import jax
import jax.lax as lax
import jax.numpy as jnp

from jaxpm.kernels import cic_compensation, fftk
from jax.sharding import PartitionSpec as P
from functools import partial
from jaxpm.distributed import autoshmap

@partial(autoshmap, 
        in_specs=(P('x', 'y'), P('x','y'), P('x','y')), 
        out_specs=P('x', 'y'))
def cic_paint(mesh, displacement, weight=None):
    """ Paints positions onto mesh
    mesh: [nx, ny, nz]
    displacement field: [nx, ny, nz, 3]
    """
    part_shape = displacement.shape
    positions = jnp.stack(jnp.meshgrid(
        jnp.arange(part_shape[0]),
        jnp.arange(part_shape[1]),
        jnp.arange(part_shape[2]),
        indexing='ij'), axis=-1) + displacement
    positions = positions.reshape([-1, 3])
    positions = jnp.expand_dims(positions, 1)
    floor = jnp.floor(positions)
    connection = jnp.array([[[0, 0, 0], [1., 0, 0], [0., 1, 0], [0., 0, 1],
                             [1., 1, 0], [1., 0, 1], [0., 1, 1], [1., 1, 1]]])

    neighboor_coords = floor + connection
    kernel = 1. - jnp.abs(positions - neighboor_coords)
    kernel = kernel[..., 0] * kernel[..., 1] * kernel[..., 2]
    if weight is not None:
        kernel = jnp.multiply(jnp.expand_dims(weight, axis=-1), kernel)

    neighboor_coords = jnp.mod(
        neighboor_coords.reshape([-1, 8, 3]).astype('int32'),
        jnp.array(mesh.shape))

    dnums = jax.lax.ScatterDimensionNumbers(update_window_dims=(),
                                            inserted_window_dims=(0, 1, 2),
                                            scatter_dims_to_operand_dims=(0, 1,
                                                                          2))
    mesh = lax.scatter_add(mesh, neighboor_coords, kernel.reshape([-1, 8]),
                           dnums)
    return mesh


@partial(autoshmap, 
        in_specs=(P('x', 'y'), P('x','y')), 
        out_specs=P('x', 'y'))
def cic_read(mesh, displacement):
    """ Paints positions onto mesh
  mesh: [nx, ny, nz]
  displacement: [nx,ny,nz, 3]
  """
    # Compute the position of the particles on a regular grid
    part_shape = displacement.shape
    positions = jnp.stack(jnp.meshgrid(
        jnp.arange(part_shape[0]),
        jnp.arange(part_shape[1]),
        jnp.arange(part_shape[2]),
        indexing='ij'), axis=-1) + displacement
    positions = positions.reshape([-1, 3])
    positions = jnp.expand_dims(positions, 1)
    floor = jnp.floor(positions)
    connection = jnp.array([[[0, 0, 0], [1., 0, 0], [0., 1, 0], [0., 0, 1],
                             [1., 1, 0], [1., 0, 1], [0., 1, 1], [1., 1, 1]]])

    neighboor_coords = floor + connection
    kernel = 1. - jnp.abs(positions - neighboor_coords)
    kernel = kernel[..., 0] * kernel[..., 1] * kernel[..., 2]

    neighboor_coords = jnp.mod(neighboor_coords.astype('int32'),
                               jnp.array(mesh.shape))

    return (mesh[neighboor_coords[..., 0], neighboor_coords[..., 1],
                 neighboor_coords[..., 3]] * kernel).sum(axis=-1).reshape(displacement.shape[:-1])


def cic_paint_2d(mesh, positions, weight):
    """ Paints positions onto a 2d mesh
  mesh: [nx, ny]
  positions: [npart, 2]
  weight: [npart]
  """
    positions = jnp.expand_dims(positions, 1)
    floor = jnp.floor(positions)
    connection = jnp.array([[0, 0], [1., 0], [0., 1], [1., 1]])

    neighboor_coords = floor + connection
    kernel = 1. - jnp.abs(positions - neighboor_coords)
    kernel = kernel[..., 0] * kernel[..., 1]
    if weight is not None:
        kernel = kernel * weight[..., jnp.newaxis]

    neighboor_coords = jnp.mod(
        neighboor_coords.reshape([-1, 4, 2]).astype('int32'),
        jnp.array(mesh.shape))

    dnums = jax.lax.ScatterDimensionNumbers(update_window_dims=(),
                                            inserted_window_dims=(0, 1),
                                            scatter_dims_to_operand_dims=(0,
                                                                          1))
    mesh = lax.scatter_add(mesh, neighboor_coords, kernel.reshape([-1, 4]),
                           dnums)
    return mesh


def compensate_cic(field):
    """
  Compensate for CiC painting
  Args:
    field: input 3D cic-painted field
  Returns:
    compensated_field
  """
    nc = field.shape
    kvec = fftk(nc)

    delta_k = jnp.fft.rfftn(field)
    delta_k = cic_compensation(kvec) * delta_k
    return jnp.fft.irfftn(delta_k)