/* 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) ;
}
scs_int factorize(const AMatrix * A, const Settings * stgs, Priv * p) {
scs_float *info;
scs_int *Pinv, amd_status, ldl_status;
cs *C, *K = formKKT(A, stgs);
if (!K) {
return -1;
}
amd_status = LDLInit(K, p->P, &info);
if (amd_status < 0)
return (amd_status);
#if EXTRAVERBOSE > 0
if(stgs->verbose) {
scs_printf("Matrix factorization info:\n");
#ifdef DLONG
amd_l_info(info);
#else
amd_info(info);
#endif
}
#endif
Pinv = cs_pinv(p->P, A->n + A->m);
C = cs_symperm(K, Pinv, 1);
ldl_status = LDLFactor(C, NULL, NULL, &p->L, &p->D);
cs_spfree(C);
cs_spfree(K);
scs_free(Pinv);
scs_free(info);
return (ldl_status);
}
css *cs_schol(int order, const cs *A) {
int n, *c, *post, *P;
cs *C;
css *S;
if (!CS_CSC (A))
return (NULL); /* check inputs */
n = A->n;
S = (css *) cs_calloc(1, sizeof(css)); /* allocate result S */
if (!S)
return (NULL); /* out of memory */
P = cs_amd(order, A); /* P = amd(A+A'), or natural */
S->pinv = cs_pinv(P, n); /* find inverse permutation */
cs_free(P);
if (order && !S->pinv)
return (cs_sfree(S));
C = cs_symperm(A, S->pinv, 0); /* C = spones(triu(A(P,P))) */
S->parent = cs_etree(C, 0); /* find etree of C */
post = cs_post(S->parent, n); /* postorder the etree */
c = cs_counts(C, S->parent, post, 0); /* find column counts of chol(C) */
cs_free(post);
cs_spfree(C);
S->cp = (int *) cs_malloc(n + 1, sizeof(int)); /* allocate result S->cp */
S->unz = S->lnz = cs_cumsum(S->cp, c, n); /* find column pointers for L */
cs_free(c);
return ((S->lnz >= 0) ? S : cs_sfree(S));
}
/* 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) ;
}
/* Modified version of Tim Davis's cs_lu_mex.c file for MATLAB */
void install_lu(SEXP Ap, int order, double tol, Rboolean err_sing)
{
// (order, tol) == (1, 1) by default, when called from R.
SEXP ans;
css *S;
csn *N;
int n, *p, *dims;
CSP A = AS_CSP__(Ap), D;
R_CheckStack();
n = A->n;
if (A->m != n)
error(_("LU decomposition applies only to square matrices"));
if (order) { /* not using natural order */
order = (tol == 1) ? 2 /* amd(S'*S) w/dense rows or I */
: 1; /* amd (A+A'), or natural */
}
S = cs_sqr(order, A, /*qr = */ 0); /* symbolic ordering */
N = cs_lu(A, S, tol); /* numeric factorization */
if (!N) {
if(err_sing)
error(_("cs_lu(A) failed: near-singular A (or out of memory)"));
else {
/* No warning: The useR should be careful :
* Put NA into "LU" factor */
set_factors(Ap, ScalarLogical(NA_LOGICAL), "LU");
return;
}
}
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' */
ans = PROTECT(NEW_OBJECT(MAKE_CLASS("sparseLU")));
dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
dims[0] = n; dims[1] = n;
SET_SLOT(ans, install("L"),
Matrix_cs_to_SEXP(N->L, "dtCMatrix", 0));
SET_SLOT(ans, install("U"),
Matrix_cs_to_SEXP(N->U, "dtCMatrix", 0));
Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, /* "p" */
INTSXP, n)), p, n);
if (order)
Memcpy(INTEGER(ALLOC_SLOT(ans, install("q"),
INTSXP, n)), S->q, n);
cs_nfree(N);
cs_sfree(S);
cs_free(p);
UNPROTECT(1);
set_factors(Ap, ans, "LU");
}
/* 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) ;
}
// Modified version of Tim Davis's cs_qr_mex.c file for MATLAB (in CSparse)
// Usage: [V,beta,p,R,q] = cs_qr(A) ;
SEXP dgCMatrix_QR(SEXP Ap, SEXP order)
{
CSP A = AS_CSP__(Ap), D;
int io = INTEGER(order)[0];
Rboolean verbose = (io < 0);
int m = A->m, n = A->n, ord = asLogical(order) ? 3 : 0, *p;
R_CheckStack();
if (m < n) error(_("A must have #{rows} >= #{columns}")) ;
SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("sparseQR")));
int *dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
dims[0] = m; dims[1] = n;
css *S = cs_sqr(ord, A, 1); /* symbolic QR ordering & analysis*/
if (!S) error(_("cs_sqr failed"));
