<gh_stars>1-10
from lenstronomy.Data.psf import PSF
import lenstronomy.Util.util as util
import lenstronomy.Util.image_util as image_util
import lenstronomy.Util.kernel_util as kernel_util
import lenstronomy.Util.mask as mask_util

import numpy as np
import copy
import scipy.ndimage.interpolation as interp


class PsfFitting(object):
    """
    class to find subsequently a better psf
    The method make use of a model and subtracts all the non-point source components of the model from the data.
    If the model is sufficient, then the data will be a (better) representation of the actual PSF. The method cuts out
    those point sources and combines them to update the estimate of the PSF. This is done in an iterative procedure as
    the model components of the extended features is PSF-dependent (hopefully not too much).

    Various options can be chosen. There is no quarante that the method works for specific data and models.

    'stacking_method': 'median', 'mean'; the different estimates of the PSF are stacked and combined together. The choices are:
        'mean': mean of pixel values as the estimator (not robust to outliers)
        'median': median of pixel values as the estimator (outlier rejection robust but needs >2 point sources in the data

    'block_center_neighbour': angle, radius of neighbouring point sources around their centers the estimates is ignored.
        Default is zero, meaning a not optimal subtraction of the neighbouring point sources might contaminate the estimate.

    'keep_error_map': bool, if True, does not replace the error term associated with the PSF estimate.
        If false, re-estimates the variance between the PSF estimates.


    The procedure only requires and changes the 'point_source_kernel' in the PSF() class and the 'psf_error_map'.
    Any previously set subgrid kernels or pixel_kernels are removed and constructed from the 'point_source_kernel'.

    """
    def __init__(self, image_model_class, kwargs_psf_iter={}):
        self._image_model_class = image_model_class
        self._stacking_method = kwargs_psf_iter.get('stacking_method', 'median')
        self._block_center_neighbour = kwargs_psf_iter.get('block_center_neighbour', 0)
        self._keep_psf_error_map = kwargs_psf_iter.get('keep_error_map', True)
        self._psf_symmetry = kwargs_psf_iter.get('psf_symmetry', 1)

    def update_psf(self, kwargs_psf, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, factor=1):
        """

        :param kwargs_data:
        :param kwargs_psf:
        :param kwargs_options:
        :param kwargs_lens:
        :param kwargs_source:
        :param kwargs_lens_light:
        :param kwargs_ps:
        :return:
        """
        psf_class = PSF(kwargs_psf)
        self._image_model_class.update_psf(psf_class)

        kernel_old = psf_class.kernel_point_source
        kernel_size = len(kernel_old)
        #kwargs_numerics_psf['psf_error_map'] = False
        kwargs_psf_copy = copy.deepcopy(kwargs_psf)
        kwargs_psf_new = {'psf_type': 'PIXEL', 'kernel_point_source': kwargs_psf_copy['kernel_point_source']}
        if 'psf_error_map' in kwargs_psf_copy:
            kwargs_psf_new['psf_error_map'] = kwargs_psf_copy['psf_error_map'] / 10
        self._image_model_class.update_psf(PSF(kwargs_psf_new))
        image_single_point_source_list = self.image_single_point_source(self._image_model_class, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)
        ra_image, dec_image, amp = self._image_model_class.PointSource.point_source_list(kwargs_ps, kwargs_lens)
        x_, y_ = self._image_model_class.Data.map_coord2pix(ra_image, dec_image)

        point_source_list = self.cutout_psf(ra_image, dec_image, x_, y_, image_single_point_source_list, kernel_size, kernel_old)

        kernel_new, error_map = self.combine_psf(point_source_list, kernel_old,
                                                 sigma_bkg=self._image_model_class.Data.background_rms, factor=factor,
                                                 stacking_option=self._stacking_method, symmetry=self._psf_symmetry)
        kernel_new = kernel_util.cut_psf(kernel_new, psf_size=kernel_size)

        kwargs_psf_new['kernel_point_source'] = kernel_new
        if 'psf_error_map' in kwargs_psf_new:
            kwargs_psf_new['psf_error_map'] *= 10
        self._image_model_class.update_psf(PSF(kwargs_psf_new))
        logL_after = self._image_model_class.likelihood_data_given_model(kwargs_lens, kwargs_source,
                                                               kwargs_lens_light, kwargs_ps)
        return kwargs_psf_new, logL_after, error_map

    def update_iterative(self, kwargs_psf, kwargs_lens, kwargs_source, kwargs_lens_light,
                   kwargs_ps, factor=1, num_iter=10, verbose=True, no_break=False):
        """

