NAME
DTPSV - solve one of the systems of equations A*x = b, or A’*x = b,
SYNOPSIS
SUBROUTINE DTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
INTEGER INCX, N
CHARACTER*1 DIAG, TRANS, UPLO
DOUBLE PRECISION AP( * ), X( * )
PURPOSE
DTPSV 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.
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’ 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.
AP - DOUBLE PRECISION 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 )
respectively, 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 - DOUBLE PRECISION 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.
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.