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