Expressions

Mathematical expressions

biogeme.expressions module

Defines the various arithmetic expressions accepted by Biogeme.

author: Michel Bierlaire
date: Tue Mar 26 16:47:49 2019

class biogeme.expressions.And(left, right)[source]

Bases: BinaryOperator

Logical and

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.Beta(name, value, lowerbound, upperbound, status)[source]

Bases: Elementary

Unknown parameters to be estimated from data.

__init__(name, value, lowerbound, upperbound, status)[source]

Constructor

Parameters

name (string) – name of the parameter.
value (float) – default value.
lowerbound (float) – if different from None, imposes a lower bound on the value of the parameter during the optimization.
upperbound (float) – if different from None, imposes an upper bound on the value of the parameter during the optimization.
status (int) – if different from 0, the parameter is fixed to its default value, and not modified by the optimization algorithm.

Raises

biogemeError – if the first parameter is not a str.
biogemeError – if the second parameter is not a int or a float.

changeInitValues(betas)[source]

Modifies the initial values of the Beta parameters.

The fact that the parameters are fixed or free is irrelevant here.

Parameters: betas (dict(string:float)) – dictionary where the keys are the names of the parameters, and the values are the new value for the parameters.

dictOfBetas(free=True, fixed=False)[source]

Extract the set of parameters from the expression. Overload the generic function.

Parameters

free (bool) – if True, the free parameters are included. Default: True.
fixed (bool) – if True, the fixed parameters are included. Default: False.

Returns

a dict with the beta parameters appearing in the expression, the keys being the names of the parameters.

Return type

dict(string:biogeme.expressions.Expression)

fix_betas(beta_values, prefix=None, suffix=None)[source]

Fix all the values of the beta parameters appearing in the dictionary

Parameters

beta_values (dict(str: float)) – dictionary containing the betas to be fixed (as key) and their value.
prefix (str) – if not None, the parameter is renamed, with a prefix defined by this argument.
suffix (str) – if not None, the parameter is renamed, with a suffix defined by this argument.

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the name of the expression between < >

the id of the expression between { }

the name of the parameter,

the status between [ ]

the unique ID, preceeded by a comma

the beta ID, preceeded by a comma

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
     (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns

list of the signatures of an expression and its children.

Return type

list(string)

Raises

biogeme.exceptions.biogemeError – if no id has been defined for elementary expression
biogeme.exceptions.biogemeError – if no id has been defined for parameter

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

setIdManager(id_manager=None)[source]

The ID manager contains the IDs of the elementary expressions.

It is externally created, as it may nee to coordinate the numbering of several expressions. It is stored only in the expressions of type Elementary.

Parameters: id_manager (class IdManager) – ID manager to be propagated to the elementary expressions. If None, all the IDs are set to None.

setOfBetas(free=True, fixed=False)[source]

Extract the set of parameters from the expression. Overload the generic function.

Parameters

free (bool) – if True, the free parameters are included. Default: True.
fixed (bool) – if True, the fixed parameters are included. Default: False.

Returns

returns a set with the beta parameters appearing in the expression.

Return type

set(biogeme.expressions.Expression)

class biogeme.expressions.BinaryOperator(left, right)[source]

Bases: Expression

Base class for arithmetic expressions that are binary operators. This expression is the result of the combination of two expressions, typically addition, substraction, multiplication or division.

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

Raises

biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

left: left child

right: right child

class biogeme.expressions.ComparisonOperator(left, right)[source]

Bases: BinaryOperator

Base class for comparison expressions.

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

audit(database=None)[source]: Performs various checks on the expression.

class biogeme.expressions.DefineVariable(name, expression, database)[source]

Bases: Variable

Expression that defines a new variable and add a column in the database.

This expression allows the use to define a new variable that will be added to the database. It avoids that it is recalculated each time it is needed.

__init__(name, expression, database)[source]

Constructor

Parameters

name (string) – name of the variable.
expression – formula that defines the variable
type – biogeme.expressions.Expression
database (biogeme.database.Database) – object identifying the database.

