stdlib_zherk Subroutine

     pure subroutine stdlib_zherk(uplo,trans,n,k,alpha,a,lda,beta,c,ldc)
     !! ZHERK performs one of the hermitian rank k operations
     !! C := alpha*A*A**H + beta*C,
     !! or
     !! C := alpha*A**H*A + beta*C,
     !! where  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.
        ! -- reference blas level3 routine --
        ! -- reference blas is a software package provided by univ. of tennessee,    --
        ! -- univ. of california berkeley, univ. of colorado denver and nag ltd..--
           ! Scalar Arguments 
           real(dp), intent(in) :: alpha, beta
           integer(ilp), intent(in) :: k, lda, ldc, n
           character, intent(in) :: trans, uplo
           ! Array Arguments 
           complex(dp), intent(in) :: a(lda,*)
           complex(dp), intent(inout) :: c(ldc,*)
        ! =====================================================================
           ! Intrinsic Functions 
           intrinsic :: real,cmplx,conjg,max
           ! Local Scalars 
           complex(dp) :: temp
           real(dp) :: rtemp
           integer(ilp) :: i, info, j, l, nrowa
           logical(lk) :: upper
           
           ! test the input parameters.
           if (stdlib_lsame(trans,'N')) then
               nrowa = n
           else
               nrowa = k
           end if
           upper = stdlib_lsame(uplo,'U')
           info = 0
           if ((.not.upper) .and. (.not.stdlib_lsame(uplo,'L'))) then
               info = 1
           else if ((.not.stdlib_lsame(trans,'N')) .and.(.not.stdlib_lsame(trans,'C'))) &
                     then
               info = 2
           else if (n<0) then
               info = 3
           else if (k<0) then
               info = 4
           else if (lda<max(1,nrowa)) then
               info = 7
           else if (ldc<max(1,n)) then
               info = 10
           end if
           if (info/=0) then
               call stdlib_xerbla('ZHERK ',info)
               return
           end if
           ! quick return if possible.
           if ((n==0) .or. (((alpha==zero).or.(k==0)).and. (beta==one))) return
           ! and when  alpha.eq.zero.
           if (alpha==zero) then
               if (upper) then
                   if (beta==zero) then
                       do j = 1,n
                           do i = 1,j
                               c(i,j) = zero
                           end do
                       end do
                   else
                       do j = 1,n
                           do i = 1,j - 1
                               c(i,j) = beta*c(i,j)
                           end do
                           c(j,j) = beta*real(c(j,j),KIND=dp)
                       end do
                   end if
               else
                   if (beta==zero) then
                       do j = 1,n
                           do i = j,n
                               c(i,j) = zero
                           end do
                       end do
                   else
                       do j = 1,n
                           c(j,j) = beta*real(c(j,j),KIND=dp)
                           do i = j + 1,n
                               c(i,j) = beta*c(i,j)
                           end do
                       end do
                   end if
               end if
               return
           end if
           ! start the operations.
           if (stdlib_lsame(trans,'N')) then
              ! form  c := alpha*a*a**h + beta*c.
               if (upper) then
                   do j = 1,n
                       if (beta==zero) then
                           do i = 1,j
                               c(i,j) = zero
                           end do
                       else if (beta/=one) then
                           do i = 1,j - 1
                               c(i,j) = beta*c(i,j)
                           end do
                           c(j,j) = beta*real(c(j,j),KIND=dp)
                       else
                           c(j,j) = real(c(j,j),KIND=dp)
                       end if
                       do l = 1,k
                           if (a(j,l)/=cmplx(zero,KIND=dp)) then
                               temp = alpha*conjg(a(j,l))
                               do i = 1,j - 1
                                   c(i,j) = c(i,j) + temp*a(i,l)
                               end do
                               c(j,j) = real(c(j,j),KIND=dp) + real(temp*a(i,l),KIND=dp)
                           end if
                       end do
                   end do
               else
                   do j = 1,n
                       if (beta==zero) then
                           do i = j,n
                               c(i,j) = zero
                           end do
                       else if (beta/=one) then
                           c(j,j) = beta*real(c(j,j),KIND=dp)
                           do i = j + 1,n
                               c(i,j) = beta*c(i,j)
                           end do
                       else
                           c(j,j) = real(c(j,j),KIND=dp)
                       end if
                       do l = 1,k
                           if (a(j,l)/=cmplx(zero,KIND=dp)) then
                               temp = alpha*conjg(a(j,l))
                               c(j,j) = real(c(j,j),KIND=dp) + real(temp*a(j,l),KIND=dp)
                               do i = j + 1,n
                                   c(i,j) = c(i,j) + temp*a(i,l)
                               end do
                           end if
                       end do
                   end do
               end if
           else
              ! form  c := alpha*a**h*a + beta*c.
               if (upper) then
                   do j = 1,n
                       do i = 1,j - 1
                           temp = zero
                           do l = 1,k
                               temp = temp + conjg(a(l,i))*a(l,j)
                           end do
                           if (beta==zero) then
                               c(i,j) = alpha*temp
                           else
                               c(i,j) = alpha*temp + beta*c(i,j)
                           end if
                       end do
                       rtemp = zero
                       do l = 1,k
                           rtemp = rtemp + conjg(a(l,j))*a(l,j)
                       end do
                       if (beta==zero) then
                           c(j,j) = alpha*rtemp
                       else
                           c(j,j) = alpha*rtemp + beta*real(c(j,j),KIND=dp)
                       end if
                   end do
               else
                   do j = 1,n
                       rtemp = zero
                       do l = 1,k
                           rtemp = rtemp + conjg(a(l,j))*a(l,j)
                       end do
                       if (beta==zero) then
                           c(j,j) = alpha*rtemp
                       else
                           c(j,j) = alpha*rtemp + beta*real(c(j,j),KIND=dp)
                       end if
                       do i = j + 1,n
                           temp = zero
                           do l = 1,k
                               temp = temp + conjg(a(l,i))*a(l,j)
                           end do
                           if (beta==zero) then
                               c(i,j) = alpha*temp
                           else
                               c(i,j) = alpha*temp + beta*c(i,j)
                           end if
                       end do
                   end do
               end if
           end if
           return
     end subroutine stdlib_zherk