## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?hpr

Performs
a rank-1 update of a Hermitian packed matrix.

## Syntax

Include Files
• mkl.fi
,
blas.f90
Description
The
?hpr
routines perform a matrix-vector operation defined as
`A := alpha*x*conjg(x') + A,`
where:
alpha
is a real scalar,
x
is an
n
-element vector,
A
is an
n
-by-
n
Hermitian matrix, supplied in packed form.
Input Parameters
uplo
CHARACTER*1
.
Specifies whether the upper or lower triangular part of the matrix
A
is supplied in the packed array
ap
.
If
uplo
=
'U'
or
'u'
, the upper triangular part of the matrix
A
is supplied in the packed array
ap
.
If
uplo
=
'L'
or
'l'
, the low triangular part of the matrix
A
is supplied in the packed array
ap
.
n
INTEGER
.
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
alpha
REAL
for
chpr
DOUBLE PRECISION
for
zhpr
Specifies the scalar
alpha
.
x
COMPLEX
for
chpr
DOUBLE COMPLEX
for
zhpr
Array, size at least
(1 + (
n
- 1)*abs(
incx
))
. Before entry, the incremented array
x
must contain the
n
-element vector
x
.
incx
INTEGER
.
Specifies the increment for the elements of
x
.
incx
must not be zero.
ap
COMPLEX
for
chpr
DOUBLE COMPLEX
for
zhpr
Array, size at least
((
n
*(
n
+ 1))/2)
.
Before entry with
uplo
=
'U'
or
'u'
, the array
ap
must contain the upper triangular part of the Hermitian 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 part of the Hermitian 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.
The imaginary parts of the diagonal elements need not be set and are assumed to be zero.
Output Parameters
ap
With
uplo
=
'U'
or
'u'
, overwritten by the upper triangular part of the updated matrix.
With
uplo
=
'L'
or
'l'
, overwritten by the lower triangular part of the updated matrix.
The imaginary parts of the diagonal elements are set to zero.
BLAS 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see BLAS 95 Interface Conventions.
Specific details for the routine
hpr
interface are the following: