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gssv(3P)		    Sun Performance Library		      gssv(3P)

NAME
       gssv:  cgssv, dgssv, sgssv, zgssv - solves a system of linear equations
       A*X=B using the LU factorization from sgstrf.

SYNOPSIS
       #include <sunperf.h>

       void sgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int
	      *perm_r,	SuperMatrix *L, SuperMatrix *U, SuperMatrix *B, Super‐
	      LUStat_t *stat, int *info)

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

       void cgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int
	      *perm_r,	SuperMatrix *L, SuperMatrix *U, SuperMatrix *B, Super‐
	      LUStat_t *stat, int *info)

       void zgssv(superlu_options_t *options, SuperMatrix *A, int *perm_c, int
	      *perm_r,	SuperMatrix *L, SuperMatrix *U, SuperMatrix *B, Super‐
	      LUStat_t *stat, int *info)

       void sgssv_64(superlu_options_t_64 *options,  SuperMatrix_64  *A,  long
	      *perm_c,	long  *perm_r,	SuperMatrix_64	*L, SuperMatrix_64 *U,
	      SuperMatrix_64 *B, SuperLUStat_t_64 *stat, long *info)

       void dgssv_64(superlu_options_t_64 *options,  SuperMatrix_64  *A,  long
	      *perm_c,	long  *perm_r,	SuperMatrix_64	*L, SuperMatrix_64 *U,
	      SuperMatrix_64 *B, SuperLUStat_t_64 *stat, long *info)

       void cgssv_64(superlu_options_t_64 *options,  SuperMatrix_64  *A,  long
	      *perm_c,	long  *perm_r,	SuperMatrix_64	*L, SuperMatrix_64 *U,
	      SuperMatrix_64 *B, SuperLUStat_t_64 *stat, long *info)

       void zgssv_64(superlu_options_t_64 *options,  SuperMatrix_64  *A,  long
	      *perm_c,	long  *perm_r,	SuperMatrix_64	*L, SuperMatrix_64 *U,
	      SuperMatrix_64 *B, SuperLUStat_t_64 *stat, long *info)

PURPOSE
       gssv solves the system of linear equations A*X=B, using the LU  factor‐
       ization from sgstrf. It performs the following steps:

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

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

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

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

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

o   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.

o   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	trian‐
    gular.

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

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

       SuperMatrix *A (input)
	      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; Dtype = SLU_S; Mtype = SLU_GE.
	      In the future, more general A may be handled.

       int *perm_c (input/output)
	      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 argu‐
	      ment.  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.

       int *perm_r (input/output)
	      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  =  SamePat‐
	      tern_SameRowPerm, perm_r is an input argument.
	      Otherwise it is an output argument.

       SuperMatrix *L (output)
	      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 com‐
	      pressed row subscripts storage for supernodes, i.e.,
	      L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.

       SuperMatrix *U (output)
	      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_S, Mtype = SLU_TRU.

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

       SuperLUStat_t *stat (output)
	      Records  the  statistics on runtime and floating-point operation
	      count.

	      int *info (output)

	    = 0:
		 successful exit

	    < 0: if info = -i, the i-th argument had an illegal value

	    > 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 sin‐
			     gular, and division by zero will occur if	it  is
			     used to solve a system of equations.

		 > A->ncol:  number  of bytes allocated when memory allocation
			     failure occurred, plus A->ncol.

COPYRIGHT
       Copyright (c) 2003,  The	 Regents  of  the  University  of  California,
       through	Lawrence  Berkeley  National Laboratory (subject to receipt of
       any required approvals from U.S. Dept. of Energy)

SEE ALSO
       SuperMatrix

       set_default_options

       StatInit

       StatFree

       gstrf

       http://crd.lbl.gov/~xiaoye/SuperLU/

       James W. Demmel, Stanley C. Eisenstat, John R. Gilbert,	Xiaoye	S.  Li
       and  Joseph  W. H. Liu, "A supernodal approach to sparse partial pivot‐
       ing", SIAM J. Matrix Analysis and Applications, Vol. 20, Num. 3,	 1999,
       pp. 720-755.

				  6 Mar 2009			      gssv(3P)
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