LogisticModel

class LogisticModel(t0=1790.0, y0=3900000.0, a=0.03134, b=1.5887e-10, populationFactor=1000000.0)

Data class for the logistic model.

In the physical model, the inputs and parameters are ordered as presented in the next table. Notice that there are no parameters in the physical model.

Index

Input variable

0

t1

1

t2

…

…

21

t22

22

a

23

c

Examples

>>> from openturns.usecases import logistic_model
>>> # Load the logistic model
>>> lm = logistic_model.LogisticModel()
>>> print(lm.data[:5])
    [ Time            U.S. Population ]
0 : [ 1790               3.9          ]
1 : [ 1800               5.3          ]
2 : [ 1810               7.2          ]
3 : [ 1820               9.6          ]
4 : [ 1830              13            ]
>>> print("Inputs:", lm.model.getInputDescription())
Inputs: [t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,a,c]#24
>>> print("Outputs:", lm.model.getOutputDescription())
Outputs: [z0,z1,z2,z3,z4,z5,z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21]#22
Attributes:
t0float, optional

Initial time. The default is 1790.

y0float, optional

Initial population (at t0). The default is 3.9e6.

afloat, optional

8Parameter of the model. The default is 0.03134.

bfloat, optional

Parameter of the model. The default is 1.5887e-10.

populationFactorfloat, optional

The multiplication factor to scale the population. The default is 1.0e6.

distY0Normal distribution

ot.Normal(y0, 0.1 * y0)

distANormal distribution

ot.Normal(a, 0.3 * a)

distBNormal distribution

ot.Normal(b, 0.3 * b)

distXJointDistribution

The joint distribution of the input parameters.

modelPythonFunction

The logistic model of growth. The input has input dimension 24 and output dimension 22. More precisely, we have \vect{X} = (t_1, ..., t_{22}, a, c) and \vect{Y} = (y_1, ..., y_{22}).

dataSample of size 22 and dimension 2

A data set containing 22 dates from 1790 to 2000. First marginal represents dates and second marginal the population in millions.

__init__(t0=1790.0, y0=3900000.0, a=0.03134, b=1.5887e-10, populationFactor=1000000.0)

Examples using the class

Logistic growth model

Logistic growth model

Calibration of the logistic model

Calibration of the logistic model