"""Grid tools for FINAM."""
from enum import Enum, IntEnum
from math import isclose, nan
import numpy as np
def point_order(order, axes_reversed=False):
"""
Determine apparent point order incorporating axes order reversion.
Parameters
----------
order : str
Point and cell ordering.
Either Fortran-like ("F") or C-like ("C"), by default "F"
axes_reversed : arraylike or None, optional
Indicate reversed axes order for the associated data, by default False
Returns
-------
str
Apparent point ordering.
"""
reverse_order = {"C": "F", "F": "C"}
return reverse_order[order] if axes_reversed else order
def order_map(shape, of="F", to="C"):
"""
Generate order mapping.
Parameters
----------
shape : tuple
Array shape of interest.
of : str, optional
Starting ordering.
Either Fortran-like ("F") or C-like ("C"), by default "F"
to : str, optional
Target ordering.
Either Fortran-like ("F") or C-like ("C"), by default "C"
Returns
-------
np.ndarray
Mapping indices.
"""
size = np.prod(shape)
return np.arange(size, dtype=int).reshape(shape, order=of).reshape(-1, order=to)
def gen_node_centers(grid):
"""
Calculate the node centers of the given grid cells.
Parameters
----------
grid : Grid
Grid to take the cells from.
Returns
-------
np.ndarray
Centroids for all cells.
"""
unique_cell_types = np.unique(grid.cell_types)
result = np.empty((grid.cell_count, grid.dim), dtype=float)
for ctype in unique_cell_types:
# select current cell type
sel = grid.cell_types == ctype
points = grid.points[grid.cells[sel][:, : NODE_COUNT[ctype]]]
result[sel] = np.mean(points, axis=1)
return result
def gen_axes(dims, spacing, origin, axes_increase=None):
"""
Generate uniform axes.
Parameters
----------
dims : iterable
Dimensions of the uniform grid for each direction.
spacing : iterable
Spacing of the uniform in each dimension. Must be positive.
origin : iterable
Origin of the uniform grid.
axes_increase : arraylike or None, optional
False to indicate a bottom up axis (in xyz order), by default None
Returns
-------
list of np.ndarray
Axes of the uniform grid.
"""
if axes_increase is None:
axes_increase = np.full(len(dims), True, dtype=bool)
if len(axes_increase) != len(dims):
raise ValueError("gen_axes: wrong length of 'axes_increase'")
axes = []
for i, d in enumerate(dims):
axes.append(np.arange(d) * spacing[i] + origin[i])
if not axes_increase[i]:
axes[i] = axes[i][::-1]
return axes
def gen_points(axes, order="F", axes_increase=None):
"""
Generate points from axes of a rectilinear grid.
Parameters
----------
axes : list of np.ndarray
Axes defining the coordinates in each direction (xyz order).
order : str, optional
Point and cell ordering.
Either Fortran-like ("F") or C-like ("C"), by default "F"
axes_increase : arraylike or None, optional
False to indicate a bottom up axis (in xyz order), by default None
Returns
-------
np.ndarray
Points of the grid in given order and orientation.
"""
if axes_increase is None:
axes_increase = np.full(len(axes), True, dtype=bool)
axes = list(axes)
for i, inc in enumerate(axes_increase):
if not inc:
axes[i] = axes[i][::-1]
dim = len(axes)
# append empty dimensions
for _ in range(dim, 3):
axes.append(np.zeros(1, dtype=float))
x_dim = len(axes[0])
y_dim = len(axes[1])
z_dim = len(axes[2])
pnt_cnt = x_dim * y_dim * z_dim
x_id, y_id, z_id = np.mgrid[0:x_dim, 0:y_dim, 0:z_dim]
points = np.empty((pnt_cnt, 3), dtype=float)
# VTK sorts points and cells in Fortran order
points[:, 0] = axes[0][x_id.reshape(-1, order=order)]
points[:, 1] = axes[1][y_id.reshape(-1, order=order)]
points[:, 2] = axes[2][z_id.reshape(-1, order=order)]
return points[:, :dim]
def gen_cells(dims, order="F"):
"""
Generate cells from dimensions of a structured grid.
Parameters
----------
dims : iterable
Dimensions of the structured grid for each direction.
order : str, optional
Point and cell ordering.
Either Fortran-like ("F") or C-like ("C"), by default "F"
Returns
-------
np.ndarray
Cell definitions containing the list of node IDs for each cell.
