Exemplo n.º 1
0
/* x=A\b where A can be rectangular; b overwritten with solution */
int cs_qrsol (int order, const cs *A, double *b)
{
    double *x ;
    css *S ;
    csn *N ;
    cs *AT = NULL ;
    int k, m, n, ok ;
    if (!CS_CSC (A) || !b) return (0) ; /* check inputs */
    n = A->n ;
    m = A->m ;
    if (m >= n)
    {
        S = cs_sqr (order, A, 1) ;          /* ordering and symbolic analysis */
        N = cs_qr (A, S) ;                  /* numeric QR factorization */
        x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ;    /* get workspace */
        ok = (S && N && x) ;
        if (ok)
        {
            cs_ipvec (S->pinv, b, x, m) ;   /* x(0:m-1) = b(p(0:m-1) */
            for (k = 0 ; k < n ; k++)       /* apply Householder refl. to x */
            {
                cs_happly (N->L, k, N->B [k], x) ;
            }
            cs_usolve (N->U, x) ;           /* x = R\x */
            cs_ipvec (S->q, x, b, n) ;      /* b(q(0:n-1)) = x(0:n-1) */
        }
    }
    else
    {
        AT = cs_transpose (A, 1) ;          /* Ax=b is underdetermined */
        S = cs_sqr (order, AT, 1) ;         /* ordering and symbolic analysis */
        N = cs_qr (AT, S) ;                 /* numeric QR factorization of A' */
        x = cs_calloc (S ? S->m2 : 1, sizeof (double)) ;    /* get workspace */
        ok = (AT && S && N && x) ;
        if (ok)
        {
            cs_pvec (S->q, b, x, m) ;       /* x(q(0:m-1)) = b(0:m-1) */
            cs_utsolve (N->U, x) ;          /* x = R'\x */
            for (k = m-1 ; k >= 0 ; k--)    /* apply Householder refl. to x */
            {
                cs_happly (N->L, k, N->B [k], x) ;
            }
            cs_pvec (S->pinv, x, b, n) ;    /* b(0:n-1) = x(p(0:n-1)) */
        }
    }
    cs_free (x) ;
    cs_sfree (S) ;
    cs_nfree (N) ;
    cs_spfree (AT) ;
    return (ok) ;
}
Exemplo n.º 2
0
/**
 * Apply Householder transformations and the row permutation P to y
 *
 * @param a sparse matrix containing the vectors defining the
 *        Householder transformations
 * @param beta scaling factors for the Householder transformations
 * @param y contents of a V->m by nrhs dense matrix
 * @param p 0-based permutation vector of length V->m
 * @param nrhs number of right hand sides (i.e. ncol(y))
 * @param trans logical value - if TRUE create Q'y[p] otherwise Qy[p]
 */
static
void sparseQR_Qmult(cs *V, double *beta, int *p, int trans,
		    double *y, int *ydims)
{
    int j, k, m = V->m, n = V->n;
    double *x = Alloca(m, double);	/* workspace */
    R_CheckStack();

