class GaussianEllipsePotential(LensProfileBase): """ this class contains functions to evaluate a Gaussian function and calculates its derivative and hessian matrix with ellipticity in the convergence the calculation follows Glenn van de Ven et al. 2009 """ param_names = ['amp', 'sigma', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = { 'amp': 0, 'sigma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100 } upper_limit_default = { 'amp': 100, 'sigma': 100, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100 } def __init__(self): self.spherical = GaussianKappa() self._diff = 0.000001 super(GaussianEllipsePotential, self).__init__() def function(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ returns Gaussian """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) x_shift = x - center_x y_shift = y - center_y cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) e = abs(1 - q) x_ = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e) y_ = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e) f_ = self.spherical.function(x_, y_, amp=amp, sigma=sigma) return f_ def derivatives(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ returns df/dx and df/dy of the function """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) x_shift = x - center_x y_shift = y - center_y cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) e = abs(1 - q) x_ = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e) y_ = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e) f_x_prim, f_y_prim = self.spherical.derivatives(x_, y_, amp=amp, sigma=sigma) f_x_prim *= np.sqrt(1 - e) f_y_prim *= np.sqrt(1 + e) f_x = cos_phi * f_x_prim - sin_phi * f_y_prim f_y = sin_phi * f_x_prim + cos_phi * f_y_prim return f_x, f_y def hessian(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ returns Hessian matrix of function d^2f/dx^2, d^2/dxdy, d^2/dydx, d^f/dy^2 """ alpha_ra, alpha_dec = self.derivatives(x, y, amp, sigma, e1, e2, center_x, center_y) diff = self._diff alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, amp, sigma, e1, e2, center_x, center_y) alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, amp, sigma, e1, e2, center_x, center_y) f_xx = (alpha_ra_dx - alpha_ra) / diff f_xy = (alpha_ra_dy - alpha_ra) / diff f_yx = (alpha_dec_dx - alpha_dec) / diff f_yy = (alpha_dec_dy - alpha_dec) / diff return f_xx, f_xy, f_yx, f_yy def density(self, r, amp, sigma, e1, e2): """ :param r: :param amp: :param sigma: :return: """ return self.spherical.density(r, amp, sigma) def density_2d(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ :param R: :param am: :param sigma_x: :param sigma_y: :return: """ return self.spherical.density_2d(x, y, amp, sigma, center_x, center_y) def mass_2d(self, R, amp, sigma, e1, e2): """ :param R: :param amp: :param sigma_x: :param sigma_y: :return: """ return self.spherical.mass_2d(R, amp, sigma) def mass_3d(self, R, amp, sigma, e1, e2): """ :param R: :param amp: :param sigma: :param e1: :param e2: :return: """ return self.spherical.mass_3d(R, amp, sigma) def mass_3d_lens(self, R, amp, sigma, e1, e2): """ :param R: :param amp: :param sigma: :param e1: :param e2: :return: """ return self.spherical.mass_3d_lens(R, amp, sigma) def mass_2d_lens(self, R, amp, sigma, e1, e2): """ :param R: :param amp: :param sigma_x: :param sigma_y: :return: """ return self.spherical.mass_2d_lens(R, amp, sigma)
