text: """
  routines that manipulate convolution kernels
  """
  import numpy as np
  import copy
  import scipy.ndimage.interpolation as interp
  import lenstronomy.Util.util as util
  import lenstronomy.Util.image_util as image_util
  from lenstronomy.LightModel.Profiles.gaussian import Gaussian
  import lenstronomy.Util.multi_gauss_expansion as mge
  
  
  def de_shift_kernel(kernel, shift_x, shift_y, iterations=20):
      """
      de-shifts a shifted kernel to the center of a pixel. This is performed iteratively.
  
      The input kernel is the solution of a linear interpolated shift of a sharper kernel centered in the middle of the
       pixel. To find the de-shifted kernel, we perform an iterative correction of proposed de-shifted kernels and compare
       its shifted version with the input kernel.
  
      :param kernel: (shifted) kernel, e.g. a star in an image that is not centered in the pixel grid
      :param shift_x: x-offset relative to the center of the pixel (sub-pixel shift)
      :param shift_y: y-offset relative to the center of the pixel (sub-pixel shift)
      :return: de-shifted kernel such that the interpolated shift boy (shift_x, shift_y) results in the input kernel
      """
      nx, ny = np.shape(kernel)
      kernel_new = np.zeros((nx+2, ny+2)) + (kernel[0, 0] + kernel[0, -1] + kernel[-1, 0] + kernel[-1, -1]) / 4.
      kernel_new[1:-1, 1:-1] = kernel
      int_shift_x = int(round(shift_x))
      frac_x_shift = shift_x - int_shift_x
      int_shift_y = int(round(shift_y))
      frac_y_shift = shift_y - int_shift_y
      kernel_init = copy.deepcopy(kernel_new)
      kernel_init_shifted = copy.deepcopy(interp.shift(kernel_init, [int_shift_y, int_shift_x], order=1))
      kernel_new = interp.shift(kernel_new, [int_shift_y, int_shift_x], order=1)
      norm = np.sum(kernel_init_shifted)
      for i in range(iterations):
          kernel_shifted_inv = interp.shift(kernel_new, [-frac_y_shift, -frac_x_shift], order=1)
          delta = kernel_init_shifted - kernel_norm(kernel_shifted_inv) * norm
          kernel_new += delta * 1.
          kernel_new = kernel_norm(kernel_new) * norm
      return kernel_new[1:-1, 1:-1]
  
  
  def center_kernel(kernel, iterations=20):
      """
      given a kernel that might not be perfectly centered, this routine computes its light weighted center and then
      moves the center in an iterative process such that it is centered
  
      :param kernel: 2d array (odd numbers)
      :param iterations: int, number of iterations
      :return: centered kernel
      """
      kernel = kernel_norm(kernel)
      nx, ny = np.shape(kernel)
      if nx %2 == 0:
          raise ValueError("kernel needs odd number of pixels")
      # make coordinate grid of kernel
      x_grid, y_grid = util.make_grid(nx, deltapix=1, left_lower=False)
      # compute 1st moments to get light weighted center
      x_w = np.sum(kernel * util.array2image(x_grid))
      y_w = np.sum(kernel * util.array2image(y_grid))
      # de-shift kernel
      kernel_centered = de_shift_kernel(kernel, shift_x=-x_w, shift_y=-y_w, iterations=iterations)
      return kernel_norm(kernel_centered)
  
  
  def kernel_norm(kernel):
      """
  
      :param kernel:
      :return: normalisation of the psf kernel
      """
      norm = np.sum(np.array(kernel))
      kernel /= norm
      return kernel
  
  
  def subgrid_kernel(kernel, subgrid_res, odd=False, num_iter=100):
      """
      creates a higher resolution kernel with subgrid resolution as an interpolation of the original kernel in an
      iterative approach
  
