TimeSeries¶

(Source code, png)

class TimeSeries(*args)¶

Time series.

Available constructors:

TimeSeries(nSteps,dim)

TimeSeries(timeGrid, dim)

TimeSeries(timeGrid, sample)

TimeSeries(field)

Parameters:

nStepsint: Enables to create a regular time grid on $[0, nSteps]$ which time step is equal to 1.
timeGridRegularGrid: Regular time grid of the time series.
dimint: Dimension of the values of the time series at each time stamp. By default, the values are equal to the null vector.
sample2-d sequence of float: Values assigned to each time stamp of the time series.
fieldField: Maps a field into a time series when the associated lesh cn be interpretated as a regular time grid.

Examples

Create a time series:

>>> import openturns as ot
>>> tmin = 0.0
>>> timeStep = 0.1
>>> n = 5
>>> myTimeGrid = ot.RegularGrid(tmin, timeStep, n)
>>> myValues = [[1.0], [2.0], [1.5], [4.5], [0.5]]
>>> myTimeSeries = ot.TimeSeries(myTimeGrid, myValues)

Draw the time series:

>>> graph = myTimeSeries.draw()

Methods

`add`(*args)	Add a new value to the time series and extend the associated time grid.
`asDeformedMesh`(*args)	Get the mesh deformed according to the values of the field.
`asSample`()	Convert to Sample.
`draw`()	Draw the first marginal of the field if the input dimension is less than 2.
`drawMarginal`([index, interpolate])	Draw one marginal field if the input dimension is less than 2.
`exportToVTKFile`(fileName)	Create the VTK format file of the field.
`getClassName`()	Accessor to the object's name.
`getDescription`()	Get the description of the field values.
`getId`()	Accessor to the object's id.
`getInputDimension`()	Get the dimension of the domain $\cD$ .
`getInputMean`()	Get the input weighted mean of the values of the field.
`getMarginal`(*args)	Marginal accessor.
`getMesh`()	Get the mesh on which the field is defined.
`getName`()	Accessor to the object's name.
`getOutputDimension`()	Get the dimension $d$ of the values.
`getOutputMean`()	Get the mean of the values of the field.
`getShadowedId`()	Accessor to the object's shadowed id.
`getSize`()	Get the number of values inside the field.
`getTimeGrid`()	Get the mesh as a time grid if it is 1D and regular.
`getValueAtIndex`(index)	Get the value of the field at the vertex of the given index.
`getValues`()	Get the values of the field.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`norm`()	Compute the ( $L^2$ ) norm.
`setDescription`(description)	Set the description of the vertices and values of the field.
`setName`(name)	Accessor to the object's name.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setValueAtIndex`(index, val)	Assign the value of the field to the vertex at the given index.
`setValues`(values)	Assign values to a field.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

add(*args)¶

Add a new value to the time series and extend the associated time grid.

Available usages:

add(sample)

add(timeSeries)

Parameters:

sample2-d sequence of float, of dimension the same as the dimension of the values of the time series.
timeSeriesTimeSeries, which time grid must match with the initial time grid (one follows the other).

Returns:

newTimeSeries: TimeSeries, which regular grid has been extended with a new time stamp or a second time grid, associated to the new values.

asDeformedMesh(*args)¶

Get the mesh deformed according to the values of the field.

Parameters:

verticesPaddingsequence of int: The positions at which the coordinates of vertices are set to zero when extending the vertices dimension. By default the sequence is empty.
valuesPaddingsequence of int: The positions at which the components of values are set to zero when extending the values dimension. By default the sequence is empty.

Returns:

deformedMeshMesh: The initial mesh is deformed as follows: each vertex of the mesh is translated by the value of the field at this vertex. Only works when the input dimension $n$ : is equal to the dimension of the field $d$ after extension.

asSample()¶

Convert to Sample.

Returns:

sampleSample: Data as a Sample object.

draw()¶

Draw the first marginal of the field if the input dimension is less than 2.

Returns:

graphGraph: Calls drawMarginal(0, False).

See also

drawMarginal

drawMarginal(index=0, interpolate=True)¶

Draw one marginal field if the input dimension is less than 2.

Parameters:

indexint: The selected marginal.
interpolatebool: Indicates whether the values at the vertices are linearly interpolated.

