# cexprtk: Mathematical Expression Parsing and Evaluation in Python
`cexprtk` is a cython wrapper around the "[ExprTK: C++ Mathematical Expression Toolkit Library ][ExprTK]" by Arash Partow. Using `cexprtk` a powerful mathematical expression engine can be incorporated into your python project.
## Table of Contents
- [Installation](#installation)
- [Usage](#usage)
- [Example: Evaluate a simple equation](#example-evaluate-a-simple-equation)
- [Example: Using Variables](#example-using-variables)
- [Example: Re-using expressions](#example-re-using-expressions)
- [Example: Defining custom functions](#example-defining-custom-functions)
- [Example: Defining an unknown symbol resolver](#example-defining-an-unknown-symbol-resolver)
- [Example: expressions that contain return statements to produce multiple values](#example-expressions-that-contain-return-statements-to-produce-multiple-values)
- [API Reference](#api-reference)
- [Class Reference](#class-reference)
- [class Expression:](#class-expression)
- [Defining unknown symbol-resolver:](#defining-unknown-symbol-resolver)
- [def __init__(self, *expression*, *symbol_table*, *unknown_symbol_resolver_callback* = None):](#def-__init__self-expression-symbol_table-unknown_symbol_resolver_callback--none)
- [def results(self):](#def-resultsself)
- [def value(self):](#def-valueself)
- [def __call__(self):](#def-__call__self)
- [symbol_table](#symbol_table)
- [class Symbol_Table:](#class-symbol_table)
- [def __init__(self, *variables*, *constants* = {}, *add_constants* = False, functions = {}):](#def-__init__self-variables-constants---add_constants--false-functions--)
- [variables](#variables)
- [constants](#constants)
- [functions](#functions)
- [class USRSymbolType:](#class-usrsymboltype)
- [VARIABLE](#variable)
- [CONSTANT](#constant)
- [Utility Functions](#utility-functions)
- [def check_expression (*expression*)](#def-check_expression-expression)
- [def evaluate_expression (*expression*, *variables*)](#def-evaluate_expression-expression-variables)
- [Authors](#authors)
- [License](#license)
## Installation
The latest version of `cexprtk` can be installed using [pip][pip] :
```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:
# 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`
```python
>>> 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:
```python
>>> 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:
```python
>>> 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:
```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 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:
```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.
* __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:__
```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`.
##### string_variables
Returns dictionary like object containing string variable values. `Symbol_Table` values can be updated through this object.
__Example:__
```python
>>> 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](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][ExprTK] library.
Thanks to:
* [jciskey][jciskey] for adding the `Expression.results()` support.
* [Caleb Hattingh][cjrh] for getting cexprtk to build using MSVC on Windows.
## License
`cexprtk` is released under the same terms as the [ExprTK][ExprTK] library the [Common Public License Version 1.0][] (CPL).
[pip]: http://www.pip-installer.org/en/latest/index.html
[Common Public License Version 1.0]: http://opensource.org/licenses/cpl1.0.php
[ExprTK]: http://www.partow.net/programming/exprtk/index.html
[jciskey]: https://github.com/jciskey
[cjrh]: https://github.com/cjrh
