# MarginalTransformationEvaluation¶

class MarginalTransformationEvaluation(*args)

Marginal transformation evaluation.

Available constructors:

MarginalTransformationEvaluation(distCol)

MarginalTransformationEvaluation(distCol, direction, standardMarginal)

MarginalTransformationEvaluation(distCol, outputDistCol)

Parameters: distCol : DistributionCollection A collection of distributions. direction : integer 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. standardMarginal : Distribution Target distribution marginal Default is Uniform(0, 1) outputDistCol : DistributionCollection 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 , the created operator transforms a Point into its rank according to the marginal distributions described in distCol. Let be the CDF of the distributions contained in distCol, then the created operator works as follows:

If , the created operator works in the opposite direction:

In that case, it requires that all the values be in .

• In the third usage, the created operator transforms a Point into the following one, where outputDistCol contains the distributions:

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.Weibull(), ot.Exponential()]
>>> margTransEvalComposed = ot.MarginalTransformationEvaluation(distCol, outputDistCol)
>>> print(margTransEvalComposed([1, 3]))
[1.84102,1.99533]


Methods

 __call__(…) <==> x(…) addCacheContent(inSample, outSample) Add input numerical points and associated output to the cache. clearCache() Empty the content of the cache. clearHistory() Empty the content of the history. disableCache() Disable the cache mechanism. disableHistory() Disable the history mechanism. draw(*args) Draw the output of function as a Graph. enableCache() Enable the cache mechanism. enableHistory() Enable the history mechanism. getCacheHits() Accessor to the number of computations saved thanks to the cache mecanism. getCacheInput() Accessor to all the input numerical points stored in the cache mecanism. getCacheOutput() Accessor to all the output numerical points stored in the cache mecanism. getCallsNumber() Accessor to the number of times the function has been called. getClassName() Accessor to the object’s name. getDescription() Accessor to the description of the inputs and outputs. getExpressions() Accessor to the numerical math function. getHistoryInput() Accessor to the history of the input values. getHistoryOutput() Accessor to the history of the output values. getId() Accessor to the object’s id. getInputDescription() Accessor to the description of the inputs. getInputDimension() Accessor to the number of the inputs. getInputDistributionCollection() Accessor to the input distribution collection. getInputParameterHistory() Accessor to the history of the input parameter values. getInputPointHistory() Accessor to the history of the input points values. getMarginal(*args) Accessor to marginal. getName() Accessor to the object’s name. getOutputDescription() Accessor to the description of the outputs. getOutputDimension() Accessor to the number of the outputs. getOutputDistributionCollection() Accessor to the output distribution collection. getParameter() Accessor to the parameter values. getParameterDescription() Accessor to the parameter description. getParameterDimension() Accessor to the dimension of the parameter. getShadowedId() Accessor to the object’s shadowed id. getSimplifications() Try to simplify the transformations if it is possible. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. isActualImplementation() Accessor to the validity flag. isCacheEnabled() Test whether the cache mechanism is enabled or not. isHistoryEnabled() Test whether the history mechanism is enabled or not. parameterGradient(inP) Gradient against the parameters. setDescription(description) Accessor to the description of the inputs and outputs. setInputDescription(inputDescription) Accessor to the description of the inputs. setInputDistributionCollection(…) Accessor to the input distribution collection. setName(name) Accessor to the object’s name. setOutputDescription(outputDescription) Accessor to the description of the outputs. setOutputDistributionCollection(…) Accessor to the output distribution collection. setParameter(parameter) Accessor to the parameter values. setParameterDescription(description) Accessor to the parameter description. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

addCacheContent(inSample, outSample)

Add input numerical points and associated output to the cache.

Parameters: input_sample : 2-d sequence of float Input numerical points to be added to the cache. output_sample : 2-d sequence of float Output numerical points associated with the input_sample to be added to the cache.
clearCache()

Empty the content of the cache.

clearHistory()

Empty the content of the history.

disableCache()

Disable the cache mechanism.

disableHistory()

Disable the history mechanism.

draw(*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, inputMarg : int, outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg. firstInputMarg, secondInputMarg : int, In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg. CP : sequence of float Central point. xiMin, xiMax : float Define the interval where the curve is plotted. xiMin_xjMin, xiMax_xjMax : sequence of float of dimension 2. In the 2D case, define the intervals where the curves are plotted. ptNb : int or list of ints of dimension 2 The number of points to draw the curves.

Notes

We note where and , with and .

