DualLinearCombinationEvaluation

class DualLinearCombinationEvaluation(*args)

Dual linear combination evaluation implementation.

Available constructors:

DualLinearCombinationEvaluation(scalarFctColl, vectCoefColl)

Parameters:
scalarFctCollsequence of Function

A collection of functions (f_i)_{i = 1, \ldots, l} of size l, such that \forall i \in \{1, \ldots, l\}, f_i : \Rset^n \rightarrow \Rset.

vectCoefColl2-d sequence of float

Sample \cC = \{\vect{c}_1, \ldots, \vect{c}_l \} of size l and dimension p.

Methods

draw(*args)

Draw the output of function as a Graph.

drawCrossCuts(*args)

Draw the 2D and 1D cross cuts of a 1D output function as a GridLayout.

getCallsNumber()

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

getCheckOutput()

Accessor to the output verification flag.

getClassName()

Accessor to the object's name.

getCoefficients()

Accessor to the coefficients.

getDescription()

Accessor to the description of the inputs and outputs.

getFunctionsCollection()

Accessor to the collection of functions.

getInputDescription()

Accessor to the description of the inputs.

getInputDimension()

Accessor to the number of the inputs.

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.

getParameter()

Accessor to the parameter values.

getParameterDescription()

Accessor to the parameter description.

getParameterDimension()

Accessor to the dimension of the parameter.

hasName()

Test if the object is named.

isActualImplementation()

Accessor to the validity flag.

isLinear()

Accessor to the linearity of the evaluation.

isLinearlyDependent(index)

Accessor to the linearity of the evaluation with regard to a specific variable.

parameterGradient(inP)

Gradient against the parameters.

setCheckOutput(checkOutput)

Accessor to the output verification flag.

setDescription(description)

Accessor to the description of the inputs and outputs.

setFunctionsCollectionAndCoefficients(...)

Accessor to the coefficients and the collection of functions.

setInputDescription(inputDescription)

Accessor to the description of the inputs.

setName(name)

Accessor to the object's name.

setOutputDescription(outputDescription)

Accessor to the description of the outputs.

setParameter(parameter)

Accessor to the parameter values.

setParameterDescription(description)

Accessor to the parameter description.

setStopCallback(callBack[, state])

Set up a stop callback.

Notes

It returns a Function which is the function f: \Rset^n \rightarrow \Rset^p defined as the linear combination of the functions f_i with vector coefficients in \cC:

\forall \vect{x} \in \Rset^n, f(\vect{x}) = \left\{ \sum_{i=1}^l f_i( \vect{x} ) c_i^{(j)} \right\}_{j = 1, \ldots, p}

__init__(*args)
draw(*args)

Draw the output of function as a Graph.

Available usages:

draw(inputMarg, outputMarg, CP, xiMin, xiMax, ptNb, scale)

draw(firstInputMarg, secondInputMarg, outputMarg, CP, xiMin_xjMin, xiMax_xjMax, ptNbs, scale, isFilled)

draw(xiMin, xiMax, ptNb, scale)

draw(xiMin_xjMin, xiMax_xjMax, ptNbs, scale)

Parameters:
outputMarg, inputMargint, outputMarg, inputMarg \geq 0

outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg.

firstInputMarg, secondInputMargint, firstInputMarg, secondInputMarg \geq 0

In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg.

CPsequence of float

Central point.

xiMin, xiMaxfloat

Define the interval where the curve is plotted.

xiMin_xjMin, xiMax_xjMaxsequence of float of dimension 2.

In the 2D case, define the intervals where the curves are plotted.

ptNbint ptNb > 0

The number of points to draw the curves.

ptNbssequence of int of dimension 2 ptNbs_k > 0, k=1,2

The number of points to draw the contour in the 2D case.

scalebool

scale indicates whether the logarithmic scale is used either for one or both axes:

  • ot.GraphImplementation.NONE or 0: no log scale is used,

  • ot.GraphImplementation.LOGX or 1: log scale is used only for horizontal data,

  • ot.GraphImplementation.LOGY or 2: log scale is used only for vertical data,

  • ot.GraphImplementation.LOGXY or 3: log scale is used for both data.

isFilledbool

isFilled indicates whether the contour graph is filled or not

Notes

We note f: \Rset^n \rightarrow \Rset^p where \vect{x} = (x_1, \dots, x_n) and f(\vect{x}) = (f_1(\vect{x}), \dots,f_p(\vect{x})), with n\geq 1 and p\geq 1.