        :param kwargs_data:
        :param kwargs_psf:
        :param kwargs_options:
        :param kwargs_lens:
        :param kwargs_source:
        :param kwargs_lens_light:
        :param kwargs_ps:
        :param factor:
        :param num_iter:
        :return:
        """
        self._image_model_class.PointSource.set_save_cache(True)
        if not 'kernel_point_source_init' in kwargs_psf:
            kernel_point_source_init = copy.deepcopy(kwargs_psf['kernel_point_source'])
        else:
            kernel_point_source_init = kwargs_psf['kernel_point_source_init']
        kwargs_psf_new = copy.deepcopy(kwargs_psf)
        kwargs_psf_final = copy.deepcopy(kwargs_psf)
        if 'psf_error_map' in kwargs_psf:
            error_map_final = kwargs_psf['psf_error_map']
        else:
            error_map_final = np.zeros_like(kernel_point_source_init)
        error_map_init = copy.deepcopy(error_map_final)
        psf_class = PSF(kwargs_psf)
        self._image_model_class.update_psf(psf_class)
        logL_before = self._image_model_class.likelihood_data_given_model(kwargs_lens, kwargs_source,
                                                                          kwargs_lens_light, kwargs_ps)
        logL_best = copy.deepcopy(logL_before)
        i_best = 0
        for i in range(num_iter):
            kwargs_psf_new, logL_after, error_map = self.update_psf(kwargs_psf_new, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, factor=factor)
            if logL_after > logL_best:
                kwargs_psf_final = copy.deepcopy(kwargs_psf_new)
                error_map_final = copy.deepcopy(error_map)
                logL_best = logL_after
                i_best = i + 1
            else:
                if not no_break:
                    if verbose:
                        print("iterative PSF reconstruction makes reconstruction worse in step %s - aborted" % i)
                    break
        if verbose is True:
            print("iteration of step %s gave best reconstruction." % i_best)
            print("log likelihood before: %s and log likelihood after: %s" % (logL_before, logL_best))
        if self._keep_psf_error_map is True:
            kwargs_psf_final['psf_error_map'] = error_map_init
        else:
            kwargs_psf_final['psf_error_map'] = error_map_final
        kwargs_psf_final['kernel_point_source_init'] = kernel_point_source_init
        return kwargs_psf_final

    def image_single_point_source(self, image_model_class, kwargs_lens, kwargs_source, kwargs_lens_light,
                                  kwargs_ps):
        """
        return model without including the point source contributions as a list (for each point source individually)
        :param image_model_class: ImageModel class instance
        :param kwargs_lens: lens model kwargs list
        :param kwargs_source: source model kwargs list
        :param kwargs_lens_light: lens light model kwargs list
        :param kwargs_ps: point source model kwargs list
        :return: list of images with point source isolated
        """
        # reconstructed model with given psf
        model, error_map, cov_param, param = image_model_class.image_linear_solve(kwargs_lens, kwargs_source,
                                                                              kwargs_lens_light, kwargs_ps)
        #model = image_model_class.image(kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)
        data = image_model_class.Data.data
        mask = image_model_class.ImageNumerics.mask
        point_source_list = image_model_class.point_sources_list(kwargs_ps, kwargs_lens)
        n = len(point_source_list)
        model_single_source_list = []
        for i in range(n):
            model_single_source = (data - model + point_source_list[i]) * mask
            model_single_source_list.append(model_single_source)
        return model_single_source_list

    def cutout_psf(self, ra_image, dec_image, x, y, image_list, kernelsize, kernel_init):
        """

