ZGBTRS (3lapack)

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, * )

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