Raises

biogemeError – if the expression is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

class biogeme.expressions.Derive(child, name)[source]

Bases: UnaryOperator

Derivative with respect to an elementary expression

__init__(child, name)[source]

Constructor

Parameters: child (biogeme.expressions.Expression) – first arithmetic expression

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the signatures of the child expression,

the name of the expression between < >

the id of the expression between { }

the id of the child, preceeded by a comma.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

class biogeme.expressions.Divide(left, right)[source]

Bases: BinaryOperator

Division expression

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.Elem(dictOfExpressions, keyExpression)[source]

Bases: Expression

This returns the element of a dictionary. The key is evaluated from an expression.

__init__(dictOfExpressions, keyExpression)[source]

Constructor

Parameters

dictOfExpressions (dict(int: biogeme.expressions.Expression)) – dict of objects with numerical keys.
keyExpression (biogeme.expressions.Expression) – object providing the key of the element to be evaluated.

Raises

biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

dictOfExpressions: dict of expressions

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the signature of the expression defining the key

the signatures of all the children expressions,

the name of the expression between < >

the id of the expression between { }

the number of elements between ( )

the id of the expression defining the key

for each element: the value of the key and the id of the expression, separated by commas.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float
Raises: biogemeError – if the calcuated key is not present in the dictionary.

keyExpression: expression for the key

class biogeme.expressions.Elementary(name)[source]

Bases: Expression

Elementary expression.

It is typically defined by a name appearing in an expression. It can be a variable (from the database), or a parameter (fixed or to be estimated using maximum likelihood), a random variable for numrerical integration, or Monte-Carlo integration.

__init__(name)[source]

Constructor

Parameters: name (string) – name of the elementary experession.

elementaryIndex: The id should be unique for all elementary expressions appearing in a given set of formulas.

getElementaryExpression(name)[source]

Returns: an elementary expression from its name if it appears in the expression. None otherwise.
Return type: biogeme.Expression

getStatusIdManager()[source]

Check the elementary expressions that are associated with an ID manager.

Returns: two lists of elementary expressions, those with and without an ID manager.
Return type: tuple(list(str), list(str))

name: name of the elementary expressiom

rename_elementary(names, prefix=None, suffix=None)[source]

Rename elementary expressions by adding a prefix and/or a suffix

Parameters

names (list(str)) – names of expressions to rename
prefix (str) – if not None, the expression is renamed, with a prefix defined by this argument.
suffix (str) – if not None, the expression is renamed, with a suffix defined by this argument.

class biogeme.expressions.Equal(left, right)[source]

Bases: ComparisonOperator

Logical equal

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.Expression[source]

Bases: object

This is the general arithmetic expression in biogeme. It serves as a base class for concrete expressions.

__add__(other)[source]

Operator overloading. Generate an expression for addition.

Parameters: other (biogeme.expressions.Expression) – expression to be added
Returns: self + other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__and__(other)[source]

Operator overloading. Generate an expression for logical and.

Parameters: other (biogeme.expressions.Expression) – expression for logical and
Returns: self and other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__div__(other)[source]

Operator overloading. Generate an expression for division.

Parameters: other (biogeme.expressions.Expression) – expression for division
Returns: self / other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__eq__(other)[source]

Operator overloading. Generate an expression for comparison.

Parameters: other (biogeme.expressions.Expression) – expression for equality
Returns: self == other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__ge__(other)[source]

Operator overloading. Generate an expression for comparison.

Parameters: other (biogeme.expressions.Expression) – expression for greater or equal
Returns: self >= other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__gt__(other)[source]

Operator overloading. Generate an expression for comparison.

Parameters: other (biogeme.expressions.Expression) – expression for greater than
Returns: self > other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__init__()[source]: Constructor

__le__(other)[source]

Operator overloading. Generate an expression for comparison.

Parameters: other (biogeme.expressions.Expression) – expression for less or equal
Returns: self <= other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__lt__(other)[source]

Operator overloading. Generate an expression for comparison.

Parameters: other (biogeme.expressions.Expression) – expression for less than
Returns: self < other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__mul__(other)[source]

Operator overloading. Generate an expression for multiplication.

Parameters: other (biogeme.expressions.Expression) – expression to be multiplied
Returns: self * other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__ne__(other)[source]

Operator overloading. Generate an expression for comparison.

Parameters: other (biogeme.expressions.Expression) – expression for difference
Returns: self != other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__neg__()[source]

Operator overloading. Generate an expression for unary minus.

