Spatialhash regional spherical improvements

docs/development/unstructured_grid_search.md

@@ -42,12 +42,12 @@ The algorithm has two phases: **initialisation** (once, when the grid is first u
 
 The hash grid is three-dimensional regardless of the source grid:
 
-| Source grid | Mesh type | Hash-grid space                       |
-| ----------- | --------- | ------------------------------------- |
-| `XGrid`     | spherical | Cartesian unit cube (lon/lat → x,y,z) |
-| `XGrid`     | flat      | 2-D lon/lat bounding box (z set to 0) |
-| `UxGrid`    | spherical | Cartesian unit cube                   |
-| `UxGrid`    | flat      | 2-D lon/lat bounding box              |
+| Source grid | Mesh type | Hash-grid space                          |
+| ----------- | --------- | ---------------------------------------- |
+| `XGrid`     | spherical | Cartesian bounding box (lon/lat → x,y,z) |
+| `XGrid`     | flat      | 2-D lon/lat bounding box (z set to 0)    |
+| `UxGrid`    | spherical | Cartesian bounding box (lon/lat → x,y,z) |
+| `UxGrid`    | flat      | 2-D lon/lat bounding box                 |
 
 For spherical grids, node coordinates are converted from degrees to radians and then to Cartesian (x, y, z) on the unit sphere using `parcels._core.index_search._latlon_rad_to_xyz`:
 
@@ -57,7 +57,7 @@ y = sin(lon) * cos(lat)
 z = sin(lat)
 ```
 
-The hash grid then spans the unit cube `[-1, 1]³`. Working in Cartesian space avoids the longitude wrap-around discontinuity that would otherwise cause the bounding boxes of cells crossing the antimeridian to erroneously span the entire domain.
+The hash grid then spans the axis-aligned Cartesian bounding box of the transformed grid nodes. For a global grid this is (nearly) the unit cube `[-1, 1]³`; for a regional grid it is much tighter, so the full quantization resolution (1024 bins per axis) is spent on the region actually covered by the grid rather than the whole sphere. Working in Cartesian space avoids the longitude wrap-around discontinuity that would otherwise cause the bounding boxes of cells crossing the antimeridian to erroneously span the entire domain.
 
 For flat meshes the hash grid simply spans `[lon_min, lon_max] × [lat_min, lat_max]`, with z fixed at 0.
 

src/parcels/_core/spatialhash.py

@@ -11,6 +11,17 @@
 from parcels._core.warnings import FieldSetWarning
 from parcels._python import isinstance_noimport
 
+# Budget on the total number of (face, hash cell) pairs in the hash table:
+# max(_HASH_ENTRIES_PER_FACE * nfaces, _HASH_ENTRY_BUDGET_MIN).
+# When the hash grid cell size, set by the bitwidth, would result in too many
+# hash entries per face, the hash grid is coarsened by lowering the bitwidth
+# The target value for the number of hash entries per face is chosen to keep
+# the number of particle in cell checks as small as possible, while also
+# minimizing the hash table construction memory footprint.