      :param kernel: initial kernel
      :param subgrid_res: subgrid resolution required
      :return: kernel with higher resolution (larger)
      """
      subgrid_res = int(subgrid_res)
      if subgrid_res == 1:
          return kernel
      nx, ny = np.shape(kernel)
      d_x = 1. / nx
      x_in = np.linspace(d_x/2, 1-d_x/2, nx)
      d_y = 1. / nx
      y_in = np.linspace(d_y/2, 1-d_y/2, ny)
      nx_new = nx * subgrid_res
      ny_new = ny * subgrid_res
      if odd is True:
          if nx_new % 2 == 0:
              nx_new -= 1
          if ny_new % 2 == 0:
              ny_new -= 1
  
      d_x_new = 1. / nx_new
      d_y_new = 1. / ny_new
      x_out = np.linspace(d_x_new/2., 1-d_x_new/2., nx_new)
      y_out = np.linspace(d_y_new/2., 1-d_y_new/2., ny_new)
      kernel_input = copy.deepcopy(kernel)
      kernel_subgrid = image_util.re_size_array(x_in, y_in, kernel_input, x_out, y_out)
      kernel_subgrid = kernel_norm(kernel_subgrid)
      for i in range(max(num_iter, 1)):
          # given a proposition, re-size it to original pixel size
          if subgrid_res % 2 == 0:
              kernel_pixel = averaging_even_kernel(kernel_subgrid, subgrid_res)
          else:
              kernel_pixel = util.averaging(kernel_subgrid, numGrid=nx_new, numPix=nx)
          delta = kernel - kernel_pixel
          #plt.matshow(delta)
          #plt.colorbar()
          #plt.show()
          temp_kernel = kernel_input + delta
          kernel_subgrid = image_util.re_size_array(x_in, y_in, temp_kernel, x_out, y_out)#/norm_subgrid
          kernel_subgrid = kernel_norm(kernel_subgrid)
          kernel_input = temp_kernel
  
      #from scipy.ndimage import zoom
  
      #ratio = subgrid_res
      #kernel_subgrid = zoom(kernel, ratio, order=4) / ratio ** 2
      #print(np.shape(kernel_subgrid))
      # whatever has not been matched is added to zeroth order (in squares of the undersampled PSF)
      if subgrid_res % 2 == 0:
          return kernel_subgrid
      kernel_pixel = util.averaging(kernel_subgrid, numGrid=nx_new, numPix=nx)
      kernel_pixel = kernel_norm(kernel_pixel)
      delta_kernel = kernel_pixel - kernel_norm(kernel)
      id = np.ones((subgrid_res, subgrid_res))
      delta_kernel_sub = np.kron(delta_kernel, id)/subgrid_res**2
      return kernel_norm(kernel_subgrid - delta_kernel_sub)
  
  
  def averaging_even_kernel(kernel_high_res, subgrid_res):
      """
      makes a lower resolution kernel based on the kernel_high_res (odd numbers) and the subgrid_res (even number), both
      meant to be centered.
  
      :param kernel_high_res: high resolution kernel with even subsampling resolution, centered
      :param subgrid_res: subsampling resolution (even number)
      :return: averaged undersampling kernel
      """
      n_kernel_high_res = len(kernel_high_res)
      n_low = int(round(n_kernel_high_res / subgrid_res + 0.5))
      if n_low % 2 == 0:
          n_low += 1
      n_high = int(n_low * subgrid_res - 1)
      assert n_high % 2 == 1
      if n_high == n_kernel_high_res:
          kernel_high_res_edges = kernel_high_res
      else:
          i_start = int((n_high - n_kernel_high_res) / 2)
          kernel_high_res_edges = np.zeros((n_high, n_high))
          kernel_high_res_edges[i_start:-i_start, i_start:-i_start] = kernel_high_res
      kernel_low_res = np.zeros((n_low, n_low))
      # adding pixels that are fully within a single re-binned pixel
      for i in range(subgrid_res-1):
          for j in range(subgrid_res-1):
              kernel_low_res += kernel_high_res_edges[i::subgrid_res, j::subgrid_res]
      # adding half of a pixel that has over-lap with two pixels
      i = subgrid_res - 1
      for j in range(subgrid_res - 1):
          kernel_low_res[1:, :] += kernel_high_res_edges[i::subgrid_res, j::subgrid_res] / 2
          kernel_low_res[:-1, :] += kernel_high_res_edges[i::subgrid_res, j::subgrid_res] / 2
      j = subgrid_res - 1
      for i in range(subgrid_res - 1):
          kernel_low_res[:, 1:] += kernel_high_res_edges[i::subgrid_res, j::subgrid_res] / 2
          kernel_low_res[:, :-1] += kernel_high_res_edges[i::subgrid_res, j::subgrid_res] / 2
      # adding a quarter of a pixel value that is at the boarder of four pixels
      i = subgrid_res - 1
      j = subgrid_res - 1
      kernel_edge = kernel_high_res_edges[i::subgrid_res, j::subgrid_res]
      kernel_low_res[1:, 1:] += kernel_edge / 4
      kernel_low_res[:-1, 1:] += kernel_edge / 4
      kernel_low_res[1:, :-1] += kernel_edge / 4
      kernel_low_res[:-1, :-1] += kernel_edge / 4
      return kernel_low_res
  