Returns: -self
Return type: biogeme.expressions.Expression

__or__(other)[source]

Operator overloading. Generate an expression for logical or.

Parameters: other (biogeme.expressions.Expression) – expression for logical or
Returns: self or other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__pow__(other)[source]

Operator overloading. Generate an expression for power.

Parameters: other (biogeme.expressions.Expression) – expression for power
Returns: self ^ other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__radd__(other)[source]

Operator overloading. Generate an expression for addition.

Parameters: other (biogeme.expressions.Expression) – expression to be added
Returns: other + self
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__rdiv__(other)[source]

Operator overloading. Generate an expression for division.

Parameters: other (biogeme.expressions.Expression) – expression for division
Returns: other / self
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__rmul__(other)[source]

Operator overloading. Generate an expression for multiplication.

Parameters: other (biogeme.expressions.Expression) – expression to be multiplied
Returns: other * self
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__rpow__(other)[source]

Operator overloading. Generate an expression for power.

Parameters: other (biogeme.expressions.Expression) – expression for power
Returns: other ^ self
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__rsub__(other)[source]

Operator overloading. Generate an expression for substraction.

Parameters: other (biogeme.expressions.Expression) – expression to be substracted
Returns: other - self
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__rtruediv__(other)[source]

Operator overloading. Generate an expression for division.

Parameters: other (biogeme.expressions.Expression) – expression for division
Returns: other / self
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__sub__(other)[source]

Operator overloading. Generate an expression for substraction.

Parameters: other (biogeme.expressions.Expression) – expression to substract
Returns: self - other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

__truediv__(other)[source]

Operator overloading. Generate an expression for division.

Parameters: other (biogeme.expressions.Expression) – expression for division
Returns: self / other
Return type: biogeme.expressions.Expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

audit(database=None)[source]

Performs various checks on the expressions.

Parameters: database (biogeme.database.Database) – database object
Returns: tuple listOfErrors, listOfWarnings
Return type: list(string), list(string)

changeInitValues(betas)[source]

Modifies the initial values of the Beta parameters.

The fact that the parameters are fixed or free is irrelevant here.

Parameters: betas (dict(string:float)) – dictionary where the keys are the names of the parameters, and the values are the new value for the parameters.

check_draws()[source]

Set of draws defined outside of ‘MonteCarlo’

Returns: List of names of variables
Return type: set(str)

check_panel_trajectory()[source]

Set of variables defined outside of ‘PanelLikelihoodTrajectory’

Returns: List of names of variables
Return type: set(str)

check_rv()[source]

Set of random variables defined outside of ‘Integrate’

Returns: List of names of variables
Return type: set(str)

children: List of children expressions

countPanelTrajectoryExpressions()[source]

Count the number of times the PanelLikelihoodTrajectory is used in the formula. It should trigger an error if it is used more than once.

Returns: number of times the PanelLikelihoodTrajectory is used in the formula
Return type: int

cpp: Interface to the C++ implementation

createFunction(database=None, numberOfDraws=1000, gradient=True, hessian=True, bhhh=False)[source]

Create a function based on the expression. The function takes as argument an array for the free parameters, and return the value of the function, the gradient, the hessian and the BHHH. The calculation of the derivatives is optional.

Parameters

database (biogeme.database.Database) – database. If no database is provided, the expression must not contain any variable.
numberOfDraws (int) – number of draws if needed by Monte-Carlo integration.
gradient (bool) – if True, the gradient is calculated.
hessian (bool) – if True, the hessian is calculated.
bhhh (bool) – if True, the BHHH matrix is calculated.

Returns

the function. It will return, in that order, the value of the function, the gradient, the hessian and the BHHH matrix. Only requested quantities will be returned. For instance, if the gradient and the BHHH matrix are requested, and not the hessian, the tuple that is returned is f, g, bhhh.

Return type

fct(np.array)

Raises

biogemeError – if gradient is False and hessian or BHHH is True.

dictOfBetas(free=True, fixed=False)[source]

Extract the set of parameters from the expression.

Parameters

free (bool) – if True, the free parameters are included. Default: True.
fixed (bool) – if True, the fixed parameters are included. Default: False.

Returns

a dict with the beta parameters appearing in the expression, the keys being the names of the parameters.

