ctrsv

CTRSV(1)                         BLAS routine                         CTRSV(1)



NAME
       CTRSV - solves one of the systems of equations   A*x = b, or A'*x = b,
       or conjg( A' )*x = b,

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

           INTEGER                                      INCX,LDA,N

           CHARACTER                                    DIAG,TRANS,UPLO

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

PURPOSE
       CTRSV  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.


ARGUMENTS
       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          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          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.

FURTHER DETAILS
       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.




BLAS routine                     November 2008                        CTRSV(1)