# dtpsv

```DTPSV(1)                         BLAS routine                         DTPSV(1)

NAME
DTPSV - solves 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                                 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.

ARGUMENTS
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.

FURTHER DETAILS
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.

BLAS routine                     November 2008                        DTPSV(1)```