"""
# sort out empty dimensions
c_dim = [d - 1 for d in dims if d > 1]
c_cnt = int(np.prod(c_dim))
mesh_dim = len(c_dim)
c_rng = np.arange(c_cnt, dtype=int)
if mesh_dim == 0:
# cells are vertices in 0D
c = np.array([[0]], dtype=int)
elif mesh_dim == 1:
# cells are lines in 1D
c = np.empty((c_cnt, 2), dtype=int)
c[:, 0] = c_rng
c[:, 1] = c[:, 0] + 1
elif mesh_dim == 2:
# cells are quad in 2D
c = np.empty((c_cnt, 4), dtype=int)
# top left corner (last node in cell definition)
c[:, 3] = c_rng
c[:, 3] += c_rng // c_dim[0]
# top right corner one ID higher than left
c[:, 2] = c[:, 3] + 1
# lower right corner two IDs higher than top left in next row
c[:, 1] = c[:, 3] + 2 + c_dim[0]
# lower left corner one ID lower than right
c[:, 0] = c[:, 1] - 1
else:
# cells are hex in 3D
c = np.empty((c_cnt, 8), dtype=int)
# ? should upper and lower layer be swapped?
# upper layer
c[:, 3] = c_rng
c[:, 3] += (c_dim[0] + c_dim[1] + 1) * (c_rng // (c_dim[0] * c_dim[1]))
c[:, 3] += (c_rng % (c_dim[0] * c_dim[1])) // c_dim[0]
c[:, 2] = c[:, 3] + 1
c[:, 1] = c[:, 3] + 2 + c_dim[0]
c[:, 0] = c[:, 1] - 1
# lower layer
c[:, 7] = c[:, 3] + (1 + c_dim[0]) * (1 + c_dim[1])
c[:, 6] = c[:, 7] + 1
c[:, 5] = c[:, 7] + 2 + c_dim[0]
c[:, 4] = c[:, 5] - 1
if order == "C" and mesh_dim > 1:
# inverse reorder point ids
c = order_map(dims, of="C", to="F")[c]
# reorder cells
c = c[order_map(c_dim, of="F", to="C")]
return c
[docs]
def check_axes_monotonicity(axes):
"""
Check axes to be strictly monotonic, and makes them strictly monotonic increasing.
Parameters
----------
axes : list of np.ndarray
Axes defining the coordinates in each direction (xyz order).
Will be modified inplace to be increasing.
Returns
-------
axes_increase : list of bool
False to indicate a bottom up axis.
Raises
------
ValueError
In case an axis in not strictly monotonic.
"""
axes_increase = np.empty(len(axes), dtype=bool)
for i, ax in enumerate(axes):
if len(ax) == 1:
axes_increase[i] = True
continue
dx = ax[1:] - ax[:-1]
if np.all(dx > 0):
axes_increase[i] = True
elif np.all(dx < 0):
ax[:] = ax[::-1]
axes_increase[i] = False
else:
raise ValueError(f"Grid: axes[{i}] not strictly monotonic.")
return axes_increase
def prepare_vtk_kwargs(data_location, data, cell_data, point_data, field_data):
"""
Prepare keyword arguments for evtk routines.
Parameters
----------
data_location : Location
Data location in the grid, by default Location.CELLS
data : dict or None
Data in the corresponding shape given by name
cell_data : dict or None
Additional cell data
point_data : dict or None
Additional point data
field_data : dict or None
Additional field data
Returns
-------
dict
Keyword arguments.
"""
cdat = data_location == Location.CELLS
kw = {"cellData": None, "pointData": None, "fieldData": None}
kw["cellData" if cdat else "pointData"] = data
if kw["cellData"]:
kw["cellData"].update(cell_data if cell_data is not None else {})
else:
kw["cellData"] = cell_data
if kw["pointData"]:
kw["pointData"].update(point_data if point_data is not None else {})
else:
kw["pointData"] = point_data
kw["fieldData"] = field_data
return kw
def prepare_vtk_data(
data, axes_reversed=False, axes_increase=None, flat=False, order="F"
):
"""
Prepare data dictionary for VTK export.
Parameters
----------
data : dict or None
Dictionary containing data arrays by name.
axes_reversed : bool, optional
Indicate reversed axes order for the associated data, by default False
axes_increase : arraylike or None, optional
False to indicate a bottom up axis (xyz order), by default None
flat : bool, optional
True to flatten data, by default False
order : str, optional
Point and cell ordering.
Either Fortran-like ("F") or C-like ("C"), by default "F"
Returns
-------
dict or None
Prepared data.
"""
if data is not None:
data = dict(data)
for name, value in data.items():
data[name] = np.ascontiguousarray(
_prepare(value, axes_reversed, axes_increase, flat, order)
)
return data
def _prepare(data, axes_reversed, axes_increase, flat, order):
if axes_increase is not None and data.ndim != len(axes_increase):
raise ValueError("prepare_vtk_data: data has wrong dimension.")
if axes_increase is None:
axes_increase = np.full(data.ndim, True, dtype=bool)
if axes_reversed and data.ndim > 1:
data = data.T
for i, inc in enumerate(axes_increase):
# only flip if not converting to unstructured
if not (inc or flat):
data = np.flip(data, axis=i)
# get 3D or flat shape
shape = -1 if flat else (data.shape + (1,) * (3 - data.ndim))
return data.reshape(shape, order=order)
def flatten_cells(cells):
"""
Flatten cells array.
