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.

## Table of Contents

[TOC]

## 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

## 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.

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.

## License

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

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