from functools import partial

import jax.numpy as jnp
import numpy as np
from jax.sharding import PartitionSpec as P

from jaxpm.distributed import autoshmap


def fftk(shape, dtype=np.float32):
    """
    Generate Fourier transform wave numbers for a given mesh.

    Args:
        nc (int): Shape of the mesh grid.

    Returns:
        list: List of wave number arrays for each dimension in
        the order [kx, ky, kz].
  """
    kx, ky, kz = [jnp.fft.fftfreq(s, dtype=dtype) * 2 * np.pi for s in shape]

    @partial(autoshmap,
             in_specs=(P('x'), P('y'), P(None)),
             out_specs=(P('x'), P(None, 'y'), P(None)))
    def get_kvec(ky, kz, kx):
        return (ky.reshape([-1, 1, 1]),
                kz.reshape([1, -1, 1]),
                kx.reshape([1, 1, -1])) # yapf: disable
    ky, kz, kx = get_kvec(ky, kz, kx)  # The order corresponds
    # to the order of dimensions in the transposed FFT
    return kx, ky, kz


def gradient_kernel(kvec, direction, order=1):
    """
  Computes the gradient kernel in the requested direction
  Parameters:
  -----------
  kvec: array
    Array of k values in Fourier space
  direction: int
    Index of the direction in which to take the gradient
  Returns:
  --------
  wts: array
    Complex kernel
  """
    if order == 0:
        wts = 1j * kvec[direction]
        wts = jnp.squeeze(wts)
        wts[len(wts) // 2] = 0
        wts = wts.reshape(kvec[direction].shape)
        return wts
    else:
        w = kvec[direction]
        a = 1 / 6.0 * (8 * jnp.sin(w) - jnp.sin(2 * w))
        wts = a * 1j
        return wts


def laplace_kernel(kvec):
    """
  Compute the Laplace kernel from a given K vector
  Parameters:
  -----------
  kvec: array
    Array of k values in Fourier space
  Returns:
  --------
  wts: array
    Complex kernel
  """
    kk = sum(ki**2 for ki in kvec)
    wts = jnp.where(kk == 0, 1., 1. / kk)
    return wts


def longrange_kernel(kvec, r_split):
    """
  Computes a long range kernel
  Parameters:
  -----------
  kvec: array
    Array of k values in Fourier space
  r_split: float
    TODO: @modichirag add documentation
  Returns:
  --------
  wts: array
    kernel
  """
    if r_split != 0:
        kk = sum(ki**2 for ki in kvec)
        return np.exp(-kk * r_split**2)
    else:
        return 1.


def cic_compensation(kvec):
    """
  Computes cic compensation kernel.
  Adapted from https://github.com/bccp/nbodykit/blob/a387cf429d8cb4a07bb19e3b4325ffdf279a131e/nbodykit/source/mesh/catalog.py#L499
  Itself based on equation 18 (with p=2) of
        `Jing et al 2005 <https://arxiv.org/abs/astro-ph/0409240>`_
  Args:
    kvec: array of k values in Fourier space
  Returns:
    v: array of kernel
  """
    kwts = [np.sinc(kvec[i] / (2 * np.pi)) for i in range(3)]
    wts = (kwts[0] * kwts[1] * kwts[2])**(-2)
    return wts


def PGD_kernel(kvec, kl, ks):
    """
  Computes the PGD kernel
  Parameters:
  -----------
  kvec: array
    Array of k values in Fourier space
  kl: float
    initial long range scale parameter
  ks: float
    initial dhort range scale parameter
  Returns:
  --------
  v: array
    kernel
  """
    kk = sum(ki**2 for ki in kvec)
    kl2 = kl**2
    ks4 = ks**4
    mask = (kk == 0).nonzero()
    kk[mask] = 1
    v = jnp.exp(-kl2 / kk) * jnp.exp(-kk**2 / ks4)
    imask = (~(kk == 0)).astype(int)
    v *= imask
    return v