4.6.5. pde.tools.expressions module¶
Handling mathematical expressions with sympy
This module provides classes representing expressions that can be provided as
human-readable strings and are converted to numpy
and numba
representations using sympy
.
return a number compiled from an expression |
|
describes a mathematical expression of a scalar quantity |
|
describes a mathematical expression of a tensorial quantity |
|
evaluate an expression involving fields |
- class ExpressionBase(expression: Basic, signature: Optional[Sequence[Union[str, List[str]]]] = None, *, user_funcs: Optional[Dict[str, Callable]] = None, consts: Optional[Dict[str, Union[int, float, complex, ndarray]]] = None)[source]¶
Bases:
object
abstract base class for handling expressions
Warning
This implementation uses
exec()
and should therefore not be used in a context where malicious input could occur.- Parameters
expression (
sympy.core.basic.Basic
) – A sympy expression or array. This could for instance be an instance ofExpr
orNDimArray
.signature (list of str, optional) – The signature defines which variables are expected in the expression. This is typically a list of strings identifying the variable names. Individual names can be specified as list, in which case any of these names can be used. The first item in such a list is the definite name and if another name of the list is used, the associated variable is renamed to the definite name. If signature is None, all variables in expressions are allowed.
user_funcs (dict, optional) – A dictionary with user defined functions that can be used in the expression.
consts (dict, optional) – A dictionary with user defined constants that can be used in the expression. The values of these constants should either be numbers or
ndarray
.
- classmethod check_reserved_symbols(symbols: Iterable[str], strict: bool = True) None [source]¶
throws an error if reserved symbols are found
- Parameters
symbols (iterable) – A sequence or set of strings with symbols to check.
strict (bool) – Flag determining whether an exception is raised
- get_compiled(single_arg: bool = False) Callable[[...], Union[int, float, complex, ndarray]] [source]¶
return numba function evaluating expression
- Parameters
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
- Returns
the compiled function
- Return type
function
- class ScalarExpression(expression: Union[float, str, ndarray, Basic, ExpressionBase] = 0, signature: Optional[Sequence[Union[str, List[str]]]] = None, *, user_funcs: Optional[Dict[str, Callable]] = None, consts: Optional[Dict[str, Union[int, float, complex, ndarray]]] = None, allow_indexed: bool = False)[source]¶
Bases:
ExpressionBase
describes a mathematical expression of a scalar quantity
Warning
This implementation uses
exec()
and should therefore not be used in a context where malicious input could occur.- Parameters
expression (str or float) – The expression, which is either a number or a string that sympy can parse
signature (list of str) – The signature defines which variables are expected in the expression. This is typically a list of strings identifying the variable names. Individual names can be specified as lists, in which case any of these names can be used. The first item in such a list is the definite name and if another name of the list is used, the associated variable is renamed to the definite name. If signature is None, all variables in expressions are allowed.
user_funcs (dict, optional) – A dictionary with user defined functions that can be used in the expression
consts (dict, optional) – A dictionary with user defined constants that can be used in the expression. The values of these constants should either be numbers or
ndarray
.allow_indexed (bool) – Whether to allow indexing of variables. If enabled, array variables are allowed to be indexed using square bracket notation.
- copy() ScalarExpression [source]¶
return a copy of the current expression
- derivatives¶
differentiate the expression with respect to all variables
- differentiate(var: str) ScalarExpression [source]¶
return the expression differentiated with respect to var
- class TensorExpression(expression: Union[float, str, ndarray, Basic, ExpressionBase], signature: Optional[Sequence[Union[str, List[str]]]] = None, *, user_funcs: Optional[Dict[str, Callable]] = None, consts: Optional[Dict[str, Union[int, float, complex, ndarray]]] = None)[source]¶
Bases:
ExpressionBase
describes a mathematical expression of a tensorial quantity
Warning
This implementation uses
exec()
and should therefore not be used in a context where malicious input could occur.- Parameters
expression (str or float) – The expression, which is either a number or a string that sympy can parse
signature (list of str) – The signature defines which variables are expected in the expression. This is typically a list of strings identifying the variable names. Individual names can be specified as list, in which case any of these names can be used. The first item in such a list is the definite name and if another name of the list is used, the associated variable is renamed to the definite name. If signature is None, all variables in expressions are allowed.
user_funcs (dict, optional) – A dictionary with user defined functions that can be used in the expression.
consts (dict, optional) – A dictionary with user defined constants that can be used in the expression. The values of these constants should either be numbers or
ndarray
.
