You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: umfpack_btf.m
    path of file: ./repos/SuiteSparse/UMFPACK/MATLAB
    
    the code of the file until where you have to start completion: function [x, info] = umfpack_btf (A, b, Control)
%UMFPACK_BTF factorize A using a block triangular form
%
% Example:
%   x = umfpack_btf (A, b, Control)
%
% solve Ax=b by first permuting the matrix A to block triangular form via dmperm
% and then using UMFPACK to factorize each diagonal block.  Adjacent 1-by-1
% blocks are merged into a single upper triang
    
function [r, nblocks, is_triangular] = merge_singletons (r)
%
% Given r from [p,q,r] = dmperm (A), where A is square, return a modified r that
% reflects the merger of adjacent singletons into a single upper triangular
% block.  is_triangular (k) is 1 if the kth block is upper triangular.  nblocks
% is the number of new blocks.

nblocks = length (r) - 1 ;
bsize = r (2:nblocks+1) - r (1:nblocks) ;
t = [0 (bsize == 1)] ;
z = (t (1:nblocks) == 0 & t (2:nblocks+1) == 1) | t (2:nblocks+1) == 0 ;
y = [(find (z)) nblocks+1] ;
r = r (y) ;
nblocks = length (y) - 1 ;
is_triangular = y (2:nblocks+1) - y (1:nblocks) > 1 ;

%-------------------------------------------------------------------------------
% solve Ax=b, but check for small and/or triangular systems
%-------------------------------------------------------------------------------

function [x, info] = solver (A, b, is_triangular, Control)
if (is_triangular)
    % back substitution only
    x = A \ b ;
    info.nnz_in_L_plus_U = nnz (A) ;
elseif (size (A,1) < 4)
    % a very small matrix, solve it as a dense linear system
    x = full (A) \ b ;
    n = size (A,1) ;
    info.nnz_in_L_plus_U = n^2 ;
else
    % solve it as a sparse linear system
    [x info] = umfpack_solve (A, '\', b, Control) ;
end