cexprtk: Mathematical Expression Parsing and Evaluation in Python

cexprtk is a cython wrapper around the "ExprTK: C++ Mathematical Expression Toolkit Library " by Arash Partow. Using cexprtk a powerful mathematical expression engine can be incorporated into your python project.

Table of Contents

• Installation
• Usage
  • Example: Evaluate a simple equation
  • Example: Using Variables
  • Example: Re-using expressions
  • Example: Defining custom functions
  • Example: Defining an unknown symbol resolver
  • Example: expressions that contain return statements to produce multiple values
• API Reference
  • Class Reference
    • class Expression:
      • Defining unknown symbol-resolver:
      • def init(self, expression, symbol_table, unknown_symbol_resolver_callback = None):
      • def results(self):
      • def value(self):
      • def call(self):
      • symbol_table
    • class Symbol_Table:
      • def init(self, variables, constants = {}, add_constants = False, functions = {}):
      • variables
      • constants
      • functions
    • class USRSymbolType:
      • VARIABLE
      • CONSTANT
  • Utility Functions
    • def check_expression (expression)
    • def evaluate_expression (expression, variables)
• Authors
• License

Installation

The latest version of cexprtk can be installed using pip :

	$ pip install cexprtk

Note: Installation requires a compatible C++ compiler to be installed (unless installing from a binary wheel).

Usage

The following examples show the major features of cexprtk.

Example: Evaluate a simple equation

The following shows how the arithmetic expression (5+5) * 23 can be evaluated:

	>>> import cexprtk
	>>> cexprtk.evaluate_expression("(5+5) * 23", {})
	230.0

Example: Using Variables

Variables can be used within expressions by passing a dictionary to the evaluate_expression function. This maps variable names to their values. The expression from the previous example can be re-calculated using variable values:

	>>> import cexprtk
	>>> cexprtk.evaluate_expression("(A+B) * C", {"A" : 5, "B" : 5, "C" : 23})
	230.0

Example: Re-using expressions

When using the evaluate_expression() function, the mathematical expression is parsed, evaluated and then immediately thrown away. This example shows how to re-use an Expression for multiple evaluations.

• An expression will be defined to calculate the circumference of circle, this will then be re-used to calculate the value for several different radii.
• First a Symbol_Table is created containing a variable r (for radius), it is also populated with some useful constants such as π.

	>>> import cexprtk
	>>> st = cexprtk.Symbol_Table({'r' : 1.0}, add_constants= True)

• Now an instance of Expression is created, defining our function:

	>>> circumference = cexprtk.Expression('2*pi*r', st)

• The Symbol_Table was initialised with r=1, the expression can be evaluated for this radius simply by calling it:

	>>> circumference()
	6.283185307179586

• Now update the radius to a value of 3.0 using the dictionary like object returned by the Symbol_Table's .variables property:

	>>> st.variables['r'] = 3.0
	>>> circumference()
	18.84955592153876

Example: Defining custom functions

Python functions can be registered with a Symbol_Table then used in an Expression. In this example a custom function will be defined which produces a random number within a given range.

A suitable function exists in the random module, namely random.uniform. As this is an instance method it needs to be wrapped in function:

>>> import random
>>> def rnd(low, high):
...   return random.uniform(low,high)
...

Our rnd function now needs to be registered with a Symbol_Table:

>>> import cexprtk
>>> st = cexprtk.Symbol_Table({})
>>> st.functions["rand"] = rnd

The functions property of the Symbol_Table is accessed like a dictionary. In the preceding code snippet, a symbol table is created and then the rnd function is assigned to the rand key. This key is used as the function's name in a cexprtk expression. The key cannot be the same as an existing variable, constant or reserved function name.

The rand function will now be used in an expression. This expression chooses a random number between 5 and 8 and then multiplies it by 10. The followin snippet shows the instantiation of the Expression which is then evaluated a few times. You will probably get different numbers out of your expression than shown, this is because your random number generator will have been initialised with a different seed than used in the example.

>>> e = cexprtk.Expression("rand(5,8) * 10", st)
>>> e()
61.4668441077191
>>> e()
77.13523163246415
>>> e()
59.14881842716157
>>> e()
69.1476535568958

Example: Defining an unknown symbol resolver

A callback can be passed to the Expression constructor through the unknown_symbol_resolver_callback parameter. This callback is invoked during expression parsing when a variable or constant is encountered that isn't in the Symbol_Table associated with the Expression.

The callback can be used to provide some logic that leads to a new symbol being registered or for an error condition to be flagged.

The Problem: The following example shows a potential use for the symbol resolver:

• An expression contains variables of the form m_VARIABLENAME and f_VARIABLENAME.
• m_ or f_ prefix the actual variable name (perhaps indicating gender).
• VARIABLENAME should be used to look up the desired value in a dictionary.
• The dictionary value of VARIABLENAME should then be weighted according to its prefix:
  • m_ variables should be multiplied by 0.8.
  • f_ variables should be multiplied by 1.1.