class MultiGaussianKappa(object): """ """ param_names = ['amp', 'sigma', 'center_x', 'center_y'] lower_limit_default = { 'amp': 0, 'sigma': 0, 'center_x': -100, 'center_y': -100 } upper_limit_default = { 'amp': 100, 'sigma': 100, 'center_x': 100, 'center_y': 100 } def __init__(self): self.gaussian_kappa = GaussianKappa() def function(self, x, y, amp, sigma, center_x=0, center_y=0, scale_factor=1): """ :param x: :param y: :param amp: :param sigma: :param center_x: :param center_y: :return: """ f_ = np.zeros_like(x, dtype=float) for i in range(len(amp)): f_ += self.gaussian_kappa.function(x, y, amp=scale_factor * amp[i], sigma=sigma[i], center_x=center_x, center_y=center_y) return f_ def derivatives(self, x, y, amp, sigma, center_x=0, center_y=0, scale_factor=1): """ :param x: :param y: :param amp: :param sigma: :param center_x: :param center_y: :return: """ f_x, f_y = np.zeros_like(x, dtype=float), np.zeros_like(x, dtype=float) for i in range(len(amp)): f_x_i, f_y_i = self.gaussian_kappa.derivatives(x, y, amp=scale_factor * amp[i], sigma=sigma[i], center_x=center_x, center_y=center_y) f_x += f_x_i f_y += f_y_i return f_x, f_y def hessian(self, x, y, amp, sigma, center_x=0, center_y=0, scale_factor=1): """ :param x: :param y: :param amp: :param sigma: :param center_x: :param center_y: :return: """ f_xx, f_yy, f_xy = np.zeros_like(x, dtype=float), np.zeros_like( x, dtype=float), np.zeros_like(x, dtype=float) for i in range(len(amp)): f_xx_i, f_yy_i, f_xy_i = self.gaussian_kappa.hessian( x, y, amp=scale_factor * amp[i], sigma=sigma[i], center_x=center_x, center_y=center_y) f_xx += f_xx_i f_yy += f_yy_i f_xy += f_xy_i return f_xx, f_yy, f_xy def density(self, r, amp, sigma, scale_factor=1): """ :param r: :param amp: :param sigma: :return: """ d_ = np.zeros_like(r, dtype=float) for i in range(len(amp)): d_ += self.gaussian_kappa.density(r, scale_factor * amp[i], sigma[i]) return d_ def density_2d(self, x, y, amp, sigma, center_x=0, center_y=0, scale_factor=1): """ :param R: :param am: :param sigma_x: :param sigma_y: :return: """ d_3d = np.zeros_like(x, dtype=float) for i in range(len(amp)): d_3d += self.gaussian_kappa.density_2d(x, y, scale_factor * amp[i], sigma[i], center_x, center_y) return d_3d def mass_3d_lens(self, R, amp, sigma, scale_factor=1): """ :param R: :param amp: :param sigma: :return: """ mass_3d = np.zeros_like(R, dtype=float) for i in range(len(amp)): mass_3d += self.gaussian_kappa.mass_3d_lens( R, scale_factor * amp[i], sigma[i]) return mass_3d
class MultiGaussian_kappa(object): """ """ def __init__(self): self.gaussian_kappa = GaussianKappa() def function(self, x, y, amp, sigma, center_x=0, center_y=0): """ :param x: :param y: :param amp: :param sigma: :param center_x: :param center_y: :return: """ f_ = np.zeros_like(x) for i in range(len(amp)): f_ += self.gaussian_kappa.function(x, y, amp=amp[i], sigma_x=sigma[i], sigma_y=sigma[i], center_x=center_x, center_y=center_y) return f_ def derivatives(self, x, y, amp, sigma, center_x=0, center_y=0): """ :param x: :param y: :param amp: :param sigma: :param center_x: :param center_y: :return: """ f_x, f_y = np.zeros_like(x), np.zeros_like(x) for i in range(len(amp)): f_x_i, f_y_i = self.gaussian_kappa.derivatives(x, y, amp=amp[i], sigma_x=sigma[i], sigma_y=sigma[i], center_x=center_x, center_y=center_y) f_x += f_x_i f_y += f_y_i return f_x, f_y def hessian(self, x, y, amp, sigma, center_x=0, center_y=0): """ :param x: :param y: :param amp: :param sigma: :param center_x: :param center_y: :return: """ f_xx, f_yy, f_xy = np.zeros_like(x), np.zeros_like(x), np.zeros_like(x) for i in range(len(amp)): f_xx_i, f_yy_i, f_xy_i = self.gaussian_kappa.hessian( x, y, amp=amp[i], sigma_x=sigma[i], sigma_y=sigma[i], center_x=center_x, center_y=center_y) f_xx += f_xx_i f_yy += f_yy_i f_xy += f_xy_i return f_xx, f_yy, f_xy def density(self, r, amp, sigma): """ :param r: :param amp: :param sigma: :return: """ d_ = np.zeros_like(r) for i in range(len(amp)): d_ += self.gaussian_kappa.density(r, amp[i], sigma[i], sigma[i]) return d_ def density_2d(self, x, y, amp, sigma, center_x=0, center_y=0): """ :param R: :param am: :param sigma_x: :param sigma_y: :return: """ d_3d = np.zeros_like(x) for i in range(len(amp)): d_3d += self.gaussian_kappa.density_2d(x, y, amp[i], sigma[i], sigma[i], center_x, center_y) return d_3d def mass_3d_lens(self, R, amp, sigma): """ :param R: :param amp: :param sigma: :return: """ mass_3d = np.zeros_like(R) for i in range(len(amp)): mass_3d += self.gaussian_kappa.mass_3d_lens( R, amp[i], sigma[i], sigma[i]) return mass_3d