Developer Reference for Intel® oneAPI Math Kernel Library for C
?her2k
Performs a Hermitian rank-2k update.
Syntax
void cblas_cher2k(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k,
const void *alpha, const void *a, const MKL_INT lda, const void *b,
const MKL_INT ldb, const float beta, void *c, const MKL_INT ldc);
void cblas_zher2k(const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo,
const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k,
const void *alpha, const void *a, const MKL_INT lda, const void *b,
const MKL_INT ldb, const double beta, void *c, const MKL_INT ldc);Include Files
mkl.h
Description
The ?her2k routines perform a rank-2k matrix-matrix operation using general matrices A and B and a Hermitian matrix C . The operation is defined as
C := alpha*A*B^{H} + conjg(alpha)B*A^{H} + beta*Cor
C := alpha*A^{H}*B + conjg(alpha)*B^{H}*A + beta*Cwhere:
alpha is a scalar and beta is a real scalar.
C is an n -by- n Hermitian matrix.
A and B are n -by- k matrices in the first case and k -by- n matrices in the second case.
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 array c is used.
If uplo = CblasUpper , then the upper triangular of the array c is used.
If uplo = CblasLower , then the low triangular of the array c is used.
trans
Specifies the operation:
if trans = CblasNoTrans , then C:=alpha*A*B^{H} + alpha*B*A^{H} + beta*C ;
if trans = CblasConjTrans , then C:=alpha*A^{H}*B + alpha*B^{H}*A + beta*C .
- n
-
Specifies the order of the matrix C . The value of n must be at least zero.
k
With trans = CblasNoTrans specifies the number of columns of the matrix A , and with trans = CblasConjTrans , k specifies the number of rows of the matrix A .
The value of k must be at least equal to zero.
- alpha
-
COMPLEX for cher2k DOUBLE COMPLEX for zher2k Specifies the scalar alpha .
- a
-
COMPLEX for cher2k DOUBLE COMPLEX for zher2k Array, size (lda, ka) , where ka is k when trans= 'N' or 'n' , and is n otherwise. Before entry with trans= 'N' or 'n' , the leading n -by- k part of the array a must contain the matrix A , otherwise the leading k -by- n part of the array a must contain the matrix A .
- lda
-
Specifies the leading dimension of a as declared in the calling (sub)program.
When trans= 'N' or 'n'trans= 'N' or 'n' , then lda must be at least max(1, n) , otherwise lda must be at least max(1, k) .
- beta
-
REAL for cher2k DOUBLE PRECISION for zher2k Specifies the scalar beta .
- b
-
COMPLEX for cher2k DOUBLE COMPLEX for zher2k Array, size (ldb, kb) , where kb is k when trans= 'N' or 'n' , and is n otherwise. Before entry with trans= 'N' or 'n' , the leading n -by- k part of the array b must contain the matrix B , otherwise the leading k -by- n part of the array b must contain the matrix B .
- ldb
-
Specifies the leading dimension of a as declared in the calling (sub)program.
When trans= 'N' or 'n' , then ldb must be at least max(1, n) , otherwise ldb must be at least max(1, k) .
- c
-
COMPLEX for cher2k DOUBLE COMPLEX for zher2k Array, size ldc by n .
Before entry with uplo = CblasUpper , the leading n -by- n upper triangular part of the array c must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of c is not referenced.
Before entry with uplo = CblasLower , the leading n -by- n lower triangular part of the array c must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of c is not referenced.
The imaginary parts of the diagonal elements need not be set, they are assumed to be zero.
- ldc
-
Specifies the leading dimension of c as declared in the calling (sub)program. The value of ldc must be at least max(1, n) .
Output Parameters
c
With uplo = CblasUpper , the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix.
With uplo = CblasLower , the lower triangular part of the array c is 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
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.