.TH ZTPSV 1 "November 2008" "BLAS routine" "BLAS routine"
.SH NAME
ZTPSV - solves one of the systems of equations A*x = b, or A\(aq*x = b, or conjg( A\(aq )*x = b,
.SH SYNOPSIS
.TP 46
SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
.TP 46
.ti +4
INTEGER
INCX,N
.TP 46
.ti +4
CHARACTER
DIAG,TRANS,UPLO
.TP 46
.ti +4
DOUBLE
COMPLEX AP(*),X(*)
.SH PURPOSE
ZTPSV 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, supplied in packed form.
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
AP - COMPLEX*16 array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, the array AP must
contain the upper triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
respectively, and so on.
Before entry with UPLO = \(aqL\(aq or \(aql\(aq, the array AP must
contain the lower triangular matrix packed sequentially,
column by column, so that AP( 1 ) contains a( 1, 1 ),
AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
respectively, and so on.
Note that when DIAG = \(aqU\(aq or \(aqu\(aq, the diagonal elements of
A are not referenced, but are assumed to be unity.
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.
.SH FURTHER DETAILS
Level 2 Blas routine.
.br
-- Written on 22-October-1986.
.br
Jack Dongarra, Argonne National Lab.
.br
Jeremy Du Croz, Nag Central Office.
.br
Sven Hammarling, Nag Central Office.
.br
Richard Hanson, Sandia National Labs.
.br