if(verbose && S->m2 > m) // in ./cs.h , m2 := # of rows for QR, after adding fictitious rows
Rprintf("Symbolic QR(): Matrix structurally rank deficient (m2-m = %d)\n",
S->m2 - m);
csn *N = cs_qr(A, S); /* numeric QR factorization */
if (!N) error(_("cs_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 */
// MM: m := S->m2 also counting the ficticious rows (Tim Davis, p.72, 74f)
p = cs_pinv(S->pinv, m); /* p = pinv' */
SET_SLOT(ans, install("V"),
Matrix_cs_to_SEXP(N->L, "dgCMatrix", 0));
Memcpy(REAL(ALLOC_SLOT(ans, install("beta"),
REALSXP, n)), N->B, n);
Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym,
INTSXP, m)), p, m);
SET_SLOT(ans, install("R"),
Matrix_cs_to_SEXP(N->U, "dgCMatrix", 0));
if (ord)
Memcpy(INTEGER(ALLOC_SLOT(ans, install("q"),
INTSXP, n)), S->q, n);
else
ALLOC_SLOT(ans, install("q"), INTSXP, 0);
cs_nfree(N);
cs_sfree(S);
cs_free(p);
UNPROTECT(1);
return ans;
}
/* 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) ;
}
/* Cholesky update/downdate */
int demo3 (problem *Prob)
{
cs *A, *C, *W = NULL, *WW, *WT, *E = NULL, *W2 ;
int n, k, *Li, *Lp, *Wi, *Wp, p1, p2, *p = NULL, ok ;
double *b, *x, *resid, *y = NULL, *Lx, *Wx, s, t, t1 ;
css *S = NULL ;
csn *N = NULL ;
if (!Prob || !Prob->sym || Prob->A->n == 0) return (0) ;
A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
n = A->n ;
if (!Prob->sym || n == 0) return (1) ;
rhs (x, b, n) ; /* compute right-hand side */
printf ("\nchol then update/downdate ") ;
print_order (1) ;
y = cs_malloc (n, sizeof (double)) ;
t = tic () ;
S = cs_schol (1, C) ; /* symbolic Chol, amd(A+A') */
printf ("\nsymbolic chol time %8.2f\n", toc (t)) ;
t = tic () ;
N = cs_chol (C, S) ; /* numeric Cholesky */
printf ("numeric chol time %8.2f\n", toc (t)) ;
if (!S || !N || !y) return (done3 (0, S, N, y, W, E, p)) ;
t = tic () ;
cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_lsolve (N->L, y) ; /* y = L\y */
cs_ltsolve (N->L, y) ; /* y = L'\y */
cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
printf ("solve chol time %8.2f\n", toc (t)) ;
printf ("original: ") ;
print_resid (1, C, x, b, resid) ; /* print residual */
k = n/2 ; /* construct W */
W = cs_spalloc (n, 1, n, 1, 0) ;
if (!W) return (done3 (0, S, N, y, W, E, p)) ;
Lp = N->L->p ; Li = N->L->i ; Lx = N->L->x ;
Wp = W->p ; Wi = W->i ; Wx = W->x ;
Wp [0] = 0 ;
p1 = Lp [k] ;
Wp [1] = Lp [k+1] - p1 ;
s = Lx [p1] ;
srand (1) ;
for ( ; p1 < Lp [k+1] ; p1++)
{
p2 = p1 - Lp [k] ;
Wi [p2] = Li [p1] ;
Wx [p2] = s * rand () / ((double) RAND_MAX) ;
}
t = tic () ;
ok = cs_updown (N->L, +1, W, S->parent) ; /* update: L*L'+W*W' */
t1 = toc (t) ;
printf ("update: time: %8.2f\n", t1) ;
if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
t = tic () ;
cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_lsolve (N->L, y) ; /* y = L\y */
cs_ltsolve (N->L, y) ; /* y = L'\y */
cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
p = cs_pinv (S->pinv, n) ;
W2 = cs_permute (W, p, NULL, 1) ; /* E = C + (P'W)*(P'W)' */
WT = cs_transpose (W2,1) ;
WW = cs_multiply (W2, WT) ;
cs_spfree (WT) ;
cs_spfree (W2) ;
E = cs_add (C, WW, 1, 1) ;
cs_spfree (WW) ;
if (!E || !p) return (done3 (0, S, N, y, W, E, p)) ;
printf ("update: time: %8.2f (incl solve) ", t1+t) ;
print_resid (1, E, x, b, resid) ; /* print residual */
cs_nfree (N) ; /* clear N */
t = tic () ;
N = cs_chol (E, S) ; /* numeric Cholesky */
if (!N) return (done3 (0, S, N, y, W, E, p)) ;
cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_lsolve (N->L, y) ; /* y = L\y */
cs_ltsolve (N->L, y) ; /* y = L'\y */
cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
printf ("rechol: time: %8.2f (incl solve) ", t) ;
print_resid (1, E, x, b, resid) ; /* print residual */
t = tic () ;
ok = cs_updown (N->L, -1, W, S->parent) ; /* downdate: L*L'-W*W' */
