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

  uplo                character*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.

  trans               character*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.

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

  k                   integer*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.

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

  a                   complex*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.

  lda                 integer*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.

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

  c                   complex*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.

  ldc                 integer*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.