('Gradient at test theta - first five values only:\n');
+fprintf(' %f \n', grad(1:5));
+fprintf('Expected gradients (approx) - first five values only:\n');
+fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ============= Part 2: Regularization and Accuracies =============
+%  Optional Exercise:
+%  In this part, you will get to try different values of lambda and
+%  see how regularization affects the decision coundart
+%
+%  Try the following values of lambda (0, 1, 10, 100).
+%
+%  How does the decision boundary change when you vary lambda? How does
+%  the training set accuracy vary?
+%
+
+% Initialize fitting parameters
+initial_theta = zeros(size(X, 2), 1);
+
+% Set regularization parameter lambda to 1 (you should vary this)
+lambda = 1;
+
+% Set Options
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+% Optimize
+[theta, J, exit_flag] = ...
+	fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
+
+% Plot Boundary
+plotDecisionBoundary(theta, X, y);
+hold on;
+title(sprintf('lambda = %g', lambda))
+
+% Labels and Legend
+xlabel('Microchip Test 1')
+ylabel('Microchip Test 2')
+
+legend('y = 1', 'y = 0', 'Decision boundary')
+hold off;
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
+
diff --git a/Programming Assignment/Week_2/jayakar_week2/mapFeature.m b/Programming Assignment/Week_2/jayakar_week2/mapFeature.m
new file mode 100644
index 0000000..d02a72a
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/mapFeature.m	
@@ -0,0 +1,21 @@
+function out = mapFeature(X1, X2)
+% MAPFEATURE Feature mapping function to polynomial features
+%
+%   MAPFEATURE(X1, X2) maps the two input features
+%   to quadratic features used in the regularization exercise.
+%
+%   Returns a new feature array with more features, comprising of 
+%   X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
+%
+%   Inputs X1, X2 must be the same size
+%
+
+degree = 6;
+out = ones(size(X1(:,1)));
+for i = 1:degree
+    for j = 0:i
+        out(:, end+1) = (X1.^(i-j)).*(X2.^j);
+    end
+end
+
+end
\ No newline at end of file
diff --git a/Programming Assignment/Week_2/jayakar_week2/plotData.m b/Programming Assignment/Week_2/jayakar_week2/plotData.m
new file mode 100644
index 0000000..d8e7f9d
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/plotData.m	
@@ -0,0 +1,32 @@
+function plotData(X, y)
+%PLOTDATA Plots the data points X and y into a new figure 
+%   PLOTDATA(x,y) plots the data points with + for the positive examples
+%   and o for the negative examples. X is assumed to be a Mx2 matrix.
+figure;
+pos = find(y==1); neg = find(y == 0);
+plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,'MarkerSize', 7);
+ hold on;
+plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
+
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Plot the positive and negative examples on a
+%               2D plot, using the option 'k+' for the positive
+%               examples and 'ko' for the negative examples.
+%
+
+
+
+
+
+
+
+
+
+% =========================================================================
+
+
+
+hold off;
+
+end
diff --git a/Programming Assignment/Week_2/jayakar_week2/plotDecisionBoundary.m b/Programming Assignment/Week_2/jayakar_week2/plotDecisionBoundary.m
new file mode 100644
index 0000000..cd36314
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/plotDecisionBoundary.m	
@@ -0,0 +1,48 @@
+function plotDecisionBoundary(theta, X, y)
+%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
+%the decision boundary defined by theta
+%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
+%   positive examples and o for the negative examples. X is assumed to be 
+%   a either 
+%   1) Mx3 matrix, where the first column is an all-ones column for the 
+%      intercept.
+%   2) MxN, N>3 matrix, where the first column is all-ones
+
+% Plot Data
+plotData(X(:,2:3), y);
+hold on
+
+if size(X, 2) <= 3
+    % Only need 2 points to define a line, so choose two endpoints
+    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
+
+    % Calculate the decision boundary line
+    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
+
+    % Plot, and adjust axes for better viewing
+    plot(plot_x, plot_y)
+    
+    % Legend, specific for the exercise
+    legend('Admitted', 'Not admitted', 'Decision Boundary')
+    axis([30, 100, 30, 100])
+else
+    % Here is the grid range
+    u = linspace(-1, 1.5, 50);
+    v = linspace(-1, 1.5, 50);
+
+    z = zeros(length(u), length(v));
+    % Evaluate z = theta*x over the grid
+    for i = 1:length(u)
+        for j = 1:length(v)
+            z(i,j) = mapFeature(u(i), v(j))*theta;
+        end
+    end
+    z = z'; % important to transpose z before calling contour
+
+    % Plot z = 0
+    % Notice you need to specify the range [0, 0]
+    contour(u, v, z, [0, 0], 'LineWidth', 2)
+end
+hold off
+
+end
diff --git a/Programming Assignment/Week_2/jayakar_week2/predict.m b/Programming Assignment/Week_2/jayakar_week2/predict.m
new file mode 100644
index 0000000..c85ac58
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/predict.m	
@@ -0,0 +1,28 @@
+function p = predict(theta, X)
+%PREDICT Predict whether the label is 0 or 1 using learned logistic 
+%regression parameters theta
+%   p = PREDICT(theta, X) computes the predictions for X using a 
+%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
+
+m = size(X, 1); % Number of training examples
+
+% You need to return the following variables correctly
+p = zeros(m, 1);
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the following code to make predictions using
+%               your learned logistic regression parameters. 
+%               You should set p to a vector of 0's and 1's
+%
+h=sigmoid(X*theta);
+for i=1:m
+  if  h(i)>=0.5
+    p(i)=1;
+  end;
+  if h(i) < 0.5
+    p(i)=0;
+   end;
+end;
+% =========================================================================
+
+
+end
diff --git a/Programming Assignment/Week_2/jayakar_week2/sigmoid.m b/Programming Assignment/Week_2/jayakar_week2/sigmoid.m
new file mode 100644
index 0000000..e36d8d0
--- /dev/null
+++ b/Programming Assignment/Week_2/jayakar_week2/sigmoid.m	
@@ -0,0 +1,20 @@
+function g = sigmoid(z)
+%SIGMOID Compute sigmoid function
+%   g = SIGMOID(z) computes the sigmoid of z.
+
+% You need to return the following variables correctly 
+g = zeros(size(z));
+z= -1*z;
+g= 1+exp(z);
+g=1./g;
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
+%               vector or scalar).
+
+
+
+
+
+% =============================================================
+
+end

