SPOT -- A linear-operator toolbox for Matlab, v1.0p

The SPOT Toolbox brings the expressiveness of Matlab's built-in matrix
notation to problems for which explicit matrices are not
practical. SPOT operators look and feel like regular Matlab
matrices, but are implicitly defined. SPOT includes a collection of
fast operators that can be stitched together using familiar Matlab
commands to form more complex operators.

The following example builds up a 1000-by-1000 circulant operator
using the discrete Fourier transform:

>> n = 1000; x = (1:n)'; % the first column defines this operator
>> F = opDFT(n); % instantiate a DFT operator
>> s = sqrt(n)*F*x; % eigenvalues of the circulant operator C
>> C = real( F'*opDiag(s)*F ); % the circulant operator C
>> w = C*x; % apply C to a vector
>> y = C'*w; % apply the adjoint of C to a vector
>> z = C(end:-1:1,:)*y; % reverse the rows of C and apply to a vector
>> double( C(1:5,1) )' % extract a few elements of the first column
ans =
           1 2 3 4 5

In this example, no explicit matrices are formed. Compare the memory
footprints of the explicit matrix against the SPOT operator:

>> A = gallery('circul',x)';
>> whos A C
 Name Size Bytes Class Attributes

 A 1000x1000 8000000 double
 C 1000x1000 70730 opReal

SPOT is available under the GNU Public License. We are glad to hear
from users -- please send your comments and suggestions!