"""Defines base class of backends that implement computations.
.. codeauthor:: David Zwicker <david.zwicker@ds.mpg.de>
"""
from __future__ import annotations
from typing import TYPE_CHECKING
import numpy as np
import torch
from ...grids import GridBase
from ..base import OperatorInfo, TFunc
from ..numpy import NumpyBackend
from .utils import get_torch_dtype
if TYPE_CHECKING:
from collections.abc import Callable
from ...grids import GridBase
from ...grids.boundaries.axes import BoundariesBase
from ...pdes import PDEBase
from ...tools.expressions import ExpressionBase
from ...tools.typing import (
NumberOrArray,
NumericArray,
TField,
)
from ..base import TFunc
from ..numpy.backend import OperatorInfo
from ..registry import BackendRegistry
from .utils import TorchOperatorType
[docs]
class TorchBackend(NumpyBackend):
"""Defines :mod:`torch` backend."""
compile_options = {
"fullgraph": True,
"dynamic": False,
"options": {"epilogue_fusion": True, "max_autotune": True},
}
def __init__(self, name: str, registry: BackendRegistry, *, device: str = "config"):
"""Initialize the torch backend.
Args:
registry (:class:`~pde.backends.registry.BackendRegistry`):
The registry to which this backend is added
name (str):
The name of the backend
device (str):
The torch device to use. Special values are "config" (read from
configuration) and "auto" (use CUDA if available, otherwise CPU)
"""
super().__init__(name=name, registry=registry)
self.device = device
@property
def device(self) -> torch.device:
"""The currently assigned torch device."""
return self._device
@device.setter
def device(self, device: str) -> None:
"""Set a new torch device."""
if device == "config":
device = self.config["device"]
if device == "auto":
device = "cuda" if torch.cuda.is_available() else "cpu"
self._device = torch.device(device)
[docs]
def compile_function(self, func: TFunc, **compile_options) -> TFunc:
r"""General method that compiles a user function.
Args:
func (callable):
The function that needs to be compiled for this backend
**compile_options:
Additional keyword arguments will be forwarded to :func:`torch.compile`
"""
if not self.config["compile"]:
return func
# compile the function using the torch backend
opts = self.compile_options | compile_options
return torch.compile(func, **opts) # type: ignore
[docs]
def make_operator_no_bc( # type: ignore
self,
grid: GridBase,
operator: str | OperatorInfo,
*,
native: bool = False,
**kwargs,
) -> TorchOperatorType:
"""Return a compiled function applying an operator without boundary conditions.
A function that takes the discretized full data as an input and an array of
valid data points to which the result of applying the operator is written.
Note:
The resulting function does not check whether the ghost cells of the input
array have been supplied with sensible values. It is the responsibility of
the user to set the values of the ghost cells beforehand. Use this function
only if you absolutely know what you're doing. In all other cases,
:meth:`make_operator` is probably the better choice.
Args:
grid (:class:`~pde.grid.base.GridBase`):
Grid for which the operator is needed
operator (str):
Identifier for the operator. Some examples are 'laplace', 'gradient', or
'divergence'. The registered operators for this grid can be obtained
from the :attr:`~pde.grids.base.GridBase.operators` attribute.
native (bool):
If True, the returned functions expects the native data representation
of the backend. Otherwise, the input and output are expected to be
:class:`~numpy.ndarray`.
**kwargs:
Specifies extra arguments influencing how the operator is created.
Returns:
callable: the function that applies the operator. This function has the
signature (arr: NumericArray, out: NumericArray), so they `out` array need
to be supplied explicitly.
"""
# obtain details about the operator
operator_info = self.get_operator_info(grid, operator)
dtype = get_torch_dtype(kwargs.pop("dtype", np.double))
# create an operator with or without BCs
torch_operator = operator_info.factory(grid, bcs=None, dtype=dtype, **kwargs)
torch_operator.eval() # type: ignore
# compile the function and move it to the device
torch_operator_jitted = self.compile_function(torch_operator)
torch_operator_jitted.to(self.device) # type: ignore
if native:
return torch_operator_jitted # type: ignore
def operator_no_bc(arr: NumericArray, out: NumericArray) -> None:
arr_torch = torch.from_numpy(arr)
out[...] = torch_operator_jitted(arr_torch) # type: ignore
return operator_no_bc # type: ignore
[docs]
def make_operator( # type: ignore
self,
grid: GridBase,
operator: str | OperatorInfo,
*,
bcs: BoundariesBase,
native: bool = False,
**kwargs,
) -> TorchOperatorType:
"""Return a torch function applying an operator with boundary conditions.
Args:
grid (:class:`~pde.grid.base.GridBase`):
Grid for which the operator is needed
operator (str):
Identifier for the operator. Some examples are 'laplace', 'gradient', or
'divergence'. The registered operators for this grid can be obtained
from the :attr:`~pde.grids.base.GridBase.operators` attribute.
bcs (:class:`~pde.grids.boundaries.axes.BoundariesBase`, optional):
The boundary conditions used before the operator is applied
native (bool):
If True, the returned functions expects the native data representation
of the backend. Otherwise, the input and output are expected to be
:class:`~numpy.ndarray`.
**kwargs:
Specifies extra arguments influencing how the operator is created.
Warning:
The same operator should not be assigned to different variables that are
used in the same code, because :mod:`torch` has problems compiling the
resulting code. This particularly precludes caching the operators, since
they then might be reused, e.g., if boundary conditions agree between
different operators.
Returns:
callable: the function that applies the operator. This function has the
signature (arr: NumericArray, out: NumericArray = None, args=None).