Parameters
----------
cells : np.ndarray
Cells given as 2D array containing cell defining node IDs.
-1 will be interpreted as used entries.
Returns
-------
np.ndarray
All cell definitions concatenated.
"""
if cells.ndim == 1:
return cells
# unused entries in "cells" marked with "-1"
return np.ma.masked_values(cells, -1).compressed()
def get_cells_matrix(cell_types, cells, connectivity=False):
"""
Create the cells matrix as used in the Grid class.
Parameters
----------
cell_types : np.ndarray
Cell types.
cells : np.ndarray
Either cell definitions given as list of number of nodes with node IDs:
``[n0, p0_0, p0_1, ..., p0_n, n1, p1_0, p1_1, ..., p1_n, ...]``
Or cell connectivity given as list of node IDs:
``[p0_0, p0_1, ..., p0_n, p1_0, p1_1, ..., p1_n, ...]``
connectivity : bool, optional
Indicate that cells are given by connectivity. Default: False
Returns
-------
np.ndarray
Cell nodes as 2D array.
"""
unique_cell_types = np.unique(cell_types)
max_nodes = np.max(NODE_COUNT[unique_cell_types])
cells_matrix = np.full((len(cell_types), max_nodes), fill_value=-1, dtype=int)
cell_sizes = NODE_COUNT[cell_types]
if connectivity:
cell_ends = np.cumsum(cell_sizes)
cell_starts = np.concatenate(
[np.array([0], dtype=cell_ends.dtype), cell_ends[:-1]]
)
else:
# adding one to skip cell size entry in cell definitions array
# [(n0), p0_0, p0_1, ..., p0_n, (n1), p1_0, p1_1, ..., p1_n, ...]
cell_ends = np.cumsum(cell_sizes + 1)
cell_starts = (
np.concatenate([np.array([0], dtype=cell_ends.dtype), cell_ends[:-1]]) + 1
)
for cell_type in unique_cell_types:
cell_size = NODE_COUNT[cell_type]
mask = cell_types == cell_type
current_cell_starts = cell_starts[mask]
cells_inds = current_cell_starts[..., np.newaxis] + np.arange(cell_size)[
np.newaxis
].astype(cell_starts.dtype)
cells_matrix[:, :cell_size][mask] = cells[cells_inds]
return cells_matrix
[docs]
class Location(Enum):
"""Data location in the grid."""
CELLS = 0
POINTS = 1
[docs]
class CellType(IntEnum):
"""Supported cell types."""
# VTK and ESMF cell node order is counter clockwise
# https://kitware.github.io/vtk-examples/site/VTKFileFormats/#legacy-file-examples
# https://earthsystemmodeling.org/docs/release/latest/ESMF_refdoc/node5.html#const:meshelemtype
# vertex for no-cell meshes
VERTEX = 0
# lines for 1D
LINE = 1
# 2D following ESMF
TRI = 2
QUAD = 3
# 3D following ESMF
TETRA = 4
HEX = 5
NODE_COUNT = np.array([1, 2, 3, 4, 4, 8], dtype=int)
"""np.ndarray: Node numbers per CellType."""
CELL_DIM = np.array([0, 1, 2, 2, 3, 3], dtype=int)
"""np.ndarray: Cell dimension per CellType."""
ESMF_TYPE_MAP = np.array([-1, -1, 3, 4, 10, 12], dtype=int)
"""np.ndarray: ESMF type per CellType (-1 for unsupported)."""
VTK_TYPE_MAP = np.array((vtk_t := [1, 3, 5, 9, 10, 12]), dtype=int)
"""np.ndarray: VTK type per CellType."""
INV_VTK_TYPE_MAP = np.array(
[vtk_t.index(i) if i in vtk_t else -1 for i in range(82)],
dtype=int,
)
"""np.ndarray: CellType per VTK type."""
# VTK v9.3
VTK_CELL_DIM = np.array(
# Linear cells (0-16)
[0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3] + 4 * [-1]
# Quadratic / Cubic, isoparametric cells (21-37)
+ [1, 2, 2, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 1, 2, 3] + 3 * [-1]
# Special class and Polyhedron cell (41-42)
+ [1, 3] + 8 * [-1]
# Higher order cells in parametric form (51-56)
+ [1, 2, 2, 2, 3, 3] + 3 * [-1]
# Higher order cells (60-67)
+ [1, 2, 2, 2, 3, 3, 3, 3]
# Arbitrary order Lagrange elements (68-74)
+ [1, 2, 2, 3, 3, 3, 3]
# Arbitrary order Bezier elements (75-81)
+ [1, 2, 2, 3, 3, 3, 3],
dtype=int,
)
"""np.ndarray: Cell dimension per VTK type."""
