Source code for lenstronomy.Plots.lens_plot


import lenstronomy.Util.util as util
import lenstronomy.Util.simulation_util as sim_util
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.axes_grid1 import make_axes_locatable
from lenstronomy.LensModel.lens_model_extensions import LensModelExtensions
from lenstronomy.LensModel.Profiles.curved_arc_spp import center_deflector
from lenstronomy.Data.imaging_data import ImageData
from lenstronomy.Plots import plot_util
import scipy.ndimage as ndimage

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


# TODO define coordinate grid beforehand, e.g. kwargs_data

[docs]@export def lens_model_plot(ax, lensModel, kwargs_lens, numPix=500, deltaPix=0.01, sourcePos_x=0, sourcePos_y=0, point_source=False, with_caustics=False, with_convergence=True, coord_center_ra=0, coord_center_dec=0, coord_inverse=False, fast_caustic=True, **kwargs): """ plots a lens model (convergence) and the critical curves and caustics :param ax: matplotlib axis instance :param kwargs_lens: lens model keyword argument list :param numPix: total nnumber of pixels (for convergence map) :param deltaPix: width of pixel (total frame size is deltaPix x numPix) :param sourcePos_x: float, x-position of point source (image positions computed by the lens equation) :param sourcePos_y: float, y-position of point source (image positions computed by the lens equation) :param point_source: bool, if True, illustrates and computes the image positions of the point source :param with_caustics: bool, if True, illustrates the critical curve and caustics of the system :param with_convergence: bool, if True, illustrates the convergence map :param coord_center_ra: float, x-coordinate of the center of the frame :param coord_center_dec: float, y-coordinate of the center of the frame :param coord_inverse: bool, if True, inverts the x-coordinates to go from right-to-left (effectively the RA definition) :param fast_caustic: boolean, if True, uses faster but less precise caustic calculation (might have troubles for the outer caustic (inner critical curve) :param with_convergence: boolean, if True, plots the convergence of the deflector :return: """ kwargs_data = sim_util.data_configure_simple(numPix, deltaPix, center_ra=coord_center_ra, center_dec=coord_center_dec, inverse=coord_inverse) data = ImageData(**kwargs_data) _coords = data _frame_size = numPix * deltaPix ra0, dec0 = data.radec_at_xy_0 if coord_inverse: extent = [ra0, ra0 - _frame_size, dec0, dec0 + _frame_size] else: extent = [ra0, ra0 + _frame_size, dec0, dec0 + _frame_size] if with_convergence: kwargs_convergence = kwargs.get('kwargs_convergence', {}) convergence_plot(ax, pixel_grid=_coords, lens_model=lensModel, kwargs_lens=kwargs_lens, extent=extent, **kwargs_convergence) if with_caustics is True: kwargs_caustics = kwargs.get('kwargs_caustics', {}) caustics_plot(ax, pixel_grid=_coords, lens_model=lensModel, kwargs_lens=kwargs_lens, fast_caustic=fast_caustic, coord_inverse=coord_inverse, **kwargs_caustics) if point_source: kwargs_point_source = kwargs.get('kwargs_point_source', {}) point_source_plot(ax, pixel_grid=_coords, lens_model=lensModel, kwargs_lens=kwargs_lens, source_x=sourcePos_x, source_y=sourcePos_y, **kwargs_point_source) if coord_inverse: ax.set_xlim([ra0, ra0 - _frame_size]) else: ax.set_xlim([ra0, ra0 + _frame_size]) ax.set_ylim([dec0, dec0 + _frame_size]) #ax.get_xaxis().set_visible(False) #ax.get_yaxis().set_visible(False) ax.autoscale(False) return ax