+_HASH_ENTRIES_PER_FACE = 16
+_HASH_ENTRY_BUDGET_MIN = 2**22
+_HASH_MAX_BITWIDTH = 1023
+
 
 class SpatialHash:
     """Custom data structure that is used for performing grid searches using Spatial Hashing. This class constructs an overlying
@@ -31,7 +42,6 @@ class SpatialHash:
     def __init__(
         self,
         grid,
-        bitwidth=1023,
     ):
         if isinstance_noimport(grid, "XGrid"):
             self._point_in_cell = curvilinear_point_in_cell
@@ -41,21 +51,23 @@ def __init__(
             raise ValueError("Expected `grid` to be a parcels.XGrid or parcels.UxGrid")
 
         self._source_grid = grid
-        self._bitwidth = bitwidth  # Max integer to use per coordinate in quantization (10 bits = 0..1023)
+        self._bitwidth = _HASH_MAX_BITWIDTH  # Max integer to use per coordinate in quantization (10 bits = 0..1023)
 
         if isinstance_noimport(grid, "XGrid"):
             self._coord_dim = 2  # Number of computational coordinates is 2 (bilinear interpolation)
             if self._source_grid._mesh == "spherical":
-                # Boundaries of the hash grid are the unit cube
-                self._xmin = -1.0
-                self._ymin = -1.0
-                self._zmin = -1.0
-                self._xmax = 1.0
-                self._ymax = 1.0
-                self._zmax = 1.0  # Compute the cell centers of the source grid (for now, assuming Xgrid)
                 lon = np.deg2rad(self._source_grid.lon)
                 lat = np.deg2rad(self._source_grid.lat)
                 x, y, z = _latlon_rad_to_xyz(lat, lon)
+                # Boundaries of the hash grid are the Cartesian bounding box of the
+                # transformed grid, so that regional domains retain full quantization
+                # resolution instead of spreading it over the whole unit cube
+                self._xmin = x.min()
+                self._xmax = x.max()
+                self._ymin = y.min()
+                self._ymax = y.max()
+                self._zmin = z.min()
+                self._zmax = z.max()
                 _xbound = np.stack(
                     (
                         x[:-1, :-1],
@@ -149,19 +161,20 @@ def __init__(
         elif isinstance_noimport(grid, "UxGrid"):
             self._coord_dim = grid.uxgrid.n_max_face_nodes  # Number of barycentric coordinates
             if self._source_grid._mesh == "spherical":
-                # Boundaries of the hash grid are the unit cube
-                self._xmin = -1.0
-                self._ymin = -1.0
-                self._zmin = -1.0
-                self._xmax = 1.0
-                self._ymax = 1.0
-                self._zmax = 1.0  # Compute the cell centers of the source grid (for now, assuming Xgrid)
                 # Reshape node coordinates to (nfaces, nnodes_per_face)
                 nids = self._source_grid.uxgrid.face_node_connectivity.values
                 lon = self._source_grid.uxgrid.node_lon.values[nids]
                 lat = self._source_grid.uxgrid.node_lat.values[nids]
-                x, y, z = _latlon_rad_to_xyz(np.deg2rad(lat), np.deg2rad(lon))
                 _xbound, _ybound, _zbound = _latlon_rad_to_xyz(np.deg2rad(lat), np.deg2rad(lon))
+                # Boundaries of the hash grid are the Cartesian bounding box of the
+                # transformed grid, so that regional domains retain full quantization
+                # resolution instead of spreading it over the whole unit cube
+                self._xmin = _xbound.min()
+                self._xmax = _xbound.max()
+                self._ymin = _ybound.min()
+                self._ymax = _ybound.max()
+                self._zmin = _zbound.min()
+                self._zmax = _zbound.max()
 
                 # Compute bounding box of each face
                 self._xlow = np.atleast_2d(np.min(_xbound, axis=-1))
@@ -193,9 +206,60 @@ def __init__(
                 self._zlow = np.zeros_like(self._xlow)
                 self._zhigh = np.zeros_like(self._xlow)
 
+        # Cap the quantization resolution so the hash table stays within a fixed entry
+        # budget.
+        budget = max(_HASH_ENTRIES_PER_FACE * np.size(self._xlow), _HASH_ENTRY_BUDGET_MIN)
+        if self._total_hash_entries(self._bitwidth) > budget:
+            # Binary search for the largest bitwidth whose table fits the budget. The
+            # entry count is not perfectly monotone in bitwidth (cell-boundary flooring
+            # effects), so the result may sit marginally below the true maximum; any
+            # in-budget bitwidth is valid. At bitwidth 1 the count equals nfaces, which
+            # is always within budget, so the search cannot fail.
