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c
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c
      subroutine cdotc3(m,n,k,a,b,c)
c purpose:      a 3-dimensional dot product.
c               c = sum (conj (a) .* b, 2), where a and b are 3d arrays.
c arguments:
c m,n,k (in)    the dimensions of a and b
c a,b (in)      complex input arrays of size (m,k,n)
c c (out)       complex output array, size (m,n)
      integer m,n,k,i,j,l
      complex a(m,k,n),b(m,k,n)
      complex c(m,n)

      complex cdotc
      external cdotc

c quick return if possible.
      if (m <= 0 .or. n <= 0) return

      if (m == 1) then
c the column-major case.
        do j = 1,n
          c(1,j) = cdotc(k,a(1,1,j),1,b(1,1,j),1)
        end do
      else
c We prefer performance here, because that's what we generally
c do by default in reduction functions. Besides, the accuracy
c of xDOT is questionable. Hence, do a cache-aligned nested loop.
        do j = 1,n
          do i = 1,m
            c(i,j) = 0e0
          end do
          do l = 1,k
            do i = 1,m
              c(i,j) = c(i,j) + conjg(a(i,l,j))*b(i,l,j)
            end do
          end do
        end do
      end if

      end subroutine