t1 = toc (t) ;
if (!ok) return (done3 (0, S, N, y, W, E, p)) ;
printf ("downdate: time: %8.2f\n", t1) ;
t = tic () ;
cs_ipvec (S->pinv, b, y, n) ; /* y = P*b */
cs_lsolve (N->L, y) ; /* y = L\y */
cs_ltsolve (N->L, y) ; /* y = L'\y */
cs_pvec (S->pinv, y, x, n) ; /* x = P'*y */
t = toc (t) ;
printf ("downdate: time: %8.2f (incl solve) ", t1+t) ;
print_resid (1, C, x, b, resid) ; /* print residual */
return (done3 (1, S, N, y, W, E, p)) ;
}
/* Given A, compute coarse and then fine dmperm */
csd *cs_dmperm (const cs *A, int seed)
{
int m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci,
*ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ;
cs *C ;
csd *D, *scc ;
/* --- Maximum matching ------------------------------------------------- */
if (!CS_CSC (A)) return (NULL) ; /* check inputs */
m = A->m ; n = A->n ;
D = cs_dalloc (m, n) ; /* allocate result */
if (!D) return (NULL) ;
p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ;
jmatch = cs_maxtrans (A, seed) ; /* max transversal */
imatch = jmatch + m ; /* imatch = inverse of jmatch */
if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ;
/* --- Coarse decomposition --------------------------------------------- */
wi = r ; wj = s ; /* use r and s as workspace */
for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */
for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */
cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/
ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/
if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ;
cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */
cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */
cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */
cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */
cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */
cs_free (jmatch) ;
/* --- Fine decomposition ----------------------------------------------- */
pinv = cs_pinv (p, m) ; /* pinv=p' */
if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ;
C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */
cs_free (pinv) ;
if (!C) return (cs_ddone (D, NULL, NULL, 0)) ;
Cp = C->p ;
nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */
if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ;
C->n = nc ;
if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */
{
cs_fkeep (C, cs_rprune, rr) ;
cnz = Cp [nc] ;
Ci = C->i ;
if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ;
}
C->m = nc ;
scc = cs_scc (C) ; /* find strongly connected components of C*/
if (!scc) return (cs_ddone (D, C, NULL, 0)) ;
/* --- Combine coarse and fine decompositions --------------------------- */
ps = scc->p ; /* C(ps,ps) is the permuted matrix */
rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */
nb1 = scc->nb ; /* # of blocks of A(R2,C2) */
for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ;
for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ;
for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ;
for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ;
nb2 = 0 ; /* create the fine block partitions */
r [0] = s [0] = 0 ;
if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */
for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */
{
r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */
s [nb2] = rs [k] + cc [2] ;
nb2++ ;
}
if (rr [2] < m)
{
r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */
s [nb2] = cc [3] ;
nb2++ ;
}
r [nb2] = m ;
s [nb2] = n ;
D->nb = nb2 ;
cs_dfree (scc) ;
return (cs_ddone (D, C, NULL, 1)) ;
}
/* Modified version of Tim Davis's cs_lu_mex.c file for MATLAB */
void install_lu(SEXP Ap, int order, double tol, Rboolean err_sing, Rboolean keep_dimnms)
{
// (order, tol) == (1, 1) by default, when called from R.