    if (ydims[0] != m)
	error(_("Dimensions of system are inconsistent"));
    for (j = 0; j < ydims[1]; j++) {
	double *yj = y + j * m;
	if (trans) {
	    cs_pvec(p, yj, x, m);	/* x(0:m-1) = y(p(0:m-1, j)) */
	    Memcpy(yj, x, m);	/* replace it */
	    for (k = 0 ; k < n ; k++)   /* apply H[1]...H[n] */
		cs_happly(V, k, beta[k], yj);
	} else {
	    for (k = n - 1 ; k >= 0 ; k--) /* apply H[n]...H[1] */
		cs_happly(V, k, beta[k], yj);
	    cs_ipvec(p, yj, x, m); /* inverse permutation */
	    Memcpy(yj, x, m);
	}
    }
}
Exemplo n.º 3
0
/**
 * @brief Solves a sparse matrix factorization.
 *
 * This solves Ax = b.
 *
 *    @param[in,out] b Input right side vector that gets set to the output solution.
 *    @param[in] fact Factorization of the sparse matrix.
 */
void cs_fact_solve( double *b, cs_fact_t *fact )
{
#ifdef USE_UMFPACK
   int ret;
   double info[ UMFPACK_INFO ];
   int fnan, finf;
#endif /* USE_UMFPACK */
   int k;
   switch (fact->type) {
      case CS_FACT_CHOLESKY:
         cs_ipvec(   fact->S->pinv, b, fact->x, fact->n );
         cs_lsolve(  fact->N->L, fact->x );
         cs_ltsolve( fact->N->L, fact->x );
         cs_pvec(    fact->S->pinv, fact->x, b, fact->n );
         break;
      case CS_FACT_LU:
         cs_ipvec(  fact->N->pinv, b, fact->x, fact->n );
         cs_lsolve( fact->N->L, fact->x );
         cs_usolve( fact->N->U, fact->x );
         cs_ipvec(  fact->S->q, fact->x, b, fact->n );
         break;
      case CS_FACT_QR:
         cs_ipvec(  fact->S->pinv, b, fact->x, fact->n );
         for (k=0; k<fact->n; k++)
            cs_happly( fact->N->L, k, fact->N->B[k], fact->x );
         cs_usolve( fact->N->U, fact->x );
         cs_ipvec(  fact->S->q, fact->x, b, fact->n );
         break;
      case CS_FACT_UMFPACK:
#ifdef USE_UMFPACK
         ret = umfpack_di_wsolve( UMFPACK_A, /* Solving Ax=b problem. */
               fact->A->p, fact->A->i, fact->A->x,
               fact->x, b, fact->numeric, NULL, info, fact->wi, fact->w );
         if (ret == UMFPACK_WARNING_singular_matrix) {
            fprintf( stderr, "UMFPACK: wsolver Matrix singular!\n" );
            fnan = 0;
            finf = 0;
            for (k=0; k<fact->n; k++) {
               if (isnan(fact->x[k])) {
                  fact->x[k] = 0.;
                  fnan       = 1;
               }
               else if (isinf(fact->x[k])) {
                  fact->x[k] = 0.;
                  finf       = 1;
               }
            }
            if (fnan)
               fprintf( stderr, "UMFPACK: NaN values detected!\n" );
            if (finf)
               fprintf( stderr, "UMFPACK: Infinity values detected!\n" );
         }
         memcpy( b, fact->x, fact->n*sizeof(double) );
#endif /* USE_UMFPACK */
      default:
         break;
   }
}
Exemplo n.º 4
0
void SparseCholeskySolver<TMatrix,TVector>::solveT(double * z, double * r) {
	int n = A.n;
	
	cs_ipvec (n, S->Pinv, r, (double*) &(tmp[0]));	//x = P*b

	cs_lsolve (N->L, (double*) &(tmp[0]));			//x = L\x
	cs_ltsolve (N->L, (double*) &(tmp[0]));			//x = L'\x/

	cs_pvec (n, S->Pinv, (double*) &(tmp[0]), z);	 //b = P'*x
}
Exemplo n.º 5
0
SEXP dgCMatrix_matrix_solve(SEXP Ap, SEXP b, SEXP give_sparse)
// FIXME:  add  'keep_dimnames' as argument
{
    Rboolean sparse = asLogical(give_sparse);
    if(sparse) {
	// FIXME: implement this
	error(_("dgCMatrix_matrix_solve(.., sparse=TRUE) not yet implemented"));

	/* Idea: in the  for(j = 0; j < nrhs ..) loop below, build the *sparse* result matrix
	 * ----- *column* wise -- which is perfect for dgCMatrix
	 * --> build (i,p,x) slots "increasingly" [well, allocate in batches ..]
	 *
	 * --> maybe first a protoype in R
	 */