        :param x_:
        :param y_:
        :param image_list: list of images (i.e. data - all models subtracted, except a single point source)
        :param kernelsize:
        :return:
        """
        mask = self._image_model_class.ImageNumerics.mask
        ra_grid, dec_grid = self._image_model_class.Data.coordinates
        ra_grid = util.image2array(ra_grid)
        dec_grid = util.image2array(dec_grid)
        radius = self._block_center_neighbour

        kernel_list = []
        for l in range(len(x)):
            mask_point_source = self.mask_point_source(ra_image, dec_image, ra_grid, dec_grid, radius, i=l)
            mask_i = mask * mask_point_source
            kernel_deshifted = self.cutout_psf_single(x[l], y[l], image_list[l], mask_i, kernelsize, kernel_init)
            kernel_list.append(kernel_deshifted)
        return kernel_list

    def cutout_psf_single(self, x, y, image, mask, kernelsize, kernel_init):
        """

        :param x: x-coordinate of point soure
        :param y: y-coordinate of point source
        :param image: image (i.e. data - all models subtracted, except a single point source)
        :param mask: mask of pixels in the image not to be considered in the PSF estimate (being replaced by kernel_init)
        :param kernelsize: width in pixel of the kernel
        :param kernel_init: initial guess of kernel (pixels that are masked are replaced by those values)
        :return: estimate of the PSF based on the image and position of the point source
        """
        # cutout the star
        x_int = int(round(x))
        y_int = int(round(y))
        star_cutout = kernel_util.cutout_source(x_int, y_int, image, kernelsize + 2, shift=False)
        # cutout the mask
        mask_cutout = kernel_util.cutout_source(x_int, y_int, mask, kernelsize + 2, shift=False)
        # enlarge the initial PSF kernel to the new cutout size
        kernel_enlarged = np.zeros((kernelsize+2, kernelsize+2))
        kernel_enlarged[1:-1, 1:-1] = kernel_init
        # shift the initial kernel to the shift of the star
        shift_x = x_int - x
        shift_y = y_int - y
        kernel_shifted = interp.shift(kernel_enlarged, [-shift_y, -shift_x], order=1)
        # compute normalization of masked and unmasked region of the shifted kernel
        # norm_masked = np.sum(kernel_shifted[mask_i == 0])
        norm_unmasked = np.sum(kernel_shifted[mask_cutout == 1])
        # normalize star within the unmasked region to the norm of the initial kernel of the same region
        star_cutout /= np.sum(star_cutout[mask_cutout == 1]) * norm_unmasked
        # replace mask with shifted initial kernel (+2 size)
        star_cutout[mask_cutout == 0] = kernel_shifted[mask_cutout == 0]
        star_cutout[star_cutout < 0] = 0
        # de-shift kernel
        kernel_deshifted = kernel_util.de_shift_kernel(star_cutout, shift_x, shift_y)
        # re-size kernel
        kernel_deshifted = image_util.cut_edges(kernel_deshifted, kernelsize)
        # re-normalize kernel again
        kernel_deshifted = kernel_util.kernel_norm(kernel_deshifted)
        return kernel_deshifted

    @staticmethod
    def combine_psf(kernel_list_new, kernel_old, sigma_bkg, factor=1, stacking_option='median', symmetry=1):
        """
        updates psf estimate based on old kernel and several new estimates
        :param kernel_list_new: list of new PSF kernels estimated from the point sources in the image
        :param kernel_old: old PSF kernel
        :param sigma_bkg: estimated background noise in the image
        :param factor: weight of updated estimate based on new and old estimate, factor=1 means new estimate,
        factor=0 means old estimate
        :param stacking_option: option of stacking, mean or median
        :param symmetry: imposed symmetry of PSF estimate
        :return: updated PSF estimate and error_map associated with it
        """