SEXP ans;
css *S;
csn *N;
int n, *p, *dims;
CSP A = AS_CSP__(Ap), D;
R_CheckStack();
n = A->n;
if (A->m != n)
error(_("LU decomposition applies only to square matrices"));
if (order) { /* not using natural order */
order = (tol == 1) ? 2 /* amd(S'*S) w/dense rows or I */
: 1; /* amd (A+A'), or natural */
}
S = cs_sqr(order, A, /*qr = */ 0); /* symbolic ordering */
N = cs_lu(A, S, tol); /* numeric factorization */
if (!N) {
if(err_sing)
error(_("cs_lu(A) failed: near-singular A (or out of memory)"));
else {
/* No warning: The useR should be careful :
* Put NA into "LU" factor */
set_factors(Ap, ScalarLogical(NA_LOGICAL), "LU");
return;
}
}
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' */
ans = PROTECT(NEW_OBJECT(MAKE_CLASS("sparseLU")));
dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
dims[0] = n; dims[1] = n;
SEXP dn; Rboolean do_dn = FALSE;
if(keep_dimnms) {
dn = GET_SLOT(Ap, Matrix_DimNamesSym);
do_dn = !isNull(VECTOR_ELT(dn, 0));
if(do_dn) {
dn = PROTECT(duplicate(dn));
// permute rownames by p : rn <- rn[ p ] :
SEXP rn = PROTECT(duplicate(VECTOR_ELT(dn, 0)));
for(int i=0; i < n; i++)
SET_STRING_ELT(VECTOR_ELT(dn, 0), i, STRING_ELT(rn, p[i]));
UNPROTECT(1); // rn
SET_VECTOR_ELT(dn, 1, R_NilValue); // colnames(.) := NULL
}
}
SET_SLOT(ans, install("L"),
Matrix_cs_to_SEXP(N->L, "dtCMatrix", 0, do_dn ? dn : R_NilValue));
if(keep_dimnms) {
if(do_dn) {
UNPROTECT(1); // dn
dn = GET_SLOT(Ap, Matrix_DimNamesSym);
}
do_dn = !isNull(VECTOR_ELT(dn, 1));
if(do_dn) {
dn = PROTECT(duplicate(dn));
if(order) { // permute colnames by S->q : cn <- cn[ S->q ] :
SEXP cn = PROTECT(duplicate(VECTOR_ELT(dn, 1)));
for(int j=0; j < n; j++)
SET_STRING_ELT(VECTOR_ELT(dn, 1), j, STRING_ELT(cn, S->q[j]));
UNPROTECT(1); // cn
}
SET_VECTOR_ELT(dn, 0, R_NilValue); // rownames(.) := NULL
}
}
SET_SLOT(ans, install("U"),
Matrix_cs_to_SEXP(N->U, "dtCMatrix", 0, do_dn ? dn : R_NilValue));
if(do_dn) UNPROTECT(1); // dn
Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, /* "p" */
INTSXP, n)), p, n);
if (order)
Memcpy(INTEGER(ALLOC_SLOT(ans, install("q"),
INTSXP, n)), S->q, n);
cs_nfree(N);
cs_sfree(S);
cs_free(p);
UNPROTECT(1);
set_factors(Ap, ans, "LU");
}
// Modified version of Tim Davis's cs_qr_mex.c file for MATLAB (in CSparse)
// Usage: [V,beta,p,R,q] = cs_qr(A) ;
SEXP dgCMatrix_QR(SEXP Ap, SEXP order, SEXP keep_dimnames)
{
CSP A = AS_CSP__(Ap), D;