    }
    SEXP ans = PROTECT(dup_mMatrix_as_dgeMatrix(b)),
	lu, qslot;
    CSP L, U;
    int *bdims = INTEGER(GET_SLOT(ans, Matrix_DimSym)), *p, *q;
    int j, n = bdims[0], nrhs = bdims[1];
    double *x, *ax = REAL(GET_SLOT(ans, Matrix_xSym));
    C_or_Alloca_TO(x, n, double);

    if (isNull(lu = get_factors(Ap, "LU"))) {
	install_lu(Ap, /* order = */ 1, /* tol = */ 1.0, /* err_sing = */ TRUE,
		   /* keep_dimnames = */ TRUE);
	lu = get_factors(Ap, "LU");
    }
    qslot = GET_SLOT(lu, install("q"));
    L = AS_CSP__(GET_SLOT(lu, install("L")));
    U = AS_CSP__(GET_SLOT(lu, install("U")));
    R_CheckStack();
    if (U->n != n)
	error(_("Dimensions of system to be solved are inconsistent"));
    if(nrhs >= 1 && n >= 1) {
	p = INTEGER(GET_SLOT(lu, Matrix_pSym));
	q = LENGTH(qslot) ? INTEGER(qslot) : (int *) NULL;

	for (j = 0; j < nrhs; j++) {
	    cs_pvec(p, ax + j * n, x, n);  /* x = b(p) */
	    cs_lsolve(L, x);	       /* x = L\x */
	    cs_usolve(U, x);	       /* x = U\x */
	    if (q)		       /* r(q) = x , hence
					  r = Q' U{^-1} L{^-1} P b = A^{-1} b */
		cs_ipvec(q, x, ax + j * n, n);
	    else
		Memcpy(ax + j * n, x, n);
	}
    }
    if(n >= SMALL_4_Alloca) Free(x);
    UNPROTECT(1);
    return ans;
}
Exemplo n.º 6
0
  void CSparseCholeskyInternal::solve(double* x, int nrhs, bool transpose) {
    casadi_assert(prepared_);
    casadi_assert(L_!=0);

    double *t = &temp_.front();
    for (int k=0; k<nrhs; ++k) {
      if (transpose) {
        cs_pvec(S_->q, x, t, AT_.n) ;   // t = P1\b
        cs_ltsolve(L_->L, t) ;               // t = L\t
        cs_lsolve(L_->L, t) ;              // t = U\t
        cs_pvec(L_->pinv, t, x, AT_.n) ;      // x = P2\t
      } else {
        cs_ipvec(L_->pinv, x, t, AT_.n) ;   // t = P1\b
        cs_lsolve(L_->L, t) ;               // t = L\t
        cs_ltsolve(L_->L, t) ;              // t = U\t
        cs_ipvec(S_->q, t, x, AT_.n) ;      // x = P2\t
      }
      x += ncol();
    }
  }
  void CSparseCholeskyInterface::solve(void* mem, double* x, int nrhs, bool tr) const {
    auto m = static_cast<CsparseCholMemory*>(mem);

    casadi_assert(m->L!=0);

    double *t = &m->temp.front();
    for (int k=0; k<nrhs; ++k) {
      if (tr) {
        cs_pvec(m->S->q, x, t, m->A.n) ;   // t = P1\b
        cs_ltsolve(m->L->L, t) ;               // t = L\t
        cs_lsolve(m->L->L, t) ;              // t = U\t
        cs_pvec(m->L->pinv, t, x, m->A.n) ;      // x = P2\t
      } else {
        cs_ipvec(m->L->pinv, x, t, m->A.n) ;   // t = P1\b
        cs_lsolve(m->L->L, t) ;               // t = L\t
        cs_ltsolve(m->L->L, t) ;              // t = U\t
        cs_ipvec(m->S->q, t, x, m->A.n) ;      // x = P2\t
      }
      x += m->ncol();
    }
  }
Exemplo n.º 8
0
void CSparseInternal::solve(double* x, int nrhs, bool transpose){
  casadi_assert(prepared_);
  casadi_assert(N_!=0);
  
