import numpy as np
import scipy.signal as scp
from lenstronomy.Util import util
from lenstronomy.Util import image_util
from lenstronomy.Util import kernel_util
"""
class to compute lensing potentials and deflection angles provided a convergence map
"""

from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()


@export
def potential_from_kappa_grid(kappa, grid_spacing):
    """
    Lensing potential :math:`\\psi ({\\vec {\\theta }})` on the convergence grid :math:`\\kappa`.

    .. math::
        \\psi ({\\vec {\\theta }})={\\frac {1}{\\pi }}\\int d^{2}\\theta ^{\\prime }
        \\kappa ({\\vec {\\theta }}^{\\prime })\\ln |{\\vec {\\theta }}-{\\vec {\\theta }}^{\\prime }|

    The computation is performed as a convolution of the Green's function with the convergence map using FFT.

    :param kappa: 2d grid of convergence values
    :param grid_spacing: scale of an individual pixel (per axis) of grid
    :return: lensing potential in a 2d grid at positions x_grid, y_grid
    """
    num_pix = len(kappa) * 2
    if num_pix % 2 == 0:
        num_pix += 1
    kernel = potential_kernel(num_pix, grid_spacing)
    f_ = scp.fftconvolve(kappa, kernel, mode='same') / np.pi * grid_spacing ** 2
    return f_


@export
def potential_from_kappa_grid_adaptive(kappa_high_res, grid_spacing, low_res_factor, high_res_kernel_size):
    """
    lensing potential on the convergence grid
    the computation is performed as a convolution of the Green's function with the convergence map using FFT

    :param kappa_high_res: 2d grid of convergence values
    :param grid_spacing: scale of an individual pixel (per axis) of grid
    :param low_res_factor: lower resolution factor of larger scale kernel.
    :param high_res_kernel_size: int, size of high resolution kernel in units of degraded pixels
    :return: lensing potential in a 2d grid at positions x_grid, y_grid
    """
    kappa_low_res = image_util.re_size(kappa_high_res, factor=low_res_factor)
    num_pix = len(kappa_high_res) * 2
    if num_pix % 2 == 0:
        num_pix += 1
    grid_spacing_low_res = grid_spacing * low_res_factor
    kernel = potential_kernel(num_pix, grid_spacing)
    kernel_low_res, kernel_high_res = kernel_util.split_kernel(kernel, high_res_kernel_size, low_res_factor,
                                                               normalized=False)

    f_high_res = scp.fftconvolve(kappa_high_res, kernel_high_res, mode='same') / np.pi * grid_spacing ** 2
    f_high_res = image_util.re_size(f_high_res, low_res_factor)
    f_low_res = scp.fftconvolve(kappa_low_res, kernel_low_res, mode='same') / np.pi * grid_spacing_low_res ** 2
    return f_high_res + f_low_res


@export
def deflection_from_kappa_grid(kappa, grid_spacing):
    """
    Deflection angle :math:`\\vec {\\alpha }}` from a convergence grid :math:`\\kappa`.

    .. math::
        {\\vec {\\alpha }}({\\vec {\\theta }})={\\frac {1}{\\pi }}
        \\int d^{2}\\theta ^{\\prime }{\\frac {({\\vec {\\theta }}-{\\vec {\\theta }}^{\\prime })
        \\kappa ({\\vec {\\theta }}^{\\prime })}{|{\\vec {\\theta }}-{\\vec {\\theta }}^{\\prime }|^{2}}}

    The computation is performed as a convolution of the Green's function with the convergence map using FFT.