Return type

dict(string:biogeme.expressions.Expression)

dictOfDraws()[source]

Recursively extract the random variables (draws for Monte-Carlo) appearing in the expression, and store them in a dictionary.

Returns: dict where the keys are the random variables and the elements the type of draws
Return type: dict(string:string)

dictOfRandomVariables()[source]

Recursively extract the random variables appearing in the expression, and store them in a dictionary.

Returns: returns a dict with the random variables appearing in the expression the keys being their names.
Return type: dict(string:biogeme.expressions.Expression)

dictOfVariables()[source]

Recursively extract the variables appearing in the expression, and store them in a dictionary.

Returns: returns a dict with the variables appearing in the expression the keys being their names.
Return type: dict(string:biogeme.expressions.Expression)

embedExpression(t)[source]

Check if the expression contains an expression of type t.

Typically, this would be used to check that a MonteCarlo expression contains a bioDraws expression.

Returns: True if the expression contains an expression of type t.
Return type: bool

fix_betas(beta_values, prefix=None, suffix=None)[source]

Fix all the values of the beta parameters appearing in the dictionary

Parameters

beta_values (dict(str: float)) – dictionary containing the betas to be fixed (as key) and their value.
prefix (str) – if not None, the parameter is renamed, with a prefix defined by this argument.
suffix (str) – if not None, the parameter is renamed, with a suffix defined by this argument.

fixedBetaValues: values of the Beta that are not estimated

getClassName()[source]

Obtain the name of the top class of the expression structure

Returns: the name of the class
Return type: string

getElementaryExpression(name)[source]

Return: an elementary expression from its name if it appears in the expression.

Parameters: name (string) – name of the elementary expression.
Returns: the expression if it exists. None otherwise.
Return type: biogeme.expressions.Expression

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the signatures of all the children expressions,

the name of the expression between < >

the id of the expression between { }

the number of children between ( )

the ids of each children, preceeded by a comma.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) } { \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
     (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

getStatusIdManager()[source]

Check the elementary expressions that are associated with an ID manager.

Returns: two sets of elementary expressions, those with and without an ID manager.
Return type: tuple(set(str), set(str))

getValueAndDerivatives(betas=None, database=None, numberOfDraws=1000, gradient=True, hessian=True, bhhh=True, aggregation=True, prepareIds=False)[source]

Evaluation of the expression

In Biogeme the complexity of some expressions requires a specific implementation, in C++. This function invokes the C++ code to evaluate the value of the expression for a series of entries in a database. Note that this function will generate draws if needed.

Parameters

betas (list(float)) – values of the free parameters
database (biogeme.database.Database) – database. If no database is provided, the expression must not contain any variable.
numberOfDraws (int) – number of draws if needed by Monte-Carlo integration.
gradient (bool) – If True, the gradient is calculated.
hessian (bool) – if True, the hessian is calculated.
bhhh (bool) – if True, the BHHH matrix is calculated.
aggregation (bool) – if a database is provided, and this parameter is True, the expression is applied on each entry of the database, and all values are aggregated, so that the sum is returned. If False, the list of all values is returned.
prepareIds (bool) – if True, it means that the IDs of the expression must be constructed before the evaluation of the expression.

Returns

if a database is provided, a list where each entry is the result of applying the expression on one entry of the dsatabase. It returns a float, a vector, and a matrix, depedending if derivatives are requested.

Return type

np.array or float, numpy.array, numpy.array

Raises

biogemeError – if no database is given and the expressions involves variables.
biogemeError – if gradient is False and hessian or BHHH is True.
biogemeError – if derivatives are asked, and the expression is not simple.
biogemeError – if the expression involves MonteCarlo integration, and no database is provided.

getValue_c(database=None, betas=None, numberOfDraws=1000, aggregation=False, prepareIds=False)[source]

Evaluation of the expression, without the derivatives

Parameters

betas (list(float)) – values of the free parameters
database (biogeme.database.Database) – database. If no database is provided, the expression must not contain any variable.
numberOfDraws (int) – number of draws if needed by Monte-Carlo integration.
aggregation (bool) – if a database is provided, and this parameter is True, the expression is applied on each entry of the database, and all values are aggregated, so that the sum is returned. If False, the list of all values is returned.
prepareIds (bool) – if True, it means that the IDs of the expression must be constructed before the evaluation of the expression.