  
  def kernel_pixelsize_change(kernel, deltaPix_in, deltaPix_out):
      """
      change the pixel size of a given kernel
      :param kernel:
      :param deltaPix_in:
      :param deltaPix_out:
      :return:
      """
      numPix = len(kernel)
      numPix_new = int(round(numPix * deltaPix_in/deltaPix_out))
      if numPix_new % 2 == 0:
          numPix_new -= 1
      x_in = np.linspace(-(numPix-1)/2*deltaPix_in, (numPix-1)/2*deltaPix_in, numPix)
      x_out = np.linspace(-(numPix_new-1)/2*deltaPix_out, (numPix_new-1)/2*deltaPix_out, numPix_new)
      kernel_out = image_util.re_size_array(x_in, x_in, kernel, x_out, x_out)
      kernel_out = kernel_norm(kernel_out)
      return kernel_out
  
  
  def cut_psf(psf_data, psf_size):
      """
      cut the psf properly
      :param psf_data: image of PSF
      :param psf_size: size of psf
      :return: re-sized and re-normalized PSF
      """
      kernel = image_util.cut_edges(psf_data, psf_size)
      kernel = kernel_norm(kernel)
      return kernel
  
  
  def pixel_kernel(point_source_kernel, subgrid_res=7):
      """
      converts a pixelised kernel of a point source to a kernel representing a uniform extended pixel
  
      :param point_source_kernel:
      :param subgrid_res:
      :return: convolution kernel for an extended pixel
      """
      kernel_subgrid = subgrid_kernel(point_source_kernel, subgrid_res, num_iter=10)
      kernel_size = len(point_source_kernel)
      kernel_pixel = np.zeros((kernel_size*subgrid_res, kernel_size*subgrid_res))
      for i in range(subgrid_res):
          k_x = int((kernel_size-1) / 2 * subgrid_res + i)
          for j in range(subgrid_res):
              k_y = int((kernel_size-1) / 2 * subgrid_res + j)
              kernel_pixel = image_util.add_layer2image(kernel_pixel, k_x, k_y, kernel_subgrid)
      kernel_pixel = util.averaging(kernel_pixel, numGrid=kernel_size*subgrid_res, numPix=kernel_size)
      return kernel_norm(kernel_pixel)
  
  
  def kernel_average_pixel(kernel_super, supersampling_factor):
      """
      computes the effective convolution kernel assuming a uniform surface brightness on the scale of a pixel
  
      :param kernel_super: supersampled PSF of a point source (odd number per axis
      :param supersampling_factor: supersampling factor (int)
      :return:
      """
      kernel_sum = np.sum(kernel_super)
      kernel_size = int(round(len(kernel_super)/float(supersampling_factor) + 0.5))
      if kernel_size % 2 == 0:
          kernel_size += 1
      n_high = kernel_size*supersampling_factor
      if n_high % 2 == 0:
          n_high += 1
      kernel_pixel = np.zeros((n_high, n_high))
      for i in range(supersampling_factor):
          k_x = int((kernel_size - 1) / 2 * supersampling_factor + i)
          for j in range(supersampling_factor):
              k_y = int((kernel_size - 1) / 2 * supersampling_factor + j)
              kernel_pixel = image_util.add_layer2image(kernel_pixel, k_x, k_y, kernel_super)
  
