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Stephan Seitz authoredThis adds a function for lazy people who want to write ```python dh = create_data_handling((20, 30)) dh.add_arrays('x, y(9), z') ``` instead of ```python dh = create_data_handling((20, 30)) dh.add_array('x') dh.add_array('y', values_per_cell=9) dh.add_array('z') ``` because in most cases you want to use more than one array.Stephan Seitz authoredThis adds a function for lazy people who want to write ```python dh = create_data_handling((20, 30)) dh.add_arrays('x, y(9), z') ``` instead of ```python dh = create_data_handling((20, 30)) dh.add_array('x') dh.add_array('y', values_per_cell=9) dh.add_array('z') ``` because in most cases you want to use more than one array.
field.py 46.59 KiB
import functools
import hashlib
import operator
import pickle
import re
from enum import Enum
from itertools import chain
from typing import List, Optional, Sequence, Set, Tuple
import numpy as np
import sympy as sp
from sympy.core.cache import cacheit
import pystencils
from pystencils.alignedarray import aligned_empty
from pystencils.data_types import StructType, TypedSymbol, create_type
from pystencils.kernelparameters import FieldShapeSymbol, FieldStrideSymbol
from pystencils.stencil import (
direction_string_to_offset, inverse_direction, offset_to_direction_string)
from pystencils.sympyextensions import is_integer_sequence
__all__ = ['Field', 'fields', 'FieldType', 'AbstractField']
class FieldType(Enum):
# generic fields
GENERIC = 0
# index fields are currently only used for boundary handling
# the coordinates are not the loop counters in that case, but are read from this index field
INDEXED = 1
# communication buffer, used for (un)packing data in communication.
BUFFER = 2
# unsafe fields may be accessed in an absolute fashion - the index depends on the data
# and thus may lead to out-of-bounds accesses
CUSTOM = 3
# staggered field
STAGGERED = 4
# staggered field that reverses sign when accessed via opposite direction
STAGGERED_FLUX = 5
@staticmethod
def is_generic(field):
assert isinstance(field, Field)
return field.field_type == FieldType.GENERIC
@staticmethod
def is_indexed(field):
assert isinstance(field, Field)
return field.field_type == FieldType.INDEXED
@staticmethod
def is_buffer(field):
assert isinstance(field, Field)
return field.field_type == FieldType.BUFFER
@staticmethod
def is_custom(field):
assert isinstance(field, Field)
return field.field_type == FieldType.CUSTOM
@staticmethod
def is_staggered(field):
assert isinstance(field, Field)
return field.field_type == FieldType.STAGGERED or field.field_type == FieldType.STAGGERED_FLUX
@staticmethod
def is_staggered_flux(field):
assert isinstance(field, Field)
return field.field_type == FieldType.STAGGERED_FLUX
def fields(description=None, index_dimensions=0, layout=None, field_type=FieldType.GENERIC, **kwargs):
"""Creates pystencils fields from a string description.
Examples:
Create a 2D scalar and vector field:
>>> s, v = fields("s, v(2): double[2D]")
>>> assert s.spatial_dimensions == 2 and s.index_dimensions == 0
>>> assert (v.spatial_dimensions, v.index_dimensions, v.index_shape) == (2, 1, (2,))
Create an integer field of shape (10, 20):
>>> f = fields("f : int32[10, 20]")
>>> f.has_fixed_shape, f.shape
(True, (10, 20))
Numpy arrays can be used as template for shape and data type of field:
>>> arr_s, arr_v = np.zeros([20, 20]), np.zeros([20, 20, 2])
>>> s, v = fields("s, v(2)", s=arr_s, v=arr_v)
>>> assert s.index_dimensions == 0 and s.dtype.numpy_dtype == arr_s.dtype
>>> assert v.index_shape == (2,)
Format string can be left out, field names are taken from keyword arguments.
>>> fields(f1=arr_s, f2=arr_s)
[f1: double[20,20], f2: double[20,20]]
The keyword names ``index_dimension`` and ``layout`` have special meaning, don't use them for field names
>>> f = fields(f=arr_v, index_dimensions=1)
>>> assert f.index_dimensions == 1
>>> f = fields("pdfs(19) : float32[3D]", layout='fzyx')
>>> f.layout
(2, 1, 0)
"""
result = []
if description:
field_descriptions, dtype, shape = _parse_description(description)
layout = 'numpy' if layout is None else layout
for field_name, idx_shape in field_descriptions:
if field_name in kwargs:
arr = kwargs[field_name]
idx_shape_of_arr = () if not len(idx_shape) else arr.shape[-len(idx_shape):]
assert idx_shape_of_arr == idx_shape
f = Field.create_from_numpy_array(field_name, kwargs[field_name], index_dimensions=len(idx_shape),
field_type=field_type)
elif isinstance(shape, tuple):
f = Field.create_fixed_size(field_name, shape + idx_shape, dtype=dtype,
index_dimensions=len(idx_shape), layout=layout, field_type=field_type)
elif isinstance(shape, int):
f = Field.create_generic(field_name, spatial_dimensions=shape, dtype=dtype,
index_shape=idx_shape, layout=layout, field_type=field_type)
elif shape is None:
f = Field.create_generic(field_name, spatial_dimensions=2, dtype=dtype,
index_shape=idx_shape, layout=layout, field_type=field_type)
else:
assert False
result.append(f)
else:
assert layout is None, "Layout can not be specified when creating Field from numpy array"
for field_name, arr in kwargs.items():
result.append(Field.create_from_numpy_array(field_name, arr, index_dimensions=index_dimensions,
field_type=field_type))
if len(result) == 0:
return None
elif len(result) == 1:
return result[0]
else:
return result
class AbstractField:
class AbstractAccess:
pass
class Field(AbstractField):
"""
With fields one can formulate stencil-like update rules on structured grids.
