CauchyModel¶

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class CauchyModel(*args)¶

Cauchy spectral model.

Refer to Parametric spectral density functions.

Available constructors:: CauchyModel(theta, sigma)

Parameters

thetasequence of float: Scale coefficients $\theta$ of the spectral density function. Vector of size n
sigmasequence of float: Amplitude coefficients $\sigma$ of the spectral density function. Vector of size p

Notes

The spectral density function of input dimension n and output dimension p writes:

$\forall (i,j) \in [0,p-1]^2, S(f)_{i,j} = \Sigma_{i,j} \prod_{k=1}^{n} \frac{\theta_k}{1 + (2\pi \theta_k f)^2}$

Examples

>>> import openturns as ot
>>> spectralModel = ot.CauchyModel([3.0, 2.0], [2.0])
>>> f = 0.3
>>> print(spectralModel(f))
[[ (0.191364,0) ]]
>>> f = 10
>>> print(spectralModel(f))
[[ (1.71084e-07,0) ]]

Methods

`__call__`(self, frequency)	Evaluate the spectral density function for a specific frequency.
`computeStandardRepresentative`(self, \*args)	Compute the standard representant of the spectral density function.
`draw`(self, \*args)	Draw a specific component of the spectral density function.
`getAmplitude`(self)	Get the amplitude parameter of the spectral density function.
`getClassName`(self)	Accessor to the object’s name.
`getId`(self)	Accessor to the object’s id.
`getInputDimension`(self)	Get the input dimension of the spectral density function.
`getName`(self)	Accessor to the object’s name.
`getOutputCorrelation`(self)	Get the spatial correlation matrix of the spectral density function.
`getOutputDimension`(self)	Get the dimension of the SpectralModel.
`getScale`(self)	Get the scale parameter of the spectral density function.
`getShadowedId`(self)	Accessor to the object’s shadowed id.
`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.
`setAmplitude`(self, amplitude)	Set the amplitude parameter of the spectral density function.
`setName`(self, name)	Accessor to the object’s name.
`setScale`(self, scale)	Set the scale parameter of the spectral density function.
`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.

computeStandardRepresentative(self, \*args)¶

Compute the standard representant of the spectral density function.

Parameters

taufloat: Frequency value.

Returns

rhoComplex: Standard representant factor of the spectral density function.

Notes

Using definitions in SpectralModel: the standard representative function writes:

$\forall \vect{f} \in \Rset^n, \rho(\vect{f} \odot \vect{\theta}) = \prod_{k=1}^{n} \frac{1}{1 + (2\pi \theta_k f)^2}$

where $(\vect{f} \odot \vect{\theta})_k = \vect{f}_k \vect{\theta}_k$

draw(self, \*args)¶

Draw a specific component of the spectral density function.

Parameters

rowIndexint, $0 \leq rowIndex < dimension$: The row index of the component to draw. Default value is 0.
columnIndex: int, :math:`0 leq columnIndex < dimension`: The column index of the component to draw. Default value is 0.
minimumFrequencyfloat: The lower bound of the frequency range over which the model is plotted. Default value is SpectralModel-DefaultMinimumFrequency in ResourceMap.
maximumFrequencyfloat: The upper bound of the frequency range over which the model is plotted. Default value is SpectralModel-DefaultMaximumFrequency in ResourceMap.
frequencyNumberint, $pointNumber \geq 2$: The discretization of the frequency range $[minimumFrequency, maximumFrequency]$ over which the model is plotted. Default value is SpectralModel-DefaultFrequencyNumber in class:~openturns.ResourceMap.
modulebool: Flag to tell if module has to be drawn (True) or if it is the argument to be drawn (False). Default value is True.

Returns

graphGraph: Graphic of the specified component

getAmplitude(self)¶

Get the amplitude parameter of the spectral density function.

Returns

amplitudePoint: The used amplitude parameter.

getClassName(self)¶

Accessor to the object’s name.

Returns

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

getId(self)¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getInputDimension(self)¶

Get the input dimension of the spectral density function.

Returns

inputDimensionint: SpatialDimension of the SpectralModel.

getName(self)¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getOutputCorrelation(self)¶

Get the spatial correlation matrix of the spectral density function.

Returns

spatialCorrelationCorrelationMatrix: Correlation matrix $\mat{R} \in \mathcal{M}_{dimension \times dimension}([-1, 1])$ .

getOutputDimension(self)¶

Get the dimension of the SpectralModel.

Returns

dimensionint: Dimension of the SpectralModel.

getScale(self)¶

Get the scale parameter of the spectral density function.

Returns

scalePoint: The used scale parameter.

getShadowedId(self)¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

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.

setAmplitude(self, amplitude)¶

Set the amplitude parameter of the spectral density function.

Parameters

amplitudePoint: The amplitude parameter to be used in the spectral density function.

setName(self, name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setScale(self, scale)¶

Set the scale parameter of the spectral density function.

Parameters

scalePoint: The scale parameter to be used in the spectral density function. It should be of size dimension.

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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