code: def diag_jacobian(
      x: FourierSeries,
      *,
      stagger=[0],
      correct_nyquist=True,
      params=None,
  ) -> FourierSeries:
      r"""Diagonal Jacobian operator for Fourier series fields.
  
      Args:
          x (FourierSeries): Input field
          stagger (list, optional): Staggering value for the returned fields.
            The fields are staggered in the direction of their derivative.
            Defaults to [0].
          correct_nyquist (bool, optional): If `True`, uses a correction of the
            derivative filter for the Nyquist frequency, which preserves Hermitian
            symmetric and null space. See [those notes](https://math.mit.edu/~stevenj/fft-deriv.pdf)
            for more details. Defaults to True.
  
      Returns:
          The vector field whose components are the diagonal entries
            of the Jacobian of the input field.
      """
      k_vec = params["k_vec"]
  
      # Adding staggering
      if len(stagger) == 1 and len(x.domain.N) != 1:
          stagger = stagger * len(x.domain.N)
  
      dx = x.domain.dx
      k_vec = [
          1j * k * jnp.exp(1j * k * s * delta)
          for k, delta, s in zip(k_vec, dx, stagger)
      ]
  
      # Set to zero the filter at the Nyquist frequency
      # if the dimension is even
      # see https://math.mit.edu/~stevenj/fft-deriv.pdf
      if correct_nyquist:
          for f in range(len(k_vec)):
              if x.domain.N[f] % 2 == 0:
                  f_nyq = x.domain.N[f] // 2
                  k_vec[f] = k_vec[f].at[f_nyq].set(0.0)
  
      new_params = jnp.zeros_like(x.params)
  
      def single_grad(axis, u):
          u = jnp.moveaxis(u, axis, -1)
          Fx = x._ffts[0](u, axis=-1)
          iku = Fx * k_vec[axis]
          du = x._ffts[1](iku, axis=-1, n=u.shape[-1])
          return jnp.moveaxis(du, -1, axis)
  
      for ax in range(x.domain.ndim):
          new_params = new_params.at[..., ax].set(
              single_grad(ax, x.params[..., ax])
          )
  
      return FourierSeries.from_grid(new_params, x.domain)
  
imports: from typing import Union
  import jax
  import numpy
  from jax import numpy
  from jaxdf.conv import fd_coefficients_fornberg, reflection_conv
  from jaxdf.core import operator
  from jaxdf.discretization import Continuous, FiniteDifferences, FourierSeries
label_desc: Use image node_id 13 for calling a global function with example usage: diag_jacobian(x) and returns: FourierSeries, jnp