This Field class knows about the dimension, memory layout (strides) and optionally about the size of an array.
Creating Fields:
The preferred method to create fields is the `fields` function.
Alternatively one can use one of the static functions `Field.create_generic`, `Field.create_from_numpy_array`
and `Field.create_fixed_size`. Don't instantiate the Field directly!
Fields can be created with known or unknown shapes:
1. If you want to create a kernel with fixed loop sizes i.e. the shape of the array is already known.
This is usually the case if just-in-time compilation directly from Python is done.
(see `Field.create_from_numpy_array`
2. create a more general kernel that works for variable array sizes. This can be used to create kernels
beforehand for a library. (see `Field.create_generic`)
Dimensions and Indexing:
A field has spatial and index dimensions, where the spatial dimensions come first.
The interpretation is that the field has multiple cells in (usually) two or three dimensional space which are
looped over. Additionally N values are stored per cell. In this case spatial_dimensions is two or three,
and index_dimensions equals N. If you want to store a matrix on each point in a two dimensional grid, there
are four dimensions, two spatial and two index dimensions: ``len(arr.shape) == spatial_dims + index_dims``
The shape of the index dimension does not have to be specified. Just use the 'index_dimensions' parameter.
However, it is good practice to define the shape, since out of bounds accesses can be directly detected in this
case. The shape can be passed with the 'index_shape' parameter of the field creation functions.
When accessing (indexing) a field the result is a `Field.Access` which is derived from sympy Symbol.
First specify the spatial offsets in [], then in case index_dimension>0 the indices in ()
e.g. ``f[-1,0,0](7)``
Staggered Fields:
Staggered fields are used to store a value on a second grid shifted by half a cell with respect to the usual
grid.
The first index dimension is used to specify the position on the staggered grid (e.g. 0 means half-way to the
eastern neighbor, 1 is half-way to the northern neighbor, etc.), while additional indices can be used to store
multiple values at each position.
Example using no index dimensions:
>>> a = np.zeros([10, 10])
>>> f = Field.create_from_numpy_array("f", a, index_dimensions=0)
>>> jacobi = (f[-1,0] + f[1,0] + f[0,-1] + f[0,1]) / 4
Examples for index dimensions to create LB field and implement stream pull:
>>> from pystencils import Assignment
>>> stencil = np.array([[0,0], [0,1], [0,-1]])
>>> src, dst = fields("src(3), dst(3) : double[2D]")
>>> assignments = [Assignment(dst[0,0](i), src[-offset](i)) for i, offset in enumerate(stencil)];
"""
@staticmethod
def create_generic(field_name, spatial_dimensions, dtype=np.float64, index_dimensions=0, layout='numpy',
index_shape=None, field_type=FieldType.GENERIC) -> 'Field':
"""
Creates a generic field where the field size is not fixed i.e. can be called with arrays of different sizes
Args:
field_name: symbolic name for the field
dtype: numpy data type of the array the kernel is called with later
spatial_dimensions: see documentation of Field
index_dimensions: see documentation of Field
layout: tuple specifying the loop ordering of the spatial dimensions e.g. (2, 1, 0 ) means that
the outer loop loops over dimension 2, the second outer over dimension 1, and the inner loop
over dimension 0. Also allowed: the strings 'numpy' (0,1,..d) or 'reverse_numpy' (d, ..., 1, 0)
index_shape: optional shape of the index dimensions i.e. maximum values allowed for each index dimension,
has to be a list or tuple
field_type: besides the normal GENERIC fields, there are INDEXED fields that store indices of the domain
that should be iterated over, BUFFER fields that are used to generate communication
packing/unpacking kernels, and STAGGERED fields, which store values half-way to the next
cell
"""
if index_shape is not None:
assert index_dimensions == 0 or index_dimensions == len(index_shape)
index_dimensions = len(index_shape)
if isinstance(layout, str):
layout = spatial_layout_string_to_tuple(layout, dim=spatial_dimensions)
total_dimensions = spatial_dimensions + index_dimensions
if index_shape is None or len(index_shape) == 0:
shape = tuple([FieldShapeSymbol([field_name], i) for i in range(total_dimensions)])
else:
shape = tuple([FieldShapeSymbol([field_name], i) for i in range(spatial_dimensions)] + list(index_shape))
strides = tuple([FieldStrideSymbol(field_name, i) for i in range(total_dimensions)])
np_data_type = np.dtype(dtype)
if np_data_type.fields is not None:
if index_dimensions != 0:
raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
shape += (1,)
strides += (1,)
if field_type == FieldType.STAGGERED and index_dimensions == 0:
raise ValueError("A staggered field needs at least one index dimension")
return Field(field_name, field_type, dtype, layout, shape, strides)
@staticmethod
def create_from_numpy_array(field_name: str, array: np.ndarray, index_dimensions: int = 0,
field_type=FieldType.GENERIC) -> 'Field':
"""Creates a field based on the layout, data type, and shape of a given numpy array.
