MarginalTransformationEvaluation

class MarginalTransformationEvaluation(*args)

Marginal transformation evaluation.

Available constructors:

MarginalTransformationEvaluation(distCol)

MarginalTransformationEvaluation(distCol, direction, standardMarginal)

MarginalTransformationEvaluation(distCol, outputDistCol)

Parameters
distColDistributionCollection

A collection of distributions.

directioninteger

Flag for the direction of the transformation, either integer or MarginalTransformationEvaluation.FROM (associated to the integer 0) or MarginalTransformationEvaluation.TO (associated to the integer 1). Default is 0.

standardMarginalDistribution

Target distribution marginal Default is Uniform(0, 1)

outputDistColDistributionCollection

A collection of distributions.

Notes

This class contains a Function which can be evaluated in one point but which proposes no gradient nor hessian implementation.

  • In the two first usage, if direction = 0, the created operator transforms a Point into its rank according to the marginal distributions described in distCol. Let (F_{X_1}, \ldots, F_{X_n}) be the CDF of the distributions contained in distCol, then the created operator works as follows:

    (x_1, \ldots, x_n) \rightarrow (F_{X_1}(x_1), \ldots, F_{X_n}(x_n))

    If direction = 1, the created operator works in the opposite direction:

    (x_1, \ldots, x_n) \rightarrow (F^{-1}_{X_1}(x_1), \ldots, F^{-1}_{X_n}(x_n))

    In that case, it requires that all the values x_i be in [0, 1].

  • In the third usage, the created operator transforms a Point into the following one, where outputDistCol contains the (F_{Y_1}, \ldots, F_{Y_n}) distributions:

    (x_1, \ldots, x_n) \rightarrow (F^{-1}_{Y_1} \circ F_{X_1}(x_1), \ldots, F^{-1}_{Y_n} \circ F_{X_n}(x_n))

Examples

>>> import openturns as ot
>>> distCol = [ot.Normal(), ot.LogNormal()]
>>> margTransEval = ot.MarginalTransformationEvaluation(distCol, 0)
>>> print(margTransEval([1, 3]))
[0.841345,0.864031]
>>> margTransEvalInverse = ot.MarginalTransformationEvaluation(distCol, 1)
>>> print(margTransEvalInverse([0.84, 0.86]))
[0.994458,2.94562]
>>> outputDistCol = [ot.WeibullMin(), ot.Exponential()]
>>> margTransEvalComposed = ot.MarginalTransformationEvaluation(distCol, outputDistCol)
>>> print(margTransEvalComposed([1, 3]))
[1.84102,1.99533]

Methods

__call__(self, \*args)

Call self as a function.

draw(self, \*args)

Draw the output of function as a Graph.

getCallsNumber(self)

Accessor to the number of times the function has been called.

getClassName(self)

Accessor to the object’s name.

getDescription(self)

Accessor to the description of the inputs and outputs.

getExpressions(self)

Accessor to the numerical math function.

getId(self)

Accessor to the object’s id.

getInputDescription(self)

Accessor to the description of the inputs.

getInputDimension(self)

Accessor to the number of the inputs.

getInputDistributionCollection(self)

Accessor to the input distribution collection.

getMarginal(self, \*args)

Accessor to marginal.

getName(self)

Accessor to the object’s name.

getOutputDescription(self)

Accessor to the description of the outputs.

getOutputDimension(self)

Accessor to the number of the outputs.

getOutputDistributionCollection(self)

Accessor to the output distribution collection.

getParameter(self)

Accessor to the parameter values.

getParameterDescription(self)

Accessor to the parameter description.

getParameterDimension(self)

Accessor to the dimension of the parameter.

getShadowedId(self)

Accessor to the object’s shadowed id.

getSimplifications(self)

Try to simplify the transformations if it is possible.

getVisibility(self)

Accessor to the object’s visibility state.

hasName(self)

Test if the object is named.

hasVisibleName(self)

Test if the object has a distinguishable name.

isActualImplementation(self)

Accessor to the validity flag.

isLinear(self)

Accessor to the linearity of the evaluation.

isLinearlyDependent(self, index)

Accessor to the linearity of the evaluation with regard to a specific variable.

parameterGradient(self, inP)

Gradient against the parameters.

setDescription(self, description)

Accessor to the description of the inputs and outputs.

setInputDescription(self, inputDescription)

Accessor to the description of the inputs.

setInputDistributionCollection(self, …)

Accessor to the input distribution collection.

setName(self, name)

Accessor to the object’s name.

setOutputDescription(self, outputDescription)

Accessor to the description of the outputs.

setOutputDistributionCollection(self, …)

Accessor to the output distribution collection.

setParameter(self, parameter)

Accessor to the parameter values.

setParameterDescription(self, description)

Accessor to the parameter description.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

setVisibility(self, visible)

Accessor to the object’s visibility state.

__init__(self, *args)

Initialize self. See help(type(self)) for accurate signature.

draw(self, *args)

Draw the output of function as a Graph.

Available usages:

draw(inputMarg, outputMarg, CP, xiMin, xiMax, ptNb)

draw(firstInputMarg, secondInputMarg, outputMarg, CP, xiMin_xjMin, xiMax_xjMax, ptNbs)

draw(xiMin, xiMax, ptNb)

draw(xiMin_xjMin, xiMax_xjMax, ptNbs)

Parameters
outputMarg, inputMargint, outputMarg, inputMarg \geq 0

outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg.

firstInputMarg, secondInputMargint, firstInputMarg, secondInputMarg \geq 0

In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg.