def convergence_plot(ax, pixel_grid, lens_model, kwargs_lens, extent=None, vmin=-1, vmax=1, cmap='Greys', **kwargs): """ plot convergence :param ax: matplotlib axis instance :param pixel_grid: lenstronomy PixelGrid() instance (or class with inheritance of PixelGrid() :param lens_model: LensModel() class instance :param kwargs_lens: lens model keyword argument list :param extent: [[min, max] [min, max]] of frame :param vmin: matplotlib vmin :param vmax: matplotlib vmax :param cmap: matplotlib cmap :param kwargs: keyword arguments for matshow :return: matplotlib axis instance with convergence plot """ x_grid, y_grid = pixel_grid.pixel_coordinates x_grid1d = util.image2array(x_grid) y_grid1d = util.image2array(y_grid) kappa_result = lens_model.kappa(x_grid1d, y_grid1d, kwargs_lens) kappa_result = util.array2image(kappa_result) im = ax.matshow(np.log10(kappa_result), origin='lower', extent=extent, cmap=cmap, vmin=vmin, vmax=vmax, **kwargs) return ax def caustics_plot(ax, pixel_grid, lens_model, kwargs_lens, fast_caustic=True, coord_inverse=False, color_crit='r', color_caustic='g', *args, **kwargs): """ :param ax: matplotlib axis instance :param pixel_grid: lenstronomy PixelGrid() instance (or class with inheritance of PixelGrid() :param lens_model: LensModel() class instance :param kwargs_lens: lens model keyword argument list :param fast_caustic: boolean, if True, uses faster but less precise caustic calculation (might have troubles for the outer caustic (inner critical curve) :param coord_inverse: bool, if True, inverts the x-coordinates to go from right-to-left (effectively the RA definition) :param color_crit: string, color of critical curve :param color_caustic: string, color of caustic curve :param kwargs: keyword arguments for plotting curves :return: updated matplotlib axis instance """ lens_model_ext = LensModelExtensions(lens_model) pixel_width = pixel_grid.pixel_width frame_size = np.max(pixel_grid.width) coord_center_ra, coord_center_dec = pixel_grid.center ra0, dec0 = pixel_grid.radec_at_xy_0 origin = [ra0, dec0] if fast_caustic: ra_crit_list, dec_crit_list, ra_caustic_list, dec_caustic_list = lens_model_ext.critical_curve_caustics( kwargs_lens, compute_window=frame_size, grid_scale=pixel_width, center_x=coord_center_ra, center_y=coord_center_dec) else: ra_crit_list, dec_crit_list = lens_model_ext.critical_curve_tiling(kwargs_lens, compute_window=frame_size, start_scale=pixel_width, max_order=10, center_x=coord_center_ra, center_y=coord_center_dec) ra_caustic_list, dec_caustic_list = lens_model.ray_shooting(ra_crit_list, dec_crit_list, kwargs_lens) #ra_crit_list, dec_crit_list = list(ra_crit_list), list(dec_crit_list) #ra_caustic_list, dec_caustic_list = list(ra_caustic_list), list(dec_caustic_list) plot_util.plot_line_set(ax, pixel_grid, ra_caustic_list, dec_caustic_list, color=color_caustic, origin=origin, flipped_x=coord_inverse, *args, **kwargs) plot_util.plot_line_set(ax, pixel_grid, ra_crit_list, dec_crit_list, color=color_crit, origin=origin, flipped_x=coord_inverse, *args, **kwargs) return ax def point_source_plot(ax, pixel_grid, lens_model, kwargs_lens, source_x, source_y, **kwargs): """ plots and illustrates images of a point source The plotting routine orders the image labels according to the arrival time and illustrates a diamond shape of the size of the magnification. The coordinates are chosen in pixel coordinates :param ax: matplotlib axis instance :param pixel_grid: lenstronomy