function b = gee_its_simple_backsolve (U, b)%GEE_ITS_SIMPLE_BACKSOLVE x=U\b where U is upper triangular% Perform back substitution to solve x=U\b.  U must be square.  The lower% triangular part of U is ignored (this allows L and U to be packed into a% single matrix).%% Example:%%   x = gee_its_simple_backsolve (U,b) ;%%   % which is the same as%   x = triu (U) \ b ;%% See also: mldivide, gee_its_simple, gee_its_short, gee_its_simple_forwardsolve% Copyright 2007, Timothy A. Davis.% http://www.cise.ufl.edu/research/sparse%-------------------------------------------------------------------------------% check inputs%-------------------------------------------------------------------------------if (nargin ~= 2 | nargout > 1)                                              %#ok    error ('Usage: x = ge_its_simple_backsolve (U,b)') ;end% ensure U is square, and that U and b have the same number of rowsgee_its_simple_check (U, 'U', b) ;%-------------------------------------------------------------------------------% backsolve solve, overwriting b with the solution U\b%-------------------------------------------------------------------------------n = size (U,1) ;for k = n:-1:1    b (k,:) = b (k,:) / U (k,k) ;    b (1:k-1,:) = b (1:k-1,:) - U (1:k-1,k) * b (k,:) ;end