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/*! @file cgssv.c
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 * \brief Solves the system of linear equations A*X=B 
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 *
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 * 
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 * -- SuperLU routine (version 3.0) --
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 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
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 * and Lawrence Berkeley National Lab.
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 * October 15, 2003
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 *   
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 */
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#include "slu_cdefs.h"
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/*! \brief
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 *
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 * 
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 * Purpose
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 * =======
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 *
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 * CGSSV solves the system of linear equations A*X=B, using the
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 * LU factorization from CGSTRF. It performs the following steps:
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 *
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 *   1. If A is stored column-wise (A->Stype = SLU_NC):
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 *
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 *      1.1. Permute the columns of A, forming A*Pc, where Pc
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 *           is a permutation matrix. For more details of this step, 
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 *           see sp_preorder.c.
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 *
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 *      1.2. Factor A as Pr*A*Pc=L*U with the permutation Pr determined
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 *           by Gaussian elimination with partial pivoting.
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 *           L is unit lower triangular with offdiagonal entries
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 *           bounded by 1 in magnitude, and U is upper triangular.
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 *
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 *      1.3. Solve the system of equations A*X=B using the factored
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 *           form of A.
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 *
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 *   2. If A is stored row-wise (A->Stype = SLU_NR), apply the
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 *      above algorithm to the transpose of A:
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 *
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 *      2.1. Permute columns of transpose(A) (rows of A),
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 *           forming transpose(A)*Pc, where Pc is a permutation matrix. 
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 *           For more details of this step, see sp_preorder.c.
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 *
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 *      2.2. Factor A as Pr*transpose(A)*Pc=L*U with the permutation Pr
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 *           determined by Gaussian elimination with partial pivoting.
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 *           L is unit lower triangular with offdiagonal entries
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 *           bounded by 1 in magnitude, and U is upper triangular.
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 *
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 *      2.3. Solve the system of equations A*X=B using the factored
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 *           form of A.
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 *
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 *   See supermatrix.h for the definition of 'SuperMatrix' structure.
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 * 
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 * Arguments
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 * =========
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 *
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 * options (input) superlu_options_t*
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 *         The structure defines the input parameters to control
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 *         how the LU decomposition will be performed and how the
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 *         system will be solved.
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 *
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 * A       (input) SuperMatrix*
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 *         Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
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 *         of linear equations is A->nrow. Currently, the type of A can be:
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 *         Stype = SLU_NC or SLU_NR; Dtype = SLU_C; Mtype = SLU_GE.
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 *         In the future, more general A may be handled.
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 *
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 * perm_c  (input/output) int*
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 *         If A->Stype = SLU_NC, column permutation vector of size A->ncol
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 *         which defines the permutation matrix Pc; perm_c[i] = j means 
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 *         column i of A is in position j in A*Pc.
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 *         If A->Stype = SLU_NR, column permutation vector of size A->nrow
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 *         which describes permutation of columns of transpose(A) 
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 *         (rows of A) as described above.
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 * 
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 *         If options->ColPerm = MY_PERMC or options->Fact = SamePattern or
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 *            options->Fact = SamePattern_SameRowPerm, it is an input argument.
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 *            On exit, perm_c may be overwritten by the product of the input
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 *            perm_c and a permutation that postorders the elimination tree
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 *            of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
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 *            is already in postorder.
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 *         Otherwise, it is an output argument.
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 * 
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 * perm_r  (input/output) int*
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 *         If A->Stype = SLU_NC, row permutation vector of size A->nrow, 
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 *         which defines the permutation matrix Pr, and is determined 
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 *         by partial pivoting.  perm_r[i] = j means row i of A is in 
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 *         position j in Pr*A.
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 *         If A->Stype = SLU_NR, permutation vector of size A->ncol, which
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 *         determines permutation of rows of transpose(A)
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 *         (columns of A) as described above.
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 *
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 *         If options->RowPerm = MY_PERMR or
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 *            options->Fact = SamePattern_SameRowPerm, perm_r is an
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 *            input argument.
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 *         otherwise it is an output argument.
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 *
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 * L       (output) SuperMatrix*
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 *         The factor L from the factorization 
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 *             Pr*A*Pc=L*U              (if A->Stype = SLU_NC) or
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 *             Pr*transpose(A)*Pc=L*U   (if A->Stype = SLU_NR).
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 *         Uses compressed row subscripts storage for supernodes, i.e.,
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 *         L has types: Stype = SLU_SC, Dtype = SLU_C, Mtype = SLU_TRLU.
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 *         
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 * U       (output) SuperMatrix*
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 *	   The factor U from the factorization 
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 *             Pr*A*Pc=L*U              (if A->Stype = SLU_NC) or
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 *             Pr*transpose(A)*Pc=L*U   (if A->Stype = SLU_NR).