        n = int(len(kernel_list_new) * symmetry)
        angle = 360. / symmetry
        kernelsize = len(kernel_old)
        kernel_list = np.zeros((n, kernelsize, kernelsize))
        i = 0
        for kernel_new in kernel_list_new:
            for k in range(symmetry):
                kernel_rotated = image_util.rotateImage(kernel_new, angle * k)
                kernel_norm = kernel_util.kernel_norm(kernel_rotated)
                kernel_list[i, :, :] = kernel_norm
                i += 1

        kernel_old_rotated = np.zeros((symmetry, kernelsize, kernelsize))
        for i in range(symmetry):
            kernel_old_rotated[i, :, :] = kernel_old

        kernel_list_new = np.append(kernel_list, kernel_old_rotated, axis=0)
        if stacking_option == 'median':
            kernel_new = np.median(kernel_list_new, axis=0)
        elif stacking_option == 'mean':
            kernel_new = np.mean(kernel_list_new, axis=0)
        else:
            raise ValueError(" stack_option must be 'median' or 'mean', %s is not supported." % stacking_option)
        kernel_new[kernel_new < 0] = 0
        kernel_new = kernel_util.kernel_norm(kernel_new)
        kernel_return = factor * kernel_new + (1.-factor)* kernel_old

        kernel_bkg = copy.deepcopy(kernel_return)
        kernel_bkg[kernel_bkg < sigma_bkg] = sigma_bkg
        error_map = np.var(kernel_list_new, axis=0) / kernel_bkg**2 / 2.
        return kernel_return, error_map

    @staticmethod
    def mask_point_source(x_pos, y_pos, x_grid, y_grid, radius, i=0):
        """

        :param x_pos: x-position of list of point sources
        :param y_pos: y-position of list of point sources
        :param x_grid: x-coordinates of grid
        :param y_grid: y-coordinates of grid
        :param i: index of point source not to mask out
        :param radius: radius to mask out other point sources
        :return: a mask of the size of the image with cutouts around the position
        """
        mask = np.ones_like(x_grid)
        for k in range(len(x_pos)):
            if k != i:
                mask_point = 1 - mask_util.mask_sphere(x_grid, y_grid, x_pos[k], y_pos[k], radius)
                mask *= mask_point
        return util.array2image(mask)

from lenstronomy.Data.psf import PSF
import lenstronomy.Util.util as util
import lenstronomy.Util.image_util as image_util
import lenstronomy.Util.kernel_util as kernel_util
import lenstronomy.Util.mask as mask_util

import numpy as np
import copy
import scipy.ndimage.interpolation as interp


class PsfFitting(object):
    """
    class to find subsequently a better psf
    The method make use of a model and subtracts all the non-point source components of the model from the data.
    If the model is sufficient, then the data will be a (better) representation of the actual PSF. The method cuts out
    those point sources and combines them to update the estimate of the PSF. This is done in an iterative procedure as
    the model components of the extended features is PSF-dependent (hopefully not too much).

    Various options can be chosen. There is no quarante that the method works for specific data and models.

    'stacking_method': 'median', 'mean'; the different estimates of the PSF are stacked and combined together. The choices are:
        'mean': mean of pixel values as the estimator (not robust to outliers)
        'median': median of pixel values as the estimator (outlier rejection robust but needs >2 point sources in the data

    'block_center_neighbour': angle, radius of neighbouring point sources around their centers the estimates is ignored.
        Default is zero, meaning a not optimal subtraction of the neighbouring point sources might contaminate the estimate.

    'keep_error_map': bool, if True, does not replace the error term associated with the PSF estimate.
        If false, re-estimates the variance between the PSF estimates.


    The procedure only requires and changes the 'point_source_kernel' in the PSF() class and the 'psf_error_map'.
    Any previously set subgrid kernels or pixel_kernels are removed and constructed from the 'point_source_kernel'.

