hemm(3F)

NAME
     CHEMM, ZHEMM - Multiplies a complex general matrix by a complex
     Hermitian matrix

SYNOPSIS
     Complex

        CALL CHEMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

     Double complex

        CALL ZHEMM (side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc)

DESCRIPTION
     These routines multiply a complex general matrix by a complex
     Hermitian matrix. They perform one of the following matrix-matrix
     operations:

          C  <-  alpha AB + beta C

          C  <- alpha BA + beta C
     where alpha and beta are scalars, A is a Hermitian matrix, and B and C
     are m-by-n matrices.

     These routines have the following arguments:

     side      Character*1.  (input)
               Specifies whether the Hermitian matrix A appears on the left
               or right in the operation, as follows:
               side = 'L' or 'l':  C <- alpha AB + beta C
               side = 'R' or 'r':  C <- alpha BA + beta C

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

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

     m         Integer.  (input)
               Specifies the number of rows in matrix C.  m must be >= 0.

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

     alpha     First scalar factor.  (input)
               CHEMM: Complex.
               ZHEMM: Double complex.

     a         Array of dimension (lda,ka).  (input)
               CHEMM: Complex array.
               ZHEMM: Double complex array.

               Contains matrix A.  When side = 'L' or 'l', ka is m;
               otherwise, it is n.

               Before entry with side = 'L' or 'l', the m-by-m part of
               array a must contain the Hermitian matrix, such that:

               * If uplo = 'U' or 'u', the leading m-by-m upper triangular
                 part of array a must contain the upper triangular part of
                 the Hermitian matrix.  The strictly lower triangular part
                 of a is not referenced.

               * If uplo = 'L' or 'l', the leading m-by-m lower triangular
                 part of array a must contain the lower triangular part of
                 the Hermitian matrix.  The strictly upper triangular part
                 of a is not referenced.

               Before entry with side = 'R' or 'r', the n-by-n part of
               array a must contain the Hermitian matrix, such that:

               * If uplo = 'U' or 'u', the leading n-by-n upper triangular
                 part of array a must contain the upper triangular part of
                 the Hermitian matrix.  The strictly lower triangular part
                 of a is not referenced.

               * If uplo = 'L' or 'l', the leading n-by-n lower triangular
                 part of array a must contain the lower triangular part of
                 the Hermitian matrix.  The strictly upper triangular part
                 of a is not referenced.

               The imaginary parts of the diagonal elements need not be
               set.  They are assumed to be 0.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  When side = 'L' or 'l', lda >= MAX(1,m);
               otherwise, lda >= MAX(1,n).

     b         Array of dimension (ldb,n).  (input)
               CHEMM: Complex array.
               ZHEMM: Double complex array.
               Contains matrix B.  Before entry, the leading m-by-n part of
               array b must contain matrix B.

     ldb       Integer.  (input)
               Specifies the first dimension of b as declared in the
               calling program.  ldb >= MAX(1,m).

     beta      Second scalar factor.  (input)
               CHEMM: Complex.
               ZHEMM: Double complex.
               When beta is supplied as 0, c need not be set on input.

     c         Array of dimension (ldc,n).  (input and output)
               CHEMM: Complex array.
               ZHEMM: Double complex array.
               Contains matrix C.  Before entry, the leading m-by-n part of
               array c must contain matrix C, except when beta is 0; in
               which case, c need not be set.  On exit, the m-by-n updated
               matrix overwrites array c.

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

NOTES
     CHEMM/ZHEMM is a Level 3 Basic Linear Algebra Subprogram (Level 3
     BLAS).

SEE ALSO
     SYMM(3F)