Visible to Intel only — GUID: GUID-A529894C-A503-476F-BF8A-4F1C4634F142
Visible to Intel only — GUID: GUID-A529894C-A503-476F-BF8A-4F1C4634F142
?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, 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
- 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*AH + beta*C;
if trans= 'C' or 'c', then C := alpha*AH*A + beta*C.
- n
-
INTEGER. Specifies the order of the matrix C. The value of n must be at least zero.
- k
-
INTEGER. Withtrans= '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.