From 1f47d897659df155e774df7993adf2c54cecdbfc Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:08:36 +0530
Subject: [PATCH 18/27] Delete costFunction.m

---
 .../Week 1/jayakar_week2/costFunction.m       | 35 -------------------
 1 file changed, 35 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/costFunction.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/costFunction.m b/Programming Assignment/Week 1/jayakar_week2/costFunction.m
deleted file mode 100644
index 9f7d711..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/costFunction.m	
+++ /dev/null
@@ -1,35 +0,0 @@
-function [J, grad] = costFunction(theta, X, y)
-%COSTFUNCTION Compute cost and gradient for logistic regression
-%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
-%   parameter for logistic regression and the gradient of the cost
-%   w.r.t. to the parameters.
-
-% Initialize some useful values
-m = length(y); % number of training examples
-% You need to return the following variables correctly 
-h=X*theta;
-h=sigmoid(h);
-J = 0;
-J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
-J=J/m;
-grad = zeros(size(theta));
-grad=(1/m)*(X'*(h-y));
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the cost of a particular choice of theta.
-%               You should set J to the cost.
-%               Compute the partial derivatives and set grad to the partial
-%               derivatives of the cost w.r.t. each parameter in theta
-%
-% Note: grad should have the same dimensions as theta
-%
-
-
-
-
-
-
-
-
-% =============================================================
-
-end

From 91ea3e2b2e5a5d0ed21417bf073ec29e34d7b7ed Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:08:49 +0530
Subject: [PATCH 19/27] Delete sigmoid.m

---
 .../Week 1/jayakar_week2/sigmoid.m            | 20 -------------------
 1 file changed, 20 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/sigmoid.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/sigmoid.m b/Programming Assignment/Week 1/jayakar_week2/sigmoid.m
deleted file mode 100644
index e36d8d0..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/sigmoid.m	
+++ /dev/null
@@ -1,20 +0,0 @@
-function g = sigmoid(z)
-%SIGMOID Compute sigmoid function
-%   g = SIGMOID(z) computes the sigmoid of z.
-
-% You need to return the following variables correctly 
-g = zeros(size(z));
-z= -1*z;
-g= 1+exp(z);
-g=1./g;
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
-%               vector or scalar).
-
-
-
-
-
-% =============================================================
-
-end

From 9f827be3533ae1bd03c5aaa773f6d9de29277d6d Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:08:56 +0530
Subject: [PATCH 20/27] Delete predict.m