Kernels created for these kind of fields can only be called with arrays of the same layout, shape and type.
Args:
field_name: symbolic name for the field
array: numpy array
index_dimensions: see documentation of Field
field_type: kind of field
"""
spatial_dimensions = len(array.shape) - index_dimensions
if spatial_dimensions < 1:
raise ValueError("Too many index dimensions. At least one spatial dimension required")
full_layout = get_layout_of_array(array)
spatial_layout = tuple([i for i in full_layout if i < spatial_dimensions])
assert len(spatial_layout) == spatial_dimensions
strides = tuple([s // np.dtype(array.dtype).itemsize for s in array.strides])
shape = tuple(int(s) for s in array.shape)
numpy_dtype = np.dtype(array.dtype)
if numpy_dtype.fields is not None:
if index_dimensions != 0:
raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
shape += (1,)
strides += (1,)
if field_type == FieldType.STAGGERED and index_dimensions == 0:
raise ValueError("A staggered field needs at least one index dimension")
return Field(field_name, field_type, array.dtype, spatial_layout, shape, strides)
@staticmethod
def create_fixed_size(field_name: str, shape: Tuple[int, ...], index_dimensions: int = 0,
dtype=np.float64, layout: str = 'numpy', strides: Optional[Sequence[int]] = None,
field_type=FieldType.GENERIC) -> 'Field':
"""
Creates a field with fixed sizes i.e. can be called only with arrays of the same size and layout
Args:
field_name: symbolic name for the field
shape: overall shape of the array
index_dimensions: how many of the trailing dimensions are interpreted as index (as opposed to spatial)
dtype: numpy data type of the array the kernel is called with later
layout: full layout of array, not only spatial dimensions
strides: strides in bytes or None to automatically compute them from shape (assuming no padding)
field_type: kind of field
"""
spatial_dimensions = len(shape) - index_dimensions
assert spatial_dimensions >= 1
if isinstance(layout, str):
layout = layout_string_to_tuple(layout, spatial_dimensions + index_dimensions)
shape = tuple(int(s) for s in shape)
if strides is None:
strides = compute_strides(shape, layout)
else:
assert len(strides) == len(shape)
strides = tuple([s // np.dtype(dtype).itemsize for s in strides])
numpy_dtype = np.dtype(dtype)
if numpy_dtype.fields is not None:
if index_dimensions != 0:
raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
shape += (1,)
strides += (1,)
if field_type == FieldType.STAGGERED and index_dimensions == 0:
raise ValueError("A staggered field needs at least one index dimension")
spatial_layout = list(layout)
for i in range(spatial_dimensions, len(layout)):
spatial_layout.remove(i)
return Field(field_name, field_type, dtype, tuple(spatial_layout), shape, strides)
def __init__(self, field_name, field_type, dtype, layout, shape, strides):
"""Do not use directly. Use static create* methods"""
self._field_name = field_name
assert isinstance(field_type, FieldType)
assert len(shape) == len(strides)
self.field_type = field_type
self._dtype = create_type(dtype)
self._layout = normalize_layout(layout)
self.shape = shape
self.strides = strides
self.latex_name: Optional[str] = None
self.coordinate_origin: tuple[float, sp.Symbol] = sp.Matrix(tuple(
0 for _ in range(self.spatial_dimensions)
)) # type
self.coordinate_transform = sp.eye(self.spatial_dimensions)
if field_type == FieldType.STAGGERED:
assert self.staggered_stencil
def new_field_with_different_name(self, new_name):
if self.has_fixed_shape:
return Field(new_name, self.field_type, self._dtype, self._layout, self.shape, self.strides)
else:
return Field.create_generic(new_name, self.spatial_dimensions, self.dtype.numpy_dtype,
self.index_dimensions, self._layout, self.index_shape, self.field_type)
@property
def spatial_dimensions(self) -> int:
return len(self._layout)
@property
def index_dimensions(self) -> int:
return len(self.shape) - len(self._layout)
@property
def ndim(self) -> int:
return len(self.shape)
def values_per_cell(self) -> int:
return functools.reduce(operator.mul, self.index_shape, 1)
@property
def layout(self):
return self._layout
@property
def name(self) -> str:
return self._field_name
@property
def spatial_shape(self) -> Tuple[int, ...]:
return self.shape[:self.spatial_dimensions]
@property
def has_fixed_shape(self):
return is_integer_sequence(self.shape)
@property