The Solution:

• First the VARIABLENAME dictionary is defined:

   variable_values = { 'county_a' : 82, 'county_b' : 76}
  

• Now the callback is defined. This takes a single argument, symbol, which gives the name of the missing variable found in the expression:

   def callback(symbol):
   	# Tokenize the symbol name into prefix and VARIABLENAME components.
   	prefix,variablename = symbol.split("_", 1)
   	# Get the value for this VARIABLENAME from the variable_values dict
   	value = variable_values[variablename]
   	# Find the correct weight for the prefix
   	if prefix == 'm':
   		weight = 0.8
   	elif prefix == 'f':
   		weight = 1.1
   	else:
   		# Flag an error condition if prefix not found.
   		errormsg = "Unknown prefix "+ str(prefix)
   		return (False, cexprtk.USRSymbolType.VARIABLE, 0.0, errormsg)
   	# Apply the weight to the 
   	value *= weight
   	# Indicate success and return value to cexprtk
   	return (True, cexprtk.USRSymbolType.VARIABLE, value, "")
  

• All that remains is to register the callback with an instance of Expression and to evaluate an expression. The expression to be evaluated is:

  • (m_county_a - f_county_b)
  • This should give a value of (0.8*82) - (1.1*76) = -18

   	>>> st = cexprtk.Symbol_Table({})
   	>>> e = cexprtk.Expression("(m_county_a - f_county_b)", st, callback)
   	>>> e.value()
   	-18.0
  

Example: expressions that contain return statements to produce multiple values

Exprtk expressions can return multiple values the results these expressions can be accessed through the results() method.

The following example shows the result of adding a constant value to a vector containing numbers:

	>>> st = cexprtk.Symbol_Table({})
	>>> e = cexprtk.Expression("var v[3] := {1,2,3}; return [v+1];", st)
	>>> e.value()
	nan
	>>> e.results()
	[[2.0, 3.0, 4.0]]

Note that expression has to be evaluated before calling the results() method.

The value accessed through results() can contain a mixture of strings, vectors and real values:

	>>> st = cexprtk.Symbol_Table({'c' : 3})
	>>> e = cexprtk.Expression("if(c>1){return ['bigger than one', c];} else { return ['not bigger than one',c];};",st)
	>>> e.value()
	nan
	>>> e.results()
	['bigger than one', 3.0]
	>>> st.variables['c']=0.5
	>>> e.value()
	nan
	>>> e.results()
	['not bigger than one', 0.5]

---

API Reference

For information about expressions supported by cexprtk please refer to the original C++ ExprTK documentation:

Class Reference

class Expression:

Class representing mathematical expression.

• Following instantiation, the expression is evaluated calling the expression or invoking its value() method.
• The variable values used by the Expression can be modified through the variables property of the Symbol_Table instance associated with the expression. The Symbol_Table can be accessed using the Expression.symbol_table property.

Defining unknown symbol-resolver:

The unknown_symbol_resolver_callback argument to the Expression constructor accepts a callable which is invoked whenever a symbol (i.e. a variable or a constant), is not found in the Symbol_Table given by the symbol_table argument. The unknown_symbol_resolver_callback can be used to provide a value for the missing value or to set an error condition.

The callable should have following signature:

	def callback(symbol_name):
		...

Where symbol_name is a string identifying the missing symbol.

The callable should return a tuple of the form:

	(HANDLED_FLAG, USR_SYMBOL_TYPE, SYMBOL_VALUE, ERROR_STRING)

Where:

• HANDLED_FLAG is a boolean:
  • True indicates that callback was able handle the error condition and that SYMBOL_VALUE should be used for the missing symbol.
  • False, flags and error condition, the reason why the unknown symbol could not be resolved by the callback is described by ERROR_STRING.
• USR_SYMBOL_TYPE gives type of symbol (constant or variable) that should be added to the symbol_table when unkown symbol is resolved. Value should be one of those given in cexprtk.USRSymbolType. e.g.
  • cexprtk.USRSymbolType.VARIABLE
  • cexprtk.USRSymbolType.CONSTANT
• SYMBOL_VALUE, floating point value that should be used when resolving missing symbol.
• ERROR_STRING when HANDLED_FLAG is False this can be used to describe error condition.

def init(self, expression, symbol_table, unknown_symbol_resolver_callback = None):

Instantiate Expression from a text string giving formula and Symbol_Table instance encapsulating variables and constants used by the expression.

