Source code for ufl.differentiation

# -*- coding: utf-8 -*-
"Differential operators."

# Copyright (C) 2008-2016 Martin Sandve Aln├Žs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
# SPDX-License-Identifier:    LGPL-3.0-or-later
#
# Modified by Anders Logg, 2009.

from ufl.log import error
from ufl.core.expr import Expr
from ufl.core.terminal import Terminal
from ufl.core.operator import Operator
from ufl.core.ufl_type import ufl_type

from ufl.exprcontainers import ExprList, ExprMapping
from ufl.constantvalue import Zero
from ufl.coefficient import Coefficient
from ufl.variable import Variable
from ufl.precedence import parstr
from ufl.domain import find_geometric_dimension
from ufl.checks import is_cellwise_constant


# --- Basic differentiation objects ---

[docs]@ufl_type(is_abstract=True, is_differential=True) class Derivative(Operator): "Base class for all derivative types." __slots__ = () def __init__(self, operands): Operator.__init__(self, operands)
[docs]@ufl_type(num_ops=4, inherit_shape_from_operand=0, inherit_indices_from_operand=0) class CoefficientDerivative(Derivative): """Derivative of the integrand of a form w.r.t. the degrees of freedom in a discrete Coefficient.""" __slots__ = () def __new__(cls, integrand, coefficients, arguments, coefficient_derivatives): if not isinstance(coefficients, ExprList): error("Expecting ExprList instance with Coefficients.") if not isinstance(arguments, ExprList): error("Expecting ExprList instance with Arguments.") if not isinstance(coefficient_derivatives, ExprMapping): error("Expecting ExprMapping for coefficient derivatives.") if isinstance(integrand, Zero): return integrand return Derivative.__new__(cls) def __init__(self, integrand, coefficients, arguments, coefficient_derivatives): if not isinstance(coefficient_derivatives, ExprMapping): coefficient_derivatives = ExprMapping(coefficient_derivatives) Derivative.__init__(self, (integrand, coefficients, arguments, coefficient_derivatives)) def __str__(self): return "d/dfj { %s }, with fh=%s, dfh/dfj = %s, and coefficient derivatives %s"\ % (self.ufl_operands[0], self.ufl_operands[1], self.ufl_operands[2], self.ufl_operands[3])
[docs]@ufl_type(num_ops=4, inherit_shape_from_operand=0, inherit_indices_from_operand=0) class CoordinateDerivative(CoefficientDerivative): """Derivative of the integrand of a form w.r.t. the SpatialCoordinates.""" __slots__ = () def __str__(self): return "d/dfj { %s }, with fh=%s, dfh/dfj = %s, and coordinate derivatives %s"\ % (self.ufl_operands[0], self.ufl_operands[1], self.ufl_operands[2], self.ufl_operands[3])
[docs]@ufl_type(num_ops=2) class VariableDerivative(Derivative): __slots__ = ( "ufl_shape", "ufl_free_indices", "ufl_index_dimensions", ) def __new__(cls, f, v): # Checks if not isinstance(f, Expr): error("Expecting an Expr in VariableDerivative.") if not isinstance(v, (Variable, Coefficient)): error("Expecting a Variable in VariableDerivative.") if v.ufl_free_indices: error("Differentiation variable cannot have free indices.") # Simplification # Return zero if expression is trivially independent of variable if f._ufl_is_terminal_ and f != v: return Zero(f.ufl_shape + v.ufl_shape, f.ufl_free_indices, f.ufl_index_dimensions) # Construction return Derivative.__new__(cls) def __init__(self, f, v): Derivative.__init__(self, (f, v)) self.ufl_free_indices = f.ufl_free_indices self.ufl_index_dimensions = f.ufl_index_dimensions self.ufl_shape = f.ufl_shape + v.ufl_shape def __str__(self): if isinstance(self.ufl_operands[0], Terminal): return "d%s/d[%s]" % (self.ufl_operands[0], self.ufl_operands[1]) return "d/d[%s] %s" % (self.ufl_operands[1], parstr(self.ufl_operands[0], self))
# --- Compound differentiation objects ---
[docs]@ufl_type(is_abstract=True) class CompoundDerivative(Derivative): "Base class for all compound derivative types." __slots__ = () def __init__(self, operands): Derivative.__init__(self, operands)
