switched psi tensor computation to double precision and implemented a…

… fudge factor for theta_cutoff to avoid aliasing issues with the grid width

tests/test_convolution.py

@@ -84,11 +84,11 @@ def _normalize_convolution_tensor_dense(psi, quad_weights, transpose_normalizati
 def _precompute_convolution_tensor_dense(
     in_shape,
     out_shape,
-    kernel_shape,
     filter_basis,
     grid_in="equiangular",
     grid_out="equiangular",
     theta_cutoff=0.01 * math.pi,
+    theta_eps=1e-3,
     transpose_normalization=False,
     basis_norm_mode="none",
     merge_quadrature=False,
@@ -106,21 +106,25 @@ def _precompute_convolution_tensor_dense(
     nlat_out, nlon_out = out_shape
 
     lats_in, win = quadrature._precompute_latitudes(nlat_in, grid=grid_in)
-    lats_in = torch.from_numpy(lats_in).float()
+    lats_in = torch.from_numpy(lats_in)
     lats_out, wout = quadrature._precompute_latitudes(nlat_out, grid=grid_out)
-    lats_out = torch.from_numpy(lats_out).float()  # array for accumulating non-zero indices
+    lats_out = torch.from_numpy(lats_out)
 
     # compute the phi differences. We need to make the linspace exclusive to not double the last point
-    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1)[:-1]
-    lons_out = torch.linspace(0, 2 * math.pi, nlon_out + 1)[:-1]
+    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1, dtype=torch.float64)[:-1]
+    lons_out = torch.linspace(0, 2 * math.pi, nlon_out + 1, dtype=torch.float64)[:-1]
+
+    # effective theta cutoff if multiplied with a fudge factor to avoid aliasing with grid width (especially near poles)
+    theta_cutoff_eff = (1.0 + theta_eps) * theta_cutoff
 
     # compute quadrature weights that will be merged into the Psi tensor
     if transpose_normalization:
-        quad_weights = torch.from_numpy(wout).float().reshape(-1, 1) / nlon_in / 2.0
+        quad_weights = torch.from_numpy(wout).reshape(-1, 1) / nlon_in / 2.0
     else:
-        quad_weights = torch.from_numpy(win).float().reshape(-1, 1) / nlon_in / 2.0
+        quad_weights = torch.from_numpy(win).reshape(-1, 1) / nlon_in / 2.0
 
-    out = torch.zeros(kernel_size, nlat_out, nlon_out, nlat_in, nlon_in)
+    # array for accumulating non-zero indices
+    out = torch.zeros(kernel_size, nlat_out, nlon_out, nlat_in, nlon_in, dtype=torch.float64)
 
     for t in range(nlat_out):
         for p in range(nlon_out):
@@ -147,13 +151,14 @@ def _precompute_convolution_tensor_dense(
             phi = torch.where(phi < 0.0, phi + 2 * torch.pi, phi)
 
             # find the indices where the rotated position falls into the support of the kernel
-            iidx, vals = filter_basis.compute_support_vals(theta, phi, r_cutoff=theta_cutoff)
+            iidx, vals = filter_basis.compute_support_vals(theta, phi, r_cutoff=theta_cutoff_eff)
             out[iidx[:, 0], t, p, iidx[:, 1], iidx[:, 2]] = vals
 
-    # take care of normalization
+    # take care of normalization and cast to float
     out = _normalize_convolution_tensor_dense(
         out, quad_weights=quad_weights, transpose_normalization=transpose_normalization, basis_norm_mode=basis_norm_mode, merge_quadrature=merge_quadrature
     )
+    out = out.to(dtype=torch.float32)
 
