/* C = cs_transpose (A), computes C=A', where A must be sparse.
C = cs_transpose (A,kind) computes C=A.' if kind <= 0, C=A' if kind > 0 */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT values ;
if (nargout > 1 || nargin < 1 || nargin > 2)
{
mexErrMsgTxt ("Usage: C = cs_transpose(A,kind)") ;
}
values = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ;
values = (values <= 0) ? -1 : 1 ;
if (mxIsComplex (pargin [0]))
{
#ifndef NCOMPLEX
cs_cl Amatrix, *A, *C ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
C = cs_cl_transpose (A, values) ; /* C = A' */
pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl Amatrix, *A, *C ;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
C = cs_dl_transpose (A, values) ; /* C = A' */
pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
}
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT n, nel, s ;
cs *A, *AT ;
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: C = cs_frand(n,nel,s)") ;
}
n = mxGetScalar (pargin [0]) ;
nel = mxGetScalar (pargin [1]) ;
s = mxGetScalar (pargin [2]) ;
n = CS_MAX (1,n) ;
nel = CS_MAX (1,nel) ;
s = CS_MAX (1,s) ;
AT = cs_dl_frand (n, nel, s) ;
A = cs_dl_transpose (AT, 1) ;
cs_dl_spfree (AT) ;
cs_dl_dropzeros (A) ;
pargout [0] = cs_dl_mex_put_sparse (&A) ;
}
/* cs_sparse: convert triplet form into compress-column form sparse matrix */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ;
}
if (mxIsComplex (pargin [2]))
{
#ifndef NCOMPLEX
cs_cl *A, *C, *T, Tmatrix ;
T = &Tmatrix ; /* get i,j,x and copy to triplet form */
T->nz = mxGetM (pargin [0]) ;
T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ;
T->nzmax = T->nz ;
C = cs_cl_compress (T) ; /* create sparse matrix C */
cs_cl_dupl (C) ; /* remove duplicates from C */
cs_cl_dropzeros (C) ; /* remove zeros from C */
A = cs_cl_transpose (C, -1) ; /* A=C.' */
cs_cl_spfree (C) ;
pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */
cs_free (T->p) ;
cs_free (T->i) ;
cs_free (T->x) ; /* free copy of complex values*/
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl *A, *C, *T, Tmatrix ;
T = &Tmatrix ; /* get i,j,x and copy to triplet form */
T->nz = mxGetM (pargin [0]) ;
T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ;
T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ;
cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ;
T->x = mxGetPr (pargin [2]) ;
T->nzmax = T->nz ;
C = cs_dl_compress (T) ; /* create sparse matrix C */
cs_dl_dupl (C) ; /* remove duplicates from C */
cs_dl_dropzeros (C) ; /* remove zeros from C */
A = cs_dl_transpose (C, 1) ; /* A=C' */
cs_dl_spfree (C) ;
pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */
cs_free (T->p) ;
cs_free (T->i) ;
}
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
if (nargout > 1 || nargin < 2 || nargin > 4)
{
mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ;
}
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1])
|| (nargin > 2 && mxIsComplex (pargin [2]))
|| (nargin > 3 && mxIsComplex (pargin [3])))
{
#ifndef NCOMPLEX
cs_complex_t alpha, beta ;
cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */
alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */
beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */
C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
cs_cl_dropzeros (C) ; /* drop zeros */
D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */
cs_cl_spfree (C) ;
C = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
double alpha, beta ;
cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */
beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */
C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
cs_dl_dropzeros (C) ; /* drop zeros */
D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */
cs_dl_spfree (C) ;
C = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */
}
}
/* cs_updown: sparse Cholesky update/downdate (rank-1 or multiple rank) */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT ignore, j, k, n, lnz, *parent, sigma = 1, cp [2], ok ;
char sigma_string [20] ;
if (nargout > 1 || nargin < 3 || nargin > 4)
{
mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