      if supersampling_factor % 2 == 0:
          kernel_pixel = averaging_even_kernel(kernel_pixel, supersampling_factor)
      else:
          kernel_pixel = util.averaging(kernel_pixel, numGrid=n_high,
                                                     numPix=kernel_size)
      kernel_pixel /= np.sum(kernel_pixel)
      return kernel_pixel * kernel_sum
  
  
  def kernel_gaussian(kernel_numPix, deltaPix, fwhm):
      sigma = util.fwhm2sigma(fwhm)
      #if kernel_numPix % 2 == 0:
      #    kernel_numPix += 1
      x_grid, y_grid = util.make_grid(kernel_numPix, deltaPix)
      gaussian = Gaussian()
      kernel = gaussian.function(x_grid, y_grid, amp=1., sigma=sigma, center_x=0, center_y=0)
      kernel /= np.sum(kernel)
      kernel = util.array2image(kernel)
      return kernel
  
  
  def split_kernel(kernel_super, supersampling_kernel_size, supersampling_factor, normalized=True):
      """
      pixel kernel and subsampling kernel such that the convolution of both applied on an image can be
      performed, i.e. smaller subsampling PSF and hole in larger PSF
  
      :param kernel: PSF kernel of the size of the pixel
      :param kernel_super: super-sampled kernel
      :param supersampling_kernel_size: size of super-sampled PSF in units of degraded pixels
      :param normalized: boolean, if True returns a split kernel that is area normalized=1 representing a convolution kernel
      :return: degraded kernel with hole and super-sampled kernel
      """
      if supersampling_factor <= 1:
          raise ValueError('To split a kernel, the supersampling_factor needs to be > 1, givn %s' %supersampling_factor)
      if supersampling_kernel_size % 2 == 0:
          raise ValueError('supersampling_kernel_size needs to be an odd number!')
      n_super = len(kernel_super)
      n_sub = supersampling_kernel_size * supersampling_factor
      if n_sub % 2 == 0:
          n_sub += 1
      if n_sub > n_super:
          n_sub = n_super
  
      kernel_hole = copy.deepcopy(kernel_super)
      n_min = int((n_super-1) / 2 - (n_sub - 1) / 2)
      n_max = int((n_super-1) / 2 + (n_sub - 1) / 2 + 1)
      kernel_hole[n_min:n_max, n_min:n_max] = 0
      kernel_hole_resized = degrade_kernel(kernel_hole, degrading_factor=supersampling_factor)
      kernel_subgrid_cut = kernel_super[n_min:n_max, n_min:n_max]
      if normalized is True:
          flux_subsampled = np.sum(kernel_subgrid_cut)
          flux_hole = np.sum(kernel_hole_resized)
          if flux_hole > 0:
              kernel_hole_resized *= (1. - flux_subsampled) / np.sum(kernel_hole_resized)
          else:
              kernel_subgrid_cut /= np.sum(kernel_subgrid_cut)
      else:
          kernel_hole_resized /= supersampling_factor ** 2
      return kernel_hole_resized, kernel_subgrid_cut
  
  
  def degrade_kernel(kernel_super, degrading_factor):
      """
  
      :param kernel_super: higher resolution kernel (odd number per axis)
      :param degrading_factor: degrading factor (effectively the super-sampling resolution of the kernel given
      :return: degraded kernel with odd axis number with the sum of the flux/values in the kernel being preserved
      """
      if degrading_factor == 1:
          return kernel_super
      if degrading_factor % 2 == 0:
          kernel_low_res = averaging_even_kernel(kernel_super, degrading_factor)
      else:
          n_kernel = len(kernel_super)
          numPix = int(round(n_kernel / degrading_factor + 0.5))
          if numPix % 2 == 0:
              numPix += 1
          n_high = numPix * degrading_factor
  
          kernel_super_ = np.zeros((n_high, n_high))
          i_start = int((n_high-n_kernel)/2)
          kernel_super_[i_start:i_start+n_kernel, i_start:i_start+n_kernel] = kernel_super
          kernel_low_res = util.averaging(kernel_super_, numGrid=n_high, numPix=numPix) * degrading_factor**2  # multiplicative factor added when providing flux conservation
      return kernel_low_res
  
