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NAME

       ZTRSV  -  solve one of the systems of equations   A*x = b, or A'*x = b, or conjg( A' )*x =
       b,

SYNOPSIS

       SUBROUTINE ZTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )

           INTEGER      INCX, LDA, N

           CHARACTER*1  DIAG, TRANS, UPLO

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

PURPOSE

       ZTRSV  solves one of the systems of equations

       where b and x are n element vectors and A is an n by n unit, or non-unit, upper  or  lower
       triangular matrix.

       No  test  for singularity or near-singularity is included in this routine. Such tests must
       be performed before calling this routine.

PARAMETERS

       UPLO   - CHARACTER*1.
              On entry, UPLO specifies whether the matrix is an upper or lower triangular  matrix
              as follows:

              UPLO = 'U' or 'u'   A is an upper triangular matrix.

              UPLO = 'L' or 'l'   A is a lower triangular matrix.

              Unchanged on exit.

       TRANS  - CHARACTER*1.
              On entry, TRANS specifies the equations to be solved as follows:

              TRANS = 'N' or 'n'   A*x = b.

              TRANS = 'T' or 't'   A'*x = b.

              TRANS = 'C' or 'c'   conjg( A' )*x = b.

              Unchanged on exit.

       DIAG   - CHARACTER*1.
              On entry, DIAG specifies whether or not A is unit triangular as follows:

              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

              DIAG = 'N' or 'n'   A is not assumed to be unit triangular.

              Unchanged on exit.

       N      - INTEGER.
              On  entry,  N  specifies  the  order  of  the  matrix  A.  N must be at least zero.
              Unchanged on exit.

       A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
              Before entry with  UPLO = 'U' or 'u', the leading n by n upper triangular  part  of
              the  array  A  must  contain  the  upper  triangular  matrix and the strictly lower
              triangular part of A is not referenced.  Before entry with UPLO = 'L' or  'l',  the
              leading  n  by  n  lower  triangular  part  of  the  array A must contain the lower
              triangular matrix and the strictly upper triangular part of A  is  not  referenced.
              Note  that  when   DIAG = 'U' or 'u', the diagonal elements of A are not referenced
              either, but are assumed to be unity.  Unchanged on exit.

       LDA    - INTEGER.
              On entry, LDA specifies the first dimension of A as declared in the  calling  (sub)
              program. LDA must be at least max( 1, n ).  Unchanged on exit.

       X      - COMPLEX*16       array of dimension at least
              (  1 + ( n - 1 )*abs( INCX ) ).  Before entry, the incremented array X must contain
              the n element right-hand side vector b. On exit, X is overwritten with the solution
              vector x.

       INCX   - INTEGER.
              On  entry,  INCX  specifies  the  increment for the elements of X. INCX must not be
              zero.  Unchanged on exit.

              Level 2 Blas routine.

              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National  Lab.   Jeremy  Du
              Croz,  Nag  Central  Office.  Sven Hammarling, Nag Central Office.  Richard Hanson,
              Sandia National Labs.