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CTRSV(1)			 BLAS routine			      CTRSV(1)

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




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

       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 rou‐
       tine. Such tests must be performed before calling this routine.

       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

	      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 refer‐
	      enced.  Before entry with UPLO = 'L' or 'l', the leading n by  n
	      lower triangular part of the array A must contain the lower tri‐
	      angular 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.

       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)

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