zgesc2(3S)

NAME
     ZGESC2 - solve a system of linear equations  A * X = scale* RHS  with a
     general N-by-N matrix A using the LU factorization with complete pivoting
     computed by ZGETC2

SYNOPSIS
     SUBROUTINE ZGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )

         INTEGER        LDA, N

         DOUBLE         PRECISION SCALE

         INTEGER        IPIV( * ), JPIV( * )

         COMPLEX*16     A( LDA, * ), RHS( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZGESC2 solves a system of linear equations A * X = scale* RHS with a
     general N-by-N matrix A using the LU factorization with complete pivoting
     computed by ZGETC2.


ARGUMENTS
     N       (input) INTEGER
             The number of columns of the matrix A.

     A       (input) COMPLEX*16 array, dimension (LDA, N)
             On entry, the  LU part of the factorization of the n-by-n matrix
             A computed by ZGETC2:  A = P * L * U * Q

     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1, N).

     RHS     (input/output) COMPLEX*16 array, dimension N.
             On entry, the right hand side vector b.  On exit, the solution
             vector X.
     IPIV    (iput) INTEGER array, dimension (N).
             The pivot indices; for 1 <= i <= N, row i of the matrix has been
             interchanged with row IPIV(i).

     JPIV    (iput) INTEGER array, dimension (N).
             The pivot indices; for 1 <= j <= N, column j of the matrix has
             been interchanged with column JPIV(j).

     SCALE    (output) DOUBLE PRECISION
              On exit, SCALE contains the scale factor. SCALE is chosen 0 <=
              SCALE <= 1 to prevent owerflow in the solution.

FURTHER DETAILS
     Based on contributions by
        Bo Kagstrom and Peter Poromaa, Department of Computing Science,
        Umea University, S-901 87 Umea, Sweden.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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