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: biogeme.expressions.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: biogeme.expressions.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)

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

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)

setSpecificIndices(indicesOfFreeBetas, indicesOfFixedBetas, indicesOfRandomVariables, indicesOfDraws)[source]¶

Provide an index to all elementary expressions, specific to their type

Parameters

indicesOfFreeBetas (dict(string:int)) – dictionary mapping the name of the free betas with their index
indicesOfFixedBetas (dict(string:int)) – dictionary mapping the name of the fixed betas with their index
indicesOfRandomVariables (dict(string:int)) – dictionary mapping the name of the random variables with their index
indicesOfDraws (dict(string:int)) – dictionary mapping the name of the draws with their index

Raises

biogemeError – if no index is available for one of the parameters

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

Bases: biogeme.expressions.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 parent

right¶: right parent

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

Bases: biogeme.expressions.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: biogeme.expressions.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)

setUniqueId(idsOfElementaryExpressions)[source]¶

Provides a unique id to the elementary expressions.

Parameters: idsOfElementaryExpressions (dict(string:int)) – dictionary mapping the name of the elementary expression with their id.
Raises: biogemeError – if no index is available for an expression.

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

Bases: biogeme.expressions.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: biogeme.expressions.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

keyExpression¶: expression for the key

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

Bases: biogeme.expressions.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.

getElementaryExpression(name)[source]¶

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

name¶: name of the elementary expressiom

setUniqueId(idsOfElementaryExpressions)[source]¶

Provides a unique id to the elementary expressions. Overloads the generic function

Parameters: idsOfElementaryExpressions (dict(string:int)) – dictionary mapping the name of the elementary expression with their id.
Raises: biogemeError – if no index is available for an expression.

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

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

Bases: biogeme.expressions.BinaryOperator

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.

allDraws¶: dict of draws

allFixedBetas¶: dict of fixed parameters

allFreeBetas¶: dict of free parameters

allRandomVariables¶: dict of random variables

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)

betaIds¶: List of ids of the free beta parameters (those to be estimated)

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.

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

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)

drawNames¶: list of draw types

elementaryExpressionIndex¶: Indices of the elementary expressions (dict)

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

See: Expression.isContainedIn

fixedBetaNames¶: list of names of fixed parameters

fixedBetaValues¶: List of values of the fixed beta parameters (those to be estimated)

freeBetaNames¶: list of names of free parameters

freeBetaValues¶: List of values of the free beta parameters (those to be 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)

getValue_c(database, numberOfDraws=1000)[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

database (biogeme.database.Database) – database
numberOfDraws (int) – number of draws if needed by Monte-Carlo integration.

Returns

a list where each entry is the result of applying the expression on one entry of the dsatabase.

Return type

numpy.array

isContainedIn(t)[source]¶

Check if the expression is contained in an expression of type t.

Typically, this would be used to check that a bioDraws expression is contained in a MonteCarlo expression. If not, it cannot be evaluated.

Returns: True if the expression is contained in an expression of type t.
Return type: bool.

See: biogeme.expressions.Expression.embedExpression()

logger¶: Logger that controls the output of messages to the screen and log file. Type: class biogeme.messaging.bioMessage.

parent¶: Parent expression

randomVariableNames¶: list of random variables names

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]¶

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

Parameters: row (int) – id of the row.

setSpecificIndices(indicesOfFreeBetas, indicesOfFixedBetas, indicesOfRandomVariables, indicesOfDraws)[source]¶

Provides an index to all elementary expressions, specific to their type

Parameters

indicesOfFreeBetas (dict(string:int)) – dictionary mapping the name of the free betas with their index
indicesOfFixedBetas (dict(string:int)) – dictionary mapping the name of the fixed betas with their index
indicesOfRandomVariables (dict(string:int)) – dictionary mapping the name of the random variables with their index
indicesOfDraws (dict(string:int)) – dictionary mapping the name of the draws with their index

setUniqueId(idsOfElementaryExpressions)[source]¶

Provides a unique id to the elementary expressions.

Parameters: idsOfElementaryExpressions (dict(string:int)) – dictionary mapping the name of the elementary expression with their id.

setVariableIndices(indicesOfVariables)[source]¶

Provide an index to all variables

Parameters: indicesOfVariables (dict(string:int)) – dictionary mapping the name of the variables with their index

variableNames¶: list of variables names

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

Bases: biogeme.expressions.BinaryOperator

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: biogeme.expressions.BinaryOperator

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: biogeme.expressions.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)

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)

setSpecificIndices(indicesOfFreeBetas, indicesOfFixedBetas, indicesOfRandomVariables, indicesOfDraws)[source]¶

Provide an index to all elementary expressions, specific to their type Overloads the generic function.

Parameters

indicesOfFreeBetas (dict(string:int)) – dictionary mapping the name of the free betas with their index
indicesOfFixedBetas (dict(string:int)) – dictionary mapping the name of the fixed betas with their index
indicesOfRandomVariables (dict(string:int)) – dictionary mapping the name of the random variables with their index
indicesOfDraws (dict(string:int)) – dictionary mapping the name of the draws with their index

Raises

biogemeError – if no index is available for a random variable.

setUniqueId(idsOfElementaryExpressions)[source]¶

Provides a unique id to the elementary expressions. Overloads the generic function

Parameters: idsOfElementaryExpressions (dict(string:int)) – dictionary mapping the name of the elementary expression with their id.
Raises: biogemeError – if no index is available for a random variable.

