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    %% Compare Sparse Matrix and LU Factorization
% The Harwell-Boeing collection of sparse matrices and the MATLAB(R) demos
% directory include a test matrix |west0479|. It is
% a matrix of order 479 resulting from a model due to Westerberg of
% an eight-stage chemical distillation column. The spy plot shows evidence
% of the eight stages. The |colamd| ordering scrambles
% this structure.

% Copyright 2015 The MathWorks, Inc.

load west0479
A = west0479;
p = colamd(A);

figure()
subplot(1,2,1), spy(A,4), title('A')
subplot(1,2,2), spy(A(:,p),4), title('A(:,p)')

%%
% Comparing the spy plot of the LU factorization of the original matrix
% with that of the reordered matrix shows that minimum degree reduces the
% time and storage requirements by better than a factor of 2.8. The nonzero
% counts are 15918 and 5920, respectively.
figure()
subplot(1,2,1), spy(lu(A),4), title('lu(A)')
subplot(1,2,2), spy(lu(A(:,p)),4), title('lu(A(:,p))')