+            lo, hi = 1, self._bitwidth
+            while lo < hi:
+                mid = (lo + hi + 1) // 2
+                if self._total_hash_entries(mid) <= budget:
+                    lo = mid
+                else:
+                    hi = mid - 1
+            self._bitwidth = lo
+
         # Generate the mapping from the hash indices to unstructured grid elements
         self._hash_table = self._initialize_hash_table()
 
+    def _total_hash_entries(self, bitwidth):
+        """Total number of (face, hash cell) pairs the hash table would hold at a given
+        quantization resolution, i.e. the summed hash-cell count of all face bounding boxes.
+        """
+        xqlow, yqlow, zqlow = quantize_coordinates(
+            self._xlow,
+            self._ylow,
+            self._zlow,
+            self._xmin,
+            self._xmax,
+            self._ymin,
+            self._ymax,
+            self._zmin,
+            self._zmax,
+            bitwidth,
+        )
+        xqhigh, yqhigh, zqhigh = quantize_coordinates(
+            self._xhigh,
+            self._yhigh,
+            self._zhigh,
+            self._xmin,
+            self._xmax,
+            self._ymin,
+            self._ymax,
+            self._zmin,
+            self._zmax,
+            bitwidth,
+        )
+        nx = xqhigh.astype(np.int64) - xqlow + 1
+        ny = yqhigh.astype(np.int64) - yqlow + 1
+        nz = zqhigh.astype(np.int64) - zqlow + 1
+        return int((nx * ny * nz).sum())
+
     def _initialize_hash_table(self):
         """Create a mapping that relates unstructured grid faces to hash indices by determining
         which faces overlap with which hash cells
@@ -238,82 +302,77 @@ def _initialize_hash_table(self):
         num_hash_per_face = (nx * ny * nz).astype(
             np.int32, copy=False
         )  # Since nx, ny, nz are in the 10-bit range, their product fits in int32
-        total_hash_entries = int(num_hash_per_face.sum())
-
-        # Preallocate output arrays
-        morton_codes = np.zeros(total_hash_entries, dtype=np.uint32)
-
-        # Compute the j, i indices corresponding to each hash entry
+        # Sums over faces can exceed int32, so accumulate in int64
+        total_hash_entries = int(num_hash_per_face.sum(dtype=np.int64))
+        # Entry indices fit in int32 for all but extreme cases; fall back to int64 when needed
+        idx_dtype = np.int64 if total_hash_entries > np.iinfo(np.int32).max else np.int32
+
+        # Every face overlaps at least one hash cell (nx, ny, nz >= 1 since quantization
+        # is monotone), and contributes one hash entry per cell of its quantized bounding
+        # box. Entries are generated in face-major order: face_ids maps each entry to its
+        # face, and intra enumerates the cells of that face's box (0..num_hash_per_face-1).
         nface = np.size(self._xlow)
-        face_ids = np.repeat(np.arange(nface, dtype=np.int32), num_hash_per_face)
-        offsets = np.concatenate(([0], np.cumsum(num_hash_per_face))).astype(np.int32)[:-1]
-
-        valid = num_hash_per_face != 0
-        if not np.any(valid):
-            # nothing to do
-            pass
-        else:
-            # Grab only valid faces to avoid empty arrays
-            nx_v = np.asarray(nx[valid], dtype=np.int32)
-            ny_v = np.asarray(ny[valid], dtype=np.int32)
-            nz_v = np.asarray(nz[valid], dtype=np.int32)
-            xlow_v = np.asarray(xqlow[valid], dtype=np.int32)
-            ylow_v = np.asarray(yqlow[valid], dtype=np.int32)
-            zlow_v = np.asarray(zqlow[valid], dtype=np.int32)
-            starts_v = np.asarray(offsets[valid], dtype=np.int32)
-
-            # Count of elements per valid face (should match num_hash_per_face[valid])
-            counts = (nx_v * ny_v * nz_v).astype(np.int32)
-            total = int(counts.sum())
-
-            # Map each global element to its face and output position
