cs *cs_rR(const cs *A, double nu, double nuR, const css *As, const cs *Roldinv, double Roldldet, const cs *pG){
cs *Rnew, *Rnewinv, *Ainv;
double Rnewldet, MH;
int dimG = A->n;
int cnt = 0;
int i, j;
Rnewinv = cs_spalloc (dimG, dimG, dimG*dimG, 1, 0);
for (i = 0 ; i < dimG; i++){
Rnewinv->p[i] = i*dimG;
for (j = 0 ; j < dimG; j++){
Rnewinv->i[cnt] = j;
Rnewinv->x[cnt] = 0.0;
A->x[i*dimG+j] -= pG->x[i*dimG+j];
cnt++;
}
}
Rnewinv->p[dimG] = dimG*dimG;
cs_cov2cor(A);
Ainv = cs_inv(A);
Rnew = cs_rinvwishart(Ainv, nu, As);
cs_cov2cor(Rnew);
Rnewldet = log(cs_invR(Rnew, Rnewinv));
/*****************************************************/
/* From Eq A.4 in Liu and Daniels (2006) */
/* using \pi_{1} = Eq 6 in Barnard (2000) */
/* using \pi_{2} = Eq 3.4 in Liu and Daniels (2006) */
/*****************************************************/
MH = Roldldet-Rnewldet;
for (i = 0 ; i < dimG; i++){
MH += log(Roldinv->x[i*dimG+i]);
MH -= log(Rnewinv->x[i*dimG+i]);
}
MH *= 0.5*nuR;
if(MH<log(runif(0.0,1.0)) || Rnewldet<log(Dtol)){
Rnewldet = cs_invR(Roldinv, Rnew); // save old R
}
for (i = 0 ; i < dimG; i++){
for (j = 0 ; j < dimG; j++){
Rnew->x[i*dimG+j] *= sqrt((pG->x[i*dimG+i])*(pG->x[j*dimG+j]));
}
}
cs_spfree(Rnewinv);
cs_spfree(Ainv);
return (cs_done (Rnew, NULL, NULL, 1)) ; /* success; free workspace, return C */
}
ACADOcsparse::~ACADOcsparse()
{
if (index1 != 0)
delete[] index1;
if (index2 != 0)
delete[] index2;
if (x != 0)
delete[] x;
if (S != 0)
cs_free(S);
if (N != 0)
{
if (N->L != 0)
cs_spfree(N->L);
if (N->U != 0)
cs_spfree(N->U);
if (N->pinv != 0)
free(N->pinv);
if (N->B != 0)
free(N->B);
free(N);
}
}
/**
* @brief Creates the penalty matrix D tilde of order k.
* Returns the matrix Dk premultipied by a diagonal
* matrix of weights.
*
* @param n number of observations
* @param k order of the trendfilter
* @param x locations of the responses
* @return pointer to a csparse matrix
* @see tf_calc_dktil
*/
cs * tf_calc_dktil (int n, int k, const double * x)
{
cs * delta_k;
cs * delta_k_cp;
cs * Dk;
cs * Dktil;
int i;
Dk = tf_calc_dk(n, k, x);
/* Deal with k=0 separately */
if(k == 0)
return Dk;
/* Construct diagonal matrix of differences: */
delta_k = cs_spalloc(n-k, n-k, (n-k), 1, 1);
for(i = 0; i < n - k; i++)
{
delta_k->p[i] = i;
delta_k->i[i] = i;
delta_k->x[i] = k / (x[k + i] - x[i]);
}
delta_k->nz = n-k;
delta_k_cp = cs_compress(delta_k);
Dktil = cs_multiply(delta_k_cp, Dk);
cs_spfree(Dk);
cs_spfree(delta_k);
cs_spfree(delta_k_cp);
return Dktil;
}
int main(void)
{
cs *T, *A, *B;
int m = 100, n = 3;
T = cs_load(stdin);
A = cs_compress(T);
B = blkdiag(A, m, n);
printf("B is %d x %d\n", B->m, B->n);
sparseprint(B);
cs_spfree(T);
cs_spfree(A);
cs_spfree(B);