}
if (nargin > 3 && mxIsChar (pargin [3]))
{
mxGetString (pargin [3], sigma_string, 8) ;
sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
}
n = mxGetN (pargin [0]) ;
parent = cs_dl_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent*/
if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]))
{
#ifndef NCOMPLEX
cs_cl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
/* get input L, and copy MATLAB complex to C complex type */
Lin = cs_cl_mex_get_sparse (&Lmatrix, 1, pargin [0]) ;
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_cl_spalloc (n, n, lnz, 0, 0) ;
for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
/* complex values already copied into Lin->x, use shallow copy for L */
L->x = Lin->x ;
cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
C = cs_cl_mex_get_sparse (&Cmatrix, 0, pargin [1]) ;
/* do the update one column at a time */
Cvec = &Cvector ;
Cvec->m = n ;
Cvec->n = 1 ;
Cvec->p = cp ;
Cvec->nz = -1 ;
cp [0] = 0 ;
for (k = 0 ; k < C->n ; k++)
{
/* extract C(:,k) */
cp [1] = C->p [k+1] - C->p [k] ;
Cvec->nzmax = cp [1] ;
Cvec->i = C->i + C->p [k] ;
Cvec->x = C->x + C->p [k] ;
/* update/downdate */
ok = cs_cl_updown (L, sigma, Cvec, parent) ;
if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
}
/* return new L */
pargout [0] = cs_cl_mex_put_sparse (&L) ;
cs_free (C->x) ; /* free complex copy of C */
#else
mexErrMsgTxt ("complex matrices not supported") ;
#endif
}
else
{
cs_dl Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
/* get input L */
Lin = cs_dl_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_dl_spalloc (n, n, lnz, 1, 0) ;
for (j = 0 ; j <= n ; j++) L->p [j] = Lin->p [j] ;
for (k = 0 ; k < lnz ; k++) L->i [k] = Lin->i [k] ;
for (k = 0 ; k < lnz ; k++) L->x [k] = Lin->x [k] ;
cs_mex_check (0, n, -1, 0, 1, 1, pargin [1]) ; /* get C */
C = cs_dl_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
/* do the update one column at a time */
Cvec = &Cvector ;
Cvec->m = n ;
Cvec->n = 1 ;
Cvec->p = cp ;
Cvec->nz = -1 ;
cp [0] = 0 ;
for (k = 0 ; k < C->n ; k++)
{
/* extract C(:,k) */
cp [1] = C->p [k+1] - C->p [k] ;
Cvec->nzmax = cp [1] ;
Cvec->i = C->i + C->p [k] ;
Cvec->x = C->x + C->p [k] ;
/* update/downdate */
ok = cs_dl_updown (L, sigma, Cvec, parent) ;
if (!ok) mexErrMsgTxt ("matrix is not positive definite") ;
}
/* return new L */
pargout [0] = cs_dl_mex_put_sparse (&L) ;
}
}
/*
[C, [E]] = provaKoren (A,B), computes Corr(A,B), where A and B must be sparse.
[C, [E]] = provaKoren (A,B,mode) computes Corr(A,b). If mode=0, the column average is calculated on common elements, otherwise column average is calculated on all non-zeros elements (DEFAULT)
E is a matrix contaninng the number of common elements
*/
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT modeAllElement ;
if (nargout > 2 || nargin < 2 || nargin > 3)
{
mexErrMsgTxt ("Usage: [C, [E]] = provaKoren (A,B,[mode=0])") ;
}
modeAllElement = (nargin > 2) ? mxGetScalar (pargin [2]) : 1 ; /* default = 1 */
modeAllElement = (modeAllElement == 0) ? 0 : 1 ;
if (modeAllElement && log) fprintf(stdout,"average computed on all non-zeros elements\n");
cs_dl Amatrix, Bmatrix, *A, *B, *C;
A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */
UF_long i, p, pp, Am, An, Anzmax, Anz, *Ap, *Ai ;
UF_long j, q, qq, Bm, Bn, Bnzmax, Bnz, *Bp, *Bi ;
double *Ax, *Bx;
if (!A || !B) { if (log) printf ("(null)\n") ; return ; }
Am = A->m ; An = A->n ; Ap = A->p ; Ai = A->i ; Ax = A->x ; Anzmax = A->nzmax ; Anz = A->nz ;
Bm = B->m ; Bn = B->n ; Bp = B->p ; Bi = B->i ; Bx = B->x ; Bnzmax = B->nzmax ; Bnz = B->nz ;
if (log) fprintf(stdout,"A: mxn = %dx%d\n",Am,An);
if (log) fprintf(stdout,"B: mxn = %dx%d\n",Bm,Bn);
/* allocate result */
cs *corrMatrix = cs_spalloc (An, Bn, An*Bn, 1, 1) ;
cs *commonElementMatrix = cs_spalloc (An, Bn, An*Bn, 1, 1) ;
for (i = 0 ; i < An ; i++)
{
for (j = 0 ; j < Bn ; j++)
{
p=Ap[i];
q=Bp[j];
pp = Ap[i+1];
qq = Bp[j+1];
/* mean on common elements*/
double meanA=0, meanB=0;
long countElementsA=0, countElementsB=0;
if (modeAllElement)
{
for (p=Ap[i] ; p<pp ; p++)
{
meanA += Ax[p];
