% Matlab diary from cs111, Oct 10 2007.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

A = rand(7)
A = rand(7)-.5
A = 100*(rand(7)-.5)
A = round(100*(rand(7)-.5))
lugui(A)
P = eye(5)
P(2,2)
P(1, :)
P(1, [1 2 3 4 5])
P(1, 1:5)
1:5
P
P([2 3 4 5],:)
P = [ P([2 3 4 5],:)     ;   P(1,:) ]
A
P * A
A = round(100*(rand(5)-.5))
clc
A
P
P * A
P*P
Q = P*P
A
Q*A
P ^ 5
P * P^4
P^4
inv(P)
P
P'
P
inv(P)
clc
A
P*A
A*P
P * A * P'
A
help lu
[L, U, P] = lu(A)
A
L * U
P * A
P*A - L*U
b = [ 1 ; 2 ; 3 ; 4 ; 5]
c = P*b
L
U
A
[L, U, P] = lu(A)
b
c = P*b
y = L \ c
x = U \ y
A * x
ans-b
residual = b - A*x
x
norm(x)
norm(residual)
A = [10^-20 1 ; 1 1]
A(1,1)
b = [1 ; 2]
x = A \ b
residual = b - A*x
[L, U, P] = lu(A)
x = U \ ( L \ ( P * b))
A\b
[L,U] = lugui(A)  % and then select "diagonal pivoting"
L(2,1)
U(2,2)
U(1,1)
x = U \ ( L \  b)
L*U
A
clc
help lutx
A
A = round(100*(rand(5)-.5))
[L,U,P] = lu(A)
[LL,UU,pp] = lutx(A)
P * [1;2;3;4;5]
P
pp
L - LL
U - UU
help lutx
A
pp
A(pp,:)
P*A
edit lutx
edit bslashtx