Developer Reference for Intel® oneAPI Math Kernel Library for C
?hpr
Performs a rank-1 update of a Hermitian packed matrix.
Syntax
void cblas_chpr(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const MKL_INT n,
const float alpha, const void *x, const MKL_INT incx, void *ap);
void cblas_zhpr(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const MKL_INT n,
const double alpha, const void *x, const MKL_INT incx, void *ap);Include Files
mkl.h
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
- 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 , the upper triangular part of the matrix A is supplied in the packed array ap .
If uplo = CblasLower , 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
-
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
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) . 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(1)ap[0] contains A1, 1 , ap(2)ap[1] and ap(3)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(1)ap[0] contains A1, 1 , ap(2)ap[1] and ap(3)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.
If alpha is zero, matrix A is unchanged; otherwise, the imaginary parts of the diagonal elements are set to zero.
BLAS 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.