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"description": "# cexprtk: Mathematical Expression Parsing and Evaluation in Python\n\n`cexprtk` is a cython wrapper around the \"[ExprTK: C++ Mathematical Expression Toolkit Library ][ExprTK]\" by Arash Partow. Using `cexprtk` a powerful mathematical expression engine can be incorporated into your python project.\n\n## Table of Contents\n\n- [Installation](#installation)\n- [Usage](#usage)\n - [Example: Evaluate a simple equation](#example-evaluate-a-simple-equation)\n - [Example: Using Variables](#example-using-variables)\n - [Example: Re-using expressions](#example-re-using-expressions)\n - [Example: Defining custom functions](#example-defining-custom-functions)\n - [Example: Defining an unknown symbol resolver](#example-defining-an-unknown-symbol-resolver)\n - [Example: expressions that contain return statements to produce multiple values](#example-expressions-that-contain-return-statements-to-produce-multiple-values)\n- [API Reference](#api-reference)\n - [Class Reference](#class-reference)\n - [class Expression:](#class-expression)\n - [Defining unknown symbol-resolver:](#defining-unknown-symbol-resolver)\n - [def __init__(self, *expression*, *symbol_table*, *unknown_symbol_resolver_callback* = None):](#def-__init__self-expression-symbol_table-unknown_symbol_resolver_callback--none)\n - [def results(self):](#def-resultsself)\n - [def value(self):](#def-valueself)\n - [def __call__(self):](#def-__call__self)\n - [symbol_table](#symbol_table)\n - [class Symbol_Table:](#class-symbol_table)\n - [def __init__(self, *variables*, *constants* = {}, *add_constants* = False, functions = {}):](#def-__init__self-variables-constants---add_constants--false-functions--)\n - [variables](#variables)\n - [constants](#constants)\n - [functions](#functions)\n - [class USRSymbolType:](#class-usrsymboltype)\n - [VARIABLE](#variable)\n - [CONSTANT](#constant)\n - [Utility Functions](#utility-functions)\n - [def check_expression (*expression*)](#def-check_expression-expression)\n - [def evaluate_expression (*expression*, *variables*)](#def-evaluate_expression-expression-variables)\n- [Authors](#authors)\n- [License](#license)\n\n## Installation\n\nThe latest version of `cexprtk` can be installed using [pip][pip] :\n\n```bash\n\t$ pip install cexprtk\n```\n\n__Note:__ Installation requires a compatible C++ compiler to be installed (unless installing from a binary wheel).\n\n\n## Usage\n\nThe following examples show the major features of `cexprtk`. \n\n### Example: Evaluate a simple equation\n\nThe following shows how the arithmetic expression `(5+5) * 23` can be evaluated:\n\n```python\n\t>>> import cexprtk\n\t>>> cexprtk.evaluate_expression(\"(5+5) * 23\", {})\n\t230.0\n```\n\n### Example: Using Variables\n\nVariables 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:\n\n```python\n\t>>> import cexprtk\n\t>>> cexprtk.evaluate_expression(\"(A+B) * C\", {\"A\" : 5, \"B\" : 5, \"C\" : 23})\n\t230.0\n```\n\n### Example: Re-using expressions\nWhen 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.\n\n* 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.\n* First a `Symbol_Table` is created containing a variable `r` (for radius), it is also populated with some useful constants such as \u03c0.\n\n```python\n\t>>> import cexprtk\n\t>>> st = cexprtk.Symbol_Table({'r' : 1.0}, add_constants= True)\n```\n\n* Now an instance of `Expression` is created, defining our function:\n\n```python\n\t>>> circumference = cexprtk.Expression('2*pi*r', st)\n```\n\n* The `Symbol_Table` was initialised with `r=1`, the expression can be evaluated for this radius simply by calling it:\n\n```python\n\t>>> circumference()\n\t6.283185307179586\n```\n\n* Now update the radius to a value of 3.0 using the dictionary like object returned by the `Symbol_Table`'s `.variables` property:\n\n```python\n\t>>> st.variables['r'] = 3.0\n\t>>> circumference()\n\t18.84955592153876\n```\n\n### Example: Defining custom functions\nPython 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.\n\nA suitable function exists in the `random` module, namely `random.uniform`. As this is an instance method it needs to be wrapped in function:\n\n```python\n>>> import random\n>>> def rnd(low, high):\n... return random.uniform(low,high)\n...