"""
# obtain details about the operator
operator_info = self.get_operator_info(grid, operator)
dtype = get_torch_dtype(kwargs.pop("dtype", np.double))
bcs = grid.get_boundary_conditions(bcs, rank=operator_info.rank_in)
# create an operator with or without BCs
torch_operator = operator_info.factory(grid, bcs, dtype=dtype, **kwargs) # type: ignore
torch_operator.eval() # type: ignore
# compile the function and move it to the device
torch_operator_jitted = self.compile_function(torch_operator)
torch_operator_jitted.to(self.device) # type: ignore
if native:
# return the native representation if requested
return torch_operator_jitted # type: ignore
# wrap the operator such that it can be called from numpy
shape_out = (grid.dim,) * operator_info.rank_out + grid.shape
# define numpy version of the operator
def apply_op(
arr: NumericArray, out: NumericArray | None = None, args=None
) -> NumericArray:
"""Set boundary conditions and apply operator."""
arr_torch = torch.from_numpy(arr)
arr_torch.to(self.device)
if out is None:
out = np.empty(shape_out, dtype=arr.dtype)
elif out.shape != shape_out:
msg = f"Incompatible shapes {out.shape} != {shape_out}"
raise ValueError(msg)
out[:] = torch_operator_jitted(arr_torch) # type: ignore
return out
# return the compiled versions of the operator
return apply_op # type: ignore
[docs]
def make_integrator(
self, grid: GridBase
) -> Callable[[NumericArray], NumberOrArray]:
"""Return function that integrates discretized data over a grid.
If this function is used in a multiprocessing run (using MPI), the integrals are
performed on all subgrids and then accumulated. Each process then receives the
same value representing the global integral.
Args:
grid (:class:`~pde.grid.base.GridBase`):
Grid for which the integrator is defined
Returns:
A function that takes a numpy array and returns the integral with the
correct weights given by the cell volumes.
"""
from .operators.common import IntegralOperator
# create the torch operator
integrate_torch = self.compile_function(IntegralOperator(grid))
integrate_torch.to(self.device)
def integrate_global(arr: NumericArray) -> float:
"""Integrate data.
Args:
arr (:class:`~numpy.ndarray`): discretized data on grid
"""
# move data to device
arr_torch = torch.from_numpy(arr)
arr_torch.to(self.device)
# integrate on device
res = integrate_torch(arr_torch)
# return result
res_np = res.cpu().detach().numpy()
if res_np.ndim == 0:
return res_np[()] # type: ignore
return res_np # type: ignore
return integrate_global
[docs]
def make_pde_rhs(
self, eq: PDEBase, state: TField
) -> Callable[[NumericArray, float], NumericArray]:
"""Return a function for evaluating the right hand side of the PDE.
Args:
eq (:class:`~pde.pdes.base.PDEBase`):
The object describing the differential equation
state (:class:`~pde.fields.FieldBase`):
An example for the state from which information can be extracted
Returns:
Function returning deterministic part of the right hand side of the PDE
"""
try:
make_rhs = eq.make_pde_rhs_torch # type: ignore
except AttributeError as err:
msg = (
"The right-hand side of the PDE is not implemented using the `torch` "
"backend. To add the implementation, provide the method "
"`make_pde_rhs_torch`, which should return a compilable function "
"calculating the evolution rate using a torch array as input."
)
raise NotImplementedError(msg) from err
# get the compiled right hand side
rhs_torch = self.compile_function(make_rhs(state))
def rhs(arr: NumericArray, t: float = 0) -> NumericArray:
arr_torch = torch.from_numpy(arr)
arr_torch.to(self.device)
return rhs_torch(arr_torch, t).numpy() # type: ignore
return rhs
[docs]
def make_expression_function(
self,
expression: ExpressionBase,
*,
single_arg: bool = False,
user_funcs: dict[str, Callable] | None = None,
) -> Callable[..., NumberOrArray]:
"""Return a function evaluating an expression.
Args:
expression (:class:`~pde.tools.expression.ExpressionBase`):
The expression that is converted to a function
single_arg (bool):
Determines whether the returned function accepts all variables in a
single argument as an array or whether all variables need to be
supplied separately.
user_funcs (dict):
Additional functions that can be used in the expression.
Returns:
function: the function
"""
import sympy
from sympy.printing.pycode import PythonCodePrinter
from ...tools.expressions import SPECIAL_FUNCTIONS
# collect all the user functions
user_functions = expression.user_funcs.copy()
if user_funcs is not None:
user_functions.update(user_funcs)
user_functions.update(SPECIAL_FUNCTIONS)
user_functions = {
k: self.compile_function(v) for k, v in user_functions.items()
}
# initialize the printer that deals with numpy arrays correctly
class ListArrayPrinter(PythonCodePrinter):
"""Special sympy printer returning arrays as lists."""
def _print_ImmutableDenseNDimArray(self, arr):
arrays = ", ".join(f"{self._print(expr)}" for expr in arr)
return f"[{arrays}]"
printer = ListArrayPrinter(
{
"fully_qualified_modules": False,
"inline": True,
"allow_unknown_functions": True,
"user_functions": {k: k for k in user_functions},
}
)
# determine the list of variables that the function depends on
variables = (expression.vars,) if single_arg else tuple(expression.vars)
constants = tuple(expression.consts)
# turn the expression into a callable function
self._logger.info("Parse sympy expression `%s`", expression._sympy_expr)
func = sympy.lambdify(
variables + constants,
expression._sympy_expr,
modules=[user_functions, "numpy"],
printer=printer,
)
# Apply the constants if there are any. Note that we use this pattern of a
# partial function instead of replacing the constants in the sympy expression
# directly since sympy does not work well with numpy arrays.
if constants:
const_values = tuple(expression.consts[c] for c in constants)
func = self.compile_function(func)
def result(*args):
return func(*args, *const_values)
else:
result = func
return self.compile_function(result)