zgbtrs(3S)

NAME
     ZGBTRS - solve a system of linear equations A * X = B, A**T * X = B, or
     A**H * X = B with a general band matrix A using the LU factorization
     computed by ZGBTRF

SYNOPSIS
     SUBROUTINE ZGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )

         CHARACTER      TRANS

         INTEGER        INFO, KL, KU, LDAB, LDB, N, NRHS

         INTEGER        IPIV( * )

         COMPLEX*16     AB( LDAB, * ), B( LDB, * )

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
     ZGBTRS solves a system of linear equations A * X = B, A**T * X = B, or
     A**H * X = B with a general band matrix A using the LU factorization
     computed by ZGBTRF.

ARGUMENTS
     TRANS   (input) CHARACTER*1
             Specifies the form of the system of equations.  = 'N':  A * X = B
             (No transpose)
             = 'T':  A**T * X = B  (Transpose)
             = 'C':  A**H * X = B  (Conjugate transpose)

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     KL      (input) INTEGER
             The number of subdiagonals within the band of A.  KL >= 0.

     KU      (input) INTEGER
             The number of superdiagonals within the band of A.  KU >= 0.
     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrix B.  NRHS >= 0.

     AB      (input) COMPLEX*16 array, dimension (LDAB,N)
             Details of the LU factorization of the band matrix A, as computed
             by ZGBTRF.  U is stored as an upper triangular band matrix with
             KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers
             used during the factorization are stored in rows KL+KU+2 to
             2*KL+KU+1.

     LDAB    (input) INTEGER
             The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

     IPIV    (input) INTEGER array, dimension (N)
             The pivot indices; for 1 <= i <= N, row i of the matrix was
             interchanged with row IPIV(i).

     B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
             On entry, the right hand side matrix B.  On exit, the solution
             matrix X.

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

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

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

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