     return out
 
@@ -239,7 +244,6 @@ def test_disco_convolution(
             psi_dense = _precompute_convolution_tensor_dense(
                 out_shape,
                 in_shape,
-                kernel_shape,
                 filter_basis,
                 grid_in=grid_out,
                 grid_out=grid_in,
@@ -256,7 +260,6 @@ def test_disco_convolution(
             psi_dense = _precompute_convolution_tensor_dense(
                 in_shape,
                 out_shape,
-                kernel_shape,
                 filter_basis,
                 grid_in=grid_in,
                 grid_out=grid_out,

torch_harmonics/convolution.py

@@ -134,6 +134,7 @@ def _precompute_convolution_tensor_s2(
     grid_in="equiangular",
     grid_out="equiangular",
     theta_cutoff=0.01 * math.pi,
+    theta_eps = 1e-3,
     transpose_normalization=False,
     basis_norm_mode="mean",
     merge_quadrature=False,
@@ -164,20 +165,23 @@ def _precompute_convolution_tensor_s2(
 
     # precompute input and output grids
     lats_in, win = _precompute_latitudes(nlat_in, grid=grid_in)
-    lats_in = torch.from_numpy(lats_in).float()
+    lats_in = torch.from_numpy(lats_in)
     lats_out, wout = _precompute_latitudes(nlat_out, grid=grid_out)
-    lats_out = torch.from_numpy(lats_out).float()
+    lats_out = torch.from_numpy(lats_out)
 
     # compute the phi differences
     # It's imporatant to not include the 2 pi point in the longitudes, as it is equivalent to lon=0
-    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1)[:-1]
+    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1, dtype=torch.float64)[:-1]
 
     # compute quadrature weights and merge them into the convolution tensor.
     # These quadrature integrate to 1 over the sphere.
     if transpose_normalization:
-        quad_weights = torch.from_numpy(wout).float().reshape(-1, 1) / nlon_in / 2.0
+        quad_weights = torch.from_numpy(wout).reshape(-1, 1) / nlon_in / 2.0
     else:
-        quad_weights = torch.from_numpy(win).float().reshape(-1, 1) / nlon_in / 2.0
+        quad_weights = torch.from_numpy(win).reshape(-1, 1) / nlon_in / 2.0
+
+    # effective theta cutoff if multiplied with a fudge factor to avoid aliasing with grid width (especially near poles)
+    theta_cutoff_eff = (1.0 + theta_eps) * theta_cutoff
 
     out_idx = []
     out_vals = []
@@ -207,7 +211,7 @@ def _precompute_convolution_tensor_s2(
         phi = torch.where(phi < 0.0, phi + 2 * torch.pi, phi)
 
         # find the indices where the rotated position falls into the support of the kernel
-        iidx, vals = filter_basis.compute_support_vals(theta, phi, r_cutoff=theta_cutoff)
+        iidx, vals = filter_basis.compute_support_vals(theta, phi, r_cutoff=theta_cutoff_eff)
 
         # add the output latitude and reshape such that psi has dimensions kernel_shape x nlat_out x (nlat_in*nlon_in)
         idx = torch.stack([iidx[:, 0], t * torch.ones_like(iidx[:, 0]), iidx[:, 1] * nlon_in + iidx[:, 2]], dim=0)
@@ -217,8 +221,8 @@ def _precompute_convolution_tensor_s2(
         out_vals.append(vals)
 
     # concatenate the indices and values
-    out_idx = torch.cat(out_idx, dim=-1).to(torch.long).contiguous()
-    out_vals = torch.cat(out_vals, dim=-1).to(torch.float32).contiguous()
+    out_idx = torch.cat(out_idx, dim=-1)
+    out_vals = torch.cat(out_vals, dim=-1)
 
     out_vals = _normalize_convolution_tensor_s2(
         out_idx,
@@ -232,6 +236,9 @@ def _precompute_convolution_tensor_s2(
         merge_quadrature=merge_quadrature,
     )
 
+    out_idx = out_idx.contiguous()
+    out_vals = out_vals.to(dtype=torch.float32).contiguous()
+
     return out_idx, out_vals
 
