Code Documentation¶

Documentation for FormulaLab.search module. This is the core module that aims to provide a search engine for formulas database.

class FormulaLab.search.FormulaSearch(data, formula_col='Formula', id_col='ID', save_all_derived_formulas=True)¶

FormulaSearch is a class that search in formulas database. It can go through equations to find connections between two differernt variables in different formulas. The database should be a DataFrame, list, tuple, set, or dict.

The main functionalties for FormulaSearch are:

1- find(function): Directly search for formulas.
2- derive(function (variable)): Derive all possible functions(variable).

Parameters

dataPandas.DataFrame, list, dict, set or tuple: Your formulas database.
formula_colstr, optional: The column name of formulas database if the input data is a DataFrame. The formula column name must match formula_col. The default is “Formula”.
id_colstr, optional: The ID column of the database must match the id_col. The default is ‘ID’.
save_all_derived_formulasbool: All derieved formulas are temporarily stored in ‘self.all_derived_formulas’

Returns

obj

Examples

>>> import FormulaLab as fl
>>> data = ['f = m*a', 'a = v/t', 'd = v*t']
>>> phyfos = fl.FormulaSearch(data)
>>> phyfos.data
      ID  Formula       Args
   0   1  f = m*a  [m, f, a]
   1   2  a = v/t  [v, a, t]
   2   3  d = v*t  [v, d, t]
    *The Args col. is automaticlly generated

Attributes

datapandas.DataFrame
all_derived_formulasset: Collect all derived formulas that have been found by derive().
traceslist: Once the derive method is called, one can see the traces of the derivation.

Methods

derive(func, var)	Find formulas through algebric substitutions.
find(func, vars, id)	Directly search for a function func in terms of vars or id.
function(func:symbols)	Converts a symbolic expr to a python function, wraping over sympy.
find_raw_formula(id)	Find a formula in the database based on its id, in string format.
solve_for(expr:str, var:str)	Solve for a variable from an exprestion, wraping over sympy.
trace(path)	Shows the detailed path of how to get from a function to a variable.

derive(self, func: str, var: str, shortest_path=True) → list¶

Search for the func and var, and connects them algabrically.

Parameters

funcstr: A funciton to solve for.
varstr: A variable to be present in the derived formula.

Returns

list: All found solutions by different paths.

See also

find: For direct search

Examples

>>> import FormulaLab as fl
>>> data = ['f = m*a', 'a = v/t', 'v = d/t']
>>> # Say you want to know what is f(d) = ?
>>> phyfos = fl.FormulaSearch(data)
>>> phyfos.data
      ID  Formula       Args
   0   1  f = m*a  [m, f, a]
   1   2  a = v/t  [v, a, t]
   2   3  v = d/t  [v, d, t]
>>> f_d = phyfos.derive('f', 'd')
>>> print(f_d)
[d*m/t**2, m*v**2/d]

find(self, func: str, vars: list = None, id: int = None, function: bool = False) → list¶

Direct search for a function with respect to variable(s). If id is specified, then the search is limited to one formula with id = “id”. If more than one variable are introdueced, then only formula(s) with all specified variable(s) are found.

Parameters

funcstr: Desired function.
varslist: Desired variables
idint, optional: Restrict the search to one formula
function: bool: To convert the output function to a python function

Returns

list: All found formulas in symbolic form. Or as a python function, at function=True

See also

derive: For indirect search

Examples

>>> import FormulaLab as fl
>>> data = ['f = m*a', 'a = v/t', 'd = v*t']
>>> # Say you want to know what is v(t,a) = ?
>>> phyfos = fl.FormulaSearch(data)
>>> phyfos.data
      ID  Formula       Args
   0   1  f = m*a  [m, f, a]
   1   2  a = v/t  [v, a, t]
   2   3  d = v*t  [v, d, t]
*The Args col. is automaticlly generated
>>> v_t_a = phyfos.find('v', ['t','a'])
>>> print(v_t_a)
[a*t]

Now, say you are only focused on one formula (eg., ID=3) and you want to call it in different places in your code/project, but you do not want to rewrite it again many times. Here where find becomes handy! In any place in your project, you call you formula by its id and in any form you want: func (vars). For example,

>>> a = phyfos.find(func='a', id=1)
>>> print(a)
[f/m]

If you wish the output to be as a pyhon func, then:

>>> a = phyfos.find(func='a', id=1, function=True)
>>> a(f=5,m=2)
2.5

find_raw_formula(self, id)¶

Find a formula in the database based on its id, in string format.

Parameters

idint: Formula id.

Returns

str: The formula as it is in the database.

See also

find: In symbolic format

static function(formula: <function symbols at 0x000002023BF21708>)¶

Convert a symbolic formula to a python function Similar to find(,, function=True). A static method that is wrapped over sympy.lambdify

Parameters

formulasp.symbols or list: Formula(s) in symbolic form, or list of them.

Returns

function: python function. Or list of python functions, depends on input.

See also

find: find(,, function=True)

Examples

>>> import FormulaLab as fl
>>> expr = m * a
>>> # You want to convert expr into a python function
>>> expr_f = fl.FormulaSearch.function(expr)
>>> print(expr_f(m=2, a=3))
6.0

get_formula_info(self, var: tuple, target_col: str = 'ID') → list¶

search in target_col bases on variable(s). target_col can be any column in the database

Parameters

vartuple of str: The varible of interest.
target_colstr, optional: The search col. The default is ‘ID’.

Returns

list: list of the found information.

static solve_for(expr: str, var: str) → list¶

solve for var in expr. This function wrap over sympy.solve

Parameters

exprstr: A formula in a string format.
varstr: The variable that is being solved for.

Returns

list of list: list of list of exprestions of sympy.symbols.

Examples

>>> import FormulaLab as fl
>>> fl.FormulaSearch.solve_for(expr="f = m  * a", var='a')
[[ f / m ]]

trace(self, path: list) → list¶

Shows the detailed path of how to get from a function to a variable. eg., [1, ‘a’, 2, ‘b’, 3], where [1,2,3] is the path, and [‘a’,’b’] is the connected variable list.

Parameters

pathlist: A list of connected ides of formulas

Returns

list: detailed path of connected variables and formulas’ id.

Examples

>>> import FormulaLab as fl
>>> data = ['f = m*a', 'a = v/t', 'd = v*t']
>>> phyfos = fl.FormulaSearch(data)
>>> phyfos.data
      ID  Formula       Args
   0   1  f = m*a  [m, f, a]
   1   2  a = v/t  [v, a, t]
   2   3  d = v*t  [v, d, t]
>>> phyfos.trace([1,2,3])
[[1, 'a', 2, 't', 3], [1, 'a', 2, 'v', 3]]

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