.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.