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0, is_terminal_modifier=True) class Grad(CompoundDerivative): __slots__ = ("_dim",) def __new__(cls, f): # Return zero if expression is trivially constant if is_cellwise_constant(f): dim = find_geometric_dimension(f) return Zero(f.ufl_shape + (dim,), f.ufl_free_indices, f.ufl_index_dimensions) return CompoundDerivative.__new__(cls) def __init__(self, f): CompoundDerivative.__init__(self, (f,)) self._dim = find_geometric_dimension(f) def _ufl_expr_reconstruct_(self, op): "Return a new object of the same type with new operands." if is_cellwise_constant(op): if op.ufl_shape != self.ufl_operands[0].ufl_shape: error("Operand shape mismatch in Grad reconstruct.") if self.ufl_operands[0].ufl_free_indices != op.ufl_free_indices: error("Free index mismatch in Grad reconstruct.") return Zero(self.ufl_shape, self.ufl_free_indices, self.ufl_index_dimensions) return self._ufl_class_(op)
[docs] def evaluate(self, x, mapping, component, index_values, derivatives=()): "Get child from mapping and return the component asked for." component, i = component[:-1], component[-1] derivatives = derivatives + (i,) result = self.ufl_operands[0].evaluate(x, mapping, component, index_values, derivatives=derivatives) return result
@property def ufl_shape(self): return self.ufl_operands[0].ufl_shape + (self._dim,) def __str__(self): return "grad(%s)" % self.ufl_operands[0]
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0, is_terminal_modifier=True, is_in_reference_frame=True) class ReferenceGrad(CompoundDerivative): __slots__ = ("_dim",) def __new__(cls, f): # Return zero if expression is trivially constant if is_cellwise_constant(f): dim = f.ufl_domain().topological_dimension() return Zero(f.ufl_shape + (dim,), f.ufl_free_indices, f.ufl_index_dimensions) return CompoundDerivative.__new__(cls) def __init__(self, f): CompoundDerivative.__init__(self, (f,)) self._dim = f.ufl_domain().topological_dimension() def _ufl_expr_reconstruct_(self, op): "Return a new object of the same type with new operands." if is_cellwise_constant(op): if op.ufl_shape != self.ufl_operands[0].ufl_shape: error("Operand shape mismatch in ReferenceGrad reconstruct.") if self.ufl_operands[0].ufl_free_indices != op.ufl_free_indices: error("Free index mismatch in ReferenceGrad reconstruct.") return Zero(self.ufl_shape, self.ufl_free_indices, self.ufl_index_dimensions) return self._ufl_class_(op)
[docs] def evaluate(self, x, mapping, component, index_values, derivatives=()): "Get child from mapping and return the component asked for." component, i = component[:-1], component[-1] derivatives = derivatives + (i,) result = self.ufl_operands[0].evaluate(x, mapping, component, index_values, derivatives=derivatives) return result
@property def ufl_shape(self): return self.ufl_operands[0].ufl_shape + (self._dim,) def __str__(self): return "reference_grad(%s)" % self.ufl_operands[0]
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0, is_terminal_modifier=True) class Div(CompoundDerivative): __slots__ = () def __new__(cls, f): if f.ufl_free_indices: error("Free indices in the divergence argument is not allowed.") # Return zero if expression is trivially constant if is_cellwise_constant(f): return Zero(f.ufl_shape[:-1]) # No free indices asserted above return CompoundDerivative.__new__(cls) def __init__(self, f): CompoundDerivative.__init__(self, (f,)) @property def ufl_shape(self): return self.ufl_operands[0].ufl_shape[:-1] def __str__(self): return "div(%s)" % self.ufl_operands[0]
