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function [x, rcnd] = gee_its_simple (A, b)
%GEE_ITS_SIMPLE solves A*x=b using a Gaussian Elimination Example (it's simple!)
% For details on the algorithm used (Gaussian elimination with partial
% pivoting), see gee_its_simple_factorize, gee_its_simple_forwardsolve,
% and gee_its_simple_backsolve.
%
% Example:
%
% x = gee_its_simple (A,b) ;
% [x,rcnd] = gee_its_simple (A,b) ;
%
% % which is the same as:
% x = A\b ;
%
% % or using LU:
% [L U p] = lu (A) ;
% x = U \ (L \ (b (p,:))) ;
% rcnd = min (abs (diag (U))) / max (abs (diag (U))) ;
%
% See also: lu, mldivide, rcond, gee_its_short
% GEE, Copyright (c) 2006-2007, Timothy A Davis. All Rights Reserved.
% SPDX-License-Identifier: BSD-3-clause
% check inputs
if (nargin ~= 2 | nargout > 2) %#ok
error ('Usage: [x,rcnd] = gee_its_simple (A,b)') ;
end
% ensure A is square, and that A and b have the same number of rows
gee_its_simple_check (A, 'A', b) ;
% LU factorization, using Gaussian Elimination with partial pivoting, same as
% [L,U,p] = lu (A) ; rcnd = rcond (A) ; except return L and U in one matrix LU.
[LU p rcnd] = gee_its_simple_factorize (A) ;
% forward/backsolve, same as x = U \ (L \ b (p,:))
x = gee_its_simple_backsolve (LU, gee_its_simple_forwardsolve (LU, b (p,:))) ;
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