    """
    def __init__(self, image_model_class, kwargs_psf_iter={}):
        self._image_model_class = image_model_class
        self._stacking_method = kwargs_psf_iter.get('stacking_method', 'median')
        self._block_center_neighbour = kwargs_psf_iter.get('block_center_neighbour', 0)
        self._keep_psf_error_map = kwargs_psf_iter.get('keep_error_map', True)
        self._psf_symmetry = kwargs_psf_iter.get('psf_symmetry', 1)

    def update_psf(self, kwargs_psf, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, factor=1):
        """

        :param kwargs_data:
        :param kwargs_psf:
        :param kwargs_options:
        :param kwargs_lens:
        :param kwargs_source:
        :param kwargs_lens_light:
        :param kwargs_ps:
        :return:
        """
        psf_class = PSF(kwargs_psf)
        self._image_model_class.update_psf(psf_class)

        kernel_old = psf_class.kernel_point_source
        kernel_size = len(kernel_old)
        #kwargs_numerics_psf['psf_error_map'] = False
        kwargs_psf_copy = copy.deepcopy(kwargs_psf)
        kwargs_psf_new = {'psf_type': 'PIXEL', 'kernel_point_source': kwargs_psf_copy['kernel_point_source']}
        if 'psf_error_map' in kwargs_psf_copy:
            kwargs_psf_new['psf_error_map'] = kwargs_psf_copy['psf_error_map'] / 10
        self._image_model_class.update_psf(PSF(kwargs_psf_new))
        image_single_point_source_list = self.image_single_point_source(self._image_model_class, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)
        ra_image, dec_image, amp = self._image_model_class.PointSource.point_source_list(kwargs_ps, kwargs_lens)
        x_, y_ = self._image_model_class.Data.map_coord2pix(ra_image, dec_image)

        point_source_list = self.cutout_psf(ra_image, dec_image, x_, y_, image_single_point_source_list, kernel_size, kernel_old)

        kernel_new, error_map = self.combine_psf(point_source_list, kernel_old,
                                                 sigma_bkg=self._image_model_class.Data.background_rms, factor=factor,
                                                 stacking_option=self._stacking_method, symmetry=self._psf_symmetry)
        kernel_new = kernel_util.cut_psf(kernel_new, psf_size=kernel_size)

        kwargs_psf_new['kernel_point_source'] = kernel_new
        if 'psf_error_map' in kwargs_psf_new:
            kwargs_psf_new['psf_error_map'] *= 10
        self._image_model_class.update_psf(PSF(kwargs_psf_new))
        logL_after = self._image_model_class.likelihood_data_given_model(kwargs_lens, kwargs_source,
                                                               kwargs_lens_light, kwargs_ps)
        return kwargs_psf_new, logL_after, error_map

    def update_iterative(self, kwargs_psf, kwargs_lens, kwargs_source, kwargs_lens_light,
                   kwargs_ps, factor=1, num_iter=10, verbose=True, no_break=False):
        """

        :param kwargs_data:
        :param kwargs_psf:
        :param kwargs_options:
        :param kwargs_lens:
        :param kwargs_source:
        :param kwargs_lens_light:
        :param kwargs_ps:
        :param factor:
        :param num_iter:
        :return:
        """
        self._image_model_class.PointSource.set_save_cache(True)
        if not 'kernel_point_source_init' in kwargs_psf:
            kernel_point_source_init = copy.deepcopy(kwargs_psf['kernel_point_source'])
        else:
            kernel_point_source_init = kwargs_psf['kernel_point_source_init']
        kwargs_psf_new = copy.deepcopy(kwargs_psf)
        kwargs_psf_final = copy.deepcopy(kwargs_psf)
        if 'psf_error_map' in kwargs_psf:
            error_map_final = kwargs_psf['psf_error_map']
        else:
            error_map_final = np.zeros_like(kernel_point_source_init)
        error_map_init = copy.deepcopy(error_map_final)
        psf_class = PSF(kwargs_psf)
        self._image_model_class.update_psf(psf_class)
        logL_before = self._image_model_class.likelihood_data_given_model(kwargs_lens, kwargs_source,
                                                                          kwargs_lens_light, kwargs_ps)
        logL_best = copy.deepcopy(logL_before)
        i_best = 0
        for i in range(num_iter):
            kwargs_psf_new, logL_after, error_map = self.update_psf(kwargs_psf_new, kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps, factor=factor)
            if logL_after > logL_best:
                kwargs_psf_final = copy.deepcopy(kwargs_psf_new)
                error_map_final = copy.deepcopy(error_map)
                logL_best = logL_after
                i_best = i + 1
            else:
                if not no_break:
                    if verbose:
                        print("iterative PSF reconstruction makes reconstruction worse in step %s - aborted" % i)
                    break
        if verbose is True:
            print("iteration of step %s gave best reconstruction." % i_best)
            print("log likelihood before: %s and log likelihood after: %s" % (logL_before, logL_best))
        if self._keep_psf_error_map is True:
            kwargs_psf_final['psf_error_map'] = error_map_init
        else:
            kwargs_psf_final['psf_error_map'] = error_map_final
        kwargs_psf_final['kernel_point_source_init'] = kernel_point_source_init
        return kwargs_psf_final

