# cexprtk 0.3.2

Mathematical expression parser: cython wrapper around the 'C++ Mathematical Expression Toolkit Library'

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.

[TOC]

## Installation

```\$ 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:
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
```

## 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 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 = {}):

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.
##### 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.

#### 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.

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.

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

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