  • In the first usage:

Draws graph of the given 1D outputMarg marginal f_k: \Rset^n \rightarrow \Rset as a function of the given 1D inputMarg marginal with respect to the variation of x_i in the interval [x_i^{min}, x_i^{max}], when all the other components of \vect{x} are fixed to the corresponding ones of the central point CP. Then it draws the graph: t\in [x_i^{min}, x_i^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t,  CP_{i+1} \dots, CP_n).

  • In the second usage:

Draws the iso-curves of the given outputMarg marginal f_k as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of (x_i, x_j) in the interval [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}], when all the other components of \vect{x} are fixed to the corresponding ones of the central point CP. Then it draws the graph: (t,u) \in [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}] \mapsto f_k(CP_1, \dots, CP_{i-1}, t, CP_{i+1}, \dots, CP_{j-1}, u,  CP_{j+1} \dots, CP_n).

  • In the third usage:

The same as the first usage but only for function f: \Rset \rightarrow \Rset.

  • In the fourth usage:

The same as the second usage but only for function f: \Rset^2 \rightarrow \Rset.

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()
drawCrossCuts(*args)

Draw the 2D and 1D cross cuts of a 1D output function as a GridLayout.

Parameters:
centralPointsequence of float

Central point with dimension equal to the input dimension of the function.

xMin, xMaxsequence of float

Define the interval where the curve is plotted.

pointNumbersequence of int

The number of points to draw the contours and the curves.

withMonoDimensionalCutsbool, optional

withMonoDimensionalCuts indicates whether the mono dimension cuts are drawn or not Default value is specified in the CrossCuts-DefaultWithMonoDimensionalCuts ResourceMap key.

isFilledbool, optional

isFilled indicates whether the contour graphs are filled or not Default value is specified in the Contour-DefaultIsFilled ResourceMap key

vMin, vMaxfloat, optional

Define the interval used to build the color map for the contours If not specified, these values are computed to best fit the graphs. Either specify both values or do not specify any.

Notes

We note f: \Rset^n \rightarrow \Rset^p where \vect{x} = (x_1, \dots, x_n) and f(\vect{x}) = (f_1(\vect{x}), \dots, f_p(\vect{x})), with n\geq 1 and p\geq 1.

In all usages, draw the 1D and 2D cross cuts of f_k: \Rset^n \rightarrow \Rset as a function of all input coordinates for 1D cuts and all couples of coordinates for 2D cuts. Variable coordinates x_i are sampled regularly using ptNb[i] points in the interval [x_i^{min}, x_i^{max}], when all the other components of \vect{x} are fixed to the corresponding components of the centralPoint \vect{c}. In the first usage, vMin and vMax are evaluated as the min and max of all samples of the function value calculated in all cross cuts performed.

  • For 1D cross cuts:

OpenTURNS draws the graph:

y = f_k^{(i)}(s)

for any s \in [x_i^{min}, x_i^{max}] where f_k^{(i)}(s) is defined by the equation:

f_k^{(i)}(s) = f_k(c_1, \dots, c_{i-1}, s,  c_{i+1} \dots, c_n).

  • For 2D cross cuts:

y = f_k^{(i,j)}(s, t)

for any (s, t) \in [x_i^{min}, x_i^{max}] \times [x_j^{min}, x_j^{max}] where f_k^{(i,j)} is defined by the equation:

f_k^{(i,j)}(s,t) = f_k(c_1, \dots, c_{i-1}, s, c_{i+1}, \dots, c_{j-1}, t,  c_{j+1} \dots, c_n).