PixelGrid() instance (or class with inheritance of PixelGrid() :param lens_model: LensModel() class instance :param kwargs_lens: lens model keyword argument list :param source_x: x-position of source :param source_y: y-position of source :param kwargs: additional plotting keyword arguments :return: matplotlib axis instance with figure """ from lenstronomy.LensModel.Solver.lens_equation_solver import LensEquationSolver solver = LensEquationSolver(lens_model) x_center, y_center = pixel_grid.center delta_pix = pixel_grid.pixel_width ra0, dec0 = pixel_grid.radec_at_xy_0 tranform = pixel_grid.transform_angle2pix if np.linalg.det(tranform) < 0: # if coordiate transform has negative parity (#TODO temporary fix) delta_pix_x = -delta_pix else: delta_pix_x = delta_pix origin = [ra0, dec0] theta_x, theta_y = solver.image_position_from_source(source_x, source_y, kwargs_lens, search_window=np.max(pixel_grid.width), x_center=x_center, y_center=y_center, min_distance=pixel_grid.pixel_width) mag_images = lens_model.magnification(theta_x, theta_y, kwargs_lens) #ax = plot_util.image_position_plot(ax=ax, coords=pixel_grid, ra_image=theta_x, dec_image=theta_y, color='w', image_name_list=None) x_image, y_image = pixel_grid.map_coord2pix(theta_x, theta_y) abc_list = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K'] for i in range(len(x_image)): x_ = (x_image[i] + 0.5) * delta_pix_x + origin[0] y_ = (y_image[i] + 0.5) * delta_pix + origin[1] ax.plot(x_, y_, 'dk', markersize=4 * (1 + np.log(np.abs(mag_images[i]))), alpha=0.5) ax.text(x_, y_, abc_list[i], fontsize=20, color='k') x_source, y_source = pixel_grid.map_coord2pix(source_x, source_y) ax.plot((x_source + 0.5) * delta_pix_x + origin[0], (y_source + 0.5) * delta_pix + origin[1], '*k', markersize=10) return ax
[docs]@export def arrival_time_surface(ax, lensModel, kwargs_lens, numPix=500, deltaPix=0.01, sourcePos_x=0, sourcePos_y=0, with_caustics=False, point_source=False, n_levels=10, kwargs_contours={}, image_color_list=None, letter_font_size=20): """ :param ax: matplotlib axis instance :param lens_model: LensModel() class instance :param kwargs_lens: lens model keyword argument list :param numPix: :param deltaPix: :param sourcePos_x: :param sourcePos_y: :param with_caustics: :return: """ kwargs_data = sim_util.data_configure_simple(numPix, deltaPix) data = ImageData(**kwargs_data) ra0, dec0 = data.radec_at_xy_0 origin = [ra0, dec0] _frame_size = numPix * deltaPix _coords = data x_grid, y_grid = data.pixel_coordinates lensModelExt = LensModelExtensions(lensModel) #ra_crit_list, dec_crit_list, ra_caustic_list, dec_caustic_list = lensModelExt.critical_curve_caustics( # kwargs_lens, compute_window=_frame_size, grid_scale=deltaPix/2.) x_grid1d = util.image2array(x_grid) y_grid1d = util.image2array(y_grid) fermat_surface = lensModel.fermat_potential(x_grid1d, y_grid1d, kwargs_lens, sourcePos_x, sourcePos_y) fermat_surface = util.array2image(fermat_surface) #, cmap='Greys', vmin=-1, vmax=1) #, cmap=self._cmap, vmin=v_min, vmax=v_max) if with_caustics is True: ra_crit_list, dec_crit_list = lensModelExt.critical_curve_tiling(kwargs_lens, compute_window=_frame_size, start_scale=deltaPix/5, max_order=10) ra_caustic_list, dec_caustic_list = lensModel.ray_shooting(ra_crit_list, dec_crit_list, kwargs_lens) plot_util.plot_line_set(ax, _coords, ra_caustic_list, dec_caustic_list, origin=origin, color='g') plot_util.plot_line_set(ax, _coords, ra_crit_list, dec_crit_list, origin=origin, color='r') if