# 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]

Logical and

__init__(left, right)[source]

Constructor

Parameters
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]

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:

1. the name of the expression between < >

2. the id of the expression between { }

3. the name of the parameter,

4. the status between [ ]

5. the unique ID, preceeded by a comma

6. 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
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
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]

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
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]

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]

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:

1. the signatures of the child expression,

2. the name of the expression between < >

3. the id of the expression between { }

4. 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]

Division expression

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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:

1. the signature of the expression defining the key

2. the signatures of all the children expressions,

3. the name of the expression between < >

4. the id of the expression between { }

5. the number of elements between ( )

6. the id of the expression defining the key

7. 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]

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]

Logical equal

__init__(left, right)[source]

Constructor

Parameters
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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Returns

-self

Return type

biogeme.expressions.Expression

__or__(other)[source]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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:

1. the signatures of all the children expressions,

2. the name of the expression between < >

3. the id of the expression between { }

4. the number of children between ( )

5. 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.

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
setOfVariables()[source]

Extract the set of variables used in the expression.

Returns

returns a set with the variables appearing in the expression.

Return type
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]

Logical greater

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

Logical greater or equal

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

Numerical integration

__init__(child, name)[source]

Constructor

Parameters
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:

1. the signatures of the child expression,

2. the name of the expression between < >

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

4. the id of the children, preceeded by a comma

5. 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]

Logical less

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

Logical less or equal

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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:

1. the signatures of all the children expressions,

2. the name of the expression between < >

3. the id of the expression between { }

4. the number of alternatives between ( )

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

6. for each alternative, separated by commas:

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

2. the id of the expression for the utility,

3. 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]

Substraction expression

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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]

Logical not equal

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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:

1. the name of the expression between < >

2. the id of the expression between { }

3. 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]

Logical or

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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]

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

Power expression

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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.

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:

1. the name of the expression between < >

2. the id of the expression between { }

3. the name of the random variable,

4. the unique ID, preceeded by a comma,

5. 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
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]

Multiplication expression

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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]

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]

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.

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:

1. the name of the expression between < >

2. the id of the expression between { }

3. the name of the variable,

4. the unique ID, preceeded by a comma.

5. 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
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]

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:

1. the name of the expression between < >

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

3. the name of the draws

4. the unique ID (preceeded by a comma),

5. 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
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]

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.

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:

1. the signatures of all the children expressions,

2. the name of the expression between < >

3. the id of the expression between { }

4. the number of terms in the utility ( )

5. for each term:

1. the id of the beta parameter

2. the unique id of the beta parameter

3. the name of the parameter

4. the id of the variable

5. the unique id of the variable

6. 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
variables

list of variables

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

Maximum of two expressions

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

Minimum of two expressions

__init__(left, right)[source]

Constructor

Parameters
getValue()[source]

Evaluates the value of the expression

Returns

value of the expression

Return type

float

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

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]

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:

1. free betas,

2. fixed betas,

3. random variables for numrerical integration,

4. random variables for Monte-Carlo integration,

5. 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]

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]

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