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function x = umfpack_solve (arg1, op, arg2, Control)
% UMFPACK_SOLVE
%
% x = umfpack_solve (A, '\', b, Control)
% x = umfpack_solve (b, '/', A, Control)
%
% Computes x = A\b, or b/A, where A is square. Uses UMFPACK if A is sparse.
% The Control argument is optional.
%
% See also umfpack, umfpack_make, umfpack_details, umfpack_report,
% and umfpack_simple.
% UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
% All Rights Reserved. Type umfpack_details for License.
%-------------------------------------------------------------------------------
% check inputs and get default control parameters
%-------------------------------------------------------------------------------
if (op == '\')
A = arg1 ;
b = arg2 ;
elseif (op == '/')
A = arg2 ;
b = arg1 ;
else
help umfack_solve
error ('umfpack_solve: unrecognized operator') ;
end
[m n] = size (A) ;
if (m ~= n)
help umfpack_solve
error ('umfpack_solve: A must be square') ;
end
[m1 n1] = size (b) ;
if ((op == '\' & n ~= m1) | (op == '/' & n1 ~= m))
help umfpack_solve
error ('umfpack_solve: b has the wrong dimensions') ;
end
if (nargin < 4)
Control = umfpack ;
end
%-------------------------------------------------------------------------------
% solve the system
%-------------------------------------------------------------------------------
if (op == '\')
if (~issparse (A))
% A is not sparse, so just use MATLAB
x = A\b ;
elseif (n1 == 1 & ~issparse (b))
% the UMFPACK '\' requires b to be a dense column vector
x = umfpack (A, '\', b, Control) ;
else
% factorize with UMFPACK and do the forward/back solves in MATLAB
[L, U, P, Q, R] = umfpack (A, Control) ;
x = Q * (U \ (L \ (P * (R \ b)))) ;
end
else
if (~issparse (A))
% A is not sparse, so just use MATLAB
x = b/A ;
elseif (m1 == 1 & ~issparse (b))
% the UMFPACK '\' requires b to be a dense column vector
x = umfpack (b, '/', A, Control) ;
else
% factorize with UMFPACK and do the forward/back solves in MATLAB
% this mimics the behavior of x = b/A, except for the row scaling
[L, U, P, Q, R] = umfpack (A.', Control) ;
x = (Q * (U \ (L \ (P * (R \ (b.')))))).' ;
% an alternative method:
% [L, U, P, Q, r] = umfpack (A, Control) ;
% x = (R \ (P' * (L.' \ (U.' \ (Q' * b.'))))).' ;
end
end
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