def index_shape(self):
return self.shape[self.spatial_dimensions:]
@property
def has_fixed_index_shape(self):
return is_integer_sequence(self.index_shape)
@property
def spatial_strides(self):
return self.strides[:self.spatial_dimensions]
@property
def index_strides(self):
return self.strides[self.spatial_dimensions:]
@property
def dtype(self):
return self._dtype
@property
def itemsize(self):
return self.dtype.numpy_dtype.itemsize
def __repr__(self):
if any(isinstance(s, sp.Symbol) for s in self.spatial_shape):
spatial_shape_str = f'{self.spatial_dimensions}d'
else:
spatial_shape_str = ','.join(str(i) for i in self.spatial_shape)
index_shape_str = ','.join(str(i) for i in self.index_shape)
if self.index_shape:
return f'{self._field_name}({index_shape_str}): {self.dtype}[{spatial_shape_str}]'
else:
return f'{self._field_name}: {self.dtype}[{spatial_shape_str}]'
def __str__(self):
return self.name
def neighbor(self, coord_id, offset):
offset_list = [0] * self.spatial_dimensions
offset_list[coord_id] = offset
return Field.Access(self, tuple(offset_list))
def neighbors(self, stencil):
return [self.__getitem__(s) for s in stencil]
@property
def center_vector(self):
index_shape = self.index_shape
if len(index_shape) == 0:
return sp.Matrix([self.center])
elif len(index_shape) == 1:
return sp.Matrix([self(i) for i in range(index_shape[0])])
elif len(index_shape) == 2:
return sp.Matrix([[self(i, j) for j in range(index_shape[1])] for i in range(index_shape[0])])
elif len(index_shape) == 3:
return sp.Matrix([[[self(i, j, k) for k in range(index_shape[2])]
for j in range(index_shape[1])] for i in range(index_shape[0])])
else:
raise NotImplementedError("center_vector is not implemented for more than 3 index dimensions")
@property
def center(self):
center = tuple([0] * self.spatial_dimensions)
return Field.Access(self, center)
def neighbor_vector(self, offset):
"""Like neighbor, but returns the entire vector/tensor stored at offset."""
if self.spatial_dimensions == 2 and len(offset) == 3:
assert offset[2] == 0
offset = offset[:2]
if self.index_dimensions == 0:
return sp.Matrix([self.__getitem__(offset)])
elif self.index_dimensions == 1:
return sp.Matrix([self.__getitem__(offset)(i) for i in range(self.index_shape[0])])
elif self.index_dimensions == 2:
return sp.Matrix([[self.__getitem__(offset)(i, k) for k in range(self.index_shape[1])]
for i in range(self.index_shape[0])])
else:
raise NotImplementedError("neighbor_vector is not implemented for more than 2 index dimensions")
def __getitem__(self, offset):
if type(offset) is np.ndarray:
offset = tuple(offset)
if type(offset) is str:
offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
if type(offset) is not tuple:
offset = (offset,)
if len(offset) != self.spatial_dimensions:
raise ValueError("Wrong number of spatial indices: "
"Got %d, expected %d" % (len(offset), self.spatial_dimensions))
return Field.Access(self, offset)
def absolute_access(self, offset, index):
assert FieldType.is_custom(self)
return Field.Access(self, offset, index, is_absolute_access=True)
def interpolated_access(self,
offset: Tuple,
interpolation_mode='linear',
address_mode='BORDER',
allow_textures=True):
"""Provides access to field values at non-integer positions
``interpolated_access`` is similar to :func:`Field.absolute_access` except that
it allows non-integer offsets and automatic handling of out-of-bound accesses.
:param offset: Tuple of spatial coordinates (can be floats)
:param interpolation_mode: One of :class:`pystencils.interpolation_astnodes.InterpolationMode`
:param address_mode: How boundaries are handled can be 'border', 'wrap', 'mirror', 'clamp'
:param allow_textures: Allow implementation by texture accesses on GPUs
"""
from pystencils.interpolation_astnodes import Interpolator
return Interpolator(self,
interpolation_mode,
address_mode,
allow_textures=allow_textures).at(offset)
def staggered_access(self, offset, index=None):
"""If this field is a staggered field, it can be accessed using half-integer offsets.
For example, an offset of ``(0, sp.Rational(1,2))`` or ``"E"`` corresponds to the staggered point to the east
of the cell center, i.e. half-way to the eastern-next cell.
If the field stores more than one value per staggered point (e.g. a vector or a tensor), the index (integer or
tuple of integers) refers to which of these values to access.
