ProcessSample

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../../_images/ProcessSample.png
class ProcessSample(*args)

Collection of fields.

Available constructors:

ProcessSample(mesh, K, d)

ProcessSample(mesh, coll)

ProcessSample(K, field)

Parameters:
meshMesh

The mesh shared by all the fields in the collection.

Kint

Number of fields in the collection.

dint

Dimension of the values of the field.

fieldField

One field.

collsequence of Sample

List of field values.

Notes

A ProcessSample stores a sample of fields. We note K the number of fields contained in the process sample and d the dimension of the values associated to each vertex of the common mesh \cM \in \Rset^n.

These fields can be generated by a stochastic process.

  • In the first usage, we fix the common mesh with mesh, the number of fields contained in the sample with K and the dimension of the values with d. The values of the fields are by default fixed to zero.

  • In the second usage, the collection of fields is filled with K copies of the given field field.

We note \vect{x}_i^k \in \Rset^d the value of the field k at the vertex i. We note N the number of vertices of \cM, with 0 \leq i \leq N-1 and 1 \leq k \leq K.

Examples

Create a bi dimensional mesh as a box:

>>> import openturns as ot
>>> myIndices = [10, 5]
>>> myMesher = ot.IntervalMesher(myIndices)
>>> lowerBound = [0.0, 0.0]
>>> upperBound = [2.0, 1.0]
>>> myInterval = ot.Interval(lowerBound, upperBound)
>>> myMesh = myMesher.build(myInterval)

Create a second order normal porcess of dimension 3:

>>> amplitude = [5]
>>> scale = [3, 3]
>>> model = ot.ExponentialModel(scale, amplitude)
>>> myProcess = ot.GaussianProcess(model, myMesh)

Generate a sample of different fields:

>>> n = 10
>>> mySampleFields = myProcess.getSample(n)

Duplicate the same field:

>>> myField = myProcess.getRealization()
>>> n = 10
>>> mySampleFields2 = ot.ProcessSample(n, myField)

Methods

add(*args)

Add a field to the collection.

clear()

Erase all field values.

computeCentralMoment(k)

Compute the central moment field of the collection of fields.

computeEmpiricalCDF(point[, tail])

Compute the empirical CDF field of the collection of fields.

computeKurtosis()

Compute the kurtosis field of the collection of fields.

computeMean()

Compute the mean field of the collection of fields.

computeMedian()

Compute the median field of the collection of fields.

computeQuantilePerComponent(*args)

Compute the quantile field of the collection of fields.

computeRange()

Compute the range field of the collection of fields.

computeRawMoment(k)

Compute the raw moment field of the collection of fields.

computeSkewness()

Compute the skewness field of the collection of fields.

computeSpatialMean()

Compute the spatial mean of the values of the fields.

computeStandardDeviation()

Compute the standard deviation field of the collection of fields.

computeTemporalMean()

Compute the temporal mean of the values of the fields.

computeVariance()

Compute the variance field of the collection of fields.

draw([interpolate])

Draw the whole field.

drawCorrelation()

Draw correlation between all marginals.

drawMarginal([index, interpolate])

Draw the selected field.

drawMarginalCorrelation(i, j)

Draw correlation between 2 marginals.

erase(*args)

Erase point(s) at or between index(es) (in-place).

getClassName()

Accessor to the object's name.

getDimension()

Get the dimension of the values of fields.

getField(i)

Field accessor.

getId()

Accessor to the object's id.

getImplementation()

Accessor to the underlying implementation.

getMarginal(*args)

Marginal sample accessor.

getMax()

Compute the max field of the collection of fields.

getMesh()

Get the mesh of the fields.

getMin()

Compute the min field of the collection of fields.

getName()

Accessor to the object's name.

getSampleAtVertex(index)

Extract sample at specific vertex of the mesh.

getSize()

Get the size of the collection of fields.

getTimeGrid()

Get the time grid of the fields.

setField(field, i)

Field accessor.

setName(name)

Accessor to the object's name.

computeCenteredMoment

__init__(*args)
add(*args)

Add a field to the collection.

