import jax
import jax.numpy as jnp

import jax_cosmo as jc

from jaxpm.kernels import fftk, gradient_kernel, laplace_kernel, longrange_kernel
from jaxpm.painting import cic_paint, cic_read
from jaxpm.growth import growth_factor, growth_rate, dGfa

def pm_forces(positions, mesh_shape=None, delta=None, r_split=0):
    """
    Computes gravitational forces on particles using a PM scheme
    """
    if mesh_shape is None:
        mesh_shape = delta.shape
    kvec = fftk(mesh_shape)

    if delta is None:
        delta_k = jnp.fft.rfftn(cic_paint(jnp.zeros(mesh_shape), positions))
    else:
        delta_k = jnp.fft.rfftn(delta)

    # Computes gravitational potential
    pot_k = delta_k * laplace_kernel(kvec) * longrange_kernel(kvec, r_split=r_split)
    # Computes gravitational forces
    return jnp.stack([cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i)*pot_k), positions) 
                      for i in range(3)],axis=-1)


def lpt(cosmo, initial_conditions, positions, a):
    """
    Computes first order LPT displacement
    """
    initial_force = pm_forces(positions, delta=initial_conditions)
    a = jnp.atleast_1d(a)
    dx = growth_factor(cosmo, a) * initial_force
    p = a**2 * growth_rate(cosmo, a) * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dx
    f = a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dGfa(cosmo, a) * initial_force
    return dx, p, f

def linear_field(mesh_shape, box_size, pk, seed):
    """
    Generate initial conditions.
    """
    kvec = fftk(mesh_shape)
    kmesh = sum((kk / box_size[i] * mesh_shape[i])**2 for i, kk in enumerate(kvec))**0.5
    pkmesh = pk(kmesh)

    field = jax.random.normal(seed, mesh_shape)
    field = jnp.fft.rfftn(field) * pkmesh**0.5
    field = jnp.fft.irfftn(field)
    return field

def make_ode_fn(mesh_shape):
    
    def nbody_ode(state, a, cosmo):
        """
        state is a tuple (position, velocities)
        """
        pos, vel = state

        forces = pm_forces(pos, mesh_shape=mesh_shape) * 1.5 * cosmo.Omega_m

        # Computes the update of position (drift)
        dpos = 1. / (a**3 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * vel
        
        # Computes the update of velocity (kick)
        dvel = 1. / (a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * forces
        
        return dpos, dvel

    return nbody_ode