Returns

if a database is provided, a list where each entry is the result of applying the expression on one entry of the dsatabase. It returns a float.

Return type

np.array or float

Raises

biogemeError – if no database is given, and the number of returned values is different from one.

id_manager: in charge of the IDs

keep_id_manager: a copy of the ID manager

missingData: Value interpreted as missing data

numberOfDraws: number of draws for Monte Carlo integration

prepare(database, numberOfDraws=1000)[source]

Prepare the expression to be evaluated

Parameters

database (biogeme.database.Database) – Biogeme database
numberOfDraws (int) – number of draws for Monte-Carlo integration

rename_elementary(names, prefix=None, suffix=None)[source]

Rename elementary expressions by adding a prefix and/or a suffix

Parameters

names (list(str)) – names of expressions to rename
prefix (str) – if not None, the expression is renamed, with a prefix defined by this argument.
suffix (str) – if not None, the expression is renamed, with a suffix defined by this argument.

requiresDraws()[source]

Checks if the expression requires draws

Returns: True if it requires draws.
Return type: bool

setIdManager(id_manager)[source]

The ID manager contains the IDs of the elementary expressions.

It is externally created, as it may nee to coordinate the numbering of several expressions. It is stored only in the expressions of type Elementary.

Parameters: id_manager (class IdManager) – ID manager to be propagated to the elementary expressions. If None, all the IDs are set to None.

setOfBetas(free=True, fixed=False)[source]

Extract the set of parameters from the expression.

Parameters

free (bool) – if True, the free parameters are included. Default: True.
fixed (bool) – if True, the fixed parameters are included. Default: False.

Returns

returns a set with the beta parameters appearing in the expression.

Return type

set(biogeme.expressions.Expression)

setOfVariables()[source]

Extract the set of variables used in the expression.

Returns: returns a set with the variables appearing in the expression.
Return type: set(biogeme.expressions.Expression)

setRow(row)[source]

Obsolete function. This function identifies the row of the database from which the values of the variables must be obtained.

Parameters: row (pandas.core.series.Serie) – row from the database
Raises: biogemeError – if the function is called, because it is obsolete.

class biogeme.expressions.Greater(left, right)[source]

Bases: ComparisonOperator

Logical greater

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.GreaterOrEqual(left, right)[source]

Bases: ComparisonOperator

Logical greater or equal

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.Integrate(child, name)[source]

Bases: UnaryOperator

Numerical integration

__init__(child, name)[source]

Constructor

Parameters

child (biogeme.expressions.Expression) – first arithmetic expression
name (string) – name of the random variable for the integration.

audit(database=None)[source]

Performs various checks on the expressions.

Parameters: database (biogeme.database.Database) – database object
Returns: tuple listOfErrors, listOfWarnings
Return type: list(string), list(string)

check_rv()[source]

List of random variables defined outside of ‘Integrate’

Returns: List of names of variables
Return type: list(str)

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the signatures of the child expression,

the name of the expression between < >

the id of the expression between { }, preceeded by a comma

the id of the children, preceeded by a comma

the index of the randon variable, preceeded by a comma

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) } { \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
     (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

class biogeme.expressions.Less(left, right)[source]

Bases: ComparisonOperator

Logical less

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.LessOrEqual(left, right)[source]

Bases: ComparisonOperator

Logical less or equal

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.LogLogit(util, av, choice)[source]

Bases: Expression

Expression capturing the logit formula.

It contains one formula for the target alternative, a dict of formula for the availabilities and a dict of formulas for the utilities

__init__(util, av, choice)[source]

Constructor

Parameters

util (dict(int:biogeme.expressions.Expression)) – dictionary where the keys are the identifiers of the alternatives, and the elements are objects defining the utility functions.
av (dict(int:biogeme.expressions.Expression)) – dictionary where the keys are the identifiers of the alternatives, and the elements are object of type biogeme.expressions.Expression defining the availability conditions. If av is None, all the alternatives are assumed to be always available
choice (biogeme.expressions.Expression) – formula to obtain the alternative for which the logit probability must be calculated.

Raises

biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

audit(database=None)[source]

Performs various checks on the expressions.