countElementsA++;
}
for (q=Bp[j] ; q<qq ; q++)
{
meanB += Bx[q];
countElementsB++;
}
}
else
{
while (pp && qq && p<pp && q<qq)
{
/* fprintf(stdout,"i=%d, j=%d, p=%d, q=%d, pp=%d, qq=%d, rowA=%d, rowB=%d \n",i,j,p,q,pp,qq,Ai[p],Bi[q]); */
if (Ai[p]==Bi[q])
{
meanA += Ax[p];
meanB += Bx[q];
countElementsA++;
countElementsB++;
/* fprintf(stdout,"(%d,%d) - sum A = %f, sum B = %f \n",Ai[p],Bi[q],meanA,meanB); */
p++;
q++;
/* values Ax[p] and Bx[q] referring to the same row */
}
else if (Ai[p]>Bi[q])
{
q++;
}
else
{
p++;
}
}
}
meanA = meanA / ((double)countElementsA);
meanB = meanB / ((double)countElementsB);
/* fprintf(stdout,"common elements = %d - mean A = %f, mean B = %f \n",countCommonElements,meanA,meanB); */
/* correleation on common elements*/
double corr;
double corrNum=0, corrDenA=0, corrDenB=0;
double entryA, entryB;
p=Ap[i];
q=Bp[j];
pp = Ap[i+1];
qq = Bp[j+1];
long countCommonElements=0;
while (pp && qq && p<pp && q<qq)
{
/* fprintf(stdout,"i=%d, j=%d, p=%d, q=%d, pp=%d, qq=%d, rowA=%d, rowB=%d \n",i,j,p,q,pp,qq,Ai[p],Bi[q]); */
if (Ai[p]==Bi[q])
{
entryA=Ax[p]-meanA;
entryB=Bx[q]-meanB;
corrNum += entryA * entryB;
corrDenA += entryA*entryA;
corrDenB += entryB*entryB;
p++;
q++;
countCommonElements++;
/* values Ax[p] and Bx[q] referring to the same row */
}
else if (Ai[p]>Bi[q])
{
q++;
}
else
{
p++;
}
}
/* fprintf(stdout,"corrNum=%f, corrDenA=%f, corrDenB=%f\n",corrNum,corrDenA,corrDenB); */
corrDenA = (corrDenA==0) ? 1 : corrDenA;
corrDenB = (corrDenB==0) ? 1 : corrDenB;
corr = corrNum / (sqrt(corrDenA*corrDenB));
/* fprintf(stdout,"corr(%d,%d)=%f\n",i,j,corr); */
cs_entry(corrMatrix,i,j,corr);
cs_entry(commonElementMatrix,i,j,countCommonElements);
}
}
if (log) fprintf(stdout,"provaKoren: outputing computed matrices \n");
corrMatrix=cs_compress(corrMatrix);
pargout [0] = cs_dl_mex_put_sparse (&corrMatrix) ; /* return C */
if (nargout>1)
{
commonElementMatrix=cs_compress(commonElementMatrix);
pargout [1] = cs_dl_mex_put_sparse (&commonElementMatrix) ; /* return E */
}
}
/* 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) ;
}
}
/* cs_qr: sparse QR factorization */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
CS_INT m, n, order, *p ;
if (nargout > 5 || nargin != 1)
{
mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ;
}
order = (nargout == 5) ? 3 : 0 ; /* determine ordering */
m = mxGetM (pargin [0]) ;
n = mxGetN (pargin [0]) ;
if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
if (mxIsComplex (pargin [0]))
{
#ifndef NCOMPLEX
cs_cls *S ;
cs_cln *N ;
cs_cl Amatrix, *A, *D ;
A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */
S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
N = cs_cl_qr (A, S) ; /* numeric QR factorization */
cs_free (A->x) ;
if (!N) mexErrMsgTxt ("qr failed") ;
cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */
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 R and sort */
D = cs_cl_transpose (N->U, 1) ;
cs_cl_spfree (N->U) ;
N->U = cs_cl_transpose (D, 1) ;
cs_cl_spfree (D) ;
m = N->L->m ; /* m may be larger now */
p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */
pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */
cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */
pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
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, 0, 1, pargin [0]) ; /* get A */
S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
N = cs_dl_qr (A, S) ; /* numeric QR factorization */
if (!N) mexErrMsgTxt ("qr failed") ;
cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */
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 R and sort */
D = cs_dl_transpose (N->U, 1) ;
cs_dl_spfree (N->U) ;
N->U = cs_dl_transpose (D, 1) ;
cs_dl_spfree (D) ;
m = N->L->m ; /* m may be larger now */
p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */
pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */
cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */
pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */
pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */
cs_dl_nfree (N) ;
cs_dl_sfree (S) ;
}
}