int io = INTEGER(order)[0];
Rboolean verbose = (io < 0);// verbose=TRUE, encoded with negative 'order'
int m0 = A->m, m = m0, n = A->n, ord = asLogical(order) ? 3 : 0, *p;
R_CheckStack();
if (m < n) error(_("A must have #{rows} >= #{columns}")) ;
SEXP ans = PROTECT(NEW_OBJECT(MAKE_CLASS("sparseQR")));
int *dims = INTEGER(ALLOC_SLOT(ans, Matrix_DimSym, INTSXP, 2));
dims[0] = m; dims[1] = n;
css *S = cs_sqr(ord, A, 1); /* symbolic QR ordering & analysis*/
if (!S) error(_("cs_sqr failed"));
int keep_dimnms = asLogical(keep_dimnames);
if(keep_dimnms == NA_LOGICAL) { keep_dimnms = TRUE;
warning(_("dgcMatrix_QR(*, keep_dimnames = NA): NA taken as TRUE"));
}
if(verbose && S->m2 > m) // in ./cs.h , m2 := # of rows for QR, after adding fictitious rows
Rprintf("Symbolic QR(): Matrix structurally rank deficient (m2-m = %d)\n",
S->m2 - m);
csn *N = cs_qr(A, S); /* numeric QR factorization */
if (!N) error(_("cs_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 */
// MM: m := S->m2 also counting the ficticious rows (Tim Davis, p.72, 74f)
p = cs_pinv(S->pinv, m); /* p = pinv' */
SEXP dn = R_NilValue; Rboolean do_dn = FALSE;
if(keep_dimnms) {
dn = GET_SLOT(Ap, Matrix_DimNamesSym);
do_dn = !isNull(VECTOR_ELT(dn, 0)) && m == m0;
// FIXME? also deal with case m > m0 ?
if(do_dn) { // keep rownames
dn = PROTECT(duplicate(dn));
SET_VECTOR_ELT(dn, 1, R_NilValue);
} else dn = R_NilValue;
}
SET_SLOT(ans, Matrix_VSym, Matrix_cs_to_SEXP(N->L, "dgCMatrix", 0, dn)); // "V"
Memcpy(REAL(ALLOC_SLOT(ans, Matrix_betaSym, REALSXP, n)), N->B, n);
Memcpy(INTEGER(ALLOC_SLOT(ans, Matrix_pSym, INTSXP, m)), p, m);
if(do_dn) {
UNPROTECT(1); // dn
dn = R_NilValue; do_dn = FALSE;
}
if (ord) {
Memcpy(INTEGER(ALLOC_SLOT(ans, install("q"), INTSXP, n)), S->q, n);
if(keep_dimnms) {
dn = GET_SLOT(Ap, Matrix_DimNamesSym);
do_dn = !isNull(VECTOR_ELT(dn, 1));
if(do_dn) {
dn = PROTECT(duplicate(dn));
// permute colnames by S->q : cn <- cn[ S->q ] :
SEXP cns = PROTECT(duplicate(VECTOR_ELT(dn, 1)));
for(int j=0; j < n; j++)
SET_STRING_ELT(VECTOR_ELT(dn, 1), j, STRING_ELT(cns, S->q[j]));
UNPROTECT(1);
SET_VECTOR_ELT(dn, 0, R_NilValue);
} else dn = R_NilValue;
}
} else
ALLOC_SLOT(ans, install("q"), INTSXP, 0);
SET_SLOT(ans, install("R"), Matrix_cs_to_SEXP(N->U, "dgCMatrix", 0, dn));
if(do_dn) UNPROTECT(1); // dn
cs_nfree(N);
cs_sfree(S);
cs_free(p);
UNPROTECT(1);
return ans;
}