// Test the block diagonal feature
// cs *T, *L, *Lt, *A, *X, *B;
// css *S;
// T = cs_load(stdin);
// L = cs_compress(T);
// Lt = cs_transpose(L, 1);
// A = cs_multiply(L, Lt);
// cs_spfree(T);
// sparseprint(A);
// S = cs_schol(0, A);
// B = speye(A->n);
// X = mldivide_chol(A, S, B);
// sparseprint(X);
}
/* 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) ;
}
returnValue ACADOcsparse::setMatrix(double *A_)
{
int run1;
int order = 0;
if (dim <= 0)
return ACADOERROR(RET_MEMBER_NOT_INITIALISED);
if (nDense <= 0)
return ACADOERROR(RET_MEMBER_NOT_INITIALISED);
cs *C, *D;
C = cs_spalloc(0, 0, 1, 1, 1);
for (run1 = 0; run1 < nDense; run1++)
cs_entry(C, index1[run1], index2[run1], A_[run1]);
D = cs_compress(C);
S = cs_sqr(order, D, 0);
N = cs_lu(D, S, TOL);
cs_spfree(C);
cs_spfree(D);
return SUCCESSFUL_RETURN;
}
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);
}
/* 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) ;
}
NumericsSparseMatrix* freeNumericsSparseMatrix(NumericsSparseMatrix* A)
{
if (A->linearSolverParams)
{
freeNumericsSparseLinearSolverParams(A->linearSolverParams);
A->linearSolverParams = NULL;
}
if (A->triplet)
{
cs_spfree(A->triplet);
A->triplet = NULL;
}
if (A->csc)
{
cs_spfree(A->csc);
A->csc = NULL;
}
if (A->trans_csc)
{
cs_spfree(A->trans_csc);
A->trans_csc = NULL;
}
if (A->csr)
{
cs_spfree(A->csr);
A->csr = NULL;
}
return NULL;
}
/* 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 */
}
/* 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");
}
int cs_rechol(const cs *A, const csn *N, int *pinv, int *c, double *x) {
double d, lki;
double *Lx, *Cx;
int t, i, p, k, n, *Li, *Lp, *Ui, *Up, *Cp, *Ci;
cs *C, *E;
if (!CS_CSC (A) || !N || !N->L || !N->U || !c || !x)
return (0);
n = A->n;
C = pinv ? cs_symperm(A, pinv, 1) : ((cs *) A);
E = pinv ? C : NULL; /* E is alias for A, or a copy E=A(p,p) */
if (!C) {
cs_spfree(E);
return (0);
}
Cp = C->p;
Ci = C->i;
Cx = C->x;
Lp = N->L->p;
Li = N->L->i;
Lx = N->L->x;
Up = N->U->p;
Ui = N->U->i;
for (k = 0; k < n; k++) /* compute L(k,:) for L*L' = C */
{
x[k] = 0; /* x (0:k) is now zero */
for (p = Cp[k]; p < Cp[k + 1]; p++) /* x = full(triu(C(:,k))) */
{
if (Ci[p] <= k)
x[Ci[p]] = Cx[p];
}
d = x[k]; /* d = C(k,k) */
x[k] = 0; /* clear x for k+1st iteration */
for (t = Up[k]; t < Up[k + 1] - 1; t++) /* solve L(0:k-1,0:k-1) * x = C(:,k) */
/* the loop does not include the diagonal element of row k of L - or column k of U - */
/* (which is placed at the end of column k for a sorted matrix - after its transposition), */
/* because it is treated outside the loop */
{
i = Ui[t]; /* pattern of L(k,:) */
lki = x[i] / Lx[Lp[i]]; /* L(k,i) = x (i) / L(i,i) */
x[i] = 0; /* clear x for k+1st iteration */
