Machine Learning Example 2

clc

clear

close all

x=load('ex2x.dat');

y=load('ex2y.dat');

figure

plot(x,y,'o')

ylabel('Height in meters')

xlabel('Age in years')

m = length(y); % store the size of data

x = [ ones(m,1),x]; %add a column to the x

%% linear regresion

theta = [0 0];

ss_old =theta;

ss_new = [inf inf];

alpha = 0.007;

while (abs(ss_new-ss_old)>0.0000000001)

ss_old = ss_new;

h_the = x*theta'; % prediction

theta(1)=theta(1)-alpha*(1/m).*sum(((h_the-y) .* x(:,1)));

theta(2)=theta(2)-alpha*(1/m).*sum(((h_the-y) .* x(:,2)));

MATCHING NETWORKS AND SIGNAL FLOW GRAPHS

2.1 Introduction, 92

2.2 The Smith Chart, 93

2.3 .The Normalized Impedance and Admittance

Smith Chart, 105

2.4 Impedance Matching Networks, 112

2.5 Microstrip Matching Networks, 141

Microstrip Lines, 141

Design ofMatching Ne!works, 152

2.6 Signal Flow Graphs and Applications, 175

Applications ofSignal Flow Graphs, 180

2.7 Power-Gain Expressions: Alternate

Derivations, 185

Power-Gain Expressions in Terms ofSp

parameters, 192

2.8 VSWR Calculations, 194

Problems, 200

3 MICROWAVE TRANSISTOR AMPLIFIER DESIGN

3.1 Introduction, 212

3.2 Power Gain Equations, 213

3.3 Stability Considerations, 217

3.4 Constant-Gain Circles: Unilateral Case, 228

Unconditionally Stable Case, ISi;1 < 1, 231

Potentially Unstable Case, ISi;1 > 1, 234

3.5 Unilateral Figure of Merit, 238

3.6 Simultaneous Conjugate Match:

Bilateral Case, 240

3.7 Operating and Available Power-Gain Circles, 247

Operating Power-Gain Circles, 247

Unconditionally stable bilateral case, 247

Potentially unstable bilateral case, 252

Available Power-Gain Circles, 257

Unconditionally stable bilateral case, 257

Potentially unstable bilateral case, 260

3.8 Constant VSWR Circles, 260

3.9 DC Bias Networks, 273

BIT Bias Networks, 273

GaAs FET Bias Networks, 280

ss_new=theta;

end

hold on

plot(x(:,2), x*theta', '-') % remember that x is now a matrix with 2 columns

% and the second column contains the time info

legend('Training data', 'Linear regression')

theta

[1 3.5]*theta'

[1 7]*theta'