    def image_single_point_source(self, image_model_class, kwargs_lens, kwargs_source, kwargs_lens_light,
                                  kwargs_ps):
        """
        return model without including the point source contributions as a list (for each point source individually)
        :param image_model_class: ImageModel class instance
        :param kwargs_lens: lens model kwargs list
        :param kwargs_source: source model kwargs list
        :param kwargs_lens_light: lens light model kwargs list
        :param kwargs_ps: point source model kwargs list
        :return: list of images with point source isolated
        """
        # reconstructed model with given psf
        model, error_map, cov_param, param = image_model_class.image_linear_solve(kwargs_lens, kwargs_source,
                                                                              kwargs_lens_light, kwargs_ps)
        #model = image_model_class.image(kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps)
        data = image_model_class.Data.data
        mask = image_model_class.ImageNumerics.mask
        point_source_list = image_model_class.point_sources_list(kwargs_ps, kwargs_lens)
        n = len(point_source_list)
        model_single_source_list = []
        for i in range(n):
            model_single_source = (data - model + point_source_list[i]) * mask
            model_single_source_list.append(model_single_source)
        return model_single_source_list

    def cutout_psf(self, ra_image, dec_image, x, y, image_list, kernelsize, kernel_init):
        """

        :param x_:
        :param y_:
        :param image_list: list of images (i.e. data - all models subtracted, except a single point source)
        :param kernelsize:
        :return:
        """
        mask = self._image_model_class.ImageNumerics.mask
        ra_grid, dec_grid = self._image_model_class.Data.coordinates
        ra_grid = util.image2array(ra_grid)
        dec_grid = util.image2array(dec_grid)
        radius = self._block_center_neighbour

        kernel_list = []
        for l in range(len(x)):
            mask_point_source = self.mask_point_source(ra_image, dec_image, ra_grid, dec_grid, radius, i=l)
            mask_i = mask * mask_point_source
            kernel_deshifted = self.cutout_psf_single(x[l], y[l], image_list[l], mask_i, kernelsize, kernel_init)
            kernel_list.append(kernel_deshifted)
        return kernel_list

    def cutout_psf_single(self, x, y, image, mask, kernelsize, kernel_init):
        """

