cblas_?hpr2

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

Syntax

void cblas_chpr2 (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const MKL_INT n, const void *alpha, const void *x, const MKL_INT incx, const void *y, const MKL_INT incy, void *ap);

void cblas_zhpr2 (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const MKL_INT n, const void *alpha, const void *x, const MKL_INT incx, const void *y, const MKL_INT incy, void *ap);

Include Files

  • mkl.h

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

Layout

Specifies whether two-dimensional array storage is row-major (CblasRowMajor) or column-major (CblasColMajor).

uplo

Specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array ap.

If uplo = CblasUpper, then the upper triangular part of the matrix A is supplied in the packed array ap .

If uplo = CblasLower, then the low triangular part of the matrix A is supplied in the packed array ap .

n

Specifies the order of the matrix A. The value of n must be at least zero.

alpha

Specifies the scalar alpha.

x

Array, dimension at least (1 +(n - 1)*abs(incx)). Before entry, the incremented array x must contain the n-element vector x.

incx

Specifies the increment for the elements of x.

The value of incx must not be zero.

y

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

incy

Specifies the increment for the elements of y.

The value of incy must not be zero.

ap

Array, size at least ((n*(n + 1))/2).

For Layout = CblasColMajor:

Before entry with uplo = CblasUpper, the array ap must contain the upper triangular part of the Hermitian matrix packed sequentially, column-by-column, so that ap[0] contains A1, 1, ap[1] and ap[2] contain A1, 2 and A2, 2 respectively, and so on.

Before entry with uplo = CblasLower, the array ap must contain the lower triangular part of the Hermitian matrix packed sequentially, column-by-column, so that ap[0] contains A1, 1, ap[1] and ap[2] contain A2, 1 and A3, 1 respectively, and so on.

For Layout = CblasRowMajor:

Before entry with uplo = CblasUpper, the array ap must contain the upper triangular part of the Hermitian matrix packed sequentially, row-by-row, ap[0] contains A1, 1, ap[1] and ap[2] contain A1, 2 and A1, 3 respectively, and so on.

Before entry with uplo = CblasLower, the array ap must contain the lower triangular part of the Hermitian matrix packed sequentially, row-by-row, so that ap[0] contains A1, 1, ap[1] and ap[2] contain A2, 1 and A2, 2 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 = CblasUpper, overwritten by the upper triangular part of the updated matrix.

With uplo = CblasLower, overwritten by the lower triangular part of the updated matrix.

The imaginary parts of the diagonal elements need are set to zero.

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