Parameters:
fieldField

A new field to add. This field shares the same mesh and the same dimension as the other fields of the collection.

clear()

Erase all field values.

computeCentralMoment(k)

Compute the central moment field of the collection of fields.

Parameters:
kint

Order of the moment.

Returns:
momentField

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise central moment of order n.

computeEmpiricalCDF(point, tail=False)

Compute the empirical CDF field of the collection of fields.

Parameters:
pointsequence of float

The point at which all the marginal CDF are computed. Its dimension must match the process sample dimension.

tailbool (optional, default=False)

Flag to if it is the CDF or the complementary CDF which is computed.

Returns:
cdfField

This field is scalar and has the same size as the process sample. At each vertex of the mesh, we compute the component-wise empirical CDF at the given point.

computeKurtosis()

Compute the kurtosis field of the collection of fields.

Returns:
kurtosisField

The squewness field has the same dimension d and the same mesh as the fields contained in the collection. At each vertex of the mesh, we compute the kurtosis of the values at this vertex of the K fields contained in the process sample.

computeMean()

Compute the mean field of the collection of fields.

Returns:
meanField

The mean field has the same dimension d and the same mesh as the fields contained in the collection. At each vertex of the mesh, we compute the mean of the values at this vertex of the K fields contained in the process sample:

\forall i \in [0,N-1], \quad \dfrac{1}{K} \sum_{k=1}^K \vect{x}_i^k

computeMedian()

Compute the median field of the collection of fields.

Returns:
medianField

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise empirical median. It is the same as computeQuantilePerComponent(0.5).

computeQuantilePerComponent(*args)

Compute the quantile field of the collection of fields.

Parameters:
pfloat, 0 \leq p \leq 1, or sequence of float

Order of the quantile.

Returns:
quantileField or ProcessSample

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise empirical quantile of order p.

computeRange()

Compute the range field of the collection of fields.

Returns:
rangeField

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise range, i.e. the difference between the largest and the lowest value in the field collection.

computeRawMoment(k)

Compute the raw moment field of the collection of fields.

Parameters:
kint

Order of the moment.

Returns:
momentField

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise raw moment of order n.

computeSkewness()

Compute the skewness field of the collection of fields.

Returns:
skewnessField

The squewness field has the same dimension d and the same mesh as the fields contained in the collection. At each vertex of the mesh, we compute the skewness of the values at this vertex of the K fields contained in the process sample.

computeSpatialMean()

Compute the spatial mean of the values of the fields.

Returns:
spatialMeanSample

Its size is the number K of fields in the collection. Its dimension is d. The k numerical point is the spatial mean of the field k:

\forall k \in [1,K], \quad \dfrac{1}{N}\sum_{i=0}^{N-1} \vect{x}_i^k

computeStandardDeviation()

Compute the standard deviation field of the collection of fields.

Returns:
stddevField

The standard deviation field has the same dimension d and the same mesh as the fields contained in the collection. At each vertex of the mesh, we compute the standard deviation of the values at this vertex of the K fields contained in the process sample:

\forall i \in [0,N-1], \quad \sqrt{\dfrac{1}{K-1} \sum_{k=1}^K (\vect{x}_i^k - \hat{\mu}_i)^2}

computeTemporalMean()

Compute the temporal mean of the values of the fields.

Returns:
spatialMeanSample

Its size is the number K of fields in the collection. Its dimension is d. The k numerical point is the temporal mean of the field k:

\forall k \in [1,K], \quad \dfrac{1}{N}\sum_{i=0}^{N-1} \vect{x}_i^k

This method can be used only when the mesh can be interpreted as a regular grid.
computeVariance()

Compute the variance field of the collection of fields.

Returns:
varianceField

The variance field has the same dimension d and the same mesh as the fields contained in the collection. At each vertex of the mesh, we compute the variance of the values at this vertex of the K fields contained in the process sample.

draw(interpolate=True)

Draw the whole field.

Parameters:
interpolatebool (optional, default=True)

Whether to draw interpolated values.

