update Subroutine

  pure subroutine update(self, dw, db, eta)
    !! Updates network weights and biases with gradients dw and db,
    !! scaled by learning rate eta.
    class(network_type), intent(in out) :: self
    class(array2d), intent(in) :: dw(:)
    class(array1d), intent(in) :: db(:)
    real(rk), intent(in) :: eta
    integer(ik) :: n

    associate(layers => self % layers, nm => size(self % dims))
      !! update biases
      do concurrent(n = 2:nm)
        layers(n) % b = layers(n) % b - eta * db(n) % array
      end do
      !! update weights
      do concurrent(n = 1:nm-1)
        layers(n) % w = layers(n) % w - eta * dw(n) % array
      end do
    end associate

  end subroutine update