Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?herk
Performs a Hermitian rank-k update.
Syntax
call cherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
call zherk(uplo, trans, n, k, alpha, a, lda, beta, c, ldc)call herk(a, c [, uplo] [, trans] [, alpha] [, beta])Include Files
mkl.fi, mkl_blas.f90
Description
The ?herk routines perform a rank-k matrix-matrix operation using a general matrix A and a Hermitian matrix C . The operation is defined as: C := alpha * A * AH + beta * C ,
or C := alpha * AH * A + beta * C ,
where:
alpha and beta are real scalars,
C is an n -by- n Hermitian matrix,
A is an n -by- k matrix in the first case and a k -by- n matrix in the second case.
Input Parameters
- Layout
-
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
uplo
CHARACTER*1 . Specifies whether the upper or lower triangular part of the array c is used.
If uplo = 'U' or ‘u’ , then the upper triangular part of the array c is used.
If uplo = 'L' or ‘l’ , then the low triangular part of the array c is used.
trans
CHARACTER*1 . Specifies the operation:
if trans= 'N' or 'n' , then C := alpha*A*A^{H} + beta*C ;
if trans= 'C' or 'c' , then C := alpha*A^{H}*A + beta*C .
n
INTEGER . Specifies the order of the matrix C . The value of n must be at least zero.
k
INTEGER . With trans= 'N' or 'n' , k specifies the number of columns of the matrix A , and with trans= 'C' or 'c' , k specifies the number of rows of the matrix A .
The value of k must be at least zero.
- alpha
-
REAL for cherk DOUBLE PRECISION for zherk Specifies the scalar alpha .
- a
-
COMPLEX for cherk DOUBLE COMPLEX for zherk 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
INTEGER . Specifies the leading dimension of a as declared in the calling (sub)program. When 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 cherk DOUBLE PRECISION for zherk Specifies the scalar beta .
- c
-
COMPLEX for cherk DOUBLE COMPLEX for zherk Array, size ldc by n .
Before entry with uplo = 'U' or ‘u’ , 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 = 'L' or ‘l’ , 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
INTEGER . 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 = 'U' or ‘u’ , the upper triangular part of the array c is overwritten by the upper triangular part of the updated matrix.
With uplo = 'L' or ‘l’ , 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
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 herk interface are the following:
- a
-
Holds the matrix A of size ( ma , ka ) where ka = k if trans='N' , ka = n otherwise, ma = n if trans='N' , ma = k otherwise.
- c
-
Holds the matrix C of size ( n , n ).
- uplo
-
Must be ‘U’ or ‘L’ . The default value is ‘U’ .
- trans
-
Must be ‘N’ or ‘C’ . The default value is ‘N’ .
- alpha
-
The default value is 1.
- beta
-
The default value is 0.