        :param x: x-coordinate of point soure
        :param y: y-coordinate of point source
        :param image: image (i.e. data - all models subtracted, except a single point source)
        :param mask: mask of pixels in the image not to be considered in the PSF estimate (being replaced by kernel_init)
        :param kernelsize: width in pixel of the kernel
        :param kernel_init: initial guess of kernel (pixels that are masked are replaced by those values)
        :return: estimate of the PSF based on the image and position of the point source
        """
        # cutout the star
        x_int = int(round(x))
        y_int = int(round(y))
        star_cutout = kernel_util.cutout_source(x_int, y_int, image, kernelsize + 2, shift=False)
        # cutout the mask
        mask_cutout = kernel_util.cutout_source(x_int, y_int, mask, kernelsize + 2, shift=False)
        # enlarge the initial PSF kernel to the new cutout size
        kernel_enlarged = np.zeros((kernelsize+2, kernelsize+2))
        kernel_enlarged[1:-1, 1:-1] = kernel_init
        # shift the initial kernel to the shift of the star
        shift_x = x_int - x
        shift_y = y_int - y
        kernel_shifted = interp.shift(kernel_enlarged, [-shift_y, -shift_x], order=1)
        # compute normalization of masked and unmasked region of the shifted kernel
        # norm_masked = np.sum(kernel_shifted[mask_i == 0])
        norm_unmasked = np.sum(kernel_shifted[mask_cutout == 1])
        # normalize star within the unmasked region to the norm of the initial kernel of the same region
        star_cutout /= np.sum(star_cutout[mask_cutout == 1]) * norm_unmasked
        # replace mask with shifted initial kernel (+2 size)
        star_cutout[mask_cutout == 0] = kernel_shifted[mask_cutout == 0]
        star_cutout[star_cutout < 0] = 0
        # de-shift kernel
        kernel_deshifted = kernel_util.de_shift_kernel(star_cutout, shift_x, shift_y)
        # re-size kernel
        kernel_deshifted = image_util.cut_edges(kernel_deshifted, kernelsize)
        # re-normalize kernel again
        kernel_deshifted = kernel_util.kernel_norm(kernel_deshifted)
        return kernel_deshifted

    @staticmethod
    def combine_psf(kernel_list_new, kernel_old, sigma_bkg, factor=1, stacking_option='median', symmetry=1):
        """
        updates psf estimate based on old kernel and several new estimates
        :param kernel_list_new: list of new PSF kernels estimated from the point sources in the image
        :param kernel_old: old PSF kernel
        :param sigma_bkg: estimated background noise in the image
        :param factor: weight of updated estimate based on new and old estimate, factor=1 means new estimate,
        factor=0 means old estimate
        :param stacking_option: option of stacking, mean or median
        :param symmetry: imposed symmetry of PSF estimate
        :return: updated PSF estimate and error_map associated with it
        """

        n = int(len(kernel_list_new) * symmetry)
        angle = 360. / symmetry
        kernelsize = len(kernel_old)
        kernel_list = np.zeros((n, kernelsize, kernelsize))
        i = 0
        for kernel_new in kernel_list_new:
            for k in range(symmetry):
                kernel_rotated = image_util.rotateImage(kernel_new, angle * k)
                kernel_norm = kernel_util.kernel_norm(kernel_rotated)
                kernel_list[i, :, :] = kernel_norm
                i += 1

        kernel_old_rotated = np.zeros((symmetry, kernelsize, kernelsize))
        for i in range(symmetry):
            kernel_old_rotated[i, :, :] = kernel_old

        kernel_list_new = np.append(kernel_list, kernel_old_rotated, axis=0)
        if stacking_option == 'median':
            kernel_new = np.median(kernel_list_new, axis=0)
        elif stacking_option == 'mean':
            kernel_new = np.mean(kernel_list_new, axis=0)
        else:
            raise ValueError(" stack_option must be 'median' or 'mean', %s is not supported." % stacking_option)
        kernel_new[kernel_new < 0] = 0
        kernel_new = kernel_util.kernel_norm(kernel_new)
        kernel_return = factor * kernel_new + (1.-factor)* kernel_old

        kernel_bkg = copy.deepcopy(kernel_return)
        kernel_bkg[kernel_bkg < sigma_bkg] = sigma_bkg
        error_map = np.var(kernel_list_new, axis=0) / kernel_bkg**2 / 2.
        return kernel_return, error_map

    @staticmethod
    def mask_point_source(x_pos, y_pos, x_grid, y_grid, radius, i=0):
        """