"""
assert FieldType.is_staggered(self)
offset_orig = offset
if type(offset) is np.ndarray:
offset = tuple(offset)
if type(offset) is str:
offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
offset = tuple([o * sp.Rational(1, 2) for o in offset])
if type(offset) is not tuple:
offset = (offset,)
if len(offset) != self.spatial_dimensions:
raise ValueError("Wrong number of spatial indices: "
"Got %d, expected %d" % (len(offset), self.spatial_dimensions))
prefactor = 1
neighbor_vec = [0] * len(offset)
for i in range(self.spatial_dimensions):
if (offset[i] + sp.Rational(1, 2)).is_Integer:
neighbor_vec[i] = sp.sign(offset[i])
neighbor = offset_to_direction_string(neighbor_vec)
if neighbor not in self.staggered_stencil:
neighbor_vec = inverse_direction(neighbor_vec)
neighbor = offset_to_direction_string(neighbor_vec)
if FieldType.is_staggered_flux(self):
prefactor = -1
if neighbor not in self.staggered_stencil:
raise ValueError("{} is not a valid neighbor for the {} stencil".format(offset_orig,
self.staggered_stencil_name))
offset = tuple(sp.Matrix(offset) - sp.Rational(1, 2) * sp.Matrix(neighbor_vec))
idx = self.staggered_stencil.index(neighbor)
if self.index_dimensions == 1: # this field stores a scalar value at each staggered position
if index is not None:
raise ValueError("Cannot specify an index for a scalar staggered field")
return prefactor * Field.Access(self, offset, (idx,))
else: # this field stores a vector or tensor at each staggered position
if index is None:
raise ValueError("Wrong number of indices: "
"Got %d, expected %d" % (0, self.index_dimensions - 1))
if type(index) is np.ndarray:
index = tuple(index)
if type(index) is not tuple:
index = (index,)
if self.index_dimensions != len(index) + 1:
raise ValueError("Wrong number of indices: "
"Got %d, expected %d" % (len(index), self.index_dimensions - 1))
return prefactor * Field.Access(self, offset, (idx, *index))
def staggered_vector_access(self, offset):
"""Like staggered_access, but returns the entire vector/tensor stored at offset."""
assert FieldType.is_staggered(self)
if self.index_dimensions == 1:
return sp.Matrix([self.staggered_access(offset)])
elif self.index_dimensions == 2:
return sp.Matrix([self.staggered_access(offset, i) for i in range(self.index_shape[1])])
elif self.index_dimensions == 3:
return sp.Matrix([[self.staggered_access(offset, (i, k)) for k in range(self.index_shape[2])]
for i in range(self.index_shape[1])])
else:
raise NotImplementedError("staggered_vector_access is not implemented for more than 3 index dimensions")
@property
def staggered_stencil(self):
assert FieldType.is_staggered(self)
stencils = {
2: {
2: ["W", "S"], # D2Q5
4: ["W", "S", "SW", "NW"] # D2Q9
},
3: {
3: ["W", "S", "B"], # D3Q7
7: ["W", "S", "B", "BSW", "TSW", "BNW", "TNW"], # D3Q15
9: ["W", "S", "B", "SW", "NW", "BW", "TW", "BS", "TS"], # D3Q19
13: ["W", "S", "B", "SW", "NW", "BW", "TW", "BS", "TS", "BSW", "TSW", "BNW", "TNW"] # D3Q27
}
}
if not self.index_shape[0] in stencils[self.spatial_dimensions]:
raise ValueError("No known stencil has {} staggered points".format(self.index_shape[0]))
return stencils[self.spatial_dimensions][self.index_shape[0]]
@property
def staggered_stencil_name(self):
assert FieldType.is_staggered(self)
return "D%dQ%d" % (self.spatial_dimensions, self.index_shape[0] * 2 + 1)
def __call__(self, *args, **kwargs):
center = tuple([0] * self.spatial_dimensions)
return Field.Access(self, center)(*args, **kwargs)
def hashable_contents(self):
return (self._layout,
self.shape,
self.strides,
self.field_type,
self._field_name,
self.latex_name,
self._dtype)
def __hash__(self):
return hash(self.hashable_contents())
def __eq__(self, other):
if not isinstance(other, Field):
return False
return self.hashable_contents() == other.hashable_contents()
@property
def physical_coordinates(self):
if hasattr(self.coordinate_transform, '__call__'):
return self.coordinate_transform(self.coordinate_origin + pystencils.x_vector(self.spatial_dimensions))
else:
return self.coordinate_transform @ (self.coordinate_origin + pystencils.x_vector(self.spatial_dimensions))
@property
def physical_coordinates_staggered(self):
return self.coordinate_transform @ \
(self.coordinate_origin + pystencils.x_staggered_vector(self.spatial_dimensions))
def index_to_physical(self, index_coordinates, staggered=False):
if staggered:
index_coordinates = sp.Matrix([i + 0.5 for i in index_coordinates])
if hasattr(self.coordinate_transform, '__call__'):
return self.coordinate_transform(self.coordinate_origin + index_coordinates)
else:
return self.coordinate_transform @ (self.coordinate_origin + index_coordinates)
def physical_to_index(self, physical_coordinates, staggered=False):
if hasattr(self.coordinate_transform, '__call__'):
if hasattr(self.coordinate_transform, 'inv'):
return self.coordinate_transform.inv()(physical_coordinates) - self.coordinate_origin
else:
idx = sp.Matrix(sp.symbols(f'index_coordinates:{self.ndim}', real=True))
rtn = sp.solve(self.index_to_physical(idx) - physical_coordinates, idx)
assert rtn, f'Could not find inverese of coordinate_transform: {self.index_to_physical(idx)}'
return rtn
else:
rtn = self.coordinate_transform.inv() @ physical_coordinates - self.coordinate_origin
if staggered:
rtn = sp.Matrix([i - 0.5 for i in rtn])
return rtn
def index_to_staggered_physical_coordinates(self, symbol_vector):
symbol_vector += sp.Matrix([0.5] * self.spatial_dimensions)
return self.create_physical_coordinates(symbol_vector)
def set_coordinate_origin_to_field_center(self):
self.coordinate_origin = -sp.Matrix([i / 2 for i in self.spatial_shape])
# noinspection PyAttributeOutsideInit,PyUnresolvedReferences
class Access(TypedSymbol, AbstractField.AbstractAccess):
"""Class representing a relative access into a `Field`.
