herk(3F)

NAME
     CHERK, ZHERK - Performs Hermitian rank k update of a complex Hermitian
     matrix

SYNOPSIS
     Complex

        CALL CHERK (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)

     Double complex

        CALL ZHERK (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)

DESCRIPTION
     These routines perform a Hermitian rank k update of a complex
     Hermitian matrix.

     They perform one of the following Hermitian rank k operations:

          C <- alpha AAH + beta C

          C <- alpha AHA + beta C

     where the following is true:

     * alpha and beta are scalars;

     * C is an n-by-n Hermitian matrix;

     * A is an n-by-k matrix in the first operation listed previously, and
       a k-by-n matrix in the second;

     * and AH is the conjugate transpose of A.

     These routines have the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               array c is referenced, as follows:

               uplo = 'U' or 'u': only the upper triangular part of c is
               referenced.
               uplo = 'L' or 'l': only the lower triangular part of c is
               referenced.

     trans     Character*1.  (input)
               Specifies the operation to be performed, as follows:

               trans = 'N' or 'n':  C  <-  alpha AAH + beta C

               trans = 'C' or 'c':  C  <-  alpha AH A + beta C

     n         Integer.  (input)
               Specifies the order of matrix C.  n must be >= 0.

     k         Integer.  (input)

               On entry with trans = 'N' or 'n', k specifies the number of
               columns of matrix A.
               On entry with trans = 'C' or 'c', k specifies the number of
               rows of matrix A.

               k must be >= 0.

     alpha     First scalar factor.  (input)
               CHERK: Real.
               ZHERK: Double precision.

     a         Array of dimension (lda,ka).  (input)
               CHERK: Complex array.
               ZHERK: Double complex array.
               When trans = 'N' or 'n', ka is k; otherwise, it is n.
               Contains matrix A.

               Before entry with trans = 'N' or 'n', the leading n-by-k
               part of array a must contain matrix A; otherwise, the
               leading k-by-n part of array a must contain matrix A.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  If trans = 'N' or 'n', lda >= MAX(1,n);
               otherwise, lda >= MAX(1,k).

     beta      Second scalar factor.  (input)
               CHERK: Real.
               ZHERK: Double precision.

     c         Array of dimension (ldc,n).  (input and output)
               CHERK: Complex array.
               ZHERK: Double complex array.

               Contains matrix C.  Before entry with uplo = 'U' or 'u', the
               leading n-by-n upper triangular part of array c must contain
               the upper triangular part of the Hermitian matrix.  The
               strictly lower triangular part of c is not referenced.  On
               exit, the upper triangular part of the updated matrix
               overwrites the upper triangular part of array c.

               Before entry with uplo = 'L' or 'l', the leading n-by-n
               lower triangular part of array c must contain the lower
               triangular part of the Hermitian matrix.  The strictly upper
               triangular part of c is not referenced.  On exit, the lower
               triangular part of the updated matrix overwrites the lower
               triangular part of array c.

               The imaginary parts of the diagonal elements need not be set
               and are assumed to be 0.  On exit, they are set to 0.

     ldc       Integer.  (input)
               Specifies the first dimension of c as declared in the
               calling program.  ldc >= MAX(1,n).

NOTES
     CHERK/ZHERK is a Level 3 Basic Linear Algebra Subprogram (Level 3
     BLAS).

SEE ALSO
     SYRK(3F)