pwd

ans =

\\nask.man.ac.uk\home$\MATLAB

which radon
C:\Program Files\MATLAB\R2012a\toolbox\images\images\radon.m
doc radon
which siddon
\\nask.man.ac.uk\home$\MATLAB\siddon.m
I = phantom(30);
doc phantom
size(I)

ans =

    30    30

imagesc(I)
[rays, sino] = siddon(I);

h =

    0.7658

ind = find(sum(rays,2));
A = rays(ind,:);
b = sino(:); b = b(ind);
imagesc(sino)
x= A\b;
figure;imagesc(reshape(x,30,30))
I=zeros(30,30);
I(10,7) =1;
imagesc(I)
b= A*I(:);
size(sino)

ans =

    41    60

size(b)

ans =

        2456           1

imagesc(reshape(b,41,60))
{Error using <a href="matlab:helpUtils.errorDocCallback('reshape')" style="font-weight:bold">reshape</a>
To RESHAPE the number of elements must not change.
} 
[rays, sino] = siddon(I);

h =

    0.7658

A = rays(ind,:);
b = sino(:); b = b(ind);
imagesc(sino)
x= A\b;
figure;imagesc(reshape(x,30,30))
figure;imagesc(reshape(A\(b + 0.1*randn(size(b))) ,30,30))
scale
{Undefined function or variable 'scale'.
} 
x=reshape(A\(b + 0.1*randn(size(b)),30,30));
 x=reshape(A\(b + 0.1*randn(size(b)),30,30));
                                   |
{Error: Expression or statement is incorrect--possibly unbalanced (, {,
or [.
} 
x=reshape(A\(b + 0.1*randn(size(b))),30,30);
plot(x(10,:))
figure;imagesc(reshape(A\(b + 0.5*randn(size(b))) ,30,30))
figure;imagesc(reshape(A\(b + 0.3*randn(size(b))) ,30,30))
cond(A)
{Warning: Using CONDEST instead of COND for sparse matrix.} 
{> In <a href="matlab: opentoline('C:\Program Files\MATLAB\R2012a\toolbox\matlab\matfun\cond.m',28,1)">cond at 28</a>} 
{Error using <a href="matlab:helpUtils.errorDocCallback('condest', 'C:\Program Files\MATLAB\R2012a\toolbox\matlab\matfun\condest.m', 43)" style="font-weight:bold">condest</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2012a\toolbox\matlab\matfun\condest.m',43,0)">line 43</a>)
Matrix must be square.

Error in <a href="matlab:helpUtils.errorDocCallback('cond', 'C:\Program Files\MATLAB\R2012a\toolbox\matlab\matfun\cond.m', 29)" style="font-weight:bold">cond</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2012a\toolbox\matlab\matfun\cond.m',29,0)">line 29</a>)
    c = condest(A);
} 
cond(full(A))

ans =

   33.5029

bnoise = b + 0.1*randn(size(b)); % keep this as randn makes different answers each time it is called.

a=0.1; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30) 
 a=0.1; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30) 
                                                                               |
{Error: Expression or statement is incorrect--possibly unbalanced (, {,
or [.
} 
a=0.1; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30))
a=0.2; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30))
a=0.3; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30))
a=1; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30))
a=10; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30))
a=50; figure; imagesc( reshape((A'*A + a^2*eye( size(A,2) ))\A'*bnoise,30,30))
doc svd
s=svd(A);
{Error using <a href="matlab:helpUtils.errorDocCallback('svd')" style="font-weight:bold">svd</a>
Use svds for sparse singular values and vectors.
} 
s=svd(full(A));
plot(s)
loglog(s)
semilogy(s)
[U,S,V]=svd(full(A));
size(U)

ans =

        2456        2456

size(V)

ans =

   900   900

v1=V(:,1);imagesc(reshape(v1,30,30))
v1=V(:,30);imagesc(reshape(v1,30,30))
v1=V(:,500);imagesc(reshape(v1,30,30))
s(500)

ans =

    6.7159

exit