point_source is True: from lenstronomy.LensModel.Solver.lens_equation_solver import LensEquationSolver solver = LensEquationSolver(lensModel) theta_x, theta_y = solver.image_position_from_source(sourcePos_x, sourcePos_y, kwargs_lens, min_distance=deltaPix, search_window=deltaPix*numPix) fermat_pot_images = lensModel.fermat_potential(theta_x, theta_y, kwargs_lens) im = ax.contour(x_grid, y_grid, fermat_surface, origin='lower', # extent=[0, _frame_size, 0, _frame_size], levels=np.sort(fermat_pot_images), **kwargs_contours) mag_images = lensModel.magnification(theta_x, theta_y, kwargs_lens) x_image, y_image = _coords.map_coord2pix(theta_x, theta_y) abc_list = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K'] for i in range(len(x_image)): x_ = (x_image[i] + 0.5) * deltaPix - _frame_size/2 y_ = (y_image[i] + 0.5) * deltaPix - _frame_size/2 if image_color_list is None: color = 'k' else: color = image_color_list[i] ax.plot(x_, y_, 'x', markersize=10, alpha=1, color=color) # markersize=8*(1 + np.log(np.abs(mag_images[i]))) ax.text(x_ + deltaPix, y_ + deltaPix, abc_list[i], fontsize=letter_font_size, color='k') x_source, y_source = _coords.map_coord2pix(sourcePos_x, sourcePos_y) ax.plot((x_source + 0.5) * deltaPix - _frame_size/2, (y_source + 0.5) * deltaPix - _frame_size/2, '*k', markersize=20) else: vmin = np.min(fermat_surface) vmax = np.max(fermat_surface) levels = np.linspace(start=vmin, stop=vmax, num=n_levels) im = ax.contour(x_grid, y_grid, fermat_surface, origin='lower', # extent=[0, _frame_size, 0, _frame_size], levels=levels, **kwargs_contours) ax.get_xaxis().set_visible(False) ax.get_yaxis().set_visible(False) ax.autoscale(False) return ax
[docs]@export def curved_arc_illustration(ax, lensModel, kwargs_lens, with_centroid=True, stretch_scale=0.1, color='k'): """ :param ax: matplotlib axis instance :param lensModel: LensModel() instance :param kwargs_lens: list of lens model keyword arguments (only those of CURVED_ARC considered :param with_centroid: plots the center of the curvature radius :param stretch_scale: float, relative scale of banana to the tangential and radial stretches (effectively intrinsic source size) :param color: string, matplotlib color for plot :return: matplotlib axis instance """ # loop through lens models # check whether curved arc lens_model_list = lensModel.lens_model_list for i, lens_type in enumerate(lens_model_list): if lens_type in ['CURVED_ARC', 'CURVED_ARC_SIS_MST', 'CURVED_ARC_CONST', 'CURVED_ARC_CONST_MST', 'CURVED_ARC_SPT', 'CURVED_ARC_TAN_DIFF']: plot_arc(ax, with_centroid=with_centroid, stretch_scale=stretch_scale, color=color, **kwargs_lens[i]) ax.get_xaxis().set_visible(False) ax.get_yaxis().set_visible(False) ax.autoscale(False) # rectangular frame ax.axis('scaled')
# plot coordinate frame and scale
[docs]@export def plot_arc(ax, tangential_stretch, radial_stretch, curvature, direction, center_x, center_y, stretch_scale=0.1, with_centroid=True, linewidth=1, color='k', dtan_dtan=0): """ :param ax: matplotlib.axes instance :param tangential_stretch: float, stretch of intrinsic source in tangential direction :param radial_stretch: float, stretch of intrinsic source in radial direction :param curvature: 1/curvature radius :param direction: float, angle in radian :param center_x: center of source in image plane :param center_y: center of source in image plane :param with_centroid: plots the center of the curvature radius :param stretch_scale: float, relative