Source code for devito.types.grid

from collections import namedtuple

import numpy as np
from sympy import prod
from math import floor

from devito.mpi import Distributor
from devito.parameters import configuration
from import ReducerMap, as_tuple
from devito.types.args import ArgProvider
from devito.types.constant import Constant
from devito.types.dense import Function
from devito.types.dimension import (Dimension, SpaceDimension, TimeDimension,
                                    SteppingDimension, SubDimension)
from devito.equation import Eq

__all__ = ['Grid', 'SubDomain', 'SubDomainSet']

[docs]class Grid(ArgProvider): """ A cartesian grid that encapsulates a computational domain over which to discretize a Function. Parameters ---------- shape : tuple of ints Shape of the computational domain in grid points. extent : tuple of floats, optional Physical extent of the domain in m; defaults to a unit box of extent 1m in all dimensions. origin : tuple of floats, optional Physical coordinate of the origin of the domain; defaults to 0.0 in all dimensions. dimensions : tuple of SpaceDimension, optional The dimensions of the computational domain encapsulated by this Grid. time_dimension : TimeDimension, optional The dimension used to define time in a `TimeFunction` created from this Grid. dtype : data-type, optional Any object that can be interpreted as a numpy data type, used as default data type to be inherited by all Functions created from this Grid. Defaults to ``np.float32``. subdomains : tuple of SubDomain, optional If no subdomains are specified, the Grid only defines the two default subdomains ``interior`` and ``domain``. comm : MPI communicator, optional The set of processes over which the grid is distributed. Only relevant in case of MPI execution. Examples -------- >>> from devito import Grid, Function >>> grid = Grid(shape=(4, 4), extent=(3.0, 3.0)) >>> f = Function(name='f', grid=grid) >>> f.shape (4, 4) >>> f.dimensions (x, y) >>> f.dtype <class 'numpy.float32'> In a Function, the domain defined by a Grid is often surrounded by a "halo region", which guarantees the correctness of stencil updates nearby the domain boundary. However, the size of the halo region does *not* depend on the Grid; for more information, refer to ``Function.__doc__``. >>> f.shape_with_halo (6, 6) Notes ----- A Grid encapsulates the topology and geometry information of the computational domain that a Function can be discretized on. As such, it defines and provides the physical coordinate information of the logical cartesian grid underlying the discretized Functions. For example, the conventions for defining the coordinate space in 2D are: .. code-block:: python x |-----------------------> | origin | o------------o | | | | | | | | DOMAIN | extent[1] y | | | | | | | | extent[0] | | o------------o | origin + extent | v """ _default_dimensions = ('x', 'y', 'z') def __init__(self, shape, extent=None, origin=None, dimensions=None, time_dimension=None, dtype=np.float32, subdomains=None, comm=None): self._shape = as_tuple(shape) self._extent = as_tuple(extent or tuple(1. for _ in self.shape)) self._dtype = dtype if dimensions is None: # Create the spatial dimensions and constant spacing symbols assert(self.dim <= 3) dim_names = self._default_dimensions[:self.dim] dim_spacing = tuple(self._const(name='h_%s' % n, value=v, dtype=self.dtype) for n, v in zip(dim_names, self.spacing)) self._dimensions = tuple(SpaceDimension(name=n, spacing=s) for n, s in zip(dim_names, dim_spacing)) else: self._dimensions = dimensions # Initialize SubDomains subdomains = tuple(i for i in (Domain(), Interior(), *as_tuple(subdomains))) for i in subdomains: i.__subdomain_finalize__(self.dimensions, self.shape) self._subdomains = subdomains origin = as_tuple(origin or tuple(0. for _ in self.shape)) self._origin = tuple(self._const(name='o_%s' %, value=v, dtype=self.dtype) for d, v in zip(self.dimensions, origin)) # Sanity check assert (self.dim == len(self.origin) == len(self.extent) == len(self.spacing)) # Store or create default symbols for time and stepping dimensions if time_dimension is None: spacing = self._const(name='dt', dtype=self.dtype) self._time_dim = TimeDimension(name='time', spacing=spacing) self._stepping_dim = self._make_stepping_dim(self.time_dim, name='t') elif isinstance(time_dimension, TimeDimension): self._time_dim = time_dimension self._stepping_dim = self._make_stepping_dim(self.time_dim) else: raise ValueError("`time_dimension` must be None or of type TimeDimension") self._distributor = Distributor(self.shape, self.dimensions, comm) def __repr__(self): return "Grid[extent=%s, shape=%s, dimensions=%s]" % ( self.extent, self.shape, self.dimensions ) @property def extent(self): """Physical extent of the domain in m.""" return self._extent @property def dtype(self): """Data type inherited by all Functions defined on this Grid.""" return self._dtype @property def origin(self): """Physical coordinates of the domain origin.""" return self._origin @property def dimensions(self): """Spatial dimensions of the computational