CauchyModel

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../../_images/openturns-CauchyModel-1.png
class CauchyModel(*args)

Cauchy spectral model.

Available constructors:
CauchyModel(theta, sigma)
Parameters:

theta : sequence of float

Scale coefficients \theta of the spectral density function. Vector of size n

sigma : sequence 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__(frequency) Evaluate the spectral density function for a specific frequency.
computeStandardRepresentative(*args) Compute the standard representant of the spectral density function.
draw([rowIndex, columnIndex, module]) Draw a specific component of the spectral density function.
getAmplitude() Get the amplitude parameter of the spectral density function.
getClassName() Accessor to the object’s name.
getDimension() Get the dimension of the SpectralModel.
getFrequencyGrid() Return the RegularGrid associated to the SpectralModel.
getId() Accessor to the object’s id.
getName() Accessor to the object’s name.
getScale() Get the scale parameter of the spectral density function.
getShadowedId() Accessor to the object’s shadowed id.
getSpatialCorrelation() Get the spatial correlation matrix of the spectral density function.
getSpatialDimension() Get the spatial dimension of the spectral density function.
getVisibility() Accessor to the object’s visibility state.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
setAmplitude(amplitude) Set the amplitude parameter of the spectral density function.
setFrequencyGrid(frequencyGrid) Set the RegularGrid associated to the SpectralModel.
setName(name) Accessor to the object’s name.
setScale(scale) Set the scale parameter of the spectral density function.
setShadowedId(id) Accessor to the object’s shadowed id.
setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)
computeStandardRepresentative(*args)

Compute the standard representant of the spectral density function.

Parameters:

tau : float

Frequency value.

Returns:

rho : Complex

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(rowIndex=0, columnIndex=0, module=True)

Draw a specific component of the spectral density function.

Parameters:

rowIndex : int

i-th row component to draw. Default value is 0

columnIndex : int

j-th column component to draw . Default value is 0

module : bool

Tells if module has to be drawn(True) or if it is the argument to be drawn (False). Default value is True.

Returns:

graph : Graph

Graphic of the specified component

Notes

The method plots a specific component of the spectral density function over a frequency grid. Thus, this last one should be specified thanks to the setFrequencyGrid method.

getAmplitude()

Get the amplitude parameter of the spectral density function.

Returns:

amplitude : NumericalPoint

The used amplitude parameter.

getClassName()

Accessor to the object’s name.

Returns:

class_name : str

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

getDimension()

Get the dimension of the SpectralModel.

Returns:

dimension : int

Dimension of the SpectralModel.

getFrequencyGrid()

Return the RegularGrid associated to the SpectralModel.

Returns:

grid : RegularGrid

Associated frequency grid of the SpectralModel.

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getScale()

Get the scale parameter of the spectral density function.

Returns:

scale : NumericalPoint

The used scale parameter.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getSpatialCorrelation()

Get the spatial correlation matrix of the spectral density function.

Returns:

spatialCorrelation : CorrelationMatrix

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

getSpatialDimension()

Get the spatial dimension of the spectral density function.

Returns:

spatialDimension : int

SpatialDimension of the SpectralModel.

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.

setAmplitude(amplitude)

Set the amplitude parameter of the spectral density function.

Parameters:

amplitude : NumericalPoint

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

setFrequencyGrid(frequencyGrid)

Set the RegularGrid associated to the SpectralModel.

Parameters:

grid : RegularGrid

Associated frequency grid of the SpectralModel.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setScale(scale)

Set the scale parameter of the spectral density function.

Parameters:

scale : NumericalPoint

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

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.