Parameters:

• expression (str) String giving expression to be calculated.
• symbol_table (Symbol_Table) Object defining variables and constants.
• unknown_symbol_resolver_callback (callable) See description above.

def results(self):

If an expression contains a return [] statement, the returned values are accessed using this method.

A python list is returned which may contain real values, strings or vectors.

Note: the expression should be evaluated by calling value() before trying to access results.

Returns:

• (list) List of values produced by expression's return statement.

def value(self):

Evaluate expression using variable values currently set within associated Symbol_Table

Returns:

• (float) Value resulting from evaluation of expression.

def call(self):

Equivalent to calling value() method.

Returns:

• (float) Value resulting from evaluation of expression.

symbol_table

Read only property that returns Symbol_Table instance associated with this expression.

Returns:

• (Symbol_Table) Symbol_Table associated with this Expression.

---

class Symbol_Table:

Class for providing variable and constant values to Expression instances.

def init(self, variables, constants = {}, add_constants = False, functions = {}, string_variables = {}):

Instantiate Symbol_Table defining variables and constants for use with Expression class.

Example:

• To instantiate a Symbol_Table with:

  • x = 1
  • y = 5
  • define a constant k = 1.3806488e-23

• The following code would be used:

   	st = cexprtk.Symbol_Table({'x' : 1, 'y' : 5}, {'k'= 1.3806488e-23})
  

Parameters:

• variables (dict) Mapping between variable name and initial variable value.
• constants (dict) Dictionary containing values that should be added to Symbol_Table as constants. These can be used a variables within expressions but their values cannot be updated following Symbol_Table instantiation.
• add_constants (bool) If True, add the standard constants pi, inf, epsilon to the 'constants' dictionary before populating the Symbol_Table
• functions (dict) Dictionary containing custom functions to be made available to expressions. Dictionary keys specify function names and values should be functions.
• string_variables (dict) Mapping between variable name and initial variable value for string variables.

variables

Returns dictionary like object containing variable values. Symbol_Table values can be updated through this object.

Example:

	>>> import cexprtk
	>>> st = cexprtk.Symbol_Table({'x' : 5, 'y' : 5})
	>>> expression = cexprtk.Expression('x+y', st)
	>>> expression()
	10.0

Update the value of x in the symbol table and re-evaluate the expression:

	>>> expression.symbol_table.variables['x'] = 11.0
	>>> expression()
	16.0

Returns:

• Dictionary like giving variables stored in this Symbol_Table. Keys are variables names and these map to variable values.

constants

Property giving constants stored in this Symbol_Table.

Returns:

• Read-only dictionary like object mapping constant names stored in Symbol_Table to their values.

functions

Returns dictionary like object containing custom python functions to use in expressions.

Returns:

• Dictionary like giving function stored in this Symbol_Table. Keys are function names (as used in Expression) and these map to python callable objects including functions, functors, and functools.partial.

string_variables

Returns dictionary like object containing string variable values. Symbol_Table values can be updated through this object.

Example:

	>>> import cexprtk
	>>> st = cexprtk.Symbol_Table({})
	>>> st.string_variables['s1'] = 'he'
	>>> st.string_variables['s2'] = 'l'
	>>> st.string_variables['s3'] = 'lo'
	>>> expression = cexprtk.Expression("return[s1+s2+s3+' world']", st)
	>>> expression.value()
	nan
	>>> expression.results()
	['hello world']

Returns:

• Dictionary like giving the string variables stored in this Symbol_Table. Keys are variables names and these map to string values.

---

class USRSymbolType:

Defines constant values used to determine symbol type returned by unknown_symbol_resolver_callback (see Expression constructor documentation for more).

VARIABLE

Value that should be returned by an unknown_symbol_resolver_callback to define a variable.

CONSTANT

Value that should be returned by an unknown_symbol_resolver_callback to define a constant.

---

Utility Functions

def check_expression (expression)

Check that expression can be parsed. If successful do nothing, if unsuccessful raise ParseException.

Parameters:

• expression (str) Formula to be evaluated

Raises:

• ParseException: If expression is invalid.

def evaluate_expression (expression, variables)

Evaluate a mathematical formula using the exprtk library and return result.

For more information about supported functions and syntax see the exprtk C++ library website.

Parameters:

• expression (str) Expression to be evaluated.
• variables (dict) Dictionary containing variable name, variable value pairs to be used in expression.

Returns:

• (float): Evaluated expression

Raises:

• ParseException: if expression is invalid.

---

Authors

Cython wrapper by Michael Rushton (m.j.d.rushton@gmail.com), although most credit should go to Arash Partow for creating the underlying ExprTK library.

Thanks to:

• jciskey for adding the Expression.results() support.
• Caleb Hattingh for getting cexprtk to build using MSVC on Windows.

License

cexprtk is released under the same terms as the ExprTK library the Common Public License Version 1.0 (CPL).