for (p = Lp[i] + 1; p < c[i]; p++) {
x[Li[p]] -= Lx[p] * lki;
}
d -= lki * lki; /* d = d - L(k,i)*L(k,i) */
p = c[i]++;
Lx[p] = lki;
}
if (d <= 0) {
cs_spfree(E);
return (0);
} /* not pos def */
p = c[k]++;
Lx[p] = sqrt(d);
}
cs_spfree(E);
return (1); /* success */
}
cs* cs_sorted_multiply2(const cs* a, const cs* b)
{
cs* D = cs_multiply(a,b);
cs* E = cs_transpose(D,1);
cs_spfree(D);
cs* C = cs_transpose(E,1);
cs_spfree(E);
return C;
}
/* free a numeric factorization */
csn *cs_nfree (csn *N)
{
if (!N) return (NULL) ; /* do nothing if N already NULL */
cs_spfree (N->L) ;
cs_spfree (N->U) ;
cs_free (N->pinv) ;
cs_free (N->B) ;
return (cs_free (N)) ; /* free the csn struct and return NULL */
}
void computeSparseAWpB(
double *A,
NumericsMatrix *W,
double *B,
NumericsMatrix *AWpB)
{
/* unsigned int problemSize = W->size0; */
SparseBlockStructuredMatrix* Wb = W->matrix1;
assert((unsigned)W->size0 >= 3);
assert((unsigned)W->size0 / 3 >= Wb->filled1 - 1);
double Ai[9], Bi[9], tmp[9];
for (unsigned int row = 0, ip9 = 0, i0 = 0;
row < Wb->filled1 - 1; ++row, ip9 += 9, i0 += 3)
{
assert(ip9 < 3 * (unsigned)W->size0 - 8);
extract3x3(3, ip9, 0, A, Ai);
extract3x3(3, ip9, 0, B, Bi);
for (unsigned int blockn = (unsigned int) Wb->index1_data[row];
blockn < Wb->index1_data[row + 1]; ++blockn)
{
unsigned int col = (unsigned int) Wb->index2_data[blockn];
mm3x3(Ai, Wb->block[blockn], tmp);
if (col == row) add3x3(Bi, tmp);
cpy3x3(tmp, AWpB->matrix1->block[blockn]);
}
}
/* Invalidation of sparse storage, if any. */
if (AWpB->matrix2)
{
if (AWpB->matrix2->triplet)
{
cs_spfree(AWpB->matrix2->triplet);
AWpB->matrix2->triplet = NULL;
}
if (AWpB->matrix2->csc)
{
cs_spfree(AWpB->matrix2->csc);
AWpB->matrix2->csc = NULL;
}
if (AWpB->matrix2->trans_csc)
{
cs_spfree(AWpB->matrix2->trans_csc);
AWpB->matrix2->trans_csc = NULL;
}
}
}
/* free workspace for demo3 */
static int done3 (int ok, css *S, csn *N, double *y, cs *W, cs *E, int *p)
{
cs_sfree (S) ;
cs_nfree (N) ;
cs_free (y) ;
cs_spfree (W) ;
cs_spfree (E) ;
cs_free (p) ;
return (ok) ;
}
/* free a problem */
problem *free_problem (problem *Prob)
{
if (!Prob) return (NULL) ;
cs_spfree (Prob->A) ;
if (Prob->sym) cs_spfree (Prob->C) ;
cs_free (Prob->b) ;
cs_free (Prob->x) ;
cs_free (Prob->resid) ;
return (cs_free (Prob)) ;
}
cs* cs_sorted_multiply(const cs* a, const cs* b)
{
cs* A = cs_transpose (a, 1) ;
cs* B = cs_transpose (b, 1) ;
cs* D = cs_multiply (B,A) ; /* D = B'*A' */
cs_spfree (A) ;
cs_spfree (B) ;
cs_dropzeros (D) ; /* drop zeros from D */
cs* C = cs_transpose (D, 1) ; /* C = D', so that C is sorted */
cs_spfree (D) ;
return C;
}
/**
* @brief Creates the admittance matrix.
*
* @return 0 on success.