 

torch_harmonics/distributed/distributed_convolution.py

@@ -75,6 +75,7 @@ def _precompute_distributed_convolution_tensor_s2(
     grid_in="equiangular",
     grid_out="equiangular",
     theta_cutoff=0.01 * math.pi,
+    theta_eps = 1e-3,
     transpose_normalization=False,
     basis_norm_mode="mean",
     merge_quadrature=False,
@@ -103,21 +104,25 @@ def _precompute_distributed_convolution_tensor_s2(
     nlat_in, nlon_in = in_shape
     nlat_out, nlon_out = out_shape
 
+    # precompute input and output grids
     lats_in, win = _precompute_latitudes(nlat_in, grid=grid_in)
-    lats_in = torch.from_numpy(lats_in).float()
+    lats_in = torch.from_numpy(lats_in)
     lats_out, wout = _precompute_latitudes(nlat_out, grid=grid_out)
-    lats_out = torch.from_numpy(lats_out).float()
+    lats_out = torch.from_numpy(lats_out)
 
     # compute the phi differences
     # It's imporatant to not include the 2 pi point in the longitudes, as it is equivalent to lon=0
-    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1)[:-1]
+    lons_in = torch.linspace(0, 2 * math.pi, nlon_in + 1, dtype=torch.float64)[:-1]
 
     # compute quadrature weights and merge them into the convolution tensor.
     # These quadrature integrate to 1 over the sphere.
     if transpose_normalization:
-        quad_weights = torch.from_numpy(wout).float().reshape(-1, 1) / nlon_in / 2.0
+        quad_weights = torch.from_numpy(wout).reshape(-1, 1) / nlon_in / 2.0
     else:
-        quad_weights = torch.from_numpy(win).float().reshape(-1, 1) / nlon_in / 2.0
+        quad_weights = torch.from_numpy(win).reshape(-1, 1) / nlon_in / 2.0
+
+    # effective theta cutoff if multiplied with a fudge factor to avoid aliasing with grid width (especially near poles)
+    theta_cutoff_eff = (1.0 + theta_eps) * theta_cutoff
 
     out_idx = []
     out_vals = []
@@ -147,7 +152,7 @@ def _precompute_distributed_convolution_tensor_s2(
         phi = torch.where(phi < 0.0, phi + 2 * torch.pi, phi)
 
         # find the indices where the rotated position falls into the support of the kernel
-        iidx, vals = filter_basis.compute_support_vals(theta, phi, r_cutoff=theta_cutoff)
+        iidx, vals = filter_basis.compute_support_vals(theta, phi, r_cutoff=theta_cutoff_eff)
 
         # add the output latitude and reshape such that psi has dimensions kernel_shape x nlat_out x (nlat_in*nlon_in)
         idx = torch.stack([iidx[:, 0], t * torch.ones_like(iidx[:, 0]), iidx[:, 1] * nlon_in + iidx[:, 2]], dim=0)
@@ -157,8 +162,8 @@ def _precompute_distributed_convolution_tensor_s2(
         out_vals.append(vals)
 
     # concatenate the indices and values
-    out_idx = torch.cat(out_idx, dim=-1).to(torch.long).contiguous()
-    out_vals = torch.cat(out_vals, dim=-1).to(torch.float32).contiguous()
+    out_idx = torch.cat(out_idx, dim=-1)
+    out_vals = torch.cat(out_vals, dim=-1)
 
     out_vals = _normalize_convolution_tensor_s2(
         out_idx,
@@ -189,6 +194,9 @@ def _precompute_distributed_convolution_tensor_s2(
     # for the indices we need to recompute them to refer to local indices of the input tenor
     out_idx = torch.stack([out_idx[0, ilats], out_idx[1, ilats], (lats[ilats] - start_idx) * nlon_in + lons[ilats]], dim=0)
 
+    out_idx = out_idx.contiguous()
+    out_vals = out_vals.to(dtype=torch.float32).contiguous()
+
     return out_idx, out_vals