CTRSV(3)

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

NAME
ctrsv - Solve a complex triangular system of equations.

LIBRARY
SLATEC (BLAS)

CATEGORY
D1B4

TYPE
COMPLEX (STRSV-S, DTRSV-D, CTRSV-C)

KEYWORDS
LEVEL 2 BLAS, LINEAR ALGEBRA

AUTHOR
Dongarra, J. J., (ANL) Du Croz, J., (NAG) Hammarling, S., (NAG) Hanson, R. J., (SNLA)

DESCRIPTION
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 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.

REFERENCES
Dongarra, J. J., Du Croz, J., Hammarling, S., and Hanson, R. J. An extended set of Fortran basic linear algebra subprograms. ACM TOMS, Vol. 14, No. 1, pp. 1-17, March 1988.

ROUTINES CALLED
LSAME, XERBLA

REVISION HISTORY (YYMMDD)
861022 DATE WRITTEN
910605 Modified to meet SLATEC prologue standards. Only comment lines were modified. (BKS)