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.

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