mathml¶

Evaluation of formulas and MathML expressions.

A Data of type FUNCTION is a formula of other data, see sbmlsim.data. The formula is parsed into the abstract syntax tree of libsedml, which implements the L3 formula syntax of SBML, and evaluated on the arrays of the variables with sympy.

formula_expression, formula_symbols and evaluate_formula read a formula with libsbml and sbmlmath, which make a symbol of every identifier. expr_from_formula hands the text of a formula to sympify, which reads beta, gamma, lambda, S or I as the functions and constants of sympy and not as identifiers of a model. expression_to_astnode and expression_to_formula are the way back, from a sympy expression to the math of SBML.

formula_to_astnode ¶

formula_to_astnode(formula)

Parse ASTNode from formula.

astnode_to_formula ¶

astnode_to_formula(astnode)

Write ASTNode as formula.

parse_mathml_str ¶

parse_mathml_str(mathml_str)

Parse MathML string.

parse_formula ¶

parse_formula(formula)

Parse formula to ASTNode.

parse_astnode ¶

parse_astnode(astnode)

Parse ASTNode.

An AST node in libSBML is a recursive tree structure; each node has a type, a pointer to a value, and a list of children nodes. Each ASTNode node may have none, one, two, or more children depending on its type. There are node types to represent numbers (with subtypes to distinguish integer, real, and rational numbers), names (e.g., constants or variables), simple mathematical operators, logical or relational operators and functions.

:param mathml: :return:

expr_from_formula ¶

expr_from_formula(formula)

Parse sympy expression from given formula string.

evaluate ¶

evaluate(astnode, variables)

Evaluate the astnode with values.

replace_piecewise ¶

replace_piecewise(formula)

Replace libsedml piecewise with sympy piecewise.

formula_expression ¶

formula_expression(formula)

Parse an L3 formula of SBML into a sympy expression.

Every identifier of the formula is a symbol of its name, also the identifiers which are functions or constants of sympy (beta, gamma, lambda, S, I). The time of the model is the symbol time. The constant avogadro stays the csymbol of SBML, which is not an identifier: formula_symbols does not list it and evaluate_formula gives it its value. A logarithm with a base is a quotient of natural logarithms, rem and quotient truncate as they do in SBML.

Parameters:

Name	Type	Description	Default
`formula`	`str`	the formula, e.g. `prey + (alpha - 1.3)`.	required

Returns:

Type	Description
`Basic`	The expression.

Raises:

Type	Description
`ValueError`	if the formula is empty, is not valid math (units of a number are not) or uses a function which is not a function of the MathML of SBML.

formula_symbols ¶

formula_symbols(formula)

Get the identifiers a formula uses.

Parameters:

Name	Type	Description	Default
`formula`	`str`	the formula, an L3 formula of SBML.	required

Returns:

Type	Description
`set[str]`	The names of the symbols of the formula, `time` for the time of the
`set[str]`	model. Constants like `pi` or `avogadro` are no identifiers.

Raises:

Type	Description
`ValueError`	if the formula is not valid math, see `formula_expression`.

evaluate_formula ¶

evaluate_formula(formula, variables)

Evaluate an L3 formula of SBML on the values of its identifiers.

Parameters:

Name	Type	Description	Default
`formula`	`str`	the formula.	required
`variables`	`Mapping[str, Any]`	the value of every identifier of the formula, a number or an array. The values of identifiers the formula does not use are not used, but give the shape of the result.	required

Returns:

Type	Description
`Any`	The value of the formula: a float if all values are numbers, else an
`Any`	array of the shape the values broadcast to, with `nan` where the
`Any`	formula is not defined.

Raises:

Type	Description
`ValueError`	if the formula is not valid math, see `formula_expression`, if an identifier has no value, if the shapes of the values do not broadcast, or if the value of numbers is complex, overflows or divides by zero.

expression_to_astnode ¶

expression_to_astnode(expression)

Convert a sympy expression into the math of SBML.

The numbers of the expression carry no units, so the math is valid in every level of SBML. The symbol time is the time of the model.

Parameters:

Name	Type	Description	Default
`expression`	`Basic`	the expression.	required

Returns:

Type	Description
`ASTNode`	The syntax tree of the MathML of the expression.

Raises:

Type	Description
`ValueError`	if the expression uses a function the MathML of SBML does not have, e.g. the error function.

expression_to_formula ¶

expression_to_formula(expression)

Write a sympy expression as an L3 formula of SBML.

Parameters:

Name	Type	Description	Default
`expression`	`Basic`	the expression.	required

Returns:

Type	Description
`str`	The formula, which `formula_expression` and libsbml read. The
`str`	natural logarithm is `ln`: `log` is the logarithm to the base 10 in a
`str`	formula of SBML.

Raises:

Type	Description
`ValueError`	if the expression has no MathML of SBML, see `expression_to_astnode`.