# SRC/zgstrs.c File Reference

Solves a system using LU factorization. More...

`#include "slu_zdefs.h"`

## Functions
void | zusolve (int, int, doublecomplex *, doublecomplex *)
| Solves a dense upper triangular system.
void | zlsolve (int, int, doublecomplex *, doublecomplex *)
| Solves a dense UNIT lower triangular system.
void | zmatvec (int, int, int, doublecomplex *, doublecomplex *, doublecomplex *)
| Performs a dense matrix-vector multiply: Mxvec = Mxvec + M * vec.
void | zgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U, int *perm_c, int *perm_r, SuperMatrix *B, SuperLUStat_t *stat, int *info)
void | zprint_soln (int n, int nrhs, doublecomplex *soln)

## Detailed Description

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

     Copyright (c) 1994 by Xerox Corporation.  All rights reserved.

     THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
     EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.

     Permission is hereby granted to use or copy this program for any
     purpose, provided the above notices are retained on all copies.
     Permission to modify the code and to distribute modified code is
     granted, provided the above notices are retained, and a notice that
     the code was modified is included with the above copyright notice.

## Function Documentation

void zgstrs | ( | trans_t | trans,
|  | SuperMatrix * | L,
|  | SuperMatrix * | U,
|  | int * | perm_c,
|  | int * | perm_r,
|  | SuperMatrix * | B,
|  | SuperLUStat_t * | stat,
|  | int * | info |
| ) |  |  |

     Purpose
     =======

     ZGSTRS solves a system of linear equations A*X=B or A'*X=B
     with A sparse and B dense, using the LU factorization computed by
     ZGSTRF.

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

     Arguments
     =========

     trans   (input) trans_t
              Specifies the form of the system of equations:
              = NOTRANS: A * X = B  (No transpose)
              = TRANS:   A'* X = B  (Transpose)
              = CONJ:    A**H * X = B  (Conjugate transpose)

     L       (input) SuperMatrix*
             The factor L from the factorization Pr*A*Pc=L*U as computed by
             zgstrf(). Use compressed row subscripts storage for supernodes,
             i.e., L has types: Stype = SLU_SC, Dtype = SLU_Z, Mtype = SLU_TRLU.

     U       (input) SuperMatrix*
             The factor U from the factorization Pr*A*Pc=L*U as computed by
             zgstrf(). Use column-wise storage scheme, i.e., U has types:
             Stype = SLU_NC, Dtype = SLU_Z, Mtype = SLU_TRU.

     perm_c  (input) int*, dimension (L->ncol)
    	   Column permutation vector, which defines the
             permutation matrix Pc; perm_c[i] = j means column i of A is
             in position j in A*Pc.

     perm_r  (input) int*, dimension (L->nrow)
             Row permutation vector, which defines the permutation matrix Pr;
             perm_r[i] = j means row i of A is in position j in Pr*A.

     B       (input/output) SuperMatrix*
             B has types: Stype = SLU_DN, Dtype = SLU_Z, 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, the i-th argument had an illegal value

void zlsolve | ( | int | ldm,
|  | int | ncol,
|  | doublecomplex * | M,
|  | doublecomplex * | rhs |
| ) |  |  |

The unit lower triangular matrix is stored in a 2D array M(1:nrow,1:ncol). The solution will be returned in the rhs vector.

void zmatvec | ( | int | ldm,
|  | int | nrow,
|  | int | ncol,
|  | doublecomplex * | M,
|  | doublecomplex * | vec,
|  | doublecomplex * | Mxvec |
| ) |  |  |

The input matrix is M(1:nrow,1:ncol); The product is returned in Mxvec[].

void zprint_soln | ( | int | n,
|  | int | nrhs,
|  | doublecomplex * | soln |
| ) |  |  |

void zusolve | ( | int | ldm,
|  | int | ncol,
|  | doublecomplex * | M,
|  | doublecomplex * | rhs |
| ) |  |  |

The upper triangular matrix is stored in a 2-dim array M(1:ldm,1:ncol). The solution will be returned in the rhs vector.