This class behaves like a normal sympy Symbol, it is actually derived from it. One can built up
sympy expressions using field accesses, solve for them, etc.
Examples:
>>> vector_field_2d = fields("v(2): double[2D]") # create a 2D vector field
>>> northern_neighbor_y_component = vector_field_2d[0, 1](1)
>>> northern_neighbor_y_component
v_N^1
>>> central_y_component = vector_field_2d(1)
>>> central_y_component
v_C^1
>>> central_y_component.get_shifted(1, 0) # move the existing access
v_E^1
>>> central_y_component.at_index(0) # change component
v_C^0
"""
def __new__(cls, name, *args, **kwargs):
obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
return obj
def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None, is_absolute_access=False, dtype=None):
field_name = field.name
offsets_and_index = (*offsets, *idx) if idx is not None else offsets
constant_offsets = not any([isinstance(o, sp.Basic) and not o.is_Integer for o in offsets_and_index])
if not idx:
idx = tuple([0] * field.index_dimensions)
if constant_offsets:
offset_name = offset_to_direction_string(offsets)
if field.index_dimensions == 0:
superscript = None
elif field.index_dimensions == 1:
superscript = str(idx[0])
else:
idx_str = ",".join([str(e) for e in idx])
superscript = idx_str
if field.has_fixed_index_shape and not isinstance(field.dtype, StructType):
for i, bound in zip(idx, field.index_shape):
if i >= bound:
raise ValueError("Field index out of bounds")
else:
offset_name = hashlib.md5(pickle.dumps(offsets_and_index)).hexdigest()[:12]
superscript = None
symbol_name = "%s_%s" % (field_name, offset_name)
if superscript is not None:
symbol_name += "^" + superscript
obj = super(Field.Access, self).__xnew__(self, symbol_name, field.dtype)
obj._field = field
obj._offsets = []
for o in offsets:
if isinstance(o, sp.Basic):
obj._offsets.append(o)
else:
obj._offsets.append(int(o))
obj._offsets = tuple(sp.sympify(obj._offsets))
obj._offsetName = offset_name
obj._superscript = superscript
obj._index = idx
obj._indirect_addressing_fields = set()
for e in chain(obj._offsets, obj._index):
if isinstance(e, sp.Basic):
obj._indirect_addressing_fields.update(a.field for a in e.atoms(Field.Access))
obj._is_absolute_access = is_absolute_access
return obj
def __getnewargs__(self):
return self.field, self.offsets, self.index, self.is_absolute_access, self.dtype
# noinspection SpellCheckingInspection
__xnew__ = staticmethod(__new_stage2__)
# noinspection SpellCheckingInspection
__xnew_cached_ = staticmethod(cacheit(__new_stage2__))
def __call__(self, *idx):
if self._index != tuple([0] * self.field.index_dimensions):
raise ValueError("Indexing an already indexed Field.Access")
idx = tuple(idx)
if self.field.index_dimensions == 0 and idx == (0,):
idx = ()
if len(idx) != self.field.index_dimensions:
raise ValueError("Wrong number of indices: "
"Got %d, expected %d" % (len(idx), self.field.index_dimensions))
return Field.Access(self.field, self._offsets, idx, dtype=self.dtype)
def __getitem__(self, *idx):
return self.__call__(*idx)
def __iter__(self):
"""This is necessary to work with parts of sympy that test if an object is iterable (e.g. simplify).
The __getitem__ would make it iterable"""
raise TypeError("Field access is not iterable")
@property
def field(self) -> 'Field':
"""Field that the Access points to"""
return self._field
@property
def offsets(self) -> Tuple:
"""Spatial offset as tuple"""
return self._offsets
@property
def required_ghost_layers(self) -> int:
"""Largest spatial distance that is accessed."""
return int(np.max(np.abs(self._offsets)))
@property
def nr_of_coordinates(self):
return len(self._offsets)
@property
def offset_name(self) -> str:
"""Spatial offset as string, East-West for x, North-South for y and Top-Bottom for z coordinate.
Example:
>>> f = fields("f: double[2D]")
>>> f[1, 1].offset_name # north-east
'NE'
"""
return self._offsetName
@property
def index(self):
"""Value of index coordinates as tuple."""
return self._index
def neighbor(self, coord_id: int, offset: int) -> 'Field.Access':
"""Returns a new Access with changed spatial coordinates.
