%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FIRST DAY MATLAB worksheet
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for MTH 654
%%% this file helps to get familiar with basic elements of MATLAB
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%% M. Peszynska,  2009/10
%% Copyright Department of Mathematics, Oregon State University
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%% INSTRUCTIONS: please type every line yourself
%%%               ignore all lines and text beginning with %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
diary yourname
%% allocate (reserve, initialize) space for a vector
n = 100;  x = zeros(n,1);
%% how large can a vector be ? 
n = 10^5; x = zeros(n,1);
n = 10^9; x = zeros(n,1);
%% how to input a matrix
A = [2 3 5; 7 11 13; 17 19, 23]
%% how to access its elements
A(1), A(3)
%% the transpose of a matrix
A'
%% how to access the first column and rows from 1:2
A (1:2,1)
%% how to access the first column and all rows
A (1:3,1)
A (:,1)
%% how to get a matrix with random entries
B = rand (3,5)
%%%%%%%%%% EXERCISE: swap the first and last columns of B
%% input a column vector
x = [1; 2; 3]
%% input a row vector 
y = [1 2 3]
%% change from a row vector to column vector
x = y'
%% operations on vectors: multiply a vector by a scalar
pi * x
y = y'
%% (now y is a column vector)
%% dot (inner) product of two column vectors
x, y, x'*y
%% compute outer product 
x * y'
%% compute a vector as a component-by-component product of x and y
x.*y
%%%%%%%%%% EXERCISE: compute all possible products of A and B 
%% how to set-up a simple loop to compute the dot product: try
n = 3;
c = 0;
for i=1:n c = c + x(i) * y(i); end
%%%%%%%%%% EXERCISE: compute Frobenious norm of matrix A directly
%% how to get the size of a vector/matrix if forgotten
size(x)
%% identity matrix
eye(4)
%% eigenevalues of a matrix
eig (A)
%% various norms of matrices: 
norm(A), norm(A,1), norm(A,2), norm(A,infty) 
%%%%%%%%%% EXERCISE: compare these norms with eigenvalues 
%% how to plot
x = 0:.01:6*pi;
plot(x,sin(x));
%%%%%%%%%% EXERCISE: plot exp(x) and use log log plots 
%% close the session