void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Lmatrix, Bmatrix, *L, *B ;
double *x ;
int k, i, j, top, *xi, *perm ;
if (nargout > 1 || nargin != 2)
{
mexErrMsgTxt ("Usage: x = cs_reach(L,b)") ;
}
/* get inputs */
L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ;
B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;
cs_mex_check (0, L->n, 1, 0, 1, 1, pargin [1]) ;
perm = cs_malloc (L->n, sizeof (int)) ;
for (k = 0 ; k < L->n ; k++) perm [k] = k ;
xi = cs_calloc (3*L->n, sizeof (int)) ;
top = cs_reach (L, B, 0, xi, perm) ;
pargout [0] = mxCreateDoubleMatrix (L->n - top, 1, mxREAL) ;
x = mxGetPr (pargout [0]) ;
for (j = 0, i = top ; i < L->n ; i++, j++) x [j] = xi [i] ;
cs_free (xi) ;
cs_free (perm) ;
}
/* cs_add: sparse matrix addition */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
double alpha, beta ;
cs Amatrix, Bmatrix, *A, *B, *C, *D ;
if (nargout > 1 || nargin < 2 || nargin > 4)
{
mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
B = cs_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_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */
cs_dropzeros (C) ; /* drop zeros */
D = cs_transpose (C, 1) ; /* sort result via double transpose */
cs_spfree (C) ;
C = cs_transpose (D, 1) ;
cs_spfree (D) ;
pargout [0] = cs_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 Lmatrix, *Lin, Cmatrix, *C, *L, Cvector, *Cvec ;
int ignore, j, k, n, lnz, *parent, sigma = 1, cp [2] ;
char sigma_string [20] ;
if (nargout > 1 || nargin < 3 || nargin > 4)
{
mexErrMsgTxt ("Usage: L = cs_updown(L,C,parent,sigma)") ;
}
Lin = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get input L */
n = Lin->n ;
if (nargin > 3 && mxIsChar (pargin [3]))
{
mxGetString (pargin [3], sigma_string, 8) ;
sigma = (sigma_string [0] == '-') ? (-1) : 1 ;
}
/* make a copy of L (this can take more work than updating L itself) */
lnz = Lin->p [n] ;
L = cs_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_mex_get_sparse (&Cmatrix, 0, 1, pargin [1]) ;
parent = cs_mex_get_int (n, pargin [2], &ignore, 0) ; /* get parent */
/* 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] ;
cs_updown (L, sigma, Cvec, parent) ; /* update/downdate */
}
pargout [0] = cs_mex_put_sparse (&L) ; /* return new L */
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs *A, Amatrix ;
double *x ;
int i, m, n, *imatch, *jmatch ;
if (nargout > 1 || nargin != 1)
{
mexErrMsgTxt ("Usage: p = cr_maxtransr(A)") ;
}
/* get inputs */
A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ;
m = A->m ;
n = A->n ;
jmatch = maxtrans (A) ;
imatch = invmatch (jmatch, m, n) ; /* imatch = inverse of jmatch */
pargout [0] = mxCreateDoubleMatrix (1, n, mxREAL) ;
x = mxGetPr (pargout [0]) ;
for (i = 0 ; i < n ; i++) x [i] = imatch [i] + 1 ;
cs_free (jmatch) ;
cs_free (imatch) ;
}
/* cs_permute: permute a sparse matrix */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *A, *C, *D ;
int ignore, *P, *Q, *Pinv ;
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: C = cs_permute(A,p,q)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
P = cs_mex_get_int (A->m, pargin [1], &ignore, 1) ; /* get P */
Q = cs_mex_get_int (A->n, pargin [2], &ignore, 1) ; /* get Q */