\n```\n\nOur `rnd` function now needs to be registered with a `Symbol_Table`:\n\n```python\n>>> import cexprtk\n>>> st = cexprtk.Symbol_Table({})\n>>> st.functions[\"rand\"] = rnd\n```\n\nThe `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.\n\nThe `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.\n\n```python\n>>> e = cexprtk.Expression(\"rand(5,8) * 10\", st)\n>>> e()\n61.4668441077191\n>>> e()\n77.13523163246415\n>>> e()\n59.14881842716157\n>>> e()\n69.1476535568958\n```\n\n### Example: Defining an unknown symbol resolver\nA 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`. \n\nThe callback can be used to provide some logic that leads to a new symbol being registered or for an error condition to be flagged.\n\n__The Problem:__ The following example shows a potential use for the symbol resolver:\n\n* An expression contains variables of the form `m_VARIABLENAME` and `f_VARIABLENAME`.\n* `m_` or `f_` prefix the actual variable name (perhaps indicating gender).\n* `VARIABLENAME` should be used to look up the desired value in a dictionary.\n* The dictionary value of `VARIABLENAME` should then be weighted according to its prefix:\n\t+ `m_` variables should be multiplied by 0.8.\n\t+ `f_` variables should be multiplied by 1.1.\n\n__The Solution:__\n\n* First the `VARIABLENAME` dictionary is defined:\n\t\n\t```python\n\tvariable_values = { 'county_a' : 82, 'county_b' : 76}\n\t```\n\n* Now the callback is defined. This takes a single argument, *symbol*, which gives the name of the missing variable found in the expression:\n\n\t```python\n\tdef callback(symbol):\n\t\t# Tokenize the symbol name into prefix and VARIABLENAME components.\n\t\tprefix,variablename = symbol.split(\"_\", 1)\n\t\t# Get the value for this VARIABLENAME from the variable_values dict\n\t\tvalue = variable_values[variablename]\n\t\t# Find the correct weight for the prefix\n\t\tif prefix == 'm':\n\t\t\tweight = 0.8\n\t\telif prefix == 'f':\n\t\t\tweight = 1.1\n\t\telse:\n\t\t\t# Flag an error condition if prefix not found.\n\t\t\terrormsg = \"Unknown prefix \"+ str(prefix)\n\t\t\treturn (False, cexprtk.USRSymbolType.VARIABLE, 0.0, errormsg)\n\t\t# Apply the weight to the \n\t\tvalue *= weight\n\t\t# Indicate success and return value to cexprtk\n\t\treturn (True, cexprtk.USRSymbolType.VARIABLE, value, \"\")\n\t```\n\n* All that remains is to register the callback with an instance of `Expression` and to evaluate an expression. The expression to be evaluated is:\n\t- `(m_county_a - f_county_b)`\n\t- This should give a value of `(0.8*82) - (1.1*76) = -18`\n\n\t```python\n\t\t>>> st = cexprtk.Symbol_Table({})\n\t\t>>> e = cexprtk.Expression(\"(m_county_a - f_county_b)\", st, callback)\n\t\t>>> e.value()\n\t\t-18.0\n\t```\n\n### Example: expressions that contain return statements to produce multiple values\n\nExprtk expressions can return multiple values the results these expressions can be accessed through the `results()` method.\n\nThe following example shows the result of adding a constant value to a vector containing numbers:\n\n```python\n\t>>> st = cexprtk.Symbol_Table({})\n\t>>> e = cexprtk.Expression(\"var v[3] := {1,2,3}; return [v+1];\", st)\n\t>>> e.value()\n\tnan\n\t>>> e.results()\n\t[[2.0, 3.0, 4.0]]\n```\nNote that expression has to be evaluated before calling the `results()` method.\n\nThe value accessed through `results()` can contain a mixture of strings, vectors and real values:\n\n```python\n\t>>> st = cexprtk.Symbol_Table({'c' : 3})\n\t>>> e = cexprtk.Expression(\"if(c>1){return ['bigger than one', c];} else { return ['not bigger than one',c];};\",st)\n\t>>> e.value()\n\tnan\n\t>>> e.results()\n\t['bigger than one', 3.0]\n\t>>> st.variables['c']=0.5\n\t>>> e.value()\n\tnan\n\t>>> e.results()\n\t['not bigger than one', 0.5]\n```\n\n---\n\n## API Reference\n\nFor information about expressions supported by `cexprtk` please refer to the original C++ [ExprTK][] documentation:\n\n### Class Reference\n\n#### class Expression:\nClass representing mathematical expression.