?hpr2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?hpr2

Performs a rank-2 update of a Hermitian packed matrix.

Syntax

call chpr2(uplo, n, alpha, x, incx, y, incy, ap)

call zhpr2(uplo, n, alpha, x, incx, y, incy, ap)

call hpr2(ap, x, y [,uplo][,alpha])

Include Files

mkl.fi, blas.f90

Description

The ?hpr2 routines perform a matrix-vector operation defined as

A := alpha*x*conjg(y') + conjg(alpha)*y*conjg(x') + A,

where:

alpha is a scalar,

x and y are n-element vectors,

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', then the upper triangular part of the matrix A is supplied in the packed array ap .

If uplo = 'L' or 'l', then 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

COMPLEX for chpr2

DOUBLE COMPLEX for zhpr2

Specifies the scalar alpha.

x

COMPLEX for chpr2

DOUBLE COMPLEX for zhpr2

Array, dimension 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.

The value of incx must not be zero.

y

COMPLEX for chpr2

DOUBLE COMPLEX for zhpr2

Array, size at least (1 +(n - 1)*abs(incy)). Before entry, the incremented array y must contain the n-element vector y.

incy

INTEGER. Specifies the increment for the elements of y.

The value of incy must not be zero.

ap

COMPLEX for chpr2

DOUBLE COMPLEX for zhpr2

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 need 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 hpr2 interface are the following:

ap: Holds the array ap of size (n*(n+1)/2).
x: Holds the vector with the number of elements n.
y: Holds the vector with the number of elements n.
uplo: Must be 'U' or 'L'. The default value is 'U'.
alpha: The default value is 1.

Parent topic: BLAS Level 2 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hpr2