# ctpsv.f

```      SUBROUTINE CTPSV (UPLO, TRANS, DIAG, N, AP, X, INCX)
C***BEGIN PROLOGUE  CTPSV
C***PURPOSE  Solve one of the systems of equations.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1B4
C***TYPE      COMPLEX (STPSV-S, DTPSV-D, CTPSV-C)
C***KEYWORDS  LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR  Dongarra, J. J., (ANL)
C           Du Croz, J., (NAG)
C           Hammarling, S., (NAG)
C           Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C  CTPSV  solves one of the systems of equations
C
C     A*x = b,   or   A'*x = b,   or   conjg( A')*x = b,
C
C  where b and x are n element vectors and A is an n by n unit, or
C  non-unit, upper or lower triangular matrix, supplied in packed form.
C
C  No test for singularity or near-singularity is included in this
C  routine. Such tests must be performed before calling this routine.
C
C  Parameters
C  ==========
C
C  UPLO   - CHARACTER*1.
C           On entry, UPLO specifies whether the matrix is an upper or
C           lower triangular matrix as follows:
C
C              UPLO = 'U' or 'u'   A is an upper triangular matrix.
C
C              UPLO = 'L' or 'l'   A is a lower triangular matrix.
C
C           Unchanged on exit.
C
C  TRANS  - CHARACTER*1.
C           On entry, TRANS specifies the equations to be solved as
C           follows:
C
C              TRANS = 'N' or 'n'   A*x = b.
C
C              TRANS = 'T' or 't'   A'*x = b.
C
C              TRANS = 'C' or 'c'   conjg( A' )*x = b.
C
C           Unchanged on exit.
C
C  DIAG   - CHARACTER*1.
C           On entry, DIAG specifies whether or not A is unit
C           triangular as follows:
C
C              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
C
C              DIAG = 'N' or 'n'   A is not assumed to be unit
C                                  triangular.
C
C           Unchanged on exit.
C
C  N      - INTEGER.
C           On entry, N specifies the order of the matrix A.
C           N must be at least zero.
C           Unchanged on exit.
C
C  AP     - COMPLEX          array of DIMENSION at least
C           ( ( n*( n + 1 ) )/2 ).
C           Before entry with  UPLO = 'U' or 'u', the array AP must
C           contain the upper triangular matrix packed sequentially,
C           column by column, so that AP( 1 ) contains a( 1, 1 ),
C           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
C           respectively, and so on.
C           Before entry with UPLO = 'L' or 'l', the array AP must
C           contain the lower triangular matrix packed sequentially,
C           column by column, so that AP( 1 ) contains a( 1, 1 ),
C           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
C           respectively, and so on.
C           Note that when  DIAG = 'U' or 'u', the diagonal elements of
C           A are not referenced, but are assumed to be unity.
C           Unchanged on exit.
C
C  X      - COMPLEX          array of dimension at least
C           ( 1 + ( n - 1 )*abs( INCX ) ).
C           Before entry, the incremented array X must contain the n
C           element right-hand side vector b. On exit, X is overwritten
C           with the solution vector x.
C
C  INCX   - INTEGER.
C           On entry, INCX specifies the increment for the elements of
C           X. INCX must not be zero.
C           Unchanged on exit.
C
C***REFERENCES  Dongarra, J. J., Du Croz, J., Hammarling, S., and
C                 Hanson, R. J.  An extended set of Fortran basic linear
C                 algebra subprograms.  ACM TOMS, Vol. 14, No. 1,
C                 pp. 1-17, March 1988.
C***ROUTINES CALLED  LSAME, XERBLA
C***REVISION HISTORY  (YYMMDD)
C   861022  DATE WRITTEN
C   910605  Modified to meet SLATEC prologue standards.  Only comment
C           lines were modified.  (BKS)
C***END PROLOGUE  CTPSV
```