% Starting diary file diary-08-Nov-2010.txt

load grades
grades
plot(grades,'.')
median(grades)
sort(grades)
hist(grades,0:5:100)

A = [ 3 1 ; -2 4]
b = [9;8]
A \ b
x = [0;0]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
A\b
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
format long
x
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]
x = [ (9-x(2))/3   ;   (8+2*x(1))/4 ]

format short
d = diag(A)
A
D = diag(d)
C = A - D

x =[0;0]
x = (b-C*x) ./ d
x = (b-C*x) ./ d
% ... about 30 repetitions
x = (b-C*x) ./ d

residual = A*x - b
x =[0;0]
x = (b-C*x) ./ d,   resnorm = norm(A*x-b)
x = (b-C*x) ./ d,   resnorm = norm(A*x-b)
% ... about 30 repetitions
x = (b-C*x) ./ d,   resnorm = norm(A*x-b)
x = (b-C*x) ./ d,   resnorm = norm(A*x-b)
resnorm =
  7.1693e-006

clc
clear
load roomtemp
spy(A)
A(1:10,1:10)
whos

B = reshape(b,100,100);
surfc(B)
t = A \ b;
surfc(reshape(t,100,100)),shg
max(t)
ans =
    37
37 * 9/5 + 32

clc
d = diag(A);
d
C = A - diag(d);
spy(C)
n = 10000
x = zeros(n,1);
surfc(reshape(x,100,100)),shg

x = (b-C*x) ./ d;   resnorm = norm(A*x-b)
surfc(reshape(x,100,100)),shg
x = (b-C*x) ./ d;   resnorm = norm(A*x-b)
surfc(reshape(x,100,100)),shg

jacobitest1  % hit space bar for each iteration
jacobitest2  % runs 20000 iterations, plotting at each 100th one.

figure,spy(A)
[L,U,P] = lu(A);
spy(L+U)

clc
jacobitest3  % runs 20000 iterations with no output, gives resvec
size(resvec)
plot(resvec)
semilogy(resvec)

x = zeros(n,1);
[x,flag,relres,iter,resvec] = pcg(A,b,10^(-8),10000);
norm(A*x-b)
iter
hold on
semilogy(resvec,'r')

clc
A = randn(100,100);
b = randn(100,1);
x = A\b;
norm(A*x-b)
jacobitest
figure
semilogy(resvec)

diary off