add lpt2

jaxpm/pm.py

@@ -7,7 +7,8 @@ from jax.sharding import PartitionSpec as P
 
 from jaxpm.distributed import (autoshmap, fft3d, get_local_shape, ifft3d,
                                normal_field)
-from jaxpm.growth import dGfa, growth_factor, growth_rate
+from jaxpm.growth import (dGf2a, dGfa, growth_factor, growth_factor_second,
+                          growth_rate, growth_rate_second)
 from jaxpm.kernels import (PGD_kernel, fftk, gradient_kernel, laplace_kernel,
                            longrange_kernel)
 from jaxpm.painting import cic_paint, cic_paint_dx, cic_read, cic_read_dx
@@ -39,11 +40,46 @@ def pm_forces(positions, mesh_shape=None, delta=None, r_split=0, halo_size=0):
     return forces
 
 
+def lpt2_source(mesh_size, initial_conditions):
+
+    kvec = fftk(mesh_size)
+    # TODO : this has already been done for LPT1, we should reuse it
+    delta_k = fft3d(initial_conditions)
+
+    source = jnp.zeros_like(delta_k)
+
+    D1 = [1, 2, 0]
+    D2 = [2, 0, 1]
+
+    # laplace_kernel should be actually inv laplace_kernel
+    # adding a minus sign here that will be negated when computing forces
+    # because F = -grad(phi)
+    # and phi = -laplace_kernel(delta_k)
+    pot_k = delta_k * laplace_kernel(delta_k)
+
+    nabla_i_nabla_i = [
+        ifft3d(gradient_kernel(kvec, i)**2 * pot_k) for i in range(3)
+    ]
+    # for diagonal terms
+    source += nabla_i_nabla_i[D1[0]] * nabla_i_nabla_i[D2[0]]
+    source += nabla_i_nabla_i[D1[1]] * nabla_i_nabla_i[D2[1]]
+    source += nabla_i_nabla_i[D1[2]] * nabla_i_nabla_i[D2[2]]
+
+    # off diag terms
+    for i in range(3):
+        nabla_i_nabla_j = gradient_kernel(kvec, D1[i]) * gradient_kernel(
+            kvec, D2[i])
+        phi = ifft3d(nabla_i_nabla_j * pot_k)
+        source -= phi**2
+
+    return source
+
+
 def lpt(cosmo, initial_conditions, a, halo_size=0):
     """
     Computes first order LPT displacement
     """
-    local_mesh_shape = get_local_shape(initial_conditions.shape) + (3, )
+    local_mesh_shape = (*get_local_shape(initial_conditions.shape), 3)
     displacement = autoshmap(
       partial(jnp.zeros, shape=(local_mesh_shape), dtype='float32'),
       in_specs=(),
@@ -62,6 +98,39 @@ def lpt(cosmo, initial_conditions, a, halo_size=0):
     return dx, p, f
 
 
+# @Credit Hugo Simon https://github.com/hsimonfroy/montecosmo
+def lpt2(cosmo, initial_conditions, dx, p, f, a, halo_size=0):
+
+    mesh_size = initial_conditions.shape
+    local_mesh_shape = (*get_local_shape(initial_conditions.shape), 3)
+    # TODO
+    # Displacements have been created in the previous step
+    # find a way to reuse them
+    displacement = autoshmap(
+      partial(jnp.zeros, shape=(local_mesh_shape), dtype='float32'),
+      in_specs=(),
+      out_specs=P('x', 'y'))()  # yapf: disable
+
+    lpt2_delta = lpt2_source(mesh_size, initial_conditions)
+    delta2_k = fft3d(lpt2_delta)
+
+    lpt2_forces = pm_forces(displacement,
+                            mesh_size,
+                            delta_k=delta2_k,
+                            halo_size=halo_size)
+    dx2 = 3 / 7 * growth_factor_second(cosmo, a) * lpt2_forces
+    p2 = a**2 * growth_rate_second(cosmo, a) * jnp.sqrt(
+        jc.background.Esqr(cosmo, a)) * dx2
+    f2 = a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dGf2a(cosmo,
+                                                               a) * lpt2_forces
+
+    dx += dx2
+    p += p2
+    f += f2
+
+    return dx, p, f
+
+
 def linear_field(mesh_shape, box_size, pk, seed):
     """
     Generate initial conditions.