IshigamiModel

class IshigamiModel

Data class for the Ishigami model.

Attributes:

dimThe dimension of the problem

dim = 3

afloat

Constant: a = 7.0

bfloat

Constant: b = 0.1

X1Uniform

First marginal, ot.Uniform(-np.pi, np.pi)

X2Uniform

Second marginal, ot.Uniform(-np.pi, np.pi)

X3Uniform

Third marginal, ot.Uniform(-np.pi, np.pi)

inputDistributionJointDistribution

The joint distribution of the input parameters.

ishigamiSymbolicFunction

The Ishigami model with a, b as variables.

modelParametricFunction

The Ishigami model with the a=7.0 and b=0.1 parameters fixed.

expectationfloat

Expectation of the output variable.

variancefloat

Variance of the output variable.

S1float

First order Sobol index number 1

S2float

First order Sobol index number 2

S3float

First order Sobol index number 3

S12float

Second order Sobol index for marginals 1 and 2.

S13float

Second order Sobol index for marginals 1 and 3.

S23float

Second order Sobol index for marginals 2 and 3.

S123float

ST1float

Total order Sobol index number 1.

ST2float

Total order Sobol index number 2.

ST3float

Total order Sobol index number 3.

Examples

>>> from openturns.usecases import ishigami_function
>>> # Load the Ishigami model
>>> im = ishigami_function.IshigamiModel()

__init__()

Examples using the class

Estimate correlation coefficients

Estimate correlation coefficients

Visualize sensitivity

Visualize sensitivity

Compute grouped indices for the Ishigami function

Compute grouped indices for the Ishigami function

Validate a polynomial chaos

Validate a polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a sparse chaos by integration

Create a sparse chaos by integration

Conditional expectation of a polynomial chaos expansion

Conditional expectation of a polynomial chaos expansion

Polynomial chaos expansion cross-validation

Polynomial chaos expansion cross-validation

Kriging: propagate uncertainties

Kriging: propagate uncertainties

Evaluate the mean of a random vector by simulations

Evaluate the mean of a random vector by simulations

Sobol’ sensitivity indices using rank-based algorithm

Sobol' sensitivity indices using rank-based algorithm

FAST sensitivity indices

FAST sensitivity indices

Estimate Sobol’ indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis

Estimate Sobol' indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis

The HSIC sensitivity indices: the Ishigami model

The HSIC sensitivity indices: the Ishigami model

Compute the L2 error between two functions

Compute the L2 error between two functions

Compute leave-one-out error of a polynomial chaos expansion

Compute leave-one-out error of a polynomial chaos expansion