*/
static int econ_createGMatrix (void)
{
int ret;
int i, j;
double R, Rsum;
cs *M;
StarSystem *sys;
/* Create the matrix. */
M = cs_spalloc( systems_nstack, systems_nstack, 1, 1, 1 );
if (M == NULL)
ERR("Unable to create CSparse Matrix.");
/* Fill the matrix. */
for (i=0; i < systems_nstack; i++) {
sys = &systems_stack[i];
Rsum = 0.;
/* Set some values. */
for (j=0; j < sys->njumps; j++) {
/* Get the resistances. */
R = econ_calcJumpR( sys, &systems_stack[sys->jumps[j]] );
R = 1./R; /* Must be inverted. */
Rsum += R;
/* Matrix is symetrical and non-diagonal is negative. */
ret = cs_entry( M, i, sys->jumps[j], -R );
if (ret != 1)
WARN("Unable to enter CSparse Matrix Cell.");
ret = cs_entry( M, sys->jumps[j], i, -R );
if (ret != 1)
WARN("Unable to enter CSparse Matrix Cell.");
}
/* Set the diagonal. */
Rsum += 1./ECON_SELF_RES; /* We add a resistence for dampening. */
cs_entry( M, i, i, Rsum );
}
/* Compress M matrix and put into G. */
if (econ_G != NULL)
cs_spfree( econ_G );
econ_G = cs_compress( M );
if (econ_G == NULL)
ERR("Unable to create economy G Matrix.");
/* Clean up. */
cs_spfree(M);
return 0;
}
/* 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) ;
}
void KLUSystem::clear()
{
if (Y22) cs_spfree (Y22);
if (T22) cs_spfree (T22);
if (acx) delete [] acx;
if (Numeric) klu_z_free_numeric (&Numeric, &Common);
if (Symbolic) klu_free_symbolic (&Symbolic, &Common);
zero_indices ();
null_pointers ();
}
void test_ppp_dotproduct(char const * A_file, char const * B_file, char const * C_file)
{
cs * A = ppp_load_ccf(A_file);
cs * B = ppp_load_ccf(B_file);
double c;
FILE * fin;
if(C_file){
fin = fopen(C_file, "r");
if(!fin){
fprintf(stderr, "Could not open %s\n", C_file);
fflush(stderr);
abort();
}
if(!fscanf(fin, "%lf", &c)){
fprintf(stderr, "Could not read in double from %s\n", C_file);
fflush(stderr);
fclose(fin);
abort();
}
fclose(fin);
}
csi mn = A->n > A->m ? A->n : A->m;
ppp_init_cs(mn);
int err;
double r;
ppp_dotproduct(&r, A, B);
if(C_file){
/* Test equivalence */
if(r - c > PPP_EPSILON * c){
fprintf(stderr, "Diff found [%s . %s != %s]:\n", A_file, B_file, C_file);
fprintf(stdout, "Diff found [%s . %s != %s]:\n", A_file, B_file, C_file);
fprintf(stdout, "Expected: %lf\n", c);
fprintf(stdout, "Obtained: %lf\n", r);
}else{
fprintf(stdout, "Success!\n");
}
}
/* clean up*/
cs_spfree(A);
cs_spfree(B);
ppp_done();
}
/* free workspace and return a numeric factorization (Cholesky, LU, or QR) */
csn *cs_ndone (csn *N, cs *C, void *w, void *x, int ok)
{
cs_spfree (C) ; /* free temporary matrix */
cs_free (w) ; /* free workspace */
cs_free (x) ;
return (ok ? N : cs_nfree (N)) ; /* return result if OK, else free it */
}
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
csi 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_frand (n, nel, s) ;
A = cs_transpose (AT, 1) ;
cs_spfree (AT) ;
cs_dropzeros (A) ;
pargout [0] = cs_mex_put_sparse (&A) ;
}
/* symbolic ordering and analysis for QR or LU */
css *cs_sqr (CS_INT order, const cs *A, CS_INT qr)
{
CS_INT n, k, ok = 1, *post ;
css *S ;
if (!CS_CSC (A)) return (NULL) ; /* check inputs */
n = A->n ;
S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
if (!S) return (NULL) ; /* out of memory */
S->q = cs_amd (order, A) ; /* fill-reducing ordering */
if (order && !S->q) return (cs_sfree (S)) ;
if (qr) /* QR symbolic analysis */
{
cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ;
S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */
post = cs_post (S->parent, n) ;
S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */
cs_free (post) ;
ok = C && S->parent && S->cp && cs_vcount (C, S) ;
if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ;
if (order) cs_spfree (C) ;
}
else
{
S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */
S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */
}
return (ok ? S : cs_sfree (S)) ; /* return result S */
}
/* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */
static int cs_bfs (const cs *A, int n, int *wi, int *wj, int *queue,
const int *imatch, const int *jmatch, int mark)
{
int *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ;
cs *C ;
for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */
{
if (imatch [j] >= 0) continue ; /* skip j if matched */
wj [j] = 0 ; /* j in set C0 (R0 if transpose) */
queue [tail++] = j ; /* place unmatched col j in queue */
}
if (tail == 0) return (1) ; /* quick return if no unmatched nodes */
C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ;
if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */
Ap = C->p ; Ai = C->i ;
while (head < tail) /* while queue is not empty */
{
j = queue [head++] ; /* get the head of the queue */
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
i = Ai [p] ;
if (wi [i] >= 0) continue ; /* skip if i is marked */
wi [i] = mark ; /* i in set R1 (C3 if transpose) */
j2 = jmatch [i] ; /* traverse alternating path to j2 */
if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */
wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */
queue [tail++] = j2 ; /* add j2 to queue */
}
}
if (mark != 1) cs_spfree (C) ; /* free A' if it was created */
return (1) ;
}
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));
}
/**
* @brief Destroys the economy.
