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

## Project description

#cexprtk: Mathematical Expression Parsing and Evaluation in Python

`cexprtk` is a cython wrapper around the "[ExprTK: C++ Mathematical Expression Toolkit Library ](http://www.partow.net/programming/exprtk/index.html)" by Arash Partow. Using `cexprtk` a powerful mathematical expression engine can be incorporated into your python project.

[TOC]

## Installation

```bash
\$ 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:

```python
>>> 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:

```python
>>> 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.

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

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

```python
>>> 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:

```python
>>> 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:

```python
>>> 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:

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

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

```python
>>> 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.

```python
>>> 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:

```python
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:

```python
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`

```python
>>> 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:

```python
def callback(symbol_name):
...
```

Where `symbol_name` is a string identifying the missing symbol.

The callable should return a tuple of the form:

```python
(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:

```python
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:__

```python
>>> 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:

```python
>>> 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.

[exprtk C++ library website](http://www.partow.net/programming/exprtk/index.html).

__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](http://www.partow.net/programming/exprtk/index.html) library.

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

[pip]: http://www.pip-installer.org/en/latest/index.html

## Project details

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