domain.""" return self._dimensions @property def dim(self): """Problem dimension, or number of spatial dimensions.""" return len(self.shape) @property def time_dim(self): """Time dimension associated with this Grid.""" return self._time_dim @property def stepping_dim(self): """Stepping dimension associated with this Grid.""" return self._stepping_dim @property def subdomains(self): """The SubDomains defined in this Grid.""" return { i for i in self._subdomains} @property def interior(self): """The interior SubDomain of the Grid.""" return self.subdomains['interior'] @property def volume_cell(self): """Volume of a single cell e.g h_x*h_y*h_z in 3D.""" return prod(d.spacing for d in self.dimensions).subs(self.spacing_map) @property def spacing(self): """Spacing between grid points in m.""" spacing = (np.array(self.extent) / (np.array(self.shape) - 1)).astype(self.dtype) return as_tuple(spacing) @property def spacing_symbols(self): """Symbols representing the grid spacing in each SpaceDimension""" return as_tuple(d.spacing for d in self.dimensions) @property def spacing_map(self): """Map between spacing symbols and their values for each SpaceDimension.""" return dict(zip(self.spacing_symbols, self.spacing)) @property def origin_offset(self): """Offset of the local (per-process) origin from the domain origin.""" grid_origin = [min(i) for i in self.distributor.glb_numb] assert len(grid_origin) == len(self.spacing) return tuple(i*h for i, h in zip(grid_origin, self.spacing)) @property def shape(self): """Shape of the physical domain.""" return self._shape @property def shape_local(self): """Shape of the local (per-process) physical domain.""" return self._distributor.shape @property def dimension_map(self): """Map between SpaceDimensions and their global/local size.""" return {d: namedtuple('Size', 'glb loc')(g, l) for d, g, l in zip(self.dimensions, self.shape, self.shape_local)} @property def distributor(self): """The Distributor used for domain decomposition.""" return self._distributor
[docs] def is_distributed(self, dim): """True if ``dim`` is a distributed Dimension, False otherwise.""" return any(dim is d for d in self.distributor.dimensions)
@property def _const(self): """The type to be used to create constant symbols.""" return Constant def _make_stepping_dim(self, time_dim, name=None): """Create a stepping dimension for this Grid.""" if name is None: name = '%s_s' % return SteppingDimension(name=name, parent=time_dim) def _arg_defaults(self): """A map of default argument values defined by this Grid.""" args = ReducerMap() for k, v in self.dimension_map.items(): args.update(k._arg_defaults(_min=0, size=v.loc)) if configuration['mpi']: distributor = self.distributor args[] = distributor._obj_comm.value args[] = distributor._obj_neighborhood.value return args def __getstate__(self): state = self.__dict__.copy() # A Distributor wraps an MPI communicator, which can't and shouldn't be pickled state.pop('_distributor') return state def __setstate__(self, state): for k, v in state.items(): setattr(self, k, v) self._distributor = Distributor(self.shape, self.dimensions)
[docs]class SubDomain(object): """ Base class to define Grid subdomains. To create a new SubDomain, all one needs to do is overriding :meth:`define`. This method takes as input a set of Dimensions and produce a mapper ``M : Dimensions -> {d, ('left', N), ('middle', N, M), ('right', N)}`` so that: * If ``M(d) = d``, then the SubDomain spans the entire Dimension ``d``. * If ``M(d) = ('left', N)``, then the SubDomain spans a contiguous region of ``N`` points starting at ``d``\'s left extreme. * ``M(d) = ('right', N)`` is analogous to the case above. * If ``M(d) = ('middle', N, M)``, then the SubDomain spans a contiguous region of ``d_size - (N + M)`` points starting at ``N`` and finishing at ``d_sizeM - M``. Examples -------- An "Inner" SubDomain, which spans the entire domain except for an exterior boundary region of ``thickness=3``, can be implemented as follows >>> from devito import SubDomain >>> class Inner(SubDomain): ... name = 'inner' ... def define(self, dimensions): ... return {d: ('middle', 3, 3) for d in dimensions} Like before, but now spanning the entire ``y`` Dimension of a three-dimensional grid >>> class InnerY(SubDomain): ... name = 'inner_y' ... def define(self, dimensions): ... x, y, z = dimensions ... return {x: ('middle', 3, 3), y: y, z: ('middle', 3, 3)} See Also -------- Domain : An example of preset SubDomain. Interior : An example of preset Subdomain. """ name = None """A unique name for the SubDomain.""" def __init__(self): if is None: raise ValueError("SubDomain requires a `name`") self._dimensions = None def __subdomain_finalize__(self, dimensions, shape): # Create the SubDomain's SubDimensions sub_dimensions = [] for k, v in self.define(dimensions).items(): if isinstance(v, Dimension): sub_dimensions.append(v) else: try: # Case ('middle', int, int) side, thickness_left, thickness_right = v if side != 'middle': raise ValueError("Expected side 'middle', not `%s`" % side) sub_dimensions.append(SubDimension.middle('%si' %, k, thickness_left, thickness_right)) except