Parameters: database (biogeme.database.Database) – database object
Returns: tuple listOfErrors, listOfWarnings
Return type: list(string), list(string)

av: dict of availability formulas

choice: expression for the chosen alternative

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the signatures of all the children expressions,

the name of the expression between < >

the id of the expression between { }

the number of alternatives between ( )

the id of the expression for the chosen alternative, preceeded by a comma.

for each alternative, separated by commas:

the number of the alternative, as defined by the user,

the id of the expression for the utility,

the id of the expression for the availability condition.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

Raises

biogemeError – if the chosen alternative does not correspond to any of the utility functions
biogemeError – if the chosen alternative does not correspond to any of entry in the availability condition

util: dict of utility functions

class biogeme.expressions.Minus(left, right)[source]

Bases: BinaryOperator

Substraction expression

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.MonteCarlo(child)[source]

Bases: UnaryOperator

Monte Carlo integration

__init__(child)[source]

Constructor

Parameters: child (biogeme.expressions.Expression) – arithmetic expression

audit(database=None)[source]

Performs various checks on the expressions.

Parameters: database (biogeme.database.Database) – database object
Returns: tuple listOfErrors, listOfWarnings
Return type: list(string), list(string)

check_draws()[source]

List of draws defined outside of ‘MonteCarlo’

Returns: List of names of variables
Return type: list(str)

class biogeme.expressions.NotEqual(left, right)[source]

Bases: ComparisonOperator

Logical not equal

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.Numeric(value)[source]

Bases: Expression

Numerical expression for a simple number

__init__(value)[source]

Constructor

Parameters: value (float) – numerical value

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the name of the expression between < >

the id of the expression between { }

the value, preceeded by a comma.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

value: numeric value

class biogeme.expressions.Or(left, right)[source]

Bases: BinaryOperator

Logical or

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.PanelLikelihoodTrajectory(child)[source]

Bases: UnaryOperator

Likelihood of a sequences of observations for the same individual

__init__(child)[source]

Constructor

Parameters: child (biogeme.expressions.Expression) – first arithmetic expression

audit(database=None)[source]

Performs various checks on the expressions.

Parameters: database (biogeme.database.Database) – database object
Returns: tuple listOfErrors, listOfWarnings
Return type: list(string), list(string)

check_panel_trajectory()[source]

List of variables defined outside of ‘PanelLikelihoodTrajectory’

Returns: List of names of variables
Return type: list(str)

countPanelTrajectoryExpressions()[source]: Count the number of times the PanelLikelihoodTrajectory is used in the formula.

class biogeme.expressions.Plus(left, right)[source]

Bases: BinaryOperator

Addition expression

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.Power(left, right)[source]

Bases: BinaryOperator

Power expression

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.RandomVariable(name)[source]

Bases: Elementary

Random variable for numerical integration

__init__(name)[source]

Constructor

Parameters: name (string.) – name of the random variable involved in the integration.

check_rv()[source]

List of random variables defined outside of ‘Integrate’

Returns: List of names of variables
Return type: list(str)

dictOfRandomVariables()[source]

Recursively extract the random variables appearing in the expression, and store them in a dictionary.

Overloads the generic function.

Returns: returns a dict with the random variables appearing in the expression the keys being their names.
Return type: dict(string:biogeme.expressions.Expression)

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the name of the expression between < >

the id of the expression between { }

the name of the random variable,

the unique ID, preceeded by a comma,

the ID of the random variable.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns

list of the signatures of an expression and its children.

Return type

list(string)

Raises

biogeme.exceptions.biogemeError – if no id has been defined for elementary expression
biogeme.exceptions.biogemeError – if no id has been defined for random variable

setIdManager(id_manager=None)[source]

The ID manager contains the IDs of the elementary expressions.

It is externally created, as it may nee to coordinate the numbering of several expressions. It is stored only in the expressions of type Elementary.

Parameters: id_manager (class IdManager) – ID manager to be propagated to the elementary expressions. If None, all the IDs are set to None.

class biogeme.expressions.Times(left, right)[source]

Bases: BinaryOperator

Multiplication expression

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.UnaryMinus(child)[source]

Bases: UnaryOperator

Unary minus expression

__init__(child)[source]

Constructor

Parameters: child (biogeme.expressions.Expression) – first arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.UnaryOperator(child)[source]

Bases: Expression

Base class for arithmetic expressions that are unary operators.