\n\n* Following instantiation, the expression is evaluated calling the expression or invoking its `value()` method.\n* 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.\n\n##### Defining unknown symbol-resolver:\n\nThe `unknown_symbol_resolver_callback` argument to the `Expression`\nconstructor accepts a callable which is invoked whenever a symbol (i.e. a\nvariable or a constant), is not found in the `Symbol_Table` given by the\n`symbol_table` argument. The `unknown_symbol_resolver_callback` can be\nused to provide a value for the missing value or to set an error condition.\n\nThe callable should have following signature:\n\n```python\n\tdef callback(symbol_name):\n\t\t...\n```\n\nWhere `symbol_name` is a string identifying the missing symbol.\n\nThe callable should return a tuple of the form:\n\n```python\n\t(HANDLED_FLAG, USR_SYMBOL_TYPE, SYMBOL_VALUE, ERROR_STRING)\n```\n\nWhere:\n\n* `HANDLED_FLAG` is a boolean:\n\t+ `True` indicates that callback was able handle the error condition and that `SYMBOL_VALUE` should be used for the missing symbol. \n\t+ `False`, flags and error condition, the reason why the unknown symbol could not be resolved by the callback is described by `ERROR_STRING`.\n* `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.\n\t+ `cexprtk.USRSymbolType.VARIABLE` \n\t+ `cexprtk.USRSymbolType.CONSTANT` \n* `SYMBOL_VALUE`, floating point value that should be used when resolving missing symbol.\n* `ERROR_STRING` when `HANDLED_FLAG` is `False` this can be used to describe error condition.\n\n##### def __init__(self, *expression*, *symbol_table*, *unknown_symbol_resolver_callback* = None):\nInstantiate `Expression` from a text string giving formula and `Symbol_Table`\ninstance encapsulating variables and constants used by the expression.\n\n__Parameters:__\n\n* __expression__ (*str*) String giving expression to be calculated.\n* __symbol_table__ (*Symbol_Table*) Object defining variables and constants.\n* __unknown_symbol_resolver_callback__ (*callable*) See description above.\n\n##### def results(self):\nIf an expression contains a `return []` statement, the returned values are accessed using this method. \n\nA python list is returned which may contain real values, strings or vectors.\n\n**Note:** the expression should be evaluated by calling `value()` before trying to access results.\n\n__Returns:__\n\n* (*list*) List of values produced by expression's `return` statement.\n\n##### def value(self):\nEvaluate expression using variable values currently set within associated `Symbol_Table`\n\n__Returns:__\n\n* (*float*) Value resulting from evaluation of expression.\n\n##### def __call__(self):\nEquivalent to calling `value()` method.\n\n__Returns:__\n\n* (*float*) Value resulting from evaluation of expression.\n\n##### symbol_table\nRead only property that returns `Symbol_Table` instance associated with this expression.\n\n__Returns:__\n\n* (*Symbol_Table*) `Symbol_Table` associated with this `Expression`.\n\n---\n\n#### class Symbol_Table:\nClass for providing variable and constant values to `Expression` instances.\n\n\n##### def __init__(self, *variables*, *constants* = {}, *add_constants* = False, functions = {}, *string_variables* = {}):\nInstantiate `Symbol_Table` defining variables and constants for use with `Expression` class.\n\n__Example:__\n\n* To instantiate a `Symbol_Table` with:\n\t+ `x = 1`\n\t+ `y = 5`\n\t+ define a constant `k = 1.3806488e-23`\n* The following code would be used:\n\n\t```python\n\t\tst = cexprtk.Symbol_Table({'x' : 1, 'y' : 5}, {'k'= 1.3806488e-23})\n\t```\n\n__Parameters:__\n\n* __variables__ (*dict*) Mapping between variable name and initial variable value.\n* __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.\n* __add_constants__ (*bool*) If `True`, add the standard constants `pi`, `inf`, `epsilon` to the 'constants' dictionary before populating the `Symbol_Table`\n* __functions__ (*dict*) Dictionary containing custom functions to be made available to expressions. Dictionary keys specify function names and values should be functions.