-            start_for_elem = np.repeat(starts_v, counts)  # shape (total,)
-
-            # Intra-face linear index for each element (0..counts_i-1)
-            # Offsets per face within the concatenation of valid faces:
-            face_starts_local = np.cumsum(np.r_[0, counts[:-1]])
-            intra = np.arange(total, dtype=np.int32) - np.repeat(face_starts_local, counts)
-
-            # Derive (zi, yi, xi) from intra using per-face sizes
-            ny_nz = np.repeat(ny_v * nz_v, counts)
-            nz_rep = np.repeat(nz_v, counts)
-
-            xi = intra // ny_nz
-            rem = intra % ny_nz
-            yi = rem // nz_rep
-            zi = rem % nz_rep
-
-            # Add per-face lows
-            x0 = np.repeat(xlow_v, counts)
-            y0 = np.repeat(ylow_v, counts)
-            z0 = np.repeat(zlow_v, counts)
-
-            xq = x0 + xi
-            yq = y0 + yi
-            zq = z0 + zi
-
-            # Vectorized morton encode for all elements at once
-            codes_all = _encode_quantized_morton3d(xq, yq, zq)
-
-            # Scatter into the preallocated output using computed absolute indices
-            out_idx = start_for_elem + intra
-            morton_codes[out_idx] = codes_all
-
-        # Sort face indices by morton code
-        order = np.argsort(morton_codes)
-        morton_codes_sorted = morton_codes[order]
-        face_sorted = face_ids[order]
-        j_sorted, i_sorted = np.unravel_index(face_sorted, self._xlow.shape)
-
-        # Get a list of unique morton codes and their corresponding starts and counts (CSR format)
-        keys, starts, counts = np.unique(morton_codes_sorted, return_index=True, return_counts=True)
+        face_ids = np.repeat(np.arange(nface, dtype=np.uint32), num_hash_per_face)
+        face_starts = np.concatenate(([0], np.cumsum(num_hash_per_face, dtype=np.int64)))[:-1]
+        intra = np.arange(total_hash_entries, dtype=idx_dtype) - np.repeat(
+            face_starts.astype(idx_dtype, copy=False), num_hash_per_face
+        )
 
+        # Derive (xi, yi, zi) cell offsets within each face's box from intra,
+        # then shift by the per-face low corner to get quantized cell coordinates
+        ny_nz = np.repeat(ny * nz, num_hash_per_face)
+        nz_rep = np.repeat(nz, num_hash_per_face)
+
+        xi = intra // ny_nz
+        rem = intra % ny_nz
+        yi = rem // nz_rep
+        zi = rem % nz_rep
+
+        xq = np.repeat(xqlow, num_hash_per_face) + xi
+        yq = np.repeat(yqlow, num_hash_per_face) + yi
+        zq = np.repeat(zqlow, num_hash_per_face) + zi
+
+        # Vectorized morton encode for all entries at once, already in face-major order
+        morton_codes = _encode_quantized_morton3d(xq, yq, zq)
+        del intra, rem, xi, yi, zi, ny_nz, nz_rep, xq, yq, zq
+
+        # Sort entries by morton code. Each (code, face) pair is fused into one uint64
+        # with the code in the high 32 bits and the face id in the low 32 bits: unsigned
+        # comparison then orders by code, with ties broken by ascending face id. Sorting
+        # the fused array in place avoids the argsort permutation array and the gather
+        # copies it would imply. Pairs are unique, so the ordering is deterministic.
+        packed = morton_codes.astype(np.uint64)
+        del morton_codes
+        packed <<= np.uint64(32)
+        np.bitwise_or(packed, face_ids, out=packed)
+        del face_ids
+        # Perform a single sort on the packed (morton_code | face_id ) list
+        packed.sort()
+        # Trunctating back to a uint32 keeps the lower 32 bits (the face_id's)
+        face_sorted = packed.astype(np.uint32)
+        # Purge the face ids from the packed list to retain only the morton codes
+        packed >>= np.uint64(32)
+        # Cast the morton codes back to uint32
+        morton_codes_sorted = packed.astype(np.uint32)
+        del packed
+
+        # Get a list of unique morton codes and their corresponding starts and counts (CSR format).