---
 .../Week 1/jayakar_week2/predict.m            | 28 -------------------
 1 file changed, 28 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/predict.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/predict.m b/Programming Assignment/Week 1/jayakar_week2/predict.m
deleted file mode 100644
index c85ac58..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/predict.m	
+++ /dev/null
@@ -1,28 +0,0 @@
-function p = predict(theta, X)
-%PREDICT Predict whether the label is 0 or 1 using learned logistic 
-%regression parameters theta
-%   p = PREDICT(theta, X) computes the predictions for X using a 
-%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
-
-m = size(X, 1); % Number of training examples
-
-% You need to return the following variables correctly
-p = zeros(m, 1);
-% ====================== YOUR CODE HERE ======================
-% Instructions: Complete the following code to make predictions using
-%               your learned logistic regression parameters. 
-%               You should set p to a vector of 0's and 1's
-%
-h=sigmoid(X*theta);
-for i=1:m
-  if  h(i)>=0.5
-    p(i)=1;
-  end;
-  if h(i) < 0.5
-    p(i)=0;
-   end;
-end;
-% =========================================================================
-
-
-end

From a312df0d1e1acf8342b930d27bc448a5a1857cc2 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:09:03 +0530
Subject: [PATCH 21/27] Delete plotDecisionBoundary.m

---
 .../jayakar_week2/plotDecisionBoundary.m      | 48 -------------------
 1 file changed, 48 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m b/Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m
deleted file mode 100644
index cd36314..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/plotDecisionBoundary.m	
+++ /dev/null
@@ -1,48 +0,0 @@
-function plotDecisionBoundary(theta, X, y)
-%PLOTDECISIONBOUNDARY Plots the data points X and y into a new figure with
-%the decision boundary defined by theta
-%   PLOTDECISIONBOUNDARY(theta, X,y) plots the data points with + for the 
-%   positive examples and o for the negative examples. X is assumed to be 
-%   a either 
-%   1) Mx3 matrix, where the first column is an all-ones column for the 
-%      intercept.
-%   2) MxN, N>3 matrix, where the first column is all-ones
-
-% Plot Data
-plotData(X(:,2:3), y);
-hold on
-
-if size(X, 2) <= 3
-    % Only need 2 points to define a line, so choose two endpoints
-    plot_x = [min(X(:,2))-2,  max(X(:,2))+2];
-
-    % Calculate the decision boundary line
-    plot_y = (-1./theta(3)).*(theta(2).*plot_x + theta(1));
-
-    % Plot, and adjust axes for better viewing
-    plot(plot_x, plot_y)
-    
-    % Legend, specific for the exercise
-    legend('Admitted', 'Not admitted', 'Decision Boundary')
-    axis([30, 100, 30, 100])
-else
-    % Here is the grid range
-    u = linspace(-1, 1.5, 50);
-    v = linspace(-1, 1.5, 50);
-
-    z = zeros(length(u), length(v));
-    % Evaluate z = theta*x over the grid
-    for i = 1:length(u)
-        for j = 1:length(v)
-            z(i,j) = mapFeature(u(i), v(j))*theta;
-        end
-    end
-    z = z'; % important to transpose z before calling contour
-
-    % Plot z = 0
-    % Notice you need to specify the range [0, 0]
-    contour(u, v, z, [0, 0], 'LineWidth', 2)
-end
-hold off
-
-end

From 3c70f82b4c0a5ffaf2b0e84733a7eafadc659ca5 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:09:10 +0530
Subject: [PATCH 22/27] Delete plotData.m

---
 .../Week 1/jayakar_week2/plotData.m           | 32 -------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/plotData.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/plotData.m b/Programming Assignment/Week 1/jayakar_week2/plotData.m
deleted file mode 100644
index d8e7f9d..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/plotData.m	
+++ /dev/null
@@ -1,32 +0,0 @@
-function plotData(X, y)
-%PLOTDATA Plots the data points X and y into a new figure 
-%   PLOTDATA(x,y) plots the data points with + for the positive examples
-%   and o for the negative examples. X is assumed to be a Mx2 matrix.
-figure;
-pos = find(y==1); neg = find(y == 0);
-plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2,'MarkerSize', 7);
- hold on;
-plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
-
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Plot the positive and negative examples on a
-%               2D plot, using the option 'k+' for the positive
-%               examples and 'ko' for the negative examples.
-%
-
-
-
-
-
-
-
-
-
-% =========================================================================
-
-
-
-hold off;
-
-end

From bc8ee4482684dd310d5099bdfe0291dcb5760988 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:09:19 +0530
Subject: [PATCH 23/27] Delete mapFeature.m

