Name

cher2k, zher2k − Rank-2k update of a complex hermitian matrix

FORMAT

{C,Z}HER2K ( uplo, trans, n, k, alpha, a, lda, b, ldb, 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(B) + conjugate(alpha)B∗conjug_transp(A) + beta∗C)

If trans = ’C’ or ’c’, C  =  alpha∗conjug_transp(A)∗B + conjugate(alpha)∗conjug_transp(B)∗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 matrices A and B when trans = ’N’ or the number of rows of the matrices A and B when trans = ’C’ or
On exit, k is unchanged. 

alphacomplex∗8 | complex∗16
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 = ’C’ or 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 lda >= MAX(1,n). 
For trans = ’C’ or lda >= MAX(1,k). 
On exit, lda is unchanged. 

bcomplex∗8 | complex∗16
On entry, a two-dimensional array B with dimensions ldb by kb.
For trans = ’N’ or kb >= k and the leading n by k portion of the array B contains the matrix B. 
For trans = ’C’ or kb >= n and the leading k by n part of the array B contains the matrix B. 
On exit, b is unchanged. 

ldbinteger∗4
For trans = ’N’ or ’n’ ldb >= MAX(1,n). 
For trans = ’C’ or ldb >= MAX(1,k). 
On exit, ldb is unchanged. 

betareal∗4 | real∗8
On entry, specifies 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

CHER2K and ZHER2K perform the rank-2k update of a complex Hermitian matrix: C  = alpha ∗ A∗conjug_transp(B) + conjugate(alpha)∗B∗conjug_transp(A)
 + beta∗C C  = alpha∗conjug_transp(A)∗B + conjugate(alpha)∗conjug_transp(B)∗A + beta∗C

where alpha is a complex scalar, beta is a real scalar, and C is an n by n Hermitian matrix. In the first case, A and B are n by k matrices, and in the second case, they are k by n matrices. 

Example

COMPLEX∗8 A(40,10), B(40,10), C(20,20), alpha
REAL∗4 beta
LDA = 40
LDB = 30
LDC = 20
N = 18
K = 10
alpha = (1.0, 1.0)
beta = (2.0)
CALL CHER2K (’U’,’N’,N,K,alpha,A,LDA,B,LDB,beta,C,LDC)

This FORTRAN code computes the rank-2k update of the complex Hermitian matrix C: C  =  alpha ∗ A∗conjug_transp(B) + conjugate(alpha)B∗conjug_transp(A) + beta∗C). Only the upper-triangular part of C is referenced. The leading 18 by 10 part of array A contains the matrix A. The leading 18 by 10 part of array B contains the matrix B. The leading 18 by 18 upper-triangular part of array C contains the upper-triangular matrix C.