CPsequence of float

Central point.

xiMin, xiMaxfloat

Define the interval where the curve is plotted.

xiMin_xjMin, xiMax_xjMaxsequence of float of dimension 2.

In the 2D case, define the intervals where the curves are plotted.

ptNbint ptNb > 0 or list of ints of dimension 2 ptNb_k > 0, k=1,2

The number of points to draw the curves.

Notes

We note f: \Rset^n \rightarrow \Rset^p where \vect{x} = (x_1, \dots, x_n) and f(\vect{x}) = (f_1(\vect{x}), \dots,f_p(\vect{x})), with n\geq 1 and p\geq 1.

  • In the first usage:

Draws graph of the given 1D outputMarg marginal f_k: \Rset^n \rightarrow \Rset as a function of the given 1D inputMarg marginal with respect to the variation of x_i in the interval [x_i^{min}, x_i^{max}], when all the other components of \vect{x} are fixed to the corresponding ones of the central point CP. Then it draws the graph: t\in [x_i^{min}, x_i^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t,  CP_{i+1} \dots, CP_n).

  • In the second usage:

Draws the iso-curves of the given outputMarg marginal f_k as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of (x_i, x_j) in the interval [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}], when all the other components of \vect{x} are fixed to the corresponding ones of the central point CP. Then it draws the graph: (t,u) \in [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t, CP_{i+1}, \dots, CP_{j-1}, u,  CP_{j+1} \dots, CP_n).

  • In the third usage:

The same as the first usage but only for function f: \Rset \rightarrow \Rset.

  • In the fourth usage:

The same as the second usage but only for function f: \Rset^2 \rightarrow \Rset.

Examples

>>> import openturns as ot
>>> from openturns.viewer import View
>>> f = ot.SymbolicFunction(['x'], ['sin(2*pi_*x)*exp(-x^2/2)'])
>>> graph = f.draw(-1.2, 1.2, 100)
>>> View(graph).show()
getCallsNumber(self)

Accessor to the number of times the function has been called.

Returns
calls_numberint

Integer that counts the number of times the function has been called since its creation.

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getDescription(self)

Accessor to the description of the inputs and outputs.

Returns
descriptionDescription

Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]
getExpressions(self)

Accessor to the numerical math function.

Returns
listFunctionFunctionCollection

The collection of numerical math functions if the analytical expressions exist.

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getInputDescription(self)

Accessor to the description of the inputs.

Returns
descriptionDescription

Description of the inputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDescription())
[x1,x2]
getInputDimension(self)

Accessor to the number of the inputs.

Returns
number_inputsint

Number of inputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getInputDimension())
2
getInputDistributionCollection(self)

Accessor to the input distribution collection.

Returns
inputDistColDistributionCollection

The input distribution collection.

getMarginal(self, *args)

Accessor to marginal.

Parameters
indicesint or list of ints

Set of indices for which the marginal is extracted.

Returns
marginalFunction

Function corresponding to either f_i or (f_i)_{i \in indices}, with f:\Rset^n \rightarrow \Rset^p and f=(f_0 , \dots, f_{p-1}).

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getOutputDescription(self)

Accessor to the description of the outputs.

Returns
descriptionDescription

Description of the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDescription())
[y0]
getOutputDimension(self)

Accessor to the number of the outputs.

Returns
number_outputsint

Number of outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getOutputDimension())
1
getOutputDistributionCollection(self)

Accessor to the output distribution collection.

Returns
outputDistColDistributionCollection

The output distribution collection.

getParameter(self)

Accessor to the parameter values.

Returns
parameterPoint

The parameter values.

getParameterDescription(self)

Accessor to the parameter description.

Returns
parameterDescription

The parameter description.

getParameterDimension(self)

Accessor to the dimension of the parameter.

Returns
parameter_dimensionint

Dimension of the parameter.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getSimplifications(self)

Try to simplify the transformations if it is possible.

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

isActualImplementation(self)

Accessor to the validity flag.

Returns
is_implbool

Whether the implementation is valid.

isLinear(self)

Accessor to the linearity of the evaluation.

Returns
linearbool

True if the evaluation is linear, False otherwise.

isLinearlyDependent(self, index)

Accessor to the linearity of the evaluation with regard to a specific variable.

Parameters
indexint

The index of the variable with regard to which linearity is evaluated.

Returns
linearbool

True if the evaluation is linearly dependent on the specified variable, False otherwise.

parameterGradient(self, inP)

Gradient against the parameters.

Parameters
xsequence of float

Input point

Returns
parameter_gradientMatrix

The parameters gradient computed at x.

setDescription(self, description)

Accessor to the description of the inputs and outputs.

Parameters
descriptionsequence of str

Description of the inputs and the outputs.

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['x1', 'x2'],
...                         ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6'])
>>> print(f.getDescription())
[x1,x2,y0]
>>> f.setDescription(['a','b','y'])
>>> print(f.getDescription())
[a,b,y]
setInputDescription(self, inputDescription)

Accessor to the description of the inputs.

Returns
descriptionDescription

Description of the inputs.

setInputDistributionCollection(self, inputDistributionCollection)

Accessor to the input distribution collection.

Parameters
inputDistColDistributionCollection

The input distribution collection.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setOutputDescription(self, outputDescription)

Accessor to the description of the outputs.

Returns
descriptionDescription

Description of the outputs.

setOutputDistributionCollection(self, outputDistributionCollection)

Accessor to the output distribution collection.

Parameters
outputDistColDistributionCollection

The output distribution collection.

setParameter(self, parameter)

Accessor to the parameter values.

Parameters
parametersequence of float

The parameter values.

setParameterDescription(self, description)

Accessor to the parameter description.

Parameters
parameterDescription

The parameter description.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.