---
 .../Week 1/jayakar_week2/mapFeature.m         | 21 -------------------
 1 file changed, 21 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/mapFeature.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/mapFeature.m b/Programming Assignment/Week 1/jayakar_week2/mapFeature.m
deleted file mode 100644
index d02a72a..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/mapFeature.m	
+++ /dev/null
@@ -1,21 +0,0 @@
-function out = mapFeature(X1, X2)
-% MAPFEATURE Feature mapping function to polynomial features
-%
-%   MAPFEATURE(X1, X2) maps the two input features
-%   to quadratic features used in the regularization exercise.
-%
-%   Returns a new feature array with more features, comprising of 
-%   X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc..
-%
-%   Inputs X1, X2 must be the same size
-%
-
-degree = 6;
-out = ones(size(X1(:,1)));
-for i = 1:degree
-    for j = 0:i
-        out(:, end+1) = (X1.^(i-j)).*(X2.^j);
-    end
-end
-
-end
\ No newline at end of file

From 54cd225df5b9b1aa690c58faaf4bc2b60ace0425 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:09:27 +0530
Subject: [PATCH 24/27] Delete ex2_reg.m

---
 .../Week 1/jayakar_week2/ex2_reg.m            | 136 ------------------
 1 file changed, 136 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/ex2_reg.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/ex2_reg.m b/Programming Assignment/Week 1/jayakar_week2/ex2_reg.m
deleted file mode 100644
index f363318..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/ex2_reg.m	
+++ /dev/null
@@ -1,136 +0,0 @@
-%% Machine Learning Online Class - Exercise 2: Logistic Regression
-%
-%  Instructions
-%  ------------
-%
-%  This file contains code that helps you get started on the second part
-%  of the exercise which covers regularization with logistic regression.
-%
-%  You will need to complete the following functions in this exericse:
-%
-%     sigmoid.m
-%     costFunction.m
-%     predict.m
-%     costFunctionReg.m
-%
-%  For this exercise, you will not need to change any code in this file,
-%  or any other files other than those mentioned above.
-%
-
-%% Initialization
-clear ; close all; clc
-
-%% Load Data
-%  The first two columns contains the X values and the third column
-%  contains the label (y).
-
-data = load('ex2data2.txt');
-X = data(:, [1, 2]); y = data(:, 3);
-
-plotData(X, y);
-
-% Put some labels
-hold on;
-
-% Labels and Legend
-xlabel('Microchip Test 1')
-ylabel('Microchip Test 2')
-
-% Specified in plot order
-legend('y = 1', 'y = 0')
-hold off;
-
-
-%% =========== Part 1: Regularized Logistic Regression ============
-%  In this part, you are given a dataset with data points that are not
-%  linearly separable. However, you would still like to use logistic
-%  regression to classify the data points.
-%
-%  To do so, you introduce more features to use -- in particular, you add
-%  polynomial features to our data matrix (similar to polynomial
-%  regression).
-%
-
-% Add Polynomial Features
-
-% Note that mapFeature also adds a column of ones for us, so the intercept
-% term is handled
-X = mapFeature(X(:,1), X(:,2));
-
-% Initialize fitting parameters
-initial_theta = zeros(size(X, 2), 1);
-
-% Set regularization parameter lambda to 1
-lambda = 1;
-
-% Compute and display initial cost and gradient for regularized logistic
-% regression
-[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
-
-fprintf('Cost at initial theta (zeros): %f\n', cost);
-fprintf('Expected cost (approx): 0.693\n');
-fprintf('Gradient at initial theta (zeros) - first five values only:\n');
-fprintf(' %f \n', grad(1:5));
-fprintf('Expected gradients (approx) - first five values only:\n');
-fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-% Compute and display cost and gradient
-% with all-ones theta and lambda = 10
-test_theta = ones(size(X,2),1);
-[cost, grad] = costFunctionReg(test_theta, X, y, 10);
-
-fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
-fprintf('Expected cost (approx): 3.16\n');
-fprintf('Gradient at test theta - first five values only:\n');
-fprintf(' %f \n', grad(1:5));
-fprintf('Expected gradients (approx) - first five values only:\n');
-fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-%% ============= Part 2: Regularization and Accuracies =============
-%  Optional Exercise:
-%  In this part, you will get to try different values of lambda and
-%  see how regularization affects the decision coundart
-%
-%  Try the following values of lambda (0, 1, 10, 100).
-%
-%  How does the decision boundary change when you vary lambda? How does
-%  the training set accuracy vary?
-%
-
-% Initialize fitting parameters
-initial_theta = zeros(size(X, 2), 1);
-
-% Set regularization parameter lambda to 1 (you should vary this)
-lambda = 1;
-
-% Set Options
-options = optimset('GradObj', 'on', 'MaxIter', 400);
-
-% Optimize
-[theta, J, exit_flag] = ...
-	fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
-
-% Plot Boundary
-plotDecisionBoundary(theta, X, y);
-hold on;
-title(sprintf('lambda = %g', lambda))
-
-% Labels and Legend
-xlabel('Microchip Test 1')
-ylabel('Microchip Test 2')
-
-legend('y = 1', 'y = 0', 'Decision boundary')
-hold off;
-
-% Compute accuracy on our training set
-p = predict(theta, X);
-
-fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
-fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
-