Such an expression is the result of the modification of another expressions, typically changing its sign.

__init__(child)[source]

Constructor

Parameters: child (biogeme.expressions.Expression) – first arithmetic expression
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

child: child

class biogeme.expressions.Variable(name)[source]

Bases: Elementary

Explanatory variable

This represents the explanatory variables of the choice model. Typically, they come from the data set.

__init__(name)[source]

Constructor

Parameters: name (string) – name of the variable.

audit(database=None)[source]

Performs various checks on the expressions.

Parameters

database (biogeme.database.Database) – database object

Returns

tuple listOfErrors, listOfWarnings

Return type

list(string), list(string)

Raises

biogemeError – if no database is provided.
biogemeError – if the name of the variable does not appear in the database.

check_panel_trajectory()[source]

List of variables defined outside of ‘PanelLikelihoodTrajectory’

Returns: List of names of variables
Return type: list(str)

dictOfVariables()[source]

Recursively extract the variables appearing in the expression, and store them in a dictionary.

Overload the generic function.

Returns: returns a dict with the variables appearing in the expression the keys being their names. Here, it contains only one element.
Return type: dict(string:biogeme.expressions.Expression)

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the name of the expression between < >

the id of the expression between { }

the name of the variable,

the unique ID, preceeded by a comma.

the variabvle ID, preceeded by a comma.

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns

list of the signatures of an expression and its children.

Return type

list(string)

Raises

biogeme.exceptions.biogemeError – if no id has been defined for elementary expression
biogeme.exceptions.biogemeError – if no id has been defined for variable

getValue()[source]

The evaluation of a Variable requires a database. Therefore, this: function triggers an exception.

Raises: biogemeError – each time the function is calles

setIdManager(id_manager=None)[source]

The ID manager contains the IDs of the elementary expressions.

It is externally created, as it may need to coordinate the numbering of several expressions. It is stored only in the expressions of type Elementary.

Parameters: id_manager (class IdManager) – ID manager to be propagated to the elementary expressions. If None, all the IDs are set to None.

class biogeme.expressions.bioDraws(name, drawType)[source]

Bases: Elementary

Draws for Monte-Carlo integration

__init__(name, drawType)[source]

Constructor

Parameters

name (string) – name of the random variable with a series of draws.
drawType (string) – type of draws.

check_draws()[source]

List of draws defined outside of ‘MonteCarlo’

Returns: List of names of variables
Return type: list(str)

dictOfDraws()[source]

Recursively extract the random variables (draws for Monte-Carlo). Overloads the generic function. appearing in the expression, and store them in a dictionary.

Returns: dict where the keys are the random variables and the elements the type of draws. Here, contains only one element.
Return type: dict(string:string)

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the name of the expression between < >

the id of the expression between { }, preceeded by a comma

the name of the draws

the unique ID (preceeded by a comma),

the draw ID (preceeded by a comma).

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns

list of the signatures of an expression and its children.

Return type

list(string)

Raises

biogeme.exceptions.biogemeError – if no id has been defined for elementary expression
biogeme.exceptions.biogemeError – if no id has been defined for draw

setIdManager(id_manager=None)[source]

The ID manager contains the IDs of the elementary expressions.

It is externally created, as it may nee to coordinate the numbering of several expressions. It is stored only in the expressions of type Elementary.

Parameters: id_manager (class IdManager) – ID manager to be propagated to the elementary expressions. If None, all the IDs are set to None.

class biogeme.expressions.bioLinearUtility(listOfTerms)[source]

Bases: Expression

When the utility function is linear, it is expressed as a list of terms, where a parameter multiplies a variable.

__init__(listOfTerms)[source]

Constructor

Parameters: listOfTerms (list(biogeme.expressions.Expression, biogeme.expressions.Expression)) – a list of tuple. Each tuple contains first a beta parameter, second the name of a variable.
Raises: biogeme.exceptions.biogemeError – if the object is not a list of tuples (parameter, variable)

betas: list of parameters

dictOfBetas(free=True, fixed=False)[source]

Extract the set of parameters from the expression.