Pinv = cs_pinv (P, A->m) ; /* P = Pinv' */
C = cs_permute (A, Pinv, Q, 1) ; /* C = A(p,q) */
D = cs_transpose (C, 1) ; /* sort C via double transpose */
cs_spfree (C) ;
C = cs_transpose (D, 1) ;
cs_spfree (D) ;
pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
cs_free (Pinv) ;
cs_free (P) ;
cs_free (Q) ;
}
/* cs_symperm: symmetric permutation of a symmetric sparse matrix. */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *A, *C, *D ;
csi ignore, n, *P, *Pinv ;
if (nargout > 1 || nargin != 2)
{
mexErrMsgTxt ("Usage: C = cs_symperm(A,p)") ;
}
A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ;
n = A->n ;
P = cs_mex_get_int (n, pargin [1], &ignore, 1) ; /* get P */
Pinv = cs_pinv (P, n) ; /* P=Pinv' */
C = cs_symperm (A, Pinv, 1) ; /* C = A(p,p) */
D = cs_transpose (C, 1) ; /* sort C */
cs_spfree (C) ;
C = cs_transpose (D, 1) ;
cs_spfree (D) ;
pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
cs_free (P) ;
cs_free (Pinv) ;
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Umatrix, Bmatrix, *U, *B, *X ;
double *x, *b ;
int top, nz, p, *xi ;
if (nargout > 1 || nargin != 2)
{
mexErrMsgTxt ("Usage: x = cs_usolve(U,b)") ;
}
U = cs_mex_get_sparse (&Umatrix, 1, 1, pargin [0]) ; /* get U */
if (mxIsSparse (pargin [1]))
{
B = cs_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ;/* get sparse b */
cs_mex_check (0, U->n, 1, 0, 1, 1, pargin [1]) ;
xi = cs_malloc (2*U->n, sizeof (int)) ; /* get workspace */
x = cs_malloc (U->n, sizeof (double)) ;
top = cs_spsolve (U, B, 0, xi, x, NULL, 0) ; /* x = U\b */
X = cs_spalloc (U->n, 1, U->n-top, 1, 0) ; /* create sparse x*/
X->p [0] = 0 ;
nz = 0 ;
for (p = top ; p < U->n ; p++)
{
X->i [nz] = xi [p] ;
X->x [nz++] = x [xi [p]] ;
}
X->p [1] = nz ;
pargout [0] = cs_mex_put_sparse (&X) ;
cs_free (x) ;
cs_free (xi) ;
}
else
{
b = cs_mex_get_double (U->n, pargin [1]) ; /* get full b */
x = cs_mex_put_double (U->n, b, &(pargout [0])) ; /* x = b */
cs_usolve (U, x) ; /* x = U\x */
}
}
/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
css *S ;
csn *N ;
cs Amatrix, *A, *D ;
csi n, order, *p ;
double tol ;
if (nargout > 4 || nargin > 3 || nargin < 1)
{
mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ;
}
A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
n = A->n ;
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 */
}
S = cs_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */
N = cs_lu (A, S, tol) ; /* numeric factorization */
if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ;
cs_dropzeros (N->L) ; /* drop zeros from L and sort it */
D = cs_transpose (N->L, 1) ;
cs_spfree (N->L) ;
N->L = cs_transpose (D, 1) ;
cs_spfree (D) ;
cs_dropzeros (N->U) ; /* drop zeros from U and sort it */
D = cs_transpose (N->U, 1) ;
cs_spfree (N->U) ;
N->U = cs_transpose (D, 1) ;
cs_spfree (D) ;
p = cs_pinv (N->pinv, n) ; /* p=pinv' */
pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return L */
pargout [1] = cs_mex_put_sparse (&(N->U)) ; /* return U */
pargout [2] = cs_mex_put_int (p, n, 1, 1) ; /* return p */
/* return Q */
if (nargout == 4) pargout [3] = cs_mex_put_int (S->q, n, 1, 0) ;
cs_nfree (N) ;
cs_sfree (S) ;
}
/* cs_print: print the contents of a sparse matrix. */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *A ;
