#include "cs_mex.h"
/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */
void mexFunction
(
    int nargout,
    mxArray *pargout [ ],
    int nargin,
    const mxArray *pargin [ ]
)
{
    CS_INT n, order, *p ;
    double tol ;
    if (nargout > 4 || nargin > 3 || nargin < 1)
    {
	mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ;
    }
    if (nargin == 2)			    /* determine tol and ordering */
    {
	tol = mxGetScalar (pargin [1]) ;
	order = (nargout == 4) ? 1 : 0 ;    /* amd (A+A'), or natural */
    }
    else
    {
	tol = 1 ;
	order = (nargout == 4) ? 2 : 0 ;    /* amd(S'*S) w/dense rows or I */
    }
    if (mxIsComplex (pargin [0]))
    {
#ifndef NCOMPLEX
	cs_cls *S ;
	cs_cln *N ;
	cs_cl Amatrix, *A, *D ;
	A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ;	/* get A */
	n = A->n ;
	S = cs_cl_sqr (order, A, 0) ;	    /* symbolic ordering, no QR bound */
	N = cs_cl_lu (A, S, tol) ;	    /* numeric factorization */
	if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
	cs_cl_free (A->x) ;		    /* complex copy no longer needed */
	cs_cl_dropzeros (N->L) ;	    /* drop zeros from L and sort it */
	D = cs_cl_transpose (N->L, 1) ;
	cs_cl_spfree (N->L) ;
	N->L = cs_cl_transpose (D, 1) ;
	cs_cl_spfree (D) ;
	cs_cl_dropzeros (N->U) ;	    /* drop zeros from U and sort it */
	D = cs_cl_transpose (N->U, 1) ;
	cs_cl_spfree (N->U) ;
	N->U = cs_cl_transpose (D, 1) ;
	cs_cl_spfree (D) ;
	p = cs_cl_pinv (N->pinv, n) ;			    /* p=pinv' */
	pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ;	    /* return L */
	pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ;	    /* return U */
	pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ;	    /* return p */
	/* return Q */
	if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
	cs_cl_nfree (N) ;
	cs_cl_sfree (S) ;
#else
	mexErrMsgTxt ("complex matrices not supported") ;
#endif
    }
    else
    {
	cs_dls *S ;
	cs_dln *N ;
	cs_dl Amatrix, *A, *D ;
	A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ;	/* get A */
	n = A->n ;
	S = cs_dl_sqr (order, A, 0) ;	    /* symbolic ordering, no QR bound */
	N = cs_dl_lu (A, S, tol) ;	    /* numeric factorization */
	if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
	cs_dl_dropzeros (N->L) ;	    /* drop zeros from L and sort it */
	D = cs_dl_transpose (N->L, 1) ;
	cs_dl_spfree (N->L) ;
	N->L = cs_dl_transpose (D, 1) ;
	cs_dl_spfree (D) ;
	cs_dl_dropzeros (N->U) ;	    /* drop zeros from U and sort it */
	D = cs_dl_transpose (N->U, 1) ;
	cs_dl_spfree (N->U) ;
	N->U = cs_dl_transpose (D, 1) ;
	cs_dl_spfree (D) ;
	p = cs_dl_pinv (N->pinv, n) ;			    /* p=pinv' */
	pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ;	    /* return L */
	pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ;	    /* return U */
	pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ;	    /* return p */
	/* return Q */
	if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ;
	cs_dl_nfree (N) ;
	cs_dl_sfree (S) ;
    }
}