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0, is_terminal_modifier=True, is_in_reference_frame=True) class ReferenceDiv(CompoundDerivative): __slots__ = () def __new__(cls, f): if f.ufl_free_indices: error("Free indices in the divergence argument is not allowed.") # Return zero if expression is trivially constant if is_cellwise_constant(f): return Zero(f.ufl_shape[:-1]) # No free indices asserted above return CompoundDerivative.__new__(cls) def __init__(self, f): CompoundDerivative.__init__(self, (f,)) @property def ufl_shape(self): return self.ufl_operands[0].ufl_shape[:-1] def __str__(self): return "reference_div(%s)" % self.ufl_operands[0]
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0) class NablaGrad(CompoundDerivative): __slots__ = ("_dim",) def __new__(cls, f): # Return zero if expression is trivially constant if is_cellwise_constant(f): dim = find_geometric_dimension(f) return Zero((dim,) + f.ufl_shape, f.ufl_free_indices, f.ufl_index_dimensions) return CompoundDerivative.__new__(cls) def __init__(self, f): CompoundDerivative.__init__(self, (f,)) self._dim = find_geometric_dimension(f) def _ufl_expr_reconstruct_(self, op): "Return a new object of the same type with new operands." if is_cellwise_constant(op): if op.ufl_shape != self.ufl_operands[0].ufl_shape: error("Operand shape mismatch in NablaGrad reconstruct.") if self.ufl_operands[0].ufl_free_indices != op.ufl_free_indices: error("Free index mismatch in NablaGrad reconstruct.") return Zero(self.ufl_shape, self.ufl_free_indices, self.ufl_index_dimensions) return self._ufl_class_(op) @property def ufl_shape(self): return (self._dim,) + self.ufl_operands[0].ufl_shape def __str__(self): return "nabla_grad(%s)" % self.ufl_operands[0]
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0) class NablaDiv(CompoundDerivative): __slots__ = () def __new__(cls, f): if f.ufl_free_indices: error("Free indices in the divergence argument is not allowed.") # Return zero if expression is trivially constant if is_cellwise_constant(f): return Zero(f.ufl_shape[1:]) # No free indices asserted above return CompoundDerivative.__new__(cls) def __init__(self, f): CompoundDerivative.__init__(self, (f,)) @property def ufl_shape(self): return self.ufl_operands[0].ufl_shape[1:] def __str__(self): return "nabla_div(%s)" % self.ufl_operands[0]
_curl_shapes = {(): (2,), (2,): (), (3,): (3,)}
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0, is_terminal_modifier=True) class Curl(CompoundDerivative): __slots__ = ("ufl_shape",) def __new__(cls, f): # Validate input sh = f.ufl_shape if f.ufl_shape not in ((), (2,), (3,)): error("Expecting a scalar, 2D vector or 3D vector.") if f.ufl_free_indices: error("Free indices in the curl argument is not allowed.") # Return zero if expression is trivially constant if is_cellwise_constant(f): sh = {(): (2,), (2,): (), (3,): (3,)}[sh] return Zero(sh) # No free indices asserted above return CompoundDerivative.__new__(cls) def __init__(self, f): global _curl_shapes CompoundDerivative.__init__(self, (f,)) self.ufl_shape = _curl_shapes[f.ufl_shape] def __str__(self): return "curl(%s)" % self.ufl_operands[0]
[docs]@ufl_type(num_ops=1, inherit_indices_from_operand=0, is_terminal_modifier=True, is_in_reference_frame=True) class ReferenceCurl(CompoundDerivative): __slots__ = ("ufl_shape",) def __new__(cls, f): # Validate input sh = f.ufl_shape if f.ufl_shape not in ((), (2,), (3,)): error("Expecting a scalar, 2D vector or 3D vector.") if f.ufl_free_indices: error("Free indices in the curl argument is not allowed.") # Return zero if expression is trivially constant if is_cellwise_constant(f): sh = {(): (2,), (2,): (), (3,): (3,)}[sh] return Zero(sh) # No free indices asserted above return CompoundDerivative.__new__(cls) def __init__(self, f): global _curl_shapes CompoundDerivative.__init__(self, (f,)) self.ufl_shape = _curl_shapes[f.ufl_shape] def __str__(self): return "reference_curl(%s)" % self.ufl_operands[0]