% Script MkDiagMat.m
% making some banded matrices
close all;

n = 10;
p = 2;   % p is upper bandwidth, with p-1 diagonals above the main one
q = 2;   % q is lower bandwidth, with q-1 diagonals below the main one

% using tril and triu:
A = tril(rand(n),p-1); spy(A); title('A after tril command')
A = triu(A,1-q); figure; spy(A); title('A after triu command')

% really, this should be in one command

A = triu(tril(rand(n),p-1),1-q); figure; spy(A) 
title('banded A in one command')

A(1:n+1:end) = p+q-2;
[L,U,P] = lu(A);
figure; spy(L); title('L when A is diagonally dominant')
figure; spy(U); title('U when A is diagonally dominant')
P   % was there row switching?

A(1:n+1:end) = rand(n,1);
[L,U,P] = lu(A);
figure; spy(U); title('U when A is not diagonally dominant')
figure; spy(L); title('L when A is not diagonally dominant')
P   % was there row switching?