lsd_mkb/lsd_mkb_superlu/superlu_seq/dgssv.c File Reference

Solves the system of linear equations A*X=B. More...

#include "slu_ddefs.h"

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Functions
void	dgssv (superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r, SuperMatrix *L, SuperMatrix *U, SuperMatrix *B, SuperLUStat_t *stat, int *info)
	Driver routines.

---

Detailed Description

Solves the system of linear equations A*X=B.

 -- SuperLU routine (version 3.0) --
 Univ. of California Berkeley, Xerox Palo Alto Research Center,
 and Lawrence Berkeley National Lab.
 October 15, 2003
 

---

Function Documentation

void dgssv	(	superlu_options_t *	options,
		SuperMatrix *	A,
		int *	perm_c,
		int *	perm_r,
		SuperMatrix *	L,
		SuperMatrix *	U,
		SuperMatrix *	B,
		SuperLUStat_t *	stat,
		int *	info
	)

Driver routines.

 Purpose
 =======

 DGSSV solves the system of linear equations A*X=B, using the
 LU factorization from DGSTRF. It performs the following steps:

   1. If A is stored column-wise (A->Stype = SLU_NC):

      1.1. Permute the columns of A, forming A*Pc, where Pc
           is a permutation matrix. For more details of this step, 
           see sp_preorder.c.

      1.2. Factor A as Pr*A*Pc=L*U with the permutation Pr determined
           by Gaussian elimination with partial pivoting.
           L is unit lower triangular with offdiagonal entries
           bounded by 1 in magnitude, and U is upper triangular.

      1.3. Solve the system of equations A*X=B using the factored
           form of A.

   2. If A is stored row-wise (A->Stype = SLU_NR), apply the
      above algorithm to the transpose of A:

      2.1. Permute columns of transpose(A) (rows of A),
           forming transpose(A)*Pc, where Pc is a permutation matrix. 
           For more details of this step, see sp_preorder.c.

      2.2. Factor A as Pr*transpose(A)*Pc=L*U with the permutation Pr
           determined by Gaussian elimination with partial pivoting.
           L is unit lower triangular with offdiagonal entries
           bounded by 1 in magnitude, and U is upper triangular.

      2.3. Solve the system of equations A*X=B using the factored
           form of A.

   See supermatrix.h for the definition of 'SuperMatrix' structure.

 Arguments
 =========

 options (input) superlu_options_t*
         The structure defines the input parameters to control
         how the LU decomposition will be performed and how the
         system will be solved.

 A       (input) SuperMatrix*
         Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
         of linear equations is A->nrow. Currently, the type of A can be:
         Stype = SLU_NC or SLU_NR; Dtype = SLU_D; Mtype = SLU_GE.
         In the future, more general A may be handled.

 perm_c  (input/output) int*
         If A->Stype = SLU_NC, column permutation vector of size A->ncol
         which defines the permutation matrix Pc; perm_c[i] = j means 
         column i of A is in position j in A*Pc.
         If A->Stype = SLU_NR, column permutation vector of size A->nrow
         which describes permutation of columns of transpose(A) 
         (rows of A) as described above.

         If options->ColPerm = MY_PERMC or options->Fact = SamePattern or
            options->Fact = SamePattern_SameRowPerm, it is an input argument.
            On exit, perm_c may be overwritten by the product of the input
            perm_c and a permutation that postorders the elimination tree
            of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
            is already in postorder.
         Otherwise, it is an output argument.

 perm_r  (input/output) int*
         If A->Stype = SLU_NC, row permutation vector of size A->nrow, 
         which defines the permutation matrix Pr, and is determined 
         by partial pivoting.  perm_r[i] = j means row i of A is in 
         position j in Pr*A.
         If A->Stype = SLU_NR, permutation vector of size A->ncol, which
         determines permutation of rows of transpose(A)
         (columns of A) as described above.

         If options->RowPerm = MY_PERMR or
            options->Fact = SamePattern_SameRowPerm, perm_r is an
            input argument.
         otherwise it is an output argument.

 L       (output) SuperMatrix*
         The factor L from the factorization 
             Pr*A*Pc=L*U              (if A->Stype = SLU_NC) or
             Pr*transpose(A)*Pc=L*U   (if A->Stype = SLU_NR).
         Uses compressed row subscripts storage for supernodes, i.e.,
         L has types: Stype = SLU_SC, Dtype = SLU_D, Mtype = SLU_TRLU.

 U       (output) SuperMatrix*
	   The factor U from the factorization 
             Pr*A*Pc=L*U              (if A->Stype = SLU_NC) or
             Pr*transpose(A)*Pc=L*U   (if A->Stype = SLU_NR).
         Uses column-wise storage scheme, i.e., U has types:
         Stype = SLU_NC, Dtype = SLU_D, Mtype = SLU_TRU.

 B       (input/output) SuperMatrix*
         B has types: Stype = SLU_DN, Dtype = SLU_D, Mtype = SLU_GE.
         On entry, the right hand side matrix.
         On exit, the solution matrix if info = 0;

 stat   (output) SuperLUStat_t*
        Record the statistics on runtime and floating-point operation count.
        See util.h for the definition of 'SuperLUStat_t'.

 info    (output) int*
	   = 0: successful exit
         > 0: if info = i, and i is
             <= A->ncol: U(i,i) is exactly zero. The factorization has
                been completed, but the factor U is exactly singular,
                so the solution could not be computed.
             > A->ncol: number of bytes allocated when memory allocation
                failure occurred, plus A->ncol.
 

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