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 *         Uses column-wise storage scheme, i.e., U has types:
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 *         Stype = SLU_NC, Dtype = SLU_C, Mtype = SLU_TRU.
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 *
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 * B       (input/output) SuperMatrix*
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 *         B has types: Stype = SLU_DN, Dtype = SLU_C, Mtype = SLU_GE.
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 *         On entry, the right hand side matrix.
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 *         On exit, the solution matrix if info = 0;
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 *
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 * stat   (output) SuperLUStat_t*
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 *        Record the statistics on runtime and floating-point operation count.
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 *        See util.h for the definition of 'SuperLUStat_t'.
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 *
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 * info    (output) int*
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 *	   = 0: successful exit
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 *         > 0: if info = i, and i is
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 *             <= A->ncol: U(i,i) is exactly zero. The factorization has
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 *                been completed, but the factor U is exactly singular,
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 *                so the solution could not be computed.
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 *             > A->ncol: number of bytes allocated when memory allocation
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 *                failure occurred, plus A->ncol.
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 * 
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 */
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void
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cgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
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      SuperMatrix *L, SuperMatrix *U, SuperMatrix *B,
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      SuperLUStat_t *stat, int *info )
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{
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    DNformat *Bstore;
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    SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
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    SuperMatrix AC; /* Matrix postmultiplied by Pc */
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    int      lwork = 0, *etree, i;
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    /* Set default values for some parameters */
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    int      panel_size;     /* panel size */
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    int      relax;          /* no of columns in a relaxed snodes */
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    int      permc_spec;
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    trans_t  trans = NOTRANS;
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    double   *utime;
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    double   t;	/* Temporary time */
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    /* Test the input parameters ... */
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    *info = 0;
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    Bstore = B->Store;
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    if ( options->Fact != DOFACT ) *info = -1;
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    else if ( A->nrow != A->ncol || A->nrow < 0 ||
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	 (A->Stype != SLU_NC && A->Stype != SLU_NR) ||
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	 A->Dtype != SLU_C || A->Mtype != SLU_GE )
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	*info = -2;
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    else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
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	B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
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	*info = -7;
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    if ( *info != 0 ) {
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	i = -(*info);
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	xerbla_("cgssv", &i);
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	return;
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    }
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    utime = stat->utime;
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    /* Convert A to SLU_NC format when necessary. */
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    if ( A->Stype == SLU_NR ) {
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	NRformat *Astore = A->Store;
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	AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
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	cCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz, 
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			       Astore->nzval, Astore->colind, Astore->rowptr,
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			       SLU_NC, A->Dtype, A->Mtype);
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	trans = TRANS;
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    } else {
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        if ( A->Stype == SLU_NC ) AA = A;
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    }
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    t = SuperLU_timer_();
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    /*
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     * Get column permutation vector perm_c[], according to permc_spec:
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     *   permc_spec = NATURAL:  natural ordering 
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     *   permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
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     *   permc_spec = MMD_ATA:  minimum degree on structure of A'*A
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     *   permc_spec = COLAMD:   approximate minimum degree column ordering
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     *   permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
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     */
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    permc_spec = options->ColPerm;
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    if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
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      get_perm_c(permc_spec, AA, perm_c);
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    utime[COLPERM] = SuperLU_timer_() - t;
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    etree = intMalloc(A->ncol);
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    t = SuperLU_timer_();
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    sp_preorder(options, AA, perm_c, etree, &AC);
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    utime[ETREE] = SuperLU_timer_() - t;
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    panel_size = sp_ienv(1);
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    relax = sp_ienv(2);
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    /*printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n", 
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	  relax, panel_size, sp_ienv(3), sp_ienv(4));*/
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    t = SuperLU_timer_(); 
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    /* Compute the LU factorization of A. */
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    cgstrf(options, &AC, relax, panel_size, etree,
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            NULL, lwork, perm_c, perm_r, L, U, stat, info);
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    utime[FACT] = SuperLU_timer_() - t;
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    t = SuperLU_timer_();
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    if ( *info == 0 ) {
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        /* Solve the system A*X=B, overwriting B with X. */
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        cgstrs (trans, L, U, perm_c, perm_r, B, stat, info);
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    }
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    utime[SOLVE] = SuperLU_timer_() - t;
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    SUPERLU_FREE (etree);
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    Destroy_CompCol_Permuted(&AC);
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    if ( A->Stype == SLU_NR ) {
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	Destroy_SuperMatrix_Store(AA);
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	SUPERLU_FREE(AA);
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    }
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}