ValueError: side, thickness = v if side == 'left': sub_dimensions.append(SubDimension.left('%sleft' %, k, thickness)) elif side == 'right': sub_dimensions.append(SubDimension.right('%sright' %, k, thickness)) else: raise ValueError("Expected sides 'left|right', not `%s`" % side) self._dimensions = tuple(sub_dimensions) # Compute the SubDomain shape self._shape = tuple(s - (sum(d._thickness_map.values()) if d.is_Sub else 0) for d, s in zip(self._dimensions, shape)) def __eq__(self, other): if not isinstance(other, SubDomain): return False return == and self.dimensions == other.dimensions def __hash__(self): return hash((, self.dimensions)) def __str__(self): return "SubDomain %s[%s]" % (, self.dimensions) __repr__ = __str__ @property def dimensions(self): return self._dimensions @property def dimension_map(self): return {d.root: d for d in self.dimensions} @property def shape(self): return self._shape
[docs] def define(self, dimensions): """ Parametrically describe the SubDomain w.r.t. a generic Grid. Notes ----- This method should be overridden by each SubDomain subclass. For more information, refer to ``SubDomain.__doc__``. """ raise NotImplementedError
class Domain(SubDomain): """ The entire computational domain (== boundary + interior). """ name = 'domain' def define(self, dimensions): return dict(zip(dimensions, dimensions)) class Interior(SubDomain): """ The interior of the computational domain (i.e., boundaries are excluded). """ name = 'interior' def define(self, dimensions): return {d: ('middle', 1, 1) for d in dimensions} class SubDomainSet(SubDomain): """ Class to define a set of N (a positive integer) subdomains. Parameters ---------- **kwargs * N : int Number of subdomains. * bounds : tuple Tuple of numpy int32 arrays representing the bounds of each subdomain. Examples -------- Set up an iterate upon a set of two subdomains: >>> import numpy as np >>> from devito import Grid, Function, Eq, Operator, SubDomainSet >>> Nx = 10 >>> Ny = Nx >>> n_domains = 2 Create a 'SubDomainSet object': >>> class MySubdomains(SubDomainSet): ... name = 'mydomains' Set the bounds of the subdomains. The required format is: (xm, xM, ym, yM, ...) where xm is a vector specifying the number of grid points inwards from the 'left' boundary in the first grid dimension that each subdomain starts. xM is a vector specifying the number of grid points inwards from the 'right' of the domain in the first grid dimension that each subdomain ends. ym and yM are the equivalents for the second grid dimension. >>> xm = np.array([1, Nx/2+1], dtype=np.int32) >>> xM = np.array([Nx/2+1, 1], dtype=np.int32) Along a dimension where all bounds are the same we can use the following shorthand: >>> ym = 1 # which is equivalent to 'np.array([1, 1], dtype=np.int32)' >>> yM = 1 Combine the data into the required form: >>> bounds = (xm, xM, ym, yM) Create our set of subdomains passing the number of domains and the bounds: >>> my_sd = MySubdomains(N=n_domains, bounds=bounds) Create a grid and iterate a function within the defined subdomains: >>> grid = Grid(extent=(Nx, Ny), shape=(Nx, Ny), subdomains=(my_sd, )) >>> f = Function(name='f', grid=grid, dtype=np.int32) >>> eq = Eq(f, f+1, subdomain=grid.subdomains['mydomains']) >>> op = Operator(eq) >>> summary = op.apply() >>> Data([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], dtype=int32) """ implicit_dimension = None """The implicit dimension of the SubDomainSet.""" def __init__(self, **kwargs): super(SubDomainSet, self).__init__() if self.implicit_dimension is None: n = Dimension(name='n') self.implicit_dimension = n self._n_domains = kwargs.get('N', 1) self._bounds = kwargs.get('bounds', None) self._implicit_exprs = None def __subdomain_finalize__(self, dimensions, shape): # Create the SubDomain's SubDimensions sub_dimensions = [] for d in dimensions: sub_dimensions.append( SubDimension.middle('%si_%s' % (,, d, 0, 0)) self._dimensions = tuple(sub_dimensions) # Compute the SubDomain shape self._shape = tuple(s - (sum(d._thickness_map.values()) if d.is_Sub else 0) for d, s in zip(self._dimensions, shape)) @property def n_domains(self): return self._n_domains @property def bounds(self): return self._bounds def _create_implicit_exprs(self): if not len(self._bounds) == 2*len(self.dimensions): raise ValueError("Left and right bounds must be supplied for each dimension") n_domains = self.n_domains i_dim = self.implicit_dimension dat = [] # Organise the data contained in 'bounds' into a form such that the # associated implicit equations can easily be created. for j in range(len(self._bounds)): index = floor(j/2) d = self.dimensions[index] if j % 2 == 0: fname = d.min_name else: fname = d.max_name func = Function(name=fname, shape=(n_domains, ), dimensions=(i_dim, ), dtype=np.int32) # Check if shorthand notation has been provided: if isinstance(self._bounds[j], int): bounds = np.full((n_domains,), self._bounds[j], dtype=np.int32)[:] = bounds else:[:] = self._bounds[j] dat.append(Eq(d.thickness[j % 2][0], func[i_dim])) return as_tuple(dat)