scale of banana to the tangential and radial stretches (effectively intrinsic source size) :param dtan_dtan: tangential eigenvector differential in tangential direction (not implemented yet as illustration) :return: """ # plot line to centroid center_x_spp, center_y_spp = center_deflector(curvature, direction, center_x, center_y) if with_centroid: ax.plot([center_x, center_x_spp], [center_y, center_y_spp], '--', color=color, alpha=0.5, linewidth=linewidth) ax.plot([center_x_spp], [center_y_spp], '*', color=color, alpha=0.5, linewidth=linewidth) # plot radial stretch to scale x_r = np.cos(direction) * radial_stretch * stretch_scale y_r = np.sin(direction) * radial_stretch * stretch_scale ax.plot([center_x - x_r, center_x + x_r], [center_y - y_r, center_y + y_r], '--', color=color, linewidth=linewidth) # compute angle of size of the tangential stretch r = 1. / curvature # make sure tangential stretch * stretch_scale is not larger than r * 2pi such that the full circle is only plotted once tangential_stretch_ = min(tangential_stretch, np.pi * r / stretch_scale) d_phi = tangential_stretch_ * stretch_scale / r # linearly interpolate angle around center phi = np.linspace(-1, 1, 50) * d_phi + direction # plot points on circle x_curve = r * np.cos(phi) + center_x_spp y_curve = r * np.sin(phi) + center_y_spp ax.plot(x_curve, y_curve, '--', color=color, linewidth=linewidth) # make round circle with start point to end to close the circle r_c, t_c = util.points_on_circle(radius=stretch_scale, num_points=200) r_c = radial_stretch * r_c + r phi_c = t_c * tangential_stretch_ / r_c + direction x_c = r_c * np.cos(phi_c) + center_x_spp y_c = r_c * np.sin(phi_c) + center_y_spp ax.plot(x_c, y_c, '-', color=color, linewidth=linewidth) return ax
# TODO add different colors for each quarter to identify parities
[docs]@export def distortions(lensModel, kwargs_lens, num_pix=100, delta_pix=0.05, center_ra=0, center_dec=0, differential_scale=0.0001, smoothing_scale=None, **kwargs): """ :param lensModel: LensModel instance :param kwargs_lens: lens model keyword argument list :param num_pix: number of pixels per axis :param delta_pix: pixel scale per axis :param center_ra: center of the grid :param center_dec: center of the grid :param differential_scale: scale of the finite derivative length in units of angles :param smoothing_scale: float or None, Gaussian FWHM of a smoothing kernel applied before plotting :return: matplotlib instance with different panels """ kwargs_grid = sim_util.data_configure_simple(num_pix, delta_pix, center_ra=center_ra, center_dec=center_dec) _coords = ImageData(**kwargs_grid) _frame_size = num_pix * delta_pix ra_grid, dec_grid = _coords.pixel_coordinates extensions = LensModelExtensions(lensModel=lensModel) ra_grid1d = util.image2array(ra_grid) dec_grid1d = util.image2array(dec_grid) lambda_rad, lambda_tan, orientation_angle, dlambda_tan_dtan, dlambda_tan_drad, dlambda_rad_drad, dlambda_rad_dtan, dphi_tan_dtan, dphi_tan_drad, dphi_rad_drad, dphi_rad_dtan = extensions.radial_tangential_differentials( ra_grid1d, dec_grid1d, kwargs_lens=kwargs_lens, center_x=center_ra, center_y=center_dec, smoothing_3rd=differential_scale, smoothing_2nd=None) lambda_rad2d, lambda_tan2d, orientation_angle2d, dlambda_tan_dtan2d, dlambda_tan_drad2d, dlambda_rad_drad2d, dlambda_rad_dtan2d, dphi_tan_dtan2d, dphi_tan_drad2d, dphi_rad_drad2d, dphi_rad_dtan2d = util.array2image(lambda_rad), \ util.array2image(lambda_tan), util.array2image(orientation_angle), util.array2image(dlambda_tan_dtan), util.array2image(dlambda_tan_drad), util.array2image(dlambda_rad_drad), util.array2image(dlambda_rad_dtan), \ util.array2image(dphi_tan_dtan), util.array2image(dphi_tan_drad), util.array2image(dphi_rad_drad), util.array2image(dphi_rad_dtan) if smoothing_scale is not None: lambda_rad2d = ndimage.gaussian_filter(lambda_rad2d, sigma=smoothing_scale/delta_pix) dlambda_rad_drad2d = ndimage.gaussian_filter(dlambda_rad_drad2d, sigma=smoothing_scale/delta_pix) lambda_tan2d = np.abs(lambda_tan2d) # the magnification cut is made to make a stable integral/convolution lambda_tan2d[lambda_tan2d > 100] = 100 lambda_tan2d = ndimage.gaussian_filter(lambda_tan2d, sigma=smoothing_scale/delta_pix) # the magnification cut is made to make a stable integral/convolution dlambda_tan_dtan2d[dlambda_tan_dtan2d > 100] = 100 dlambda_tan_dtan2d[dlambda_tan_dtan2d < -100] = -100 dlambda_tan_dtan2d = ndimage.gaussian_filter(dlambda_tan_dtan2d, sigma=smoothing_scale/delta_pix) orientation_angle2d = ndimage.gaussian_filter(orientation_angle2d, sigma=smoothing_scale/delta_pix) dphi_tan_dtan2d = ndimage.gaussian_filter(dphi_tan_dtan2d, sigma=smoothing_scale/delta_pix) def _plot_frame(ax, map, vmin, vmax, text_string): """ :param ax: matplotlib.axis instance :param map: 2d array :param vmin: minimum plotting scale :param vmax: maximum plotting scale :param text_string: string to describe the label :return: """ font_size = 10 _arrow_size = 0.02 im = ax.matshow(map, extent=[0, _frame_size, 0, _frame_size], vmin=vmin, vmax=vmax) ax.get_xaxis().set_visible(False) ax.get_yaxis().set_visible(False) ax.autoscale(False) divider = make_axes_locatable(ax) cax = divider.append_axes("right", size="5%", pad=0.05) cb = plt.colorbar(im, cax=cax, orientation='vertical') #cb.set_label(text_string, fontsize=10) #plot_util.scale_bar(ax, _frame_size, dist=1, text='1"', font_size=font_size) plot_util.text_description(ax, _frame_size, text=text_string, color="k", backgroundcolor='w', font_size=font_size) #if 'no_arrow' not in kwargs or not kwargs['no_arrow']: # plot_util.coordinate_arrows(ax, _frame_size, _coords, # color='w', arrow_size=_arrow_size, # font_size=font_size) f, axes = plt.subplots(3, 4, figsize=(12, 8)) _plot_frame(axes[0, 0], lambda_rad2d, vmin=0.6, vmax=1.4, text_string=r"$\lambda_{rad}$") _plot_frame(axes[0, 1], lambda_tan2d, vmin=-20, vmax=20, text_string=r"$\lambda_{tan}$") _plot_frame(axes[0, 2], orientation_angle2d, vmin=-np.pi / 10, vmax=np.pi / 10, text_string=r"$\phi$") _plot_frame(axes[0, 3], util.array2image(lambda_tan * lambda_rad), vmin=-20, vmax=20, text_string='magnification') _plot_frame(axes[1, 0], dlambda_rad_drad2d/lambda_rad2d, vmin=-.1, vmax=.1, text_string='dlambda_rad_drad') _plot_frame(axes[1, 1], dlambda_tan_dtan2d/lambda_tan2d, vmin=-20, vmax=20, text_string='dlambda_tan_dtan') _plot_frame(axes[1, 2], dlambda_tan_drad2d/lambda_tan2d, vmin=-20, vmax=20, text_string='dlambda_tan_drad') _plot_frame(axes[1, 3], dlambda_rad_dtan2d/lambda_rad2d, vmin=-.1, vmax=.1, text_string='dlambda_rad_dtan') _plot_frame(axes[2, 0], dphi_rad_drad2d, vmin=-.1, vmax=.1, text_string='dphi_rad_drad') _plot_frame(axes[2, 1], dphi_tan_dtan2d, vmin=0, vmax=20, text_string='dphi_tan_dtan: curvature radius') _plot_frame(axes[2, 2], dphi_tan_drad2d, vmin=-.1, vmax=.1, text_string='dphi_tan_drad') _plot_frame(axes[2, 3], dphi_rad_dtan2d, vmin=0, vmax=20, text_string='dphi_rad_dtan') return f, axes