From 6f2243393973bf12c77e8ae6417ac93b10064c56 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:09:38 +0530
Subject: [PATCH 25/27] Delete ex2.m

---
 .../Week 1/jayakar_week2/ex2.m                | 151 ------------------
 1 file changed, 151 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/ex2.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/ex2.m b/Programming Assignment/Week 1/jayakar_week2/ex2.m
deleted file mode 100644
index 103fe11..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/ex2.m	
+++ /dev/null
@@ -1,151 +0,0 @@
-%% Machine Learning Online Class - Exercise 2: Logistic Regression
-%
-%  Instructions
-%  ------------
-% 
-%  This file contains code that helps you get started on the logistic
-%  regression exercise. You will need to complete the following functions 
-%  in this exericse:
-%
-%     sigmoid.m
-%     costFunction.m
-%     predict.m
-%     costFunctionReg.m
-%
-%  For this exercise, you will not need to change any code in this file,
-%  or any other files other than those mentioned above.
-%
-
-%% Initialization
-clear ; close all; clc
-
-%% Load Data
-%  The first two columns contains the exam scores and the third column
-%  contains the label.
-
-data = load('ex2data1.txt');
-X = data(:, [1, 2]); y = data(:, 3);
-
-%% ==================== Part 1: Plotting ====================
-%  We start the exercise by first plotting the data to understand the 
-%  the problem we are working with.
-
-fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
-         'indicating (y = 0) examples.\n']);
-
-plotData(X, y);
-
-% Put some labels 
-hold on;
-% Labels and Legend
-xlabel('Exam 1 score')
-ylabel('Exam 2 score')
-
-% Specified in plot order
-legend('Admitted', 'Not admitted')
-hold off;
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-
-%% ============ Part 2: Compute Cost and Gradient ============
-%  In this part of the exercise, you will implement the cost and gradient
-%  for logistic regression. You neeed to complete the code in 
-%  costFunction.m
-
-%  Setup the data matrix appropriately, and add ones for the intercept term
-[m, n] = size(X);
-
-% Add intercept term to x and X_test
-X = [ones(m, 1) X];
-
-% Initialize fitting parameters
-initial_theta = zeros(n + 1, 1);
-
-% Compute and display initial cost and gradient
-[cost, grad] = costFunction(initial_theta, X, y);
-
-fprintf('Cost at initial theta (zeros): %f\n', cost);
-fprintf('Expected cost (approx): 0.693\n');
-fprintf('Gradient at initial theta (zeros): \n');
-fprintf(' %f \n', grad);
-fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
-
-% Compute and display cost and gradient with non-zero theta
-test_theta = [-24; 0.2; 0.2];
-[cost, grad] = costFunction(test_theta, X, y);
-
-fprintf('\nCost at test theta: %f\n', cost);
-fprintf('Expected cost (approx): 0.218\n');
-fprintf('Gradient at test theta: \n');
-fprintf(' %f \n', grad);
-fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-
-%% ============= Part 3: Optimizing using fminunc  =============
-%  In this exercise, you will use a built-in function (fminunc) to find the
-%  optimal parameters theta.
-
-%  Set options for fminunc
-options = optimset('GradObj', 'on', 'MaxIter', 400);
-
-%  Run fminunc to obtain the optimal theta
-%  This function will return theta and the cost 
-[theta, cost] = ...
-	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
-
-% Print theta to screen
-fprintf('Cost at theta found by fminunc: %f\n', cost);
-fprintf('Expected cost (approx): 0.203\n');
-fprintf('theta: \n');
-fprintf(' %f \n', theta);
-fprintf('Expected theta (approx):\n');
-fprintf(' -25.161\n 0.206\n 0.201\n');
-
-% Plot Boundary
-plotDecisionBoundary(theta, X, y);
-
-% Put some labels 
-hold on;
-% Labels and Legend
-xlabel('Exam 1 score')
-ylabel('Exam 2 score')
-
-% Specified in plot order
-legend('Admitted', 'Not admitted')
-hold off;
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-%% ============== Part 4: Predict and Accuracies ==============
-%  After learning the parameters, you'll like to use it to predict the outcomes
-%  on unseen data. In this part, you will use the logistic regression model
-%  to predict the probability that a student with score 45 on exam 1 and 
-%  score 85 on exam 2 will be admitted.
-%
-%  Furthermore, you will compute the training and test set accuracies of 
-%  our model.
-%
-%  Your task is to complete the code in predict.m
-
-%  Predict probability for a student with score 45 on exam 1 
-%  and score 85 on exam 2 
-
-prob = sigmoid([1 45 85] * theta);
-fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
-         'probability of %f\n'], prob);
-fprintf('Expected value: 0.775 +/- 0.002\n\n');
-
-% Compute accuracy on our training set
-p = predict(theta, X);
-
-fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
-fprintf('Expected accuracy (approx): 89.0\n');
-fprintf('\n');
-
-