    :param kappa: convergence values for each pixel (2-d array)
    :param grid_spacing: scale of an individual pixel (per axis) of grid
    :return: numerical deflection angles in x- and y- direction over the convergence grid points
    """
    num_pix = len(kappa) * 2
    if num_pix % 2 == 0:
        num_pix += 1
    kernel_x, kernel_y = deflection_kernel(num_pix, grid_spacing)
    f_x = scp.fftconvolve(kappa, kernel_x, mode='same') / np.pi * grid_spacing ** 2
    f_y = scp.fftconvolve(kappa, kernel_y, mode='same') / np.pi * grid_spacing ** 2
    return f_x, f_y


@export
def deflection_from_kappa_grid_adaptive(kappa_high_res, grid_spacing, low_res_factor, high_res_kernel_size):
    """
    deflection angles on the convergence grid with adaptive FFT
    the computation is performed as a convolution of the Green's function with the convergence map using FFT
    The grid is returned in the lower resolution grid

    :param kappa_high_res: convergence values for each pixel (2-d array)
    :param grid_spacing: pixel size of high resolution grid
    :param low_res_factor: lower resolution factor of larger scale kernel.
    :param high_res_kernel_size: int, size of high resolution kernel in units of degraded pixels
    :return: numerical deflection angles in x- and y- direction
    """
    kappa_low_res = image_util.re_size(kappa_high_res, factor=low_res_factor)
    num_pix = len(kappa_high_res) * 2
    if num_pix % 2 == 0:
        num_pix += 1

    kernel_x, kernel_y = deflection_kernel(num_pix, grid_spacing)
    grid_spacing_low_res = grid_spacing * low_res_factor

    kernel_low_res_x, kernel_high_res_x = kernel_util.split_kernel(kernel_x, high_res_kernel_size, low_res_factor,
                                                                   normalized=False)
    f_x_high_res = scp.fftconvolve(kappa_high_res, kernel_high_res_x, mode='same') / np.pi * grid_spacing ** 2
    f_x_high_res = image_util.re_size(f_x_high_res, low_res_factor)
    f_x_low_res = scp.fftconvolve(kappa_low_res, kernel_low_res_x, mode='same') / np.pi * grid_spacing_low_res ** 2
    f_x = f_x_high_res + f_x_low_res

    kernel_low_res_y, kernel_high_res_y = kernel_util.split_kernel(kernel_y, high_res_kernel_size, low_res_factor,
                                                                   normalized=False)
    f_y_high_res = scp.fftconvolve(kappa_high_res, kernel_high_res_y, mode='same') / np.pi * grid_spacing ** 2
    f_y_high_res = image_util.re_size(f_y_high_res, low_res_factor)
    f_y_low_res = scp.fftconvolve(kappa_low_res, kernel_low_res_y, mode='same') / np.pi * grid_spacing_low_res ** 2
    f_y = f_y_high_res + f_y_low_res
    return f_x, f_y


@export
def potential_kernel(num_pix, delta_pix):
    """
    numerical gridded integration kernel for convergence to lensing kernel with given pixel size

    :param num_pix: integer; number of pixels of kernel per axis
    :param delta_pix: pixel size (per dimension in units of angle)
    :return: kernel for lensing potential
    """
    x_shift, y_shift = util.make_grid(numPix=num_pix, deltapix=delta_pix)
    r2 = x_shift ** 2 + y_shift ** 2
    r2_max = np.max(r2)
    r2[r2 < (delta_pix / 2) ** 2] = (delta_pix / 2) ** 2
    lnr = np.log(r2/r2_max) / 2.
    kernel = util.array2image(lnr)
    return kernel


@export
def deflection_kernel(num_pix, delta_pix):
    """
    numerical gridded integration kernel for convergence to deflection angle with given pixel size

    :param num_pix: integer; number of pixels of kernel per axis, should be odd number to have a defined center
    :param delta_pix: pixel size (per dimension in units of angle)
    :return: kernel for x-direction and kernel of y-direction deflection angles
    """
    x_shift, y_shift = util.make_grid(numPix=num_pix, deltapix=delta_pix)
    r2 = x_shift**2 + y_shift**2
    r2[r2 < (delta_pix/2)**2] = (delta_pix/2) ** 2

    kernel_x = util.array2image(x_shift / r2)
    kernel_y = util.array2image(y_shift / r2)
    return kernel_x, kernel_y