Examples

>>> import openturns as ot
>>> from openturns.viewer import View
>>> f = ot.SymbolicFunction(['x0', 'x1', 'x2'], ['sin(1*pi_*x0) + x1 - x2 ^ 2'])
>>> grid = f.drawCrossCuts([0., 0., 0.], [-3., -3, -3], [3, 3, 3], [100, 20, 20], True, True)
>>> View(grid).show()
getCallsNumber()

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

Returns:
calls_numberint

Integer that counts the number of times the function has been called since its creation.

getCheckOutput()

Accessor to the output verification flag.

Returns:
check_outputbool

Whether to check return values for nan or inf.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getCoefficients()

Accessor to the coefficients.

Returns:
coefSample

The vectorial coefficients \cC = \{\vect{c}_1, \ldots, \vect{c}_l \} which define the linear combination of f.

getDescription()

Accessor to the description of the inputs and outputs.

Returns:
descriptionDescription

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]
getFunctionsCollection()

Accessor to the collection of functions.

Returns:
fctCollFunctionCollection

The collection of scalar functions (f_i)_{i = 1, \ldots, l} which defines the linear combination of f.

getInputDescription()

Accessor to the description of the inputs.

Returns:
descriptionDescription

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_inputsint

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
getMarginal(*args)

Accessor to marginal.

Parameters:
indicesint or sequence of ints

Set of indices for which the marginal is extracted.

Returns:
marginalFunction

Function corresponding to either f_i or (f_i)_{i \in indices}, with f:\Rset^n \rightarrow \Rset^p and f=(f_0 , \dots, f_{p-1}).

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOutputDescription()

Accessor to the description of the outputs.

Returns:
descriptionDescription

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_outputsint

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
getParameter()

Accessor to the parameter values.

Returns:
parameterPoint

The parameter values.

getParameterDescription()

Accessor to the parameter description.

Returns:
parameterDescription

The parameter description.

getParameterDimension()

Accessor to the dimension of the parameter.

Returns:
parameter_dimensionint

Dimension of the parameter.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

isActualImplementation()

Accessor to the validity flag.

Returns:
is_implbool

Whether the implementation is valid.

isLinear()

Accessor to the linearity of the evaluation.

Returns:
linearbool

True if the evaluation is linear, False otherwise.

isLinearlyDependent(index)

Accessor to the linearity of the evaluation with regard to a specific variable.

Parameters:
indexint

The index of the variable with regard to which linearity is evaluated.

Returns:
linearbool

True if the evaluation is linearly dependent on the specified variable, False otherwise.

parameterGradient(inP)

Gradient against the parameters.

Parameters:
xsequence of float

Input point

Returns:
parameter_gradientMatrix

The parameters gradient computed at x.

setCheckOutput(checkOutput)

Accessor to the output verification flag.

Parameters:
check_outputbool

Whether to check return values for nan or inf.

setDescription(description)

Accessor to the description of the inputs and outputs.

Parameters:
descriptionsequence 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]
setFunctionsCollectionAndCoefficients(functionsCollection, coefficients)

Accessor to the coefficients and the collection of functions.

Parameters:
scalarFctCollsequence of Function

The collection of functions (f_i)_{i = 1, \ldots, l}.

vectCoefColl2-d sequence of float

The sample of coefficients \cC = \{\vect{c}_1, \ldots, \vect{c}_l \}.

setInputDescription(inputDescription)

Accessor to the description of the inputs.

Returns:
descriptionDescription

Description of the inputs.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

setOutputDescription(outputDescription)

Accessor to the description of the outputs.

Returns:
descriptionDescription

Description of the outputs.

setParameter(parameter)

Accessor to the parameter values.

Parameters:
parametersequence of float

The parameter values.

setParameterDescription(description)

Accessor to the parameter description.

Parameters:
parameterDescription

The parameter description.

setStopCallback(callBack, state=None)

Set up a stop callback.

Can be used to programmatically stop an evaluation.

Parameters:
callbackcallable

Returns a bool deciding whether to stop or continue.