Args:
coord_id: index of the coordinate to change (0 for x, 1 for y,...)
offset: incremental change of this coordinate
Example:
>>> f = fields('f: [2D]')
>>> f[0,0].neighbor(coord_id=1, offset=-1)
f_S
"""
offset_list = list(self.offsets)
offset_list[coord_id] += offset
return Field.Access(self.field, tuple(offset_list), self.index, dtype=self.dtype)
def get_shifted(self, *shift) -> 'Field.Access':
"""Returns a new Access with changed spatial coordinates
Example:
>>> f = fields("f: [2D]")
>>> f[0,0].get_shifted(1, 1)
f_NE
"""
return Field.Access(self.field,
tuple(a + b for a, b in zip(shift, self.offsets)),
self.index,
dtype=self.dtype)
def at_index(self, *idx_tuple) -> 'Field.Access':
"""Returns new Access with changed index.
Example:
>>> f = fields("f(9): [2D]")
>>> f(0).at_index(8)
f_C^8
"""
return Field.Access(self.field, self.offsets, idx_tuple, dtype=self.dtype)
def _eval_subs(self, old, new):
return Field.Access(self.field,
tuple(sp.sympify(a).subs(old, new) for a in self.offsets),
tuple(sp.sympify(a).subs(old, new) for a in self.index),
dtype=self.dtype)
@property
def is_absolute_access(self) -> bool:
"""Indicates if a field access is relative to the loop counters (this is the default) or absolute"""
return self._is_absolute_access
@property
def indirect_addressing_fields(self) -> Set['Field']:
"""Returns a set of fields that the access depends on.
e.g. f[index_field[1, 0]], the outer access to f depends on index_field
"""
return self._indirect_addressing_fields
def _hashable_content(self):
super_class_contents = super(Field.Access, self)._hashable_content()
return (super_class_contents, self._field.hashable_contents(), *self._index, *self._offsets)
def _staggered_offset(self, offsets, index):
assert FieldType.is_staggered(self._field)
neighbor = self._field.staggered_stencil[index]
neighbor = direction_string_to_offset(neighbor, self._field.spatial_dimensions)
return [(o + sp.Rational(int(neighbor[i]), 2)) for i, o in enumerate(offsets)]
def _latex(self, _):
n = self._field.latex_name if self._field.latex_name else self._field.name
offset_str = ",".join([sp.latex(o) for o in self.offsets])
if FieldType.is_staggered(self._field):
offset_str = ",".join([sp.latex(self._staggered_offset(self.offsets, self.index[0])[i])
for i in range(len(self.offsets))])
if self.is_absolute_access:
offset_str = "\\mathbf{}".format(offset_str)
elif self.field.spatial_dimensions > 1:
offset_str = "({})".format(offset_str)
if FieldType.is_staggered(self._field):
if self.index and self.field.index_dimensions > 1:
return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index[1:]
if len(self.index) > 2 else self.index[1])
else:
return "{{%s}_{%s}}" % (n, offset_str)
else:
if self.index and self.field.index_dimensions > 0:
return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
else:
return "{{%s}_{%s}}" % (n, offset_str)
def __str__(self):
n = self._field.latex_name if self._field.latex_name else self._field.name
offset_str = ",".join([sp.latex(o) for o in self.offsets])
if FieldType.is_staggered(self._field):
offset_str = ",".join([sp.latex(self._staggered_offset(self.offsets, self.index[0])[i])
for i in range(len(self.offsets))])
if self.is_absolute_access:
offset_str = "[abs]{}".format(offset_str)
if FieldType.is_staggered(self._field):
if self.index and self.field.index_dimensions > 1:
return "%s[%s](%s)" % (n, offset_str, self.index[1:] if len(self.index) > 2 else self.index[1])
else:
return "%s[%s]" % (n, offset_str)
else:
if self.index and self.field.index_dimensions > 0:
return "%s[%s](%s)" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
else:
return "%s[%s]" % (n, offset_str)
def get_layout_from_strides(strides: Sequence[int], index_dimension_ids: Optional[List[int]] = None):
index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
coordinates = list(range(len(strides)))
relevant_strides = [stride for i, stride in enumerate(strides) if i not in index_dimension_ids]
result = [x for (y, x) in sorted(zip(relevant_strides, coordinates), key=lambda pair: pair[0], reverse=True)]
return normalize_layout(result)
def get_layout_of_array(arr: np.ndarray, index_dimension_ids: Optional[List[int]] = None):
""" Returns a list indicating the memory layout (linearization order) of the numpy array.
Examples:
>>> get_layout_of_array(np.zeros([3,3,3]))
(0, 1, 2)
In this example the loop over the zeroth coordinate should be the outermost loop,
followed by the first and second. Elements arr[x,y,0] and arr[x,y,1] are adjacent in memory.
Normally constructed numpy arrays have this order, however by stride tricks or other frameworks, arrays
with different memory layout can be created.