Returns:

graphGraph

If the dimension of the mesh is $n=1$ and interpolate=True: it draws the graph of the piecewise linear function based on the selected marginal values of the field and the vertices coordinates (in $\Rset$ ).
If the dimension of the mesh is $n=1$ and interpolate=False: it draws the cloud of points which coordinates are (vertex, value of the marginal index).
If the dimension of the mesh is $n=2$ and interpolate=True: it draws several iso-values curves of the selected marginal, based on a piecewise linear interpolation within the simplices (triangles) of the mesh. You get an empty graph if the vertices are not connected through simplicies.
If the dimension of the mesh is $n=2$ and interpolate=False: if the vertices are connected through simplicies, each simplex is drawn with a color defined by the mean of the values of the vertices of the simplex. In the other case, it draws each vertex colored by its value.

exportToVTKFile(fileName)¶

Create the VTK format file of the field.

Parameters:

myVTKFilestr: Name of the output file. No extension is append to the filename.

Notes

Creates the VTK format file that contains the mesh and the associated values that can be visualised with the open source software Paraview .

getClassName()¶

Accessor to the object’s name.

Returns:

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

getDescription()¶

Get the description of the field values.

Returns:

descriptionDescription: Description of the vertices and values of the field, size $n+d$ .

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getInputDimension()¶

Get the dimension of the domain $\cD$ .

Returns:

nint: Dimension of the domain $\cD$ : $n$ .

getInputMean()¶

Get the input weighted mean of the values of the field.

Returns:

inputMeanPoint: Weighted mean of the values of the field, weighted by the volume of each simplex.

Notes

The input mean of the field is defined by:

$\displaystyle \frac{1}{V} \sum_{S_i \in \cM} \left( \frac{1}{n+1}\sum_{k=0}^{n} \vect{v}_{i_k}\right) |S_i|$

where $S_i$ is the simplex of index $i$ of the mesh, $|S_i|$ its volume and $(\vect{v}_{i_0}, \dots, \vect{v}_{i_n})$ the values of the field associated to the vertices of $S_i$ , and $\displaystyle V=\sum_{S_i \in \cD} |S_i|$ .

getMarginal(*args)¶

Marginal accessor.

Parameters:

iint or sequence of int: Index of the marginal.

Returns:

valueField.: Marginal field.

getMesh()¶

Get the mesh on which the field is defined.

Returns:

meshMesh: Mesh over which the domain $\cD$ is discretized.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getOutputDimension()¶

Get the dimension $d$ of the values.

Returns:

dint: Dimension of the field values: $d$ .

getOutputMean()¶

Get the mean of the values of the field.

Returns:

temporalMeanPoint: Mean of the values of the field.

Notes

If we note $(\vect{x}_0, \dots, \vect{x}_{N-1})$ the values in $\Rset^d$ of the field, then the temporal mean is defined by:

$\displaystyle \frac{1}{N} \sum_{i=0}^{N-1} \vect{v}_i$

Only makes sense in the case of a regular grid.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getSize()¶

Get the number of values inside the field.

Returns:

sizeint: Number $N$ of vertices in the mesh.

getTimeGrid()¶

Get the mesh as a time grid if it is 1D and regular.

Returns:

timeGridRegularGrid: Mesh of the field when it can be interpreted as a RegularGrid. We check if the vertices of the mesh are scalar and are regularly spaced in $\Rset$ but we don’t check if the connectivity of the mesh is conform to the one of a regular grid (without any hole and composed of ordered instants).

getValueAtIndex(index)¶

Get the value of the field at the vertex of the given index.

Parameters:

indexint: Vertex of the mesh of index index.

Returns:

valuePoint: The value of the field associated to the selected vertex, in $\Rset^d$ .

getValues()¶

Get the values of the field.

Returns:

valuesSample: Values associated to the mesh. The size of the sample is the number of vertices of the mesh and the dimension is the dimension of the values ( $d$ ). Identical to getSample().

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool: True if the name is not empty and not the default one.

norm()¶

Compute the ( $L^2$ ) norm.

Returns:

normfloat: The field’s norm computed using the mesh weights.

setDescription(description)¶

Set the description of the vertices and values of the field.

Parameters:

myDescriptionDescription: Description of the field values. Must be of size $n+d$ and give the description of the vertices and the values.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setValueAtIndex(index, val)¶

Assign the value of the field to the vertex at the given index.

Parameters:

indexint: Index that characterizes one vertex of the mesh.
valuePoint in $\Rset^d$ .: New value assigned to the selected vertex.

setValues(values)¶

Assign values to a field.

Parameters:

values2-d sequence of float: Values assigned to the mesh. The size of the values is the number of vertices of the mesh and the dimension is $d$ .

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

Examples using the class¶

Estimate a multivariate ARMA process

Estimate a scalar ARMA process

Create a discrete Markov chain process

Manipulate a time series

Create and manipulate an ARMA process

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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