Name

cherk, zherk − Rank-k update of a complex hermitian matrix

FORMAT

{C,Z}HERK ( uplo, trans, n, k, alpha, a, lda, beta, c, ldc )

Arguments

uplocharacter∗1
On entry, specifies whether the upper- or lower-triangular part of the Hermitian matrix C is to be referenced:

If uplo = ’U’ or ’u’, the upper-triangular part of C is to be referenced. 

If uplo = ’L’ or ’l’, the lower-triangular part of C is to be referenced. 
On exit, uplo is unchanged. 

transcharacter∗1
On entry, specifies the operation to be performed:

If trans = ’N’ or ’n’, C  =  alpha ∗ A∗conjug_transp(A) + beta∗C

If trans = ’C’ or ’c’, C  =  alpha∗conjug_transp(A)A + beta∗C
On exit, trans is unchanged. 

ninteger∗4
On entry, the order of the matrix C; n >= 0
On exit, n is unchanged. 

kinteger∗4
On entry,  the number of columns of the matrix A when trans = ’N’ or the number of rows of the matrix A when trans = ’C’ or
On exit, k is unchanged. 

alphareal∗4 | real∗8
On entry, specifies the scalar alpha.
On exit, alpha is unchanged. 

acomplex∗8 | complex∗16
On entry, a two-dimensional array A with dimensions lda by ka.
For trans = ’N’ or ka >= k and the leading n by k portion of the array A contains the matrix A. 
For trans = ’T’, ka >= n and the leading k by n part of the array A contains the matrix A. 
On exit, a is unchanged. 

ldainteger∗4
On entry, the first dimension of array A.
For trans = ’N’ or ’n’ lda >= MAX(1,n). 
For trans = ’C’ or lda >= MAX(1,k). 
On exit, lda is unchanged. 

betareal∗4 | real∗8
On entry, the scalar beta.
On exit, beta is unchanged. 

ccomplex∗8 | complex∗16
On entry, a two-dimensional array C of dimensions ldc by at least n.

If uplo specifies the upper part, the leading n by n upper-triangular part of the array C must contain the upper-triangular part of the Hermitian matrix C, and the strictly lower-triangular part of C is not referenced. 

If uplo specifies the lower part, the leading n by n lower-triangular part of the array C must contain the lower-triangular part of the Hermitian matrix C, 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 0, and on exit, they are set to 0. 
On exit, c is overwritten; the triangular part of the array C is overwritten by the triangular part of the updated matrix. 

ldcinteger∗4
On entry, the first dimension  of array C; ldc >= MAX(1,n)
On exit, ldc is unchanged. 

Description

CHERK and ZHERK perform the rank-k update of a complex Hermitian matrix: C  = alpha ∗ A∗conjug_transp(A) + beta∗C C  = alpha∗conjug_transp(A)A + beta∗C
alpha and beta are real scalars,  C is an n by n Hermitian matrix, and A is an n by k matrix in the first case and a k by n matrix in the second case.

Example

COMPLEX∗8 A(40,20), C(20,20)
REAL∗4 alpha, beta
LDA = 40
LDC = 20
N = 10
K = 15
alpha = (1.0)
beta = (2.0)
CALL CHERK (’U’,’N’,N,K,alpha,A,LDA,beta,C,LDC)

This FORTRAN code computes the rank-k update of the complex Hermitian matrix C: C  =  alpha ∗ A∗conjug_transp(A) + beta∗C. C is a 10 by 10 matrix, and A is a 10 by 15 matrix. Only the upper-triangular part of C is referenced. The leading 10 by 15 part of array A contains the matrix A. The leading 10 by 10 upper-triangular part of array C contains the upper-triangular matrix C.