%                              ----------------------
%                              USEFUL MATLAB COMMANDS
%                              ----------------------
% --------
% vectors:
% --------

x=[0:0.2:1], x1=[0, 0.2, 0.4, 0.6, 0.8, 1], x2=[0 0.2 0.4 0.6 0.8 1]     % row

z=[0; 0.2; 0.4; 0.6; 0.8; 1]                                          % column

x(2), z(2)

y=transpose(x)

y*x

x*y

% not defined:
% y.*x

sin(x)

sin(x(2))

% ---------
% matrices:
% ---------

z1=zeros(3), z2=zeros(2,4)

m=[1 2; 3 4]

m1=[1 2
    3 4]

transpose(m)

m^2

n=inv(m)

n*m

% compare with component-wise multiplication:
n.*m

det(m)

eig(m)

[v,lambda]=eig(m)

v1=v(:,1)

check=m*v1-lambda(1,1)*v1

m=[1 0
   0 2]

k=[ 1 -1
   -1  1]

omega2=eig(k,m), omega=sqrt(omega2)

check=det(k-omega(1)^2.*m)

a=rand(4)

a1=a([1:3],[1:3])

a2=a([1:2],4)

a3=a([1,3],[2,4])

% call function 'beam' (defined in 'beam.m'; see below):
%
s=zeros(8);
k=beam(1,1)
%
% add beam element 1:
%
s([1 2 3 4],[1 2 3 4])=s([1 2 3 4],[1 2 3 4])+k
%
% add beam element 2:
%
s([3 4 5 6],[3 4 5 6])=s([3 4 5 6],[3 4 5 6])+k
%
% add beam element 3:
%
s([5 6 7 8],[5 6 7 8])=s([5 6 7 8],[5 6 7 8])+k

% ----------
% functions:
% ----------

t=[0:0.1:2*pi];

plot(sin(t))

plot(t,sin(2*t).^2,t,sqrt(t))

integral=quad('sin(2*y)',0,2*pi)

fzero('x-tan(x)',2), fzero('x-tan(x)',4)

% -------------------
% logical structures:
% -------------------

x=0
for i=1:2:10
    x=x+i
end

i=input('Enter first number: ');
j=input('Enter second number: ');
%
if i==j
   r=1
elseif abs(i-j)>=2
   r=2
elseif i~=0 & j~=0
   r=1/(i*j)
end

% ------------------------------
% contents of the file 'beam.m':
% ------------------------------
%
%function k=beam(EI,L)
%
%k = (EI/L^3)*[ 12      6*L     -12     6*L
%                6*L    4*L^2   -6*L    2*L^2
%              -12     -6*L      12    -6*L
%                6*L    2*L^2   -6*L    4*L^2  ];