*/
void economy_destroy (void)
{
int i;
/* Must be initialized. */
if (!econ_initialized)
return;
/* Clean up the prices in the systems stack. */
for (i=0; i<systems_nstack; i++) {
if (systems_stack[i].prices != NULL) {
free(systems_stack[i].prices);
systems_stack[i].prices = NULL;
}
}
/* Destroy the economy matrix. */
if (econ_G != NULL) {
cs_spfree( econ_G );
econ_G = NULL;
}
/* Economy is now deinitialized. */
econ_initialized = 0;
}
/* read a problem from a file; use %g for integers to avoid int conflicts */
problem *get_problem (FILE *f, double tol)
{
cs *T, *A, *C ;
int sym, m, n, mn, nz1, nz2 ;
problem *Prob ;
Prob = cs_calloc (1, sizeof (problem)) ;
if (!Prob) return (NULL) ;
T = cs_load (f) ; /* load triplet matrix T from a file */
Prob->A = A = cs_compress (T) ; /* A = compressed-column form of T */
cs_spfree (T) ; /* clear T */
if (!cs_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */
Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */
m = A->m ; n = A->n ;
mn = CS_MAX (m,n) ;
nz1 = A->p [n] ;
cs_dropzeros (A) ; /* drop zero entries */
nz2 = A->p [n] ;
if (tol > 0) cs_droptol (A, tol) ; /* drop tiny entries (just to test) */
Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */
if (!C) return (free_problem (Prob)) ;
printf ("\n--- Matrix: %g-by-%g, nnz: %g (sym: %g: nnz %g), norm: %8.2e\n",
(double) m, (double) n, (double) (A->p [n]), (double) sym,
(double) (sym ? C->p [n] : 0), cs_norm (C)) ;
if (nz1 != nz2) printf ("zero entries dropped: %g\n", (double) (nz1 - nz2));
if (nz2 != A->p [n]) printf ("tiny entries dropped: %g\n",
(double) (nz2 - A->p [n])) ;
Prob->b = cs_malloc (mn, sizeof (double)) ;
Prob->x = cs_malloc (mn, sizeof (double)) ;
Prob->resid = cs_malloc (mn, sizeof (double)) ;
return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ;
}
/**
* @brief Cleans up a sparse matrix factorization.
*
* @param[in] fact Factorization to clean up.
*/
void cs_fact_free( cs_fact_t *fact )
{
if (fact == NULL)
return;
switch (fact->type) {
case CS_FACT_NULL:
break;
case CS_FACT_CHOLESKY:
case CS_FACT_LU:
case CS_FACT_QR:
cs_free( fact->x );
cs_sfree( fact->S );
cs_nfree( fact->N );
break;
case CS_FACT_UMFPACK:
#ifdef USE_UMFPACK
cs_spfree( fact->A );
umfpack_di_free_numeric( &fact->numeric );
free( fact->x );
free( fact->wi );
free( fact->w );
#endif /* USE_UMFPACK */
break;
}
free( fact );
}