From 281fbdaa63cb71e68a1e2fd37d6477401768dcaf Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Mon, 1 Jul 2019 01:09:46 +0530
Subject: [PATCH 26/27] Delete costFunctionReg.m

---
 .../Week 1/jayakar_week2/costFunctionReg.m    | 32 -------------------
 1 file changed, 32 deletions(-)
 delete mode 100644 Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m

diff --git a/Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m b/Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m
deleted file mode 100644
index 86e2e21..0000000
--- a/Programming Assignment/Week 1/jayakar_week2/costFunctionReg.m	
+++ /dev/null
@@ -1,32 +0,0 @@
-function [J, grad] = costFunctionReg(theta, X, y, lambda)
-%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
-%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
-%   theta as the parameter for regularized logistic regression and the
-%   gradient of the cost w.r.t. to the parameters. 
-
-% Initialize some useful values
-m = length(y); % number of training examples
-
-% You need to return the following variables correctly 
-J = 0;
-grad = zeros(size(theta));
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the cost of a particular choice of theta.
-%               You should set J to the cost.
-%               Compute the partial derivatives and set grad to the partial
-%               derivatives of the cost w.r.t. each parameter in theta
-h=X*theta;
-h=sigmoid(h);
-J=(-1)*(((y')*log(h))+((1-y)'*log(1-h)));
-J=J/m;
-k=ones(1,size(theta,1));
-l=theta.^2;
-J=J+(lambda/(2*m))*(k*l);
-J=J-(lambda/(2*m))*l(1,1);
-grad=(1/m)*(X'*(h-y));
-grad=grad+(lambda/m)*theta;
-grad(1)=grad(1)-(lambda/m)*theta(1);
-% =============================================================
-
-end

From 80ef8b66804e484b587b2d3940be8ca5031eba19 Mon Sep 17 00:00:00 2001
From: jayakar01 <49501623+jayakar01@users.noreply.github.com>
Date: Tue, 29 Oct 2019 14:31:35 +0530
Subject: [PATCH 27/27] Checking out a reame feature.

---
 README.md | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/README.md b/README.md
index f1919c0..a8bdd9d 100644
--- a/README.md
+++ b/README.md
@@ -2,6 +2,9 @@
 
 ### This is an attempt at teaching our juniors at IIT Bhubaneswar Machine Learning.
 
+![Student Community](https://www.google.com/imgres?imgurl=https%3A%2F%2Fdataqualitycampaign.org%2Fwp-content%2Fuploads%2F2016%2F03%2Fwhy-education-data-illustration-3.png&imgrefurl=https%3A%2F%2Fdataqualitycampaign.org%2Fwhy-education-data%2F&docid=qxzQaiCVfbwnXM&tbnid=4SzoAgqZUdpTbM%3A&vet=10ahUKEwiBubLeisHlAhVafisKHQGyBrMQMwhVKAkwCQ..i&w=1134&h=920&bih=669&biw=1299&q=students%20helping%20each%20other%20animated&ved=0ahUKEwiBubLeisHlAhVafisKHQGyBrMQMwhVKAkwCQ&iact=mrc&uact=8)
+
+
 * This repository includes their project codes, programming assignments
 
 -----