The index_dimension_ids parameter leaves specifies which coordinates should not be
"""
index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
return get_layout_from_strides(arr.strides, index_dimension_ids)
def create_numpy_array_with_layout(shape, layout, alignment=False, byte_offset=0, **kwargs):
"""Creates numpy array with given memory layout.
Args:
shape: shape of the resulting array
layout: layout as tuple, where the coordinates are ordered from slow to fast
alignment: number of bytes to align the beginning and the innermost coordinate to, or False for no alignment
byte_offset: only used when alignment is specified, align not beginning but address at this offset
mostly used to align first inner cell, not ghost cells
Example:
>>> res = create_numpy_array_with_layout(shape=(2, 3, 4, 5), layout=(3, 2, 0, 1))
>>> res.shape
(2, 3, 4, 5)
>>> get_layout_of_array(res)
(3, 2, 0, 1)
"""
assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
cur_layout = list(range(len(shape)))
swaps = []
for i in range(len(layout)):
if cur_layout[i] != layout[i]:
index_to_swap_with = cur_layout.index(layout[i])
swaps.append((i, index_to_swap_with))
cur_layout[i], cur_layout[index_to_swap_with] = cur_layout[index_to_swap_with], cur_layout[i]
assert tuple(cur_layout) == tuple(layout)
shape = list(shape)
for a, b in swaps:
shape[a], shape[b] = shape[b], shape[a]
if not alignment:
res = np.empty(shape, order='c', **kwargs)
else:
if alignment is True:
alignment = 8 * 4
res = aligned_empty(shape, alignment, byte_offset=byte_offset, **kwargs)
for a, b in reversed(swaps):
res = res.swapaxes(a, b)
return res
def spatial_layout_string_to_tuple(layout_str: str, dim: int) -> Tuple[int, ...]:
if layout_str in ('fzyx', 'zyxf'):
assert dim <= 3
return tuple(reversed(range(dim)))
if layout_str in ('fzyx', 'f', 'reverse_numpy', 'SoA'):
return tuple(reversed(range(dim)))
elif layout_str in ('c', 'numpy', 'AoS'):
return tuple(range(dim))
raise ValueError("Unknown layout descriptor " + layout_str)
def layout_string_to_tuple(layout_str, dim):
layout_str = layout_str.lower()
if layout_str == 'fzyx' or layout_str == 'soa':
assert dim <= 4
return tuple(reversed(range(dim)))
elif layout_str == 'zyxf' or layout_str == 'aos':
assert dim <= 4
return tuple(reversed(range(dim - 1))) + (dim - 1,)
elif layout_str == 'f' or layout_str == 'reverse_numpy':
return tuple(reversed(range(dim)))
elif layout_str == 'c' or layout_str == 'numpy':
return tuple(range(dim))
raise ValueError("Unknown layout descriptor " + layout_str)
def normalize_layout(layout):
"""Takes a layout tuple and subtracts the minimum from all entries"""
min_entry = min(layout)
return tuple(i - min_entry for i in layout)
def compute_strides(shape, layout):
"""
Computes strides assuming no padding exists
Args:
shape: shape (size) of array
layout: layout specification as tuple
Returns:
strides in elements, not in bytes
"""
dim = len(shape)
assert len(layout) == dim
assert len(set(layout)) == dim
strides = [0] * dim
product = 1
for j in reversed(layout):
strides[j] = product
product *= shape[j]
return tuple(strides)
# ---------------------------------------- Parsing of string in fields() function --------------------------------------
field_description_regex = re.compile(r"""
\s* # ignore leading white spaces
(\w+) # identifier is a sequence of alphanumeric characters, is stored in first group
(?: # optional index specification e.g. (1, 4, 2)
\s*
\(
([^\)]+) # read everything up to closing bracket
\)
\s*
)?
\s*,?\s* # ignore trailing white spaces and comma
""", re.VERBOSE)
type_description_regex = re.compile(r"""
\s*
(\w+)? # optional dtype
\s*
\[
([^\]]+)
\]
\s*
""", re.VERBOSE | re.IGNORECASE)
def _parse_part1(d):
result = field_description_regex.match(d)
while result:
name, index_str = result.group(1), result.group(2)
index = tuple(int(e) for e in index_str.split(",")) if index_str else ()
yield name, index
d = d[result.end():]
result = field_description_regex.match(d)
def _parse_description(description):
def parse_part2(d):
result = type_description_regex.match(d)
if result:
data_type_str, size_info = result.group(1), result.group(2).strip().lower()
if data_type_str is None:
data_type_str = 'float64'
data_type_str = data_type_str.lower().strip()
if not data_type_str:
data_type_str = 'float64'
if size_info.endswith('d'):
size_info = int(size_info[:-1])
else:
size_info = tuple(int(e) for e in size_info.split(","))
return data_type_str, size_info
else:
raise ValueError("Could not parse field description")
if ':' in description:
field_description, field_info = description.split(':')
else:
field_description, field_info = description, 'float64[2D]'
fields_info = [e for e in _parse_part1(field_description)]
if not field_info:
raise ValueError("Could not parse field description")
data_type, size = parse_part2(field_info)
return fields_info, data_type, size