  double *t = &temp_.front();
  
  for(int k=0; k<nrhs; ++k){
    if(transpose){
      cs_ipvec (N_->pinv, x, t, AT_.n) ;   // t = P1\b
      cs_lsolve (N_->L, t) ;               // t = L\t 
      cs_usolve (N_->U, t) ;               // t = U\t 
      cs_ipvec (S_->q, t, x, AT_.n) ;      // x = P2\t 
    } else {
      cs_pvec (S_->q, x, t, AT_.n) ;       // t = P2*b 
      casadi_assert(N_->U!=0);
      cs_utsolve (N_->U, t) ;              // t = U'\t 
      cs_ltsolve (N_->L, t) ;              // t = L'\t 
      cs_pvec (N_->pinv, t, x, AT_.n) ;    // x = P1*t 
    }
    x += nrow();
  }
}
Exemplo n.º 9
0
  void CsparseInterface::solve(double* x, int nrhs, bool transpose) {
    double time_start=0;
    if (CasadiOptions::profiling&& CasadiOptions::profilingBinary) {
      time_start = getRealTime(); // Start timer
      profileWriteEntry(CasadiOptions::profilingLog, this);
    }


    casadi_assert(prepared_);
    casadi_assert(N_!=0);

    double *t = &temp_.front();

    for (int k=0; k<nrhs; ++k) {
      if (transpose) {
        cs_pvec(S_->q, x, t, A_.n) ;       // t = P2*b
        casadi_assert(N_->U!=0);
        cs_utsolve(N_->U, t) ;              // t = U'\t
        cs_ltsolve(N_->L, t) ;              // t = L'\t
        cs_pvec(N_->pinv, t, x, A_.n) ;    // x = P1*t
      } else {
        cs_ipvec(N_->pinv, x, t, A_.n) ;   // t = P1\b
        cs_lsolve(N_->L, t) ;               // t = L\t
        cs_usolve(N_->U, t) ;               // t = U\t
        cs_ipvec(S_->q, t, x, A_.n) ;      // x = P2\t
      }
      x += ncol();
    }

    if (CasadiOptions::profiling && CasadiOptions::profilingBinary) {
      double time_stop = getRealTime(); // Stop timer
      profileWriteTime(CasadiOptions::profilingLog, this, 1,
                       time_stop-time_start,
                       time_stop-time_start);
      profileWriteExit(CasadiOptions::profilingLog, this, time_stop-time_start);
    }
  }
Exemplo n.º 10
0
void SparseCholeskySolver<TMatrix,TVector>::solveT(float * z, float * r) {
	int n = A.n;
	z_tmp.resize(n);
	r_tmp.resize(n);
	for (int i=0;i<n;i++) r_tmp[i] = (double) r[i];
	
	cs_ipvec (n, S->Pinv, (double*) &(r_tmp[0]), (double*) &(tmp[0]));	//x = P*b

	cs_lsolve (N->L, (double*) &(tmp[0]));			//x = L\x
	cs_ltsolve (N->L, (double*) &(tmp[0]));			//x = L'\x/

