Previous: dtpmv Up: ../lapack-blas.html Next: dtrmm

# dtpsv

```
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 triangu-
lar.

DIAG = 'N' or 'n'   A is not assumed to be unit tri-
angular.

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 triangu-
lar 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 ) con-
tains 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 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.
```