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

Bases: biogeme.expressions.BinaryOperator

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: biogeme.expressions.BinaryOperator

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: biogeme.expressions.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

util¶: dict of utility functions

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

Bases: biogeme.expressions.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: biogeme.expressions.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)

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

Bases: biogeme.expressions.BinaryOperator

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: biogeme.expressions.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: biogeme.expressions.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: biogeme.expressions.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)

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

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

Bases: biogeme.expressions.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: biogeme.expressions.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: biogeme.expressions.Elementary

Random variable for numerical integration

__init__(name)[source]¶

Constructor

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

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

setSpecificIndices(indicesOfFreeBetas, indicesOfFixedBetas, indicesOfRandomVariables, indicesOfDraws)[source]¶

Provide an index to all elementary expressions, specific to their type Overloads the generic function.

Parameters

indicesOfFreeBetas (dict(string:int)) – dictionary mapping the name of the free betas with their index
indicesOfFixedBetas (dict(string:int)) – dictionary mapping the name of the fixed betas with their index
indicesOfRandomVariables (dict(string:int)) – dictionary mapping the name of the random variables with their index
indicesOfDraws (dict(string:int)) – dictionary mapping the name of the draws with their index

Raises

biogemeError – if no index is available for a random variable.

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

Bases: biogeme.expressions.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: biogeme.expressions.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: biogeme.expressions.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: biogeme.expressions.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.

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]¶

Evaluates the value of the expression

Returns: value of the expression
Return type: float

setVariableIndices(indicesOfVariables)[source]¶

Provide an index to all variables

Parameters: indicesOfVariables (dict(string:int)) – dictionary mapping the name of the variables with their index

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

Bases: biogeme.expressions.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.

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)

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

setDrawIndex(idsOfDraws)[source]¶

Provide an index to a series of draw for a random variable. Overload the generic function.

Parameters: idsOfDraws (dict(string:int)) – dictionary mapping the name of the draws with their id.
Raises: biogemeError – if no id is available for a draw.

setSpecificIndices(indicesOfFreeBetas, indicesOfFixedBetas, indicesOfRandomVariables, indicesOfDraws)[source]¶

Provide an index to all elementary expressions, specific to their type Overloads the generic function.

Parameters

indicesOfFreeBetas (dict(string:int)) – dictionary mapping the name of the free betas with their index
indicesOfFixedBetas (dict(string:int)) – dictionary mapping the name of the fixed betas with their index
indicesOfRandomVariables (dict(string:int)) – dictionary mapping the name of the random variables with their index
indicesOfDraws (dict(string:int)) – dictionary mapping the name of the draws with their index

Raises

biogemeError – if no index is available for one draw type.

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

Bases: biogeme.expressions.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: biogeme.expressions.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: biogeme.expressions.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: biogeme.expressions.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

Returns: value of the expression
Return type: float

class biogeme.expressions.bioNormalCdf(child)[source]¶

Bases: biogeme.expressions.UnaryOperator

Cumulative Distribution Function of a normal random variable

__init__(child)[source]¶

Constructor

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

biogeme.expressions.defineNumberingOfElementaryExpressions(collectionOfFormulas, variableNames)[source]¶

Provides indices for elementary expressions

The numbering is done in the following order:

free betas,

fixed betas,

random variables for numrerical integration,

random variables for Monte-Carlo integration,

variables

The numbering convention will be performed for all expressions together, so that the same elementary expressions in several expressions will have the same index.

Parameters

collectionOfFormulas (list(biogeme.expressions.Expression)) – collection of Biogeme expressions.
variableNames (list(string)) – list of the names of the variables

Returns

dict, free, freeNames, fixed, fixedNames, rv, rvNames, draws, drawsNames where

dict is a dictionary mapping the names of the elementary expressions with their index,

free is a dict with the free betas,

freeNames is a list of the names of the free betas,

fixed is a dict with the fixed betas,

fixedNames is the list of the names of the fixed betas,

rv is a dict with the random variables for numerical integration,

rvNames is a list with their names,

draws is a dict of the draws, and

drawsNames is a list with their names.

Return type

tuple(dict(str: class Expression), dict(str: class Beta), list(str), dict(str: class Beta), list(str), dict(str: class RandomVariable), list(str), dict(str: class bioDraws), list(str))

Raises

biogemeError – if some elementary expressions are defined more than once.

class biogeme.expressions.exp(child)[source]¶

Bases: biogeme.expressions.UnaryOperator

exponential 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

biogeme.expressions.isNumeric(obj)[source]¶

Identifies if an object is numeric, that is int, float or bool.

Parameters: obj (object) – any object
Returns: True if the object is int, float or bool.
Return type: bool

class biogeme.expressions.log(child)[source]¶

Bases: biogeme.expressions.UnaryOperator

logarithm 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