\n* __string_variables__ (*dict*) Mapping between variable name and initial variable value for string variables.\n\n##### variables\nReturns dictionary like object containing variable values. `Symbol_Table` values can be updated through this object.\n\n__Example:__\n\n```python\n\t>>> import cexprtk\n\t>>> st = cexprtk.Symbol_Table({'x' : 5, 'y' : 5})\n\t>>> expression = cexprtk.Expression('x+y', st)\n\t>>> expression()\n\t10.0\n```\n\nUpdate the value of `x` in the symbol table and re-evaluate the expression:\n\n```python\n\t>>> expression.symbol_table.variables['x'] = 11.0\n\t>>> expression()\n\t16.0\n```\n\n__Returns:__\n\n* Dictionary like giving variables stored in this `Symbol_Table`. Keys are variables names and these map to variable values.\n\n##### constants\nProperty giving constants stored in this `Symbol_Table`.\n\n__Returns:__\n\n* Read-only dictionary like object mapping constant names stored in `Symbol_Table` to their values.\n\n##### functions\nReturns dictionary like object containing custom python functions to use in expressions. \n\n__Returns:__\n\n* 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`.\n\n##### string_variables\nReturns dictionary like object containing string variable values. `Symbol_Table` values can be updated through this object.\n\n__Example:__\n\n```python\n\t>>> import cexprtk\n\t>>> st = cexprtk.Symbol_Table({})\n\t>>> st.string_variables['s1'] = 'he'\n\t>>> st.string_variables['s2'] = 'l'\n\t>>> st.string_variables['s3'] = 'lo'\n\t>>> expression = cexprtk.Expression(\"return[s1+s2+s3+' world']\", st)\n\t>>> expression.value()\n\tnan\n\t>>> expression.results()\n\t['hello world']\n```\n\n__Returns:__\n\n* Dictionary like giving the string variables stored in this `Symbol_Table`. Keys are variables names and these map to string values.\n\n\n---\n\n#### class USRSymbolType:\nDefines constant values used to determine symbol type returned by `unknown_symbol_resolver_callback` (see `Expression` constructor documentation for more).\n\n##### VARIABLE\nValue that should be returned by an `unknown_symbol_resolver_callback` to define a variable.\n\n##### CONSTANT\nValue that should be returned by an `unknown_symbol_resolver_callback` to define a constant.\n\n---\n\n### Utility Functions\n#### def check_expression (*expression*)\n\nCheck that expression can be parsed. If successful do nothing, if unsuccessful raise `ParseException`.\n\n__Parameters:__\n\n* *expression* (*str*) Formula to be evaluated\n\n__Raises:__ \n\n* `ParseException`: If expression is invalid.\t\n\n\n#### def evaluate_expression (*expression*, *variables*)\nEvaluate a mathematical formula using the exprtk library and return result.\n\nFor more information about supported functions and syntax see the\n[exprtk C++ library website](http://www.partow.net/programming/exprtk/index.html).\n\n__Parameters:__\n\n* __expression__ (*str*) Expression to be evaluated.\n* __variables__ (*dict*) Dictionary containing variable name, variable value pairs to be used in expression.\n\n__Returns:__ \n\n* (*float*): Evaluated expression\n\n__Raises:__ \n\n* `ParseException`: if *expression* is invalid.\n\n---\n\n## Authors\n\nCython wrapper by Michael Rushton (m.j.d.rushton@gmail.com), although most credit should go to Arash Partow for creating the underlying [ExprTK][ExprTK] library.\n\nThanks to:\n\n* [jciskey][jciskey] for adding the `Expression.results()` support.\n* [Caleb Hattingh][cjrh] for getting cexprtk to build using MSVC on Windows.\n\n\n## License\n\n`cexprtk` is released under the same terms as the [ExprTK][ExprTK] library the [Common Public License Version 1.0][] (CPL).\n\n[pip]: http://www.pip-installer.org/en/latest/index.html\n[Common Public License Version 1.0]: http://opensource.org/licenses/cpl1.0.php\n[ExprTK]: http://www.partow.net/programming/exprtk/index.html\n[jciskey]: https://github.com/jciskey\n[cjrh]: https://github.com/cjrh\n",
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