.TH ZTRSV 1 "November 2006" "BLAS routine" "BLAS routine" .SH NAME ZTRSV - one of the systems of equations A*x = b, or A\(aq*x = b, or conjg( A\(aq )*x = b, .SH SYNOPSIS .TP 49 SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) .TP 49 .ti +4 INTEGER INCX,LDA,N .TP 49 .ti +4 CHARACTER DIAG,TRANS,UPLO .TP 49 .ti +4 DOUBLE COMPLEX A(LDA,*),X(*) .SH PURPOSE ZTRSV 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. .br No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. .SH ARGUMENTS .TP 7 UPLO - CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = \(aqU\(aq or \(aqu\(aq A is an upper triangular matrix. UPLO = \(aqL\(aq or \(aql\(aq A is a lower triangular matrix. Unchanged on exit. .TP 7 TRANS - CHARACTER*1. On entry, TRANS specifies the equations to be solved as follows: TRANS = \(aqN\(aq or \(aqn\(aq A*x = b. TRANS = \(aqT\(aq or \(aqt\(aq A\(aq*x = b. TRANS = \(aqC\(aq or \(aqc\(aq conjg( A\(aq )*x = b. Unchanged on exit. .TP 7 DIAG - CHARACTER*1. On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = \(aqU\(aq or \(aqu\(aq A is assumed to be unit triangular. DIAG = \(aqN\(aq or \(aqn\(aq A is not assumed to be unit triangular. Unchanged on exit. .TP 7 N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. .TP 7 A - COMPLEX*16 array of DIMENSION ( LDA, n ). Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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 = \(aqU\(aq or \(aqu\(aq, the diagonal elements of A are not referenced either, but are assumed to be unity. Unchanged on exit. .TP 7 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. .TP 7 X - COMPLEX*16 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. .TP 7 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.