	cs_pvec (n, S->Pinv, (double*) &(tmp[0]), (double*) &(z_tmp[0]));	 //b = P'*x
	
	for (int i=0;i<n;i++) z[i] = (float) z_tmp[i];
}
Exemplo n.º 11
0
/* x=A\b where A is symmetric positive definite; b overwritten with solution */
CS_INT cs_cholsol (CS_INT order, const cs *A, CS_ENTRY *b)
{
    CS_ENTRY *x ;
    css *S ;
    csn *N ;
    CS_INT n, ok ;
    if (!CS_CSC (A) || !b) return (0) ;     /* check inputs */
    n = A->n ;
    S = cs_schol (order, A) ;               /* ordering and symbolic analysis */
    N = cs_chol (A, S) ;                    /* numeric Cholesky factorization */
    x = cs_malloc (n, sizeof (CS_ENTRY)) ;    /* get workspace */
    ok = (S && N && x) ;
    if (ok)
    {
        cs_ipvec (S->pinv, b, x, n) ;   /* x = P*b */
        cs_lsolve (N->L, x) ;           /* x = L\x */
        cs_ltsolve (N->L, x) ;          /* x = L'\x */
        cs_pvec (S->pinv, x, b, n) ;    /* b = P'*x */
    }
    cs_free (x) ;
    cs_sfree (S) ;
    cs_nfree (N) ;
    return (ok) ;
}
void choleskyDecomp_sparse(cs* matrixA, double* matrixB, double* matrixX,int size)
{
    int i;
    css *S;
    csn *N;
 	
    S=cs_schol(1, matrixA);
    N=cs_chol(matrixA, S);
    cs_spfree(matrixA);

    if(found_dc_sweep==0){
        cs_ipvec(S->pinv, matrixB, matrixX, size);
        cs_lsolve(N->L, matrixX);
	cs_ltsolve(N->L, matrixX);
	cs_pvec(S->pinv, matrixX, matrixB, size);

	printf("X vector \n");
	for(i=0;i<size;i++){
	    printf(" %.6lf ",matrixX[i]);
	}
	printf("\n");
    }
    else{
        double value;
		double *matrixB_temp = (double *)calloc(size,sizeof(double));
		if (source > -1) {
            for(value=start_value;value<=end_value;value=value+step){
                matrixB[source-1]=value;
				cs_ipvec(S->pinv, matrixB, matrixX, size);
				cs_lsolve(N->L, matrixX);
				cs_ltsolve(N->L, matrixX);
				cs_pvec(S->pinv, matrixX, matrixB_temp, size);
		
				printf("value= %lf Matrix X: \n",value);
                for(i=0;i<size;i++){
	    	    	printf(" %.6lf ",matrixX[i]);
				}
				printf("\n");
       	    }
        }
        else { 
	    	if (sweep_node1!=0){
		 		matrixB[sweep_node1-1]+=sweep_value-start_value;
	    	}
	    	if(sweep_node2!=0){
				matrixB[sweep_node2-1]-=sweep_value-start_value;
	    	}
	    	for(value=start_value;value<=end_value;value=value+step) {
				cs_ipvec(S->pinv, matrixB, matrixX, size);
				cs_lsolve(N->L, matrixX);
				cs_ltsolve(N->L, matrixX);
				cs_pvec(S->pinv, matrixX, matrixB_temp, size);
	        
				if (sweep_node1!=0){
		    		matrixB[sweep_node1-1]-=step;
	       	 	}
	        	if(sweep_node2!=0){
		    		matrixB[sweep_node2-1]+=step;
	        	}
				printf("value= %lf Matrix X: \n",value);
                for(i=0;i<size;i++){
			   	    printf(" %.6lf ",matrixX[i]);
				}
				printf("\n");
		    } 
		}
    }                
    printf("\n");      
}
Exemplo n.º 13
0
/* 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)) ;
} 
Exemplo n.º 14
0
void solve_spdSparse(double time){
  	
	int i;
	double current_value;
	double *B_sparse_temp;

	//Adeiasma twn arxeiwn sta opoia tha apothikeutoun ta apotelesmata tis analysis gia tous komvous PLOT
	if(TRAN==0)initPlotFiles("Sparse");
	  
	if(ITER==0){
		//cholesky decomposition
		S=cs_schol(1, C_sparse);
		N=cs_chol(C_sparse, S);
		//cs_spfree(C_sparse);
	}
	if(dc_sweep==0){		//An den exoume sweep
		if(ITER==0){	

		  cs_ipvec(S->pinv, B_sparse, x_sparse, sizeB);

		  cs_lsolve(N->L, x_sparse);	//seg fault gia choleskyNetlist!LA8OS TO N!ARA ANADROMIKA LA8OS TO C_sparse.Omws C_sparce swsto vash ths CG.