• In the first usage:

Draws graph of the given 1D outputMarg marginal as a function of the given 1D inputMarg marginal with respect to the variation of in the interval , when all the other components of are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph: .

• In the second usage:

Draws the iso-curves of the given outputMarg marginal as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of in the interval , when all the other components of are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph: .

• In the third usage:

The same as the first usage but only for function .

• In the fourth usage:

The same as the second usage but only for function .

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()

enableCache()

Enable the cache mechanism.

enableHistory()

Enable the history mechanism.

getCacheHits()

Accessor to the number of computations saved thanks to the cache mecanism.

Returns: cacheHits : int Integer that counts the number of computations saved thanks to the cache mecanism.
getCacheInput()

Accessor to all the input numerical points stored in the cache mecanism.

Returns: cacheInput : Sample All the input numerical points stored in the cache mecanism.
getCacheOutput()

Accessor to all the output numerical points stored in the cache mecanism.

Returns: cacheInput : Sample All the output numerical points stored in the cache mecanism.
getCallsNumber()

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

Returns: calls_number : int Integer that counts the number of times the function has been called since its creation.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getDescription()

Accessor to the description of the inputs and outputs.

Returns: description : Description 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()

Accessor to the numerical math function.

Returns: listFunction : FunctionCollection The collection of numerical math functions if the analytical expressions exist.
getHistoryInput()

Accessor to the history of the input values.

Returns: input_history : Sample All the input numerical points stored in the history mecanism.
getHistoryOutput()

Accessor to the history of the output values.

Returns: output_history : Sample All the output numerical points stored in the history mecanism.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getInputDescription()

Accessor to the description of the inputs.

Returns: description : Description 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()

Accessor to the number of the inputs.

Returns: number_inputs : int 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()

Accessor to the input distribution collection.

Returns: inputDistCol : DistributionCollection The input distribution collection.
getInputParameterHistory()

Accessor to the history of the input parameter values.

Returns: history : Sample All the input parameters stored in the history mecanism.
getInputPointHistory()

Accessor to the history of the input points values.

Returns: history : Sample All the input points stored in the history mecanism.
getMarginal(*args)

Accessor to marginal.

Parameters: indices : int or list of ints Set of indices for which the marginal is extracted. marginal : Function Function corresponding to either or , with and .
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getOutputDescription()

Accessor to the description of the outputs.

Returns: description : Description 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()

Accessor to the number of the outputs.

Returns: number_outputs : int 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()

Accessor to the output distribution collection.

Returns: outputDistCol : DistributionCollection The output distribution collection.
getParameter()

Accessor to the parameter values.

Returns: parameter : Point The parameter values.
getParameterDescription()

Accessor to the parameter description.

Returns: parameter : Description The parameter description.
getParameterDimension()

Accessor to the dimension of the parameter.

Returns: parameter_dimension : int Dimension of the parameter.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
getSimplifications()

Try to simplify the transformations if it is possible.

getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
isActualImplementation()

Accessor to the validity flag.

Returns: is_impl : bool Whether the implementation is valid.
isCacheEnabled()

Test whether the cache mechanism is enabled or not.

Returns: isCacheEnabled : bool Flag telling whether the cache mechanism is enabled. It is disabled by default.
isHistoryEnabled()

Test whether the history mechanism is enabled or not.

Returns: isHistoryEnabled : bool Flag telling whether the history mechanism is enabled. It is disabled by default.
parameterGradient(inP)

Gradient against the parameters.

Parameters: x : sequence of float Input point parameter_gradient : Matrix The parameters gradient computed at x.
setDescription(description)

Accessor to the description of the inputs and outputs.

Parameters: description : sequence 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(inputDescription)

Accessor to the description of the inputs.

Returns: description : Description Description of the inputs.
setInputDistributionCollection(inputDistributionCollection)

Accessor to the input distribution collection.

Parameters: inputDistCol : DistributionCollection The input distribution collection.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setOutputDescription(outputDescription)

Accessor to the description of the outputs.

Returns: description : Description Description of the outputs.
setOutputDistributionCollection(outputDistributionCollection)

Accessor to the output distribution collection.

Parameters: outputDistCol : DistributionCollection The output distribution collection.
setParameter(parameter)

Accessor to the parameter values.

Parameters: parameter : sequence of float The parameter values.
setParameterDescription(description)

Accessor to the parameter description.

Parameters: parameter : Description The parameter description.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.