        :param x_pos: x-position of list of point sources
        :param y_pos: y-position of list of point sources
        :param x_grid: x-coordinates of grid
        :param y_grid: y-coordinates of grid
        :param i: index of point source not to mask out
        :param radius: radius to mask out other point sources
        :return: a mask of the size of the image with cutouts around the position
        """
        mask = np.ones_like(x_grid)
        for k in range(len(x_pos)):
            if k != i:
                mask_point = 1 - mask_util.mask_sphere(x_grid, y_grid, x_pos[k], y_pos[k], radius)
                mask *= mask_point
        return util.array2image(mask)
class to find subsequently a better psf     The method make use of a model and subtracts all the non-point source components of the model from the data.     If the model is sufficient, then the data will be a (better) representation of the actual PSF. The method cuts out     those point sources and combines them to update the estimate of the PSF. This is done in an iterative procedure as     the model components of the extended features is PSF-dependent (hopefully not too much).      Various options can be chosen. There is no quarante that the method works for specific data and models.      'stacking_method': 'median', 'mean'; the different estimates of the PSF are stacked and combined together. The choices are:         'mean': mean of pixel values as the estimator (not robust to outliers)         'median': median of pixel values as the estimator (outlier rejection robust but needs >2 point sources in the data      'block_center_neighbour': angle, radius of neighbouring point sources around their centers the estimates is ignored.         Default is zero, meaning a not optimal subtraction of the neighbouring point sources might contaminate the estimate.      'keep_error_map': bool, if True, does not replace the error term associated with the PSF estimate.         If false, re-estimates the variance between the PSF estimates.       The procedure only requires and changes the 'point_source_kernel' in the PSF() class and the 'psf_error_map'.     Any previously set subgrid kernels or pixel_kernels are removed and constructed from the 'point_source_kernel'. :param kwargs_data:         :param kwargs_psf:         :param kwargs_options:         :param kwargs_lens:         :param kwargs_source:         :param kwargs_lens_light:         :param kwargs_ps:         :return: #kwargs_numerics_psf['psf_error_map'] = False :param kwargs_data:         :param kwargs_psf:         :param kwargs_options:         :param kwargs_lens:         :param kwargs_source:         :param kwargs_lens_light:         :param kwargs_ps:         :param factor:         :param num_iter:         :return: return model without including the point source contributions as a list (for each point source individually)         :param image_model_class: ImageModel class instance         :param kwargs_lens: lens model kwargs list         :param kwargs_source: source model kwargs list         :param kwargs_lens_light: lens light model kwargs list         :param kwargs_ps: point source model kwargs list         :return: list of images with point source isolated # reconstructed model with given psf #model = image_model_class.image(kwargs_lens, kwargs_source, kwargs_lens_light, kwargs_ps) :param x_:         :param y_:         :param image_list: list of images (i.e. data - all models subtracted, except a single point source)         :param kernelsize:         :return: :param x: x-coordinate of point soure         :param y: y-coordinate of point source         :param image: image (i.e. data - all models subtracted, except a single point source)         :param mask: mask of pixels in the image not to be considered in the PSF estimate (being replaced by kernel_init)         :param kernelsize: width in pixel of the kernel         :param kernel_init: initial guess of kernel (pixels that are masked are replaced by those values)         :return: estimate of the PSF based on the image and position of the point source # cutout the star # cutout the mask # enlarge the initial PSF kernel to the new cutout size # shift the initial kernel to the shift of the star # compute normalization of masked and unmasked region of the shifted kernel # norm_masked = np.sum(kernel_shifted[mask_i == 0]) # normalize star within the unmasked region to the norm of the initial kernel of the same region # replace mask with shifted initial kernel (+2 size) # de-shift kernel # re-size kernel # re-normalize kernel again updates psf estimate based on old kernel and several new estimates         :param kernel_list_new: list of new PSF kernels estimated from the point sources in the image         :param kernel_old: old PSF kernel         :param sigma_bkg: estimated background noise in the image         :param factor: weight of updated estimate based on new and old estimate, factor=1 means new estimate,         factor=0 means old estimate         :param stacking_option: option of stacking, mean or median         :param symmetry: imposed symmetry of PSF estimate         :return: updated PSF estimate and error_map associated with it :param x_pos: x-position of list of point sources         :param y_pos: y-position of list of point sources         :param x_grid: x-coordinates of grid         :param y_grid: y-coordinates of grid         :param i: index of point source not to mask out         :param radius: radius to mask out other point sources         :return: a mask of the size of the image with cutouts around the position