		  cs_ltsolve(N->L, x_sparse);
		  cs_pvec(S->pinv, x_sparse, B_sparse, sizeB);			//solve cholesky
		  
		  for(i=0;i<sizeB;i++){
			x_sparse[i]=B_sparse[i];
		  }
		  		  
		  //printf("\n ----- SPARSE Cholesky decomposition ----- \n");
		}
		else{
		  conjugate_gradient_sparse(C_sparse,B_sparse, sizeB, x_sparse, itol_value);			//solve with Conjugated Gradient	
		  //printf("\n");
		  //printf("---- CG SPARSE ----\n");		  
		}	
		/*
		printf("X = \n");
		for(i=0;i<sizeB;i++){
		  printf(" %.6lf \n",x_sparse[i]);
		}
		printf("----------------------\n");
		printf("\n");
		*/
		if(TRAN==0){
		  plotFiles("Sparse", x_sparse, -1.0, "Analysis: DC");
		}else{
		  plotFiles("Sparse", x_sparse, time, "Analysis: TRAN");
		}
	}else{		//An exoume sweep
	  B_sparse_temp = (double *)calloc(sizeB,sizeof(double));		//Proswrini apothikeusi tou apotelesmatos anamesa sta loop
		if(sweep_source!=-1){						//pigi tasis ginetai sweep
		  for(current_value=start_value;current_value<=end_value+EPS;current_value+=sweep_step){

		    B_sparse[sweep_source-1]=current_value;
		    if(ITER==0){		
		      cs_ipvec(S->pinv, B_sparse, x_sparse, sizeB);
		      cs_lsolve(N->L, x_sparse);
		      cs_ltsolve(N->L, x_sparse);
		      cs_pvec(S->pinv, x_sparse, B_sparse_temp, sizeB);		//solve cholesky
		    }
		    else{
			
			conjugate_gradient_sparse(C_sparse,B_sparse, sizeB, x_sparse, itol_value);		

		    }
		    
		    //Apothikeusi twn apotelesmatwn tis analysis gia tous komvous PLOT se arxeia
		    plotFiles("Sparse", (ITER ? x_sparse:B_sparse_temp), current_value, "Sweep source voltage at");
		  }
		}else{		//pigi reumatos ginetai sweep
		  //Anairesi twn praksewn + kai - apo tin arxiki timi tis pigis ston pinaka B
		  //kai praksi + kai - me to start_value
		  if(sweep_posNode!=0){
		    B_sparse[sweep_posNode-1]+=sweep_value_I-start_value;
		  }
		  if(sweep_negNode!=0){
		    B_sparse[sweep_negNode-1]-=sweep_value_I-start_value;
		  }
		  
		  for(current_value=start_value;current_value<=end_value+EPS;current_value+=sweep_step){

		   if(ITER==0){
		      cs_ipvec(S->pinv, B_sparse, x_sparse, sizeB);
		      cs_lsolve(N->L, x_sparse);
		      cs_ltsolve(N->L, x_sparse);
		      cs_pvec(S->pinv, x_sparse, B_sparse_temp, sizeB);		//solve cholesky
		   }
		   else{
			
			conjugate_gradient_sparse(C_sparse,B_sparse, sizeB, x_sparse, itol_value);	
			//Arxiki proseggish h lush ths prohgoumenhs
		   }
		    
		   
		   //Allagi twn timwn ston pinaka B gia to epomeno vima tou sweep
		   if(sweep_posNode!=0){
		     B_sparse[sweep_posNode-1]-=sweep_step;
		    }
		   if(sweep_negNode!=0){
		     B_sparse[sweep_negNode-1]+=sweep_step;
		   }

		    //Apothikeusi twn apotelesmatwn tis analysis gia tous komvous PLOT se arxeia
		    plotFiles("Sparse", (ITER ? x_sparse:B_sparse_temp), current_value, "Sweep source current at");
			
		  }
		  printf("\n");
		}
	}

}