Parameters

free (bool) – if True, the free parameters are included. Default: True.
fixed (bool) – if True, the fixed parameters are included. Default: False.

Returns

a dict with the beta parameters appearing in the expression, the keys being the names of the parameters.

Return type

dict(string:biogeme.expressions.Expression)

dictOfDraws()[source]

Recursively extract the random variables (draws for Monte-Carlo). Overloads the generic function. appearing in the expression, and store them in a dictionary.

Returns: dict where the keys are the random variables and the elements the type of draws. Here, returns an empty dict.
Return type: dict(string:string)

dictOfRandomVariables()[source]

Recursively extract the random variables appearing in the expression, and store them in a dictionary.

Returns: returns a dict with the random variables appearing in the expression the keys being their names.
Return type: dict(string:biogeme.expressions.Expression)

dictOfVariables()[source]

Recursively extract the variables appearing in the expression, and store them in a dictionary.

Overloads the generic function.

Returns: returns a dict with the variables appearing in the expression the keys being their names.
Return type: dict(string:biogeme.expressions.Expression)

getSignature()[source]

The signature of a string characterizing an expression.

This is designed to be communicated to C++, so that the expression can be reconstructed in this environment.

The list contains the following elements:

the signatures of all the children expressions,

the name of the expression between < >

the id of the expression between { }

the number of terms in the utility ( )

for each term:

the id of the beta parameter

the unique id of the beta parameter

the name of the parameter

the id of the variable

the unique id of the variable

the name of the variable

Consider the following expression:

\[2 \beta_1 V_1 - \frac{\exp(-\beta_2 V_2) }{ \beta_3 (\beta_2 \geq \beta_1)}.\]

It is defined as:

2 * beta1 * Variable1 - expressions.exp(-beta2*Variable2) /
    (beta3 * (beta2 >= beta1))

And its signature is:

[b'<Numeric>{4780527008},2',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<Times>{4780526952}(2),4780527008,4780277152',
 b'<Variable>{4511837152}"Variable1",5,2',
 b'<Times>{4780527064}(2),4780526952,4511837152',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<UnaryMinus>{4780527120}(1),4780277656',
 b'<Variable>{4511837712}"Variable2",6,3',
 b'<Times>{4780527176}(2),4780527120,4511837712',
 b'<exp>{4780527232}(1),4780527176',
 b'<Beta>{4780277264}"beta3"[1],2,0',
 b'<Beta>{4780277656}"beta2"[0],1,1',
 b'<Beta>{4780277152}"beta1"[0],0,0',
 b'<GreaterOrEqual>{4780527288}(2),4780277656,4780277152',
 b'<Times>{4780527344}(2),4780277264,4780527288',
 b'<Divide>{4780527400}(2),4780527232,4780527344',
 b'<Minus>{4780527456}(2),4780527064,4780527400']

Returns: list of the signatures of an expression and its children.
Return type: list(string)

listOfTerms: List of terms

setOfBetas(free=True, fixed=False)[source]

Extract the set of parameters from the expression.

Parameters

free (bool) – if True, the free parameters are included. Default: True.
fixed (bool) – if True, the fixed parameters are included. Default: False.

Returns

returns a set with the beta parameters appearing in the expression.

Return type

set(biogeme.expressions.Expression)

variables: list of variables

class biogeme.expressions.bioMax(left, right)[source]

Bases: BinaryOperator

Maximum of two expressions

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.bioMin(left, right)[source]

Bases: BinaryOperator

Minimum of two expressions

__init__(left, right)[source]

Constructor

Parameters

left (biogeme.expressions.Expression) – first arithmetic expression
right (biogeme.expressions.Expression) – second arithmetic expression

getValue()[source]

Evaluates the value of the expression

Returns: value of the expression
Return type: float

class biogeme.expressions.bioMultSum(listOfExpressions)[source]

Bases: Expression

This expression returns the sum of several other expressions.

It is a generalization of ‘Plus’ for more than two terms

__init__(listOfExpressions)[source]

Constructor

Parameters: listOfExpressions (list(biogeme.expressions.Expression)) – list of objects representing the terms of the sum.
Raises: biogemeError – if one of the expressions is invalid, that is neither a numeric value or a biogeme.expressions.Expression object.

getValue()[source]

Evaluates the value of the expression