From c2485055c8b10b0eeba9e6d9727fc695aece19f9 Mon Sep 17 00:00:00 2001
From: Jan Grewe <jan.grewe@g-node.org>
Date: Sun, 8 Nov 2015 18:11:50 +0100
Subject: [PATCH] extra code

---
 regression/code/errorGradient.m       | 31 +++++++++++++++++++
 regression/code/gradientDescent.m     | 31 +++++++++++++++++++
 regression/code/gradientDescentPlot.m | 43 +++++++++++++++++++++++++++
 3 files changed, 105 insertions(+)
 create mode 100644 regression/code/errorGradient.m
 create mode 100644 regression/code/gradientDescent.m
 create mode 100644 regression/code/gradientDescentPlot.m

diff --git a/regression/code/errorGradient.m b/regression/code/errorGradient.m
new file mode 100644
index 0000000..5a5998b
--- /dev/null
+++ b/regression/code/errorGradient.m
@@ -0,0 +1,31 @@
+clear
+load('lin_regression.mat')
+
+ms = -1:0.5:5;
+ns = -10:1:10;
+
+error_surf = zeros(length(ms), length(ns));
+gradient_m = zeros(size(error_surf));
+gradient_n = zeros(size(error_surf));
+
+for i = 1:length(ms)
+    for j = 1:length(ns)
+        error_surf(i,j) = lsqError([ms(i), ns(j)], x, y);
+        grad = lsqGradient([ms(i), ns(j)], x, y);
+        gradient_m(i,j) = grad(1);
+        gradient_n(i,j) = grad(2);
+    end
+end
+
+figure()
+hold on
+[N, M] = meshgrid(ns, ms);
+%surface(M,N, error_surf, 'FaceAlpha', 0.5);
+contour(M,N, error_surf, 50);
+quiver(M,N, gradient_m, gradient_n)
+xlabel('slope')
+ylabel('intercept')
+zlabel('error')
+set(gcf, 'paperunits', 'centimeters', 'papersize', [15, 12.5], ... 
+    'paperposition', [0., 0., 15, 12.5])
+saveas(gcf, 'error_gradient', 'pdf')
\ No newline at end of file
diff --git a/regression/code/gradientDescent.m b/regression/code/gradientDescent.m
new file mode 100644
index 0000000..d4d18b9
--- /dev/null
+++ b/regression/code/gradientDescent.m
@@ -0,0 +1,31 @@
+clear 
+close all
+load('lin_regression.mat')
+
+position = [-2. 10.];
+gradient = [];
+errors = [];
+count = 1;
+eps = 0.01;
+
+while isempty(gradient) || norm(gradient) > 0.1
+    gradient = lsqGradient(position, x,y);
+    errors(count) = lsqError(position, x, y);
+    position = position - eps .* gradient; 
+    count = count + 1;
+end
+figure()
+subplot(2,1,1)
+hold on
+scatter(x,y, 'displayname', 'data')
+xaxis = min(x):0.01:max(x);
+f_x = position(1).*xaxis + position(2);
+plot(xaxis, f_x, 'displayname', 'fit')
+xlabel('Input')
+ylabel('Output')
+grid on
+legend show
+subplot(2,1,2)
+plot(errors)
+xlabel('optimization steps')
+ylabel('error')
\ No newline at end of file
diff --git a/regression/code/gradientDescentPlot.m b/regression/code/gradientDescentPlot.m
new file mode 100644
index 0000000..83dc2df
--- /dev/null
+++ b/regression/code/gradientDescentPlot.m
@@ -0,0 +1,43 @@
+clear 
+close all
+
+load('lin_regression.mat')
+
+ms = -1:0.5:5;
+ns = -10:1:10;
+
+position = [-2. 10.];
+gradient = [];
+error = [];
+eps = 0.01;
+
+% claculate error surface
+error_surf = zeros(length(ms), length(ns));
+for i = 1:length(ms)
+    for j = 1:length(ns)
+        error_surf(i,j) = lsqError([ms(i), ns(j)], x, y);
+    end
+end
+figure()
+hold on
+[N, M] = meshgrid(ns, ms);
+surface(M,N, error_surf, 'FaceAlpha', 0.5);
+view(3)
+xlabel('slope')
+ylabel('intersection')
+zlabel('error')
+
+% do the descent
+
+while isempty(gradient) || norm(gradient) > 0.1
+    gradient = lsqGradient(position, x,y);
+    error = lsqError(position, x, y);
+    plot3(position(1), position(2), error, '.', 'color', 'red', 'markersize', 20)
+    position = position - eps .* gradient; 
+    pause(0.05)
+end
+
+grid on
+set(gcf, 'paperunits', 'centimeters', 'papersize', [15, 15], ... 
+    'paperposition', [0., 0., 15, 15])
+saveas(gcf, 'gradient_descent', 'pdf')