int brief ;
if (nargout > 0 || nargin < 1 || nargin > 2)
{
mexErrMsgTxt ("Usage: cs_print(A,brief)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
brief = (nargin < 2) ? 0 : mxGetScalar (pargin [1]) ; /* get brief */
cs_print (A, brief) ; /* print A */
}
/* cs_qr: sparse QR factorization */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
css *S ;
csn *N ;
cs Amatrix, *A, *D ;
csi m, n, order, *p ;
if (nargout > 5 || nargin != 1)
{
mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
m = A->m ;
n = A->n ;
if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ;
order = (nargout == 5) ? 3 : 0 ; /* determine ordering */
S = cs_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/
N = cs_qr (A, S) ; /* numeric QR factorization */
if (!N) mexErrMsgTxt ("qr failed") ;
cs_dropzeros (N->L) ; /* drop zeros from V and sort */
D = cs_transpose (N->L, 1) ;
cs_spfree (N->L) ;
N->L = cs_transpose (D, 1) ;
cs_spfree (D) ;
cs_dropzeros (N->U) ; /* drop zeros from R and sort */
D = cs_transpose (N->U, 1) ;
cs_spfree (N->U) ;
N->U = cs_transpose (D, 1) ;
cs_spfree (D) ;
m = N->L->m ; /* m may be larger now */
p = cs_pinv (S->pinv, m) ; /* p = pinv' */
pargout [0] = cs_mex_put_sparse (&(N->L)) ; /* return V */
cs_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */
pargout [2] = cs_mex_put_int (p, m, 1, 1) ; /* return p */
pargout [3] = cs_mex_put_sparse (&(N->U)) ; /* return R */
pargout [4] = cs_mex_put_int (S->q, n, 1, 0) ; /* return q */
cs_nfree (N) ;
cs_sfree (S) ;
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *A ;
int m, n, mn, m2, n2, k, s, j, ij, sj, si, p, *Ap, *Ai ;
double aij, *S, *Ax ;
if (nargout > 1 || nargin < 1 || nargin > 2)
{
mexErrMsgTxt ("Usage: S = cs_thumb(A,k)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
m = A->m ;
n = A->n ;
mn = CS_MAX (m,n) ;
k = (nargin == 1) ? 256 : mxGetScalar (pargin [1]) ; /* get k */
/* s = size of each submatrix; A(1:s,1:s) maps to S(1,1) */
s = (mn < k) ? 1 : (int) ceil ((double) mn / (double) k) ;
m2 = (int) ceil ((double) m / (double) s) ;
n2 = (int) ceil ((double) n / (double) s) ;
/* create S */
pargout [0] = mxCreateDoubleMatrix (m2, n2, mxREAL) ;
S = mxGetPr (pargout [0]) ;
Ap = A->p ;
Ai = A->i ;
Ax = A->x ;
for (j = 0 ; j < n ; j++)
{
sj = j/s ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
si = Ai [p] / s ;
ij = INDEX (si,sj,m2) ;
aij = fabs (Ax [p]) ;
if (ISNAN (aij)) aij = BIG_VALUE ;
aij = CS_MIN (BIG_VALUE, aij) ;
S [ij] = CS_MAX (S [ij], aij) ;
}
}
}
/* cs_ltsolve: solve an upper triangular system L'*x=b */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Lmatrix, *L ;
double *x, *b ;
if (nargout > 1 || nargin != 2)
{
mexErrMsgTxt ("Usage: x = cs_ltsolve(L,b)") ;
}
L = cs_mex_get_sparse (&Lmatrix, 1, 1, pargin [0]) ; /* get L */
b = cs_mex_get_double (L->n, pargin [1]) ; /* get b */
x = cs_mex_put_double (L->n, b, &(pargout [0])) ; /* x = b */
cs_ltsolve (L, x) ; /* x = L'\x */
}
/* z = cs_gaxpy (A,x,y) computes z = A*x+y */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *A ;
double *x, *y, *z ;
if (nargout > 1 || nargin != 3)
{
mexErrMsgTxt ("Usage: z = cs_gaxpy(A,x,y)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
