esys.escript.symbolic Package

Classes

class esys.escript.symbolic.Evaluator(*expressions)
__init__(*expressions)

Returns a symbolic evaluator.

Parameters

expressions – optional expressions to initialise with

addExpression(expression)

Adds an expression to this evaluator.

Returns

the modified Evaluator object

evaluate(evalf=False, **args)

Evaluates all expressions in this evaluator and returns the result as a tuple.

Returns

the evaluated expressions in the order they were added to this Evaluator.

subs(**args)

Symbol substitution.

Returns

the modified Evaluator object

class esys.escript.symbolic.Symbol(*args, **kwargs)

Symbol objects are placeholders for a single mathematical symbol, such as ‘x’, or for arbitrarily complex mathematical expressions such as ‘c*x**4+alpha*exp(x)-2*sin(beta*x)’, where ‘alpha’, ‘beta’, ‘c’, and ‘x’ are also Symbols (the symbolic ‘atoms’ of the expression).

With the help of the ‘Evaluator’ class these symbols and expressions can be resolved by substituting numeric values and/or escript Data objects for the atoms. To facilitate the use of Data objects a Symbol has a shape (and thus a rank) as well as a dimension (see constructor). Symbols are useful to perform mathematical simplifications, compute derivatives and as coefficients for nonlinear PDEs which can be solved by the NonlinearPDE class.

__init__(*args, **kwargs)

Initialises a new Symbol object in one of three ways:

u=Symbol('u')

returns a scalar symbol by the name ‘u’.

alpha=Symbol(‘alpha’, (4,3))

returns a rank 2 symbol with the shape (4,3), whose elements are named ‘[alpha]_i_j’ (with i=0..3, j=0..2).

a,b,c=symbols(‘a,b,c’) x=Symbol([[a+b,0,0],[0,b-c,0],[0,0,c-a]])

returns a rank 2 symbol with the shape (3,3) whose elements are explicitly specified by numeric values and other symbols/expressions within a list or numpy array.

The dimensionality of the symbol can be specified through the dim keyword. All other keywords are passed to the underlying symbolic library (currently sympy).

Parameters
  • args – initialisation arguments as described above

  • dim (int) – dimensionality of the new Symbol (default: 2)

applyfunc(f, on_type=None)

Applies the function f to all elements (if on_type is None) or to all elements of type on_type.

atoms(*types)

Returns the atoms that form the current Symbol.

By default, only objects that are truly atomic and cannot be divided into smaller pieces are returned: symbols, numbers, and number symbols like I and pi. It is possible to request atoms of any type, however.

Note that if this symbol contains components such as [x]_i_j then only their main symbol ‘x’ is returned.

Parameters

types – types to restrict result to

Returns

list of atoms of specified type

Return type

set

coeff(x, expand=True)

Returns the coefficient of the term “x” or 0 if there is no “x”.

If “x” is a scalar symbol then “x” is searched in all components of this symbol. Otherwise the shapes must match and the coefficients are checked component by component.

Example:

x=Symbol('x', (2,2))
y=3*x
print y.coeff(x)
print y.coeff(x[1,1])

will print:

[[3 3]
 [3 3]]

[[0 0]
 [0 3]]
Parameters

x (Symbol, numpy.ndarray, list) – the term whose coefficients are to be found

Returns

the coefficient(s) of the term

Return type

Symbol

diff(*symbols, **assumptions)
evalf()

Applies the sympy.evalf operation on all elements in this symbol

expand()

Applies the sympy.expand operation on all elements in this symbol

getDataSubstitutions()

Returns a dictionary of symbol names and the escript Data objects they represent within this Symbol.

Returns

the dictionary of substituted Data objects

Return type

dict

getDim()

Returns the spatial dimensionality of this symbol.

Returns

the symbol’s spatial dimensionality, or -1 if undefined

Return type

int

getRank()

Returns the rank of this symbol.

Returns

the symbol’s rank which is equal to the length of the shape.

Return type

int

getShape()

Returns the shape of this symbol.

Returns

the symbol’s shape

Return type

tuple of int

grad(where=None)

Returns a symbol which represents the gradient of this symbol. :type where: Symbol, FunctionSpace

inverse()
is_Add = False
is_Float = False
item(*args)

Returns an element of this symbol. This method behaves like the item() method of numpy.ndarray. If this is a scalar Symbol, no arguments are allowed and the only element in this Symbol is returned. Otherwise, ‘args’ specifies a flat or nd-index and the element at that index is returned.

Parameters

args – index of item to be returned

Returns

the requested element

Return type

sympy.Symbol, int, or float

lambdarepr()
simplify()

Applies the sympy.simplify operation on all elements in this symbol

subs(old, new)

Substitutes an expression.

swap_axes(axis0, axis1)
tensorProduct(other, axis_offset)
tensorTransposedProduct(other, axis_offset)
trace(axis_offset)

Returns the trace of this Symbol.

transpose(axis_offset)

Returns the transpose of this Symbol.

transposedTensorProduct(other, axis_offset)

Functions

Others

  • HAVE_SYMBOLS

Packages