- derivatives¶
differentiate the expression with respect to all variables
- differentiate(var: str) TensorExpression [source]¶
return the expression differentiated with respect to var
- get_compiled_array(single_arg: bool = True) Callable[[ndarray, Optional[ndarray]], ndarray] [source]¶
compile the tensor expression such that a numpy array is returned
- Parameters
single_arg (bool) – Whether the compiled function expects all arguments as a single array or whether they are supplied individually.
- property value¶
the value for a constant expression
- evaluate(expression: str, fields: Dict[str, DataFieldBase], *, bc: Union[Dict[str, Union[Dict, str, BCBase]], Dict, str, BCBase, Tuple[Union[Dict, str, BCBase], Union[Dict, str, BCBase]], Sequence[Union[Dict[str, Union[Dict, str, BCBase]], Dict, str, BCBase, Tuple[Union[Dict, str, BCBase], Union[Dict, str, BCBase]]]]] = 'auto_periodic_neumann', bc_ops: Optional[Dict[str, Union[Dict[str, Union[Dict, str, BCBase]], Dict, str, BCBase, Tuple[Union[Dict, str, BCBase], Union[Dict, str, BCBase]], Sequence[Union[Dict[str, Union[Dict, str, BCBase]], Dict, str, BCBase, Tuple[Union[Dict, str, BCBase], Union[Dict, str, BCBase]]]]]]] = None, user_funcs: Optional[Dict[str, Callable]] = None, consts: Optional[Dict[str, Union[int, float, complex, ndarray]]] = None, label: str = None) DataFieldBase [source]¶
evaluate an expression involving fields
Warning
This implementation uses
exec()
and should therefore not be used in a context where malicious input could occur.- Parameters
expression (str) – The expression, which is parsed by
sympy
. The expression may contain variables (i.e., fields and spatial coordinates of the grid), standard local mathematical operators defined by sympy, and the operators defined in thepde
package. Note that operators need to be specified with their full name, i.e., laplace for a scalar Laplacian and vector_laplace for a Laplacian operating on a vector field. Moreover, the dot product between two vector fields can be denoted by using dot(field1, field2) in the expression, and outer(field1, field2) calculates an outer product. More information can be found in the expression documentation.fields (dict) – Dictionary of the fields involved in the expression.
bc – Boundary conditions for the operators used in the expression. The conditions here are applied to all operators that do not have a specialized condition given in bc_ops. Boundary conditions are generally given as a list with one condition for each axis. For periodic axis, only periodic boundary conditions are allowed (indicated by ‘periodic’ and ‘anti-periodic’). For non- periodic axes, different boundary conditions can be specified for the lower and upper end (using a tuple of two conditions). For instance, Dirichlet conditions enforcing a value NUM (specified by {‘value’: NUM}) and Neumann conditions enforcing the value DERIV for the derivative in the normal direction (specified by {‘derivative’: DERIV}) are supported. Note that the special value ‘natural’ imposes periodic boundary conditions for periodic axis and a vanishing derivative otherwise. More information can be found in the boundaries documentation.
bc_ops (dict) – Special boundary conditions for some operators. The keys in this dictionary specify the operator to which the boundary condition will be applied.
user_funcs (dict, optional) – A dictionary with user defined functions that can be used in the expressions in rhs.
consts (dict, optional) – A dictionary with user defined constants that can be used in the expression. These can be either scalar numbers or fields defined on the same grid as the actual simulation.
label (str) – Name of the field that is returned.
- Returns
The resulting field. The rank of the returned field (and thus the precise class) is determined automatically.
- Return type