x = cs_mex_get_double (A->n, pargin [1]) ; /* get x */
y = cs_mex_get_double (A->m, pargin [2]) ; /* get y */
z = cs_mex_put_double (A->m, y, &(pargout [0])) ; /* z = y */
cs_gaxpy (A, x, z) ; /* z = z + A*x */
}
/* cs_amd: approximate minimum degree ordering */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *A ;
int *P, order ;
if (nargout > 1 || nargin < 1 || nargin > 2)
{
mexErrMsgTxt ("Usage: p = cs_amd(A,order)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
order = (nargin > 1) ? mxGetScalar (pargin [1]) : 1 ; /* get ordering */
order = CS_MAX (order, 1) ;
order = CS_MIN (order, 3) ;
P = cs_amd (order, A) ; /* min. degree ordering */
pargout [0] = cs_mex_put_int (P, A->n, 1, 1) ; /* return P */
}
/* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
double seed ;
cs *A, Amatrix ;
csd *D ;
csi m, n, *jmatch, iseed ;
if (nargin < 1 || nargin > 2 || nargout > 6)
{
mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ;
}
seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */
iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
n = A->n ;
m = A->m ;
if (nargout <= 1)
{
jmatch = cs_maxtrans (A, iseed) ; /* max. matching */
pargout [0] = cs_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */
cs_free (jmatch) ;
}
else
{
D = cs_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */
pargout [0] = cs_mex_put_int (D->p, m, 1, 0) ;
pargout [1] = cs_mex_put_int (D->q, n, 1, 0) ;
pargout [2] = cs_mex_put_int (D->r, D->nb+1, 1, 0) ;
pargout [3] = cs_mex_put_int (D->s, D->nb+1, 1, 0) ;
pargout [4] = cs_mex_put_int (D->cc, 5, 1, 0) ;
pargout [5] = cs_mex_put_int (D->rr, 5, 1, 0) ;
cs_dfree (D) ;
}
}
/* cs_lusol: solve A*x=b using a sparse LU factorization */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs *A, Amatrix ;
csi order ;
double *x, *b, tol ;
if (nargout > 1 || nargin < 2 || nargin > 4)
{
mexErrMsgTxt ("Usage: x = cs_lusol(A,b,order,tol)") ;
}
A = cs_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */
b = cs_mex_get_double (A->n, pargin [1]) ; /* get b */
x = cs_mex_put_double (A->n, b, &(pargout [0])) ; /* x = b */
order = (nargin < 3) ? 2 : mxGetScalar (pargin [2]) ;
order = CS_MAX (order, 0) ;
order = CS_MIN (order, 3) ;
if (nargin == 2)
{
tol = 1 ; /* normal partial pivoting */
}
else if (nargin == 3)
{
tol = (order == 1) ? 0.001 : 1 ; /* tol = 0.001 for amd(A+A') */
}
else
{
tol = mxGetScalar (pargin [3]) ;
}
if (!cs_lusol (order, A, x, tol)) /* x = A\x */
{
mexErrMsgTxt ("LU factorization failed (singular or out of memory)") ;
}
}
/* cs_droptol: remove small entries from A */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
cs Amatrix, *C, *A ;
int j, k ;
double tol ;
if (nargout > 1 || nargin != 2)
{
mexErrMsgTxt ("Usage: C = cs_droptol(A,tol)") ;
}
A = cs_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */
tol = mxGetScalar (pargin [1]) ; /* get tol */
C = cs_spalloc (A->m, A->n, A->nzmax, 1, 0) ; /* C = A */
for (j = 0 ; j <= A->n ; j++) C->p [j] = A->p [j] ;
for (k = 0 ; k < A->nzmax ; k++) C->i [k] = A->i [k] ;
for (k = 0 ; k < A->nzmax ; k++) C->x [k] = A->x [k] ;
cs_droptol (C, tol) ; /* drop from C */
pargout [0] = cs_mex_put_sparse (&C) ; /* return C */
}
