CTPSV - solve one of the systems of equations A*x = b,
or A'*x = b, or conjg( A' )*x = b,
SYNOPSIS
SUBROUTINE CTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
INTEGER INCX, N
CHARACTER*1 DIAG, TRANS, UPLO
COMPLEX AP( * ), X( * )
PURPOSE
CTPSV 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, sup
plied in packed form.
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
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.
AP - COMPLEX array of DIMENSION at least
( ( n*( n + 1 ) )/2 ). Before entry with UPLO =
'U' or 'u', 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 ) respec
tively, and so on. Before entry with UPLO = 'L' or
'l', 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 = 'U' or 'u', the
diagonal elements of A are not referenced, but are
assumed to be unity. 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 ele
ments 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.
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