+        # The codes are already sorted at this point, first by morton code, then by face_id
+        # Starting indices of the matrix rows are located by finding indices where the morton codes differ
+        starts = np.concatenate(([0], np.flatnonzero(morton_codes_sorted[1:] != morton_codes_sorted[:-1]) + 1))
+        # The unique keys for the hash table are the unique morton codes
+        keys = morton_codes_sorted[starts]
+        # The number of faces per hash keys (morton codes) is easily calculated as the difference betwee the start values
+        counts = np.diff(np.concatenate((starts, [morton_codes_sorted.size])))
+
+        # The flat face id is stored (4 bytes per entry); query() unravels the gathered
+        # candidates to (j, i) on demand, instead of holding two precomputed int64
+        # index arrays (16 bytes per entry) for the lifetime of the grid.
         hash_table = {
             "keys": keys,
             "starts": starts,
             "counts": counts,
-            "i": i_sorted,
-            "j": j_sorted,
+            "faces": face_sorted,
         }
         return hash_table
 
@@ -341,8 +400,7 @@ def query(self, y, x):
         keys = self._hash_table["keys"]
         starts = self._hash_table["starts"]
         counts = self._hash_table["counts"]
-        i = self._hash_table["i"]
-        j = self._hash_table["j"]
+        faces = self._hash_table["faces"]
 
         y = np.asarray(y)
         x = np.asarray(x)
@@ -358,7 +416,16 @@ def query(self, y, x):
             qz = np.zeros_like(qx)
 
         query_codes = _encode_morton3d(
-            qx, qy, qz, self._xmin, self._xmax, self._ymin, self._ymax, self._zmin, self._zmax
+            qx,
+            qy,
+            qz,
+            self._xmin,
+            self._xmax,
+            self._ymin,
+            self._ymax,
+            self._zmin,
+            self._zmax,
+            bitwidth=self._bitwidth,
         ).ravel()
         num_queries = query_codes.size
 
@@ -418,9 +485,10 @@ def query(self, y, x):
         # use to quickly gather the (i,j) pairs for each query
         source_idx = starts[hash_positions].astype(np.int32) + intra
 
-        # Gather all candidate (j,i) pairs in one shot
-        j_all = j[source_idx]
-        i_all = i[source_idx]
+        # Gather all candidate face ids in one shot and unravel them to (j, i) pairs;
+        # only the gathered candidates are unraveled, not the whole table
+        face_all = faces[source_idx]
+        j_all, i_all = np.unravel_index(face_all, self._xlow.shape)
 
         # Now we need to construct arrays that repeats the y and x coordinates for each candidate
         # to enable vectorized point-in-cell checks
@@ -588,10 +656,15 @@ def quantize_coordinates(x, y, z, xmin, xmax, ymin, ymax, zmin, zmax, bitwidth=1
         zn = np.where(dz != 0, (z - zmin) / dz, 0.0)
 
     # --- 2) Quantize to (0..bitwidth). ---
-    # Multiply by bitwidth, round down, and clip to be safe against slight overshoot.
-    xq = np.clip((xn * bitwidth).astype(np.uint32), 0, bitwidth)
-    yq = np.clip((yn * bitwidth).astype(np.uint32), 0, bitwidth)
-    zq = np.clip((zn * bitwidth).astype(np.uint32), 0, bitwidth)
+    # Multiply by bitwidth, round down, and clip to be safe against overshoot.
+    # Clip in float space before casting: out-of-range queries (e.g., points outside
+    # a regional domain) would otherwise wrap around when a negative float is cast to uint32.
+    # NaN queries produce arbitrary codes here; they are discarded downstream by the
+    # finite-coordinate mask in SpatialHash.query.
+    with np.errstate(invalid="ignore"):
+        xq = np.clip(xn * bitwidth, 0, bitwidth).astype(np.uint32)
+        yq = np.clip(yn * bitwidth, 0, bitwidth).astype(np.uint32)
+        zq = np.clip(zn * bitwidth, 0, bitwidth).astype(np.uint32)
 
     return xq, yq, zq