% Introduction to MATLAB for "Numerical modelling of weather and climate"
% Springterm 2010

% delete all variables
clear
clear all

% delete single variables
clear x

% Definition of variables
a=1
b=2
c=1.3456
d=1.567e-2

% supress output of variables using ;
e=23.1045;

%print used variables and its dimensions
who     % variables

whos    % variablen, dimensions and typ

% operations:

f=a+b
g=A+b

% MATLAB destinguishes between capital and small letters

% power
f=e^2
g=e^1.4

% square root
f=sqrt(e)
f=e^0.45

% also for complex numbers
f=a-c
h=sqrt(f)
z=e+h

% Real- and Imaginary part
real(z)
imag(z)


% textvariables
%==============

text='This is text'

text=num2str(300)  % transformation from numbers to text
whos text


% Vektors and Vectoroperations
%===============================

a=[1 2 3]   % rowvector, 1x3
size(a)

b=[1;2;3]   % columnvector, 3x1
size(b)

c=[3 2 1 0] % rowvector, 1x4

% Indices of vectors (and matrices) have to be integer and 
% always lager than 0
% alternative Definition is
a=[]
a(1)=1
a(2)=2
a(3)=3

% Transpose
%--------------
at1=a'       % rowvector to columnvector
size(at1)

% for vectoroperations, pay attention to vector dimensions
d=[3 2 1]

e=a+d % 1x3 vector + 1x3 vector = 1x3 vector

f=d*at1 % 1x3 vector * 3x1 vector = 1x1 vector = scalar

% elementwise operations:
ff = a.*d % ff(i) = a(i)*d(i)

% Matrices and matrixoperations
%===============================

A=[1 2 3; 4 5 6]    % 2x3 matrix

B=[1 2; 3 4; 5 6]   % 3x2 matrix

C=[-1 -2 -3; 1 2 3] % 2x3 matrix

size(A)
size(B)

G=at1*d % 3x1 vector * 1x3 vector = 3x3 matrix

% Transpose
%--------------
AT1=A'
GT1=G'

% for matrixoperations, pay attention to matrix dimensions
E=A+C
F=A+B

F2=G^2
F3=G^3

size(F2)

H=[1 1 0; 0 1 1 ; 0 0 1]
H2=H^2
H3=H^3

K=G*H

% elementwise Operations:

He=H2.^2

% Loops, if-statements, plotting etc.


% Loops
%==========

for k=start:increment:end
    blabla
end

for k=0:2:10
    k
end

% vectorfunction
x=[1 3 6 8 10 8 6 3 1]


% 'if' statement
%==============

if (condition)
    do this
else
    do that
end

oder
if (condition)
    do this
end

x=[];
for k=1:10
    if (mod(k,2)==0)
        x(k)=0;
    else
        x(k)=1;
    end
end
x
size(x)

x=[];
for k=5:-1:-5
    if (k<=0) 
        break       %break ends the for-loop
    end
    x(k)=k;
end
x
size(x)

% plotting of functions
% Attention, the vector could already contain some elements
x=[0:12]

for k=1:10
    x(k)=2*k;
end
plot(x)     % strange plot 
x
size(x)

%better like this:
x=[]        %empty vector
for k=1:10; 
    x(k)=2*k; 
end; 
plot(x)

%or like this:
clear x
for k=1:10; 
    x(k)=2*k; 
end; 
plot(x)

%create vector x with values 0,pi/100,2*pi/100,...,2*pi
x=[0:pi/100:2*pi] 
y=sin(x)

figure(1)       % open plot window Nr 1
plot(y)         % pay attention to x-axis

plot(sin(x))

figure(2)       % open plot window Nr 2
plot(x,y)       % pay attention to x-axis
% modifications to current axis
set(gca,'XLim',[0 2*pi])
set(gca,'YLim',[-1 1])

clf(1)          % delet plot Nr 1 

close(1)        % close Plot window 1 
close(2)        % close Plot window 2


% open several frames to create a liitle clip

clear all
close all

%number of frames: 
nframes = 20;

figure(1)       % open plot window Nr 1
for i = 1:nframes
    x=0:0.1:i;
    y1=x.*2.;
    plot(x,y1);
    title('simple')
    set(gca,'XLim',[0 20]) % modifies "current axis"
    set(gca,'YLim',[0 40]) % modifies  "current axis"
    M(i)=getframe;
end

movie(M)

%number of frames: 
nframes = 20;

figure(2)       % open plot window Nr 2
for i = 1:nframes
    x=0:0.01:i;
    y1=x.*2.;
    y2=x.*x;
    plot(x,y1);
    title(['a bit more complex'])
    grid
    set(gca,'XLim',[0 20])
    set(gca,'YLim',[0 400])
    hold on
    plot(x,y2,'r')
    hold off
    M(i)=getframe;
end
%and just for the fun of it, 5 more times ...
movie(M,5)

close all
clear all

% and now it's your turn ...