Returns:
graphGridLayout

The graph of the whole field using the interpolate method.

drawCorrelation()

Draw correlation between all marginals.

This is only available on a 1-d mesh.

Returns:
graphGridLayout

The graph of the correlation between all marginals.

drawMarginal(index=0, interpolate=True)

Draw the selected field.

Parameters:
indiceint

Index of the field that is drawn in the graph.

interpolatebool (optional, default=True)

Whether to draw interpolated values.

Returns:
graphGraph

The graph of the selected field using the interpolate method.

drawMarginalCorrelation(i, j)

Draw correlation between 2 marginals.

This is only available on a 1-d mesh.

Parameters:
i, jint, i, j < d

Marginal indices.

Returns:
graphGraph

The graph of the correlation between 2 marginals.

erase(*args)

Erase point(s) at or between index(es) (in-place).

Parameters:
fint, 0 \leq f < m

The index of the first point to erase.

lint, f < l \leq m, optional

The index after the last point to erase. Default uses l = f + 1 and only removes sample[f].

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getDimension()

Get the dimension of the values of fields.

Returns:
dint

Dimension of the values of the fields.

getField(i)

Field accessor.

Parameters:
iint

Field index

Returns:
fieldField

i-th field in the sample.

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getImplementation()

Accessor to the underlying implementation.

Returns:
implImplementation

A copy of the underlying implementation object.

getMarginal(*args)

Marginal sample accessor.

Parameters:
indiceint or sequence of int

Index of the marginals.

Returns:
sampleProcessSample

The marginal sample.

getMax()

Compute the max field of the collection of fields.

Returns:
maxField

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise maximum.

getMesh()

Get the mesh of the fields.

Returns:
meshMesh

The mesh shared by all the fields of the collection.

getMin()

Compute the min field of the collection of fields.

Returns:
minField

This field has the same size and the same dimension as the fields of the collection. At each vertex of the mesh, we compute the component-wise minimum.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getSampleAtVertex(index)

Extract sample at specific vertex of the mesh.

Parameters:
indexint, index < N

Node index in the mesh.

Returns:
sample_at_iSample

The sample of all values of the trajectories at the desired node.

getSize()

Get the size of the collection of fields.

Returns:
Kint

Number of fields in the collection.

getTimeGrid()

Get the time grid of the fields.

Returns:
meshRegularGrid

The time grid shared by all the fields of the collection. Can be used only if the mesh can be interpreted as a regular time grid.

setField(field, i)

Field accessor.

Parameters:
iint

Field index

fieldField

i-th field in the sample.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

Examples using the class

Estimate a non stationary covariance function

Estimate a non stationary covariance function

Estimate a scalar ARMA process

Estimate a scalar ARMA process

Estimate a spectral density function

Estimate a spectral density function

Estimate a stationary covariance function

Estimate a stationary covariance function

Create a functional basis process

Create a functional basis process

Add a trend to a process

Add a trend to a process

Create a gaussian process from a cov. model using HMatrix

Create a gaussian process from a cov. model using HMatrix

Create a white noise process

Create a white noise process

Create a discrete Markov chain process

Create a discrete Markov chain process

Create a normal process

Create a normal process

Create a random walk process

Create a random walk process

Create a process from random vectors and processes

Create a process from random vectors and processes

Draw fields

Draw fields

Create and manipulate an ARMA process

Create and manipulate an ARMA process

Compare covariance models

Compare covariance models

Kriging : generate trajectories from a metamodel

Kriging : generate trajectories from a metamodel

Kriging : draw covariance models

Kriging : draw covariance models

Validation of a Karhunen-Loeve decomposition

Validation of a Karhunen-Loeve decomposition

Viscous free fall: metamodel of a field function

Viscous free fall: metamodel of a field function

Metamodel of a field function

Metamodel of a field function

Estimate Sobol indices on a field to point function

Estimate Sobol indices on a field to point function

Define a function with a field output: the viscous free fall example

Define a function with a field output: the viscous free fall example

Define a connection function with a field output

Define a connection function with a field output

Logistic growth model

Logistic growth model