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NAME
     ctrsv - solve 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*1 DIAG, TRANS, UPLO

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



     #include <sunperf.h>

     void ctrsv(char uplo, char trans, char diag, int n,  complex
               *ca, int lda, complex *cx, int incx) ;

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

               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 triangular matrix and the
               strictly  upper triangular part of A is not refer-
               enced.  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  overwrit-
               ten 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.

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