  
  def cutout_source(x_pos, y_pos, image, kernelsize, shift=True):
      """
      cuts out point source (e.g. PSF estimate) out of image and shift it to the center of a pixel
      :param x_pos:
      :param y_pos:
      :param image:
      :param kernelsize:
      :return:
      """
      if kernelsize % 2 == 0:
          raise ValueError("even pixel number kernel size not supported!")
      x_int = int(round(x_pos))
      y_int = int(round(y_pos))
      n = len(image)
      d = (kernelsize - 1)/2
      x_max = int(np.minimum(x_int + d + 1, n))
      x_min = int(np.maximum(x_int - d, 0))
      y_max = int(np.minimum(y_int + d + 1, n))
      y_min = int(np.maximum(y_int - d, 0))
      image_cut = copy.deepcopy(image[y_min:y_max, x_min:x_max])
      shift_x = x_int - x_pos
      shift_y = y_int - y_pos
      if shift is True:
          kernel_shift = de_shift_kernel(image_cut, shift_x, shift_y, iterations=50)
      else:
          kernel_shift = image_cut
      kernel_final = np.zeros((kernelsize, kernelsize))
  
      k_l2_x = int((kernelsize - 1) / 2)
      k_l2_y = int((kernelsize - 1) / 2)
  
      xk_min = np.maximum(0, -x_int + k_l2_x)
      yk_min = np.maximum(0, -y_int + k_l2_y)
      xk_max = np.minimum(kernelsize, -x_int + k_l2_x + n)
      yk_max = np.minimum(kernelsize, -y_int + k_l2_y + n)
  
      kernel_final[yk_min:yk_max, xk_min:xk_max] = kernel_shift
      return kernel_final
  
  
  def fwhm_kernel(kernel):
      """
  
      :param kernel:
      :return:
      """
      n = len(kernel)
      center = (n - 1) / 2.
      I_r = image_util.radial_profile(kernel, center=[center, center])
      if n % 2 == 0:
          raise ValueError('only works with odd number of pixels in kernel!')
      max_flux = kernel[int((n-1)/2), int((n-1)/2)]
      I_2 = max_flux / 2.
      r = np.linspace(0, (n - 1) / 2, int((n + 1) / 2)) + 0.33
      for i in range(1, len(I_r)):
          if I_r[i] < I_2:
              fwhm_2 = (I_2 - I_r[i - 1]) / (I_r[i] - I_r[i - 1]) + r[i - 1]
              return fwhm_2 * 2
      raise ValueError('The kernel did not drop to half the max value - fwhm not determined!')
  
  
  def estimate_amp(data, x_pos, y_pos, psf_kernel):
      """
      estimates the amplitude of a point source located at x_pos, y_pos
      :param data:
      :param x_pos:
      :param y_pos:
      :param deltaPix:
      :return:
      """
      numPix_x, numPix_y = np.shape(data)
      #data_center = int((numPix-1.)/2)
      x_int = int(round(x_pos-0.49999))#+data_center
      y_int = int(round(y_pos-0.49999))#+data_center
      # TODO: make amplitude estimate not sucecible to rounding effects on which pixels to chose to estimate the amplitude
      if x_int > 2 and x_int < numPix_x-2 and y_int > 2 and y_int < numPix_y-2:
          mean_image = max(np.sum(data[y_int - 2:y_int+3, x_int-2:x_int+3]), 0)
          num = len(psf_kernel)
          center = int((num-0.5)/2)
          mean_kernel = np.sum(psf_kernel[center-2:center+3, center-2:center+3])
          amp_estimated = mean_image/mean_kernel
      else:
          amp_estimated = 0
      return amp_estimated
  
  
  def mge_kernel(kernel, order=5):
      """
      azimutal Multi-Gaussian expansion of a pixelized kernel
  
      :param kernel: 2d numpy array
      :return:
      """
      # radial average
      n = len(kernel)
      center = (n - 1) / 2.
      psf_r = image_util.radial_profile(kernel, center=[center, center])
      # MGE of radial average
      n_r = len(psf_r)
      r_array = np.linspace(start=0., stop=n_r - 1, num=n_r)
      amps, sigmas, norm = mge.mge_1d(r_array, psf_r, N=order, linspace=True)
      return amps, sigmas, norm