Merge pull request #11 from DifferentiableUniverseInitiative/u/EiffL/…

…lensing

Adds basic utilities for Born lensing

jaxpm/lensing.py

@@ -0,0 +1,81 @@
+import jax 
+import jax.numpy as jnp
+import jax_cosmo.constants as constants
+import jax_cosmo
+
+from jax.scipy.ndimage import map_coordinates
+from jaxpm.utils import gaussian_smoothing
+from jaxpm.painting import cic_paint_2d
+
+def density_plane(positions,
+                  box_shape,
+                  center,
+                  width,
+                  plane_resolution,
+                  smoothing_sigma=None):
+    """ Extacts a density plane from the simulation
+    """
+    nx, ny, nz = box_shape
+    xy = positions[..., :2]
+    d = positions[..., 2]
+
+    # Apply 2d periodic conditions
+    xy = jnp.mod(xy, nx)
+
+    # Rescaling positions to target grid
+    xy = xy / nx * plane_resolution
+
+    # Selecting only particles that fall inside the volume of interest
+    weight = jnp.where((d > (center - width / 2)) & (d <= (center + width / 2)), 1., 0.)
+    # Painting density plane
+    density_plane = cic_paint_2d(jnp.zeros([plane_resolution, plane_resolution]), xy, weight)
+
+    # Apply density normalization
+    density_plane = density_plane / ((nx / plane_resolution) *
+                                     (ny / plane_resolution) * (width))
+
+    # Apply Gaussian smoothing if requested
+    if smoothing_sigma is not None:
+        density_plane = gaussian_smoothing(density_plane, 
+                                           smoothing_sigma)
+
+    return density_plane
+
+
+def convergence_Born(cosmo,
+                     density_planes,
+                     dx, dz,
+                     coords,
+                     z_source):
+  """
+  Compute the Born convergence
+  Args:
+    cosmo: `Cosmology`, cosmology object.
+    density_planes: list of tuples (r, a, density_plane), lens planes to use 
+    dx: float, transverse pixel resolution of the density planes [Mpc/h]
+    dz: float, width of the density planes [Mpc/h]
+    coords: a 3-D array of angular coordinates in radians of N points with shape [batch, N, 2].
+    z_source: 1-D `Tensor` of source redshifts with shape [Nz] .
+    name: `string`, name of the operation.
+  Returns:
+    `Tensor` of shape [batch_size, N, Nz], of convergence values.
+  """
+  # Compute constant prefactor:
+  constant_factor = 3 / 2 * cosmo.Omega_m * (constants.H0 / constants.c)**2
+  # Compute comoving distance of source galaxies
+  r_s = jax_cosmo.background.radial_comoving_distance(cosmo, 1 / (1 + z_source))
+
+  convergence = 0
+  for r, a, p in density_planes:
+    # Normalize density planes
+    density_normalization = dz * r / a
+    p = (p - p.mean()) * constant_factor * density_normalization
+
+    # Interpolate at the density plane coordinates
+    im = map_coordinates(p, 
+                         coords * r / dx - 0.5, 
+                         order=1, mode="wrap")
+
+    convergence += im * jnp.clip(1. - (r / r_s), 0, 1000).reshape([-1, 1, 1])
+
+  return convergence

jaxpm/painting.py

@@ -52,6 +52,34 @@ def cic_read(mesh, positions):
                neighboor_coords[...,1], 
                neighboor_coords[...,3]]*kernel).sum(axis=-1)
 
+def cic_paint_2d(mesh, positions, weight):
+  """ Paints positions onto a 2d mesh
+  mesh: [nx, ny]
+  positions: [npart, 2]
+  weight: [npart]
+  """
+  positions = jnp.expand_dims(positions, 1)
+  floor = jnp.floor(positions)
+  connection = jnp.array([[0, 0], [1., 0], [0., 1], [1., 1]])
+
+  neighboor_coords = floor + connection
+  kernel = 1. - jnp.abs(positions - neighboor_coords)
+  kernel = kernel[..., 0] * kernel[..., 1] 
+  if weight is not None:
+    kernel = kernel * weight[...,jnp.newaxis]
+
+  neighboor_coords = jnp.mod(neighboor_coords.reshape([-1,4,2]).astype('int32'), jnp.array(mesh.shape))
+
+  dnums = jax.lax.ScatterDimensionNumbers(
+    update_window_dims=(),
+    inserted_window_dims=(0, 1),
+    scatter_dims_to_operand_dims=(0, 1))
+  mesh = lax.scatter_add(mesh, 
+                         neighboor_coords, 
+                         kernel.reshape([-1,4]),
+                         dnums)
+  return mesh
+
 def compensate_cic(field):
   """
   Compensate for CiC painting

jaxpm/utils.py

@@ -1,5 +1,6 @@
 import numpy as np
 import jax.numpy as jnp
+from jax.scipy.stats import norm
 
 __all__ = ['power_spectrum']
 
@@ -79,3 +80,20 @@ def power_spectrum(field, kmin=5, dk=0.5, boxsize=False):
   kbins = kedges[:-1] + (kedges[1:] - kedges[:-1]) / 2
 
   return kbins, P / norm
+
+def gaussian_smoothing(im, sigma):
+  """
+  im: 2d image
+  sigma: smoothing scale in px 
+  """
+  # Compute k vector
+  kvec = jnp.stack(jnp.meshgrid(jnp.fft.fftfreq(im.shape[0]),
+                                jnp.fft.fftfreq(im.shape[1])),
+                 axis=-1)
+  k = jnp.linalg.norm(kvec, axis=-1)
+  # We compute the value of the filter at frequency k
+  filter = norm.pdf(k, 0, 1. / (2. * np.pi * sigma))
+  filter /= filter[0,0]
+
+  return jnp.fft.ifft2(jnp.fft.fft2(im) * filter).real
+