LinearCombinationFunction¶
-
class
LinearCombinationFunction
(*args)¶ Linear combination of functions.
Allows to create a function which is the linear combination of functions with scalar weights.
where
and
then the linear combination is:
Parameters: - functionCollection : sequence of
Function
Collection of functions to sum.
- scalarCoefficientColl : sequence of float
Collection of scalar weights.
Examples
>>> import openturns as ot >>> f1 = ot.SymbolicFunction(['x1', 'x2', 'x3'], ... ['x1^2 + x2', 'x1 + x2 + x3']) >>> f2 = ot.SymbolicFunction(['x1', 'x2', 'x3'], ... ['x1 + 2 * x2 + x3', 'x1 + x2 - x3']) >>> functions = [f1, f2] >>> coefficients = [2.0, 4.0] >>> linComb = ot.LinearCombinationFunction(functions, coefficients) >>> print(linComb([1.0, 2.0, 3.0])) [38,12]
Methods
draw
(*args)Draw the output of function as a Graph
.getCallsNumber
()Accessor to the number of times the function has been called. getClassName
()Accessor to the object’s name. getDescription
()Accessor to the description of the inputs and outputs. getEvaluation
()Accessor to the evaluation function. getEvaluationCallsNumber
()Accessor to the number of times the function has been called. getGradient
()Accessor to the gradient function. getGradientCallsNumber
()Accessor to the number of times the gradient of the function has been called. getHessian
()Accessor to the hessian function. getHessianCallsNumber
()Accessor to the number of times the hessian of the function has been called. getId
()Accessor to the object’s id. getImplementation
(*args)Accessor to the underlying implementation. getInputDescription
()Accessor to the description of the input vector. getInputDimension
()Accessor to the dimension of the input vector. getMarginal
(*args)Accessor to marginal. getName
()Accessor to the object’s name. getOutputDescription
()Accessor to the description of the output vector. 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. gradient
(inP)Return the Jacobian transposed matrix of the function at a point. hessian
(inP)Return the hessian of the function at a point. parameterGradient
(inP)Accessor to the gradient against the parameter. setDescription
(description)Accessor to the description of the inputs and outputs. setEvaluation
(evaluation)Accessor to the evaluation function. setGradient
(gradient)Accessor to the gradient function. setHessian
(hessian)Accessor to the hessian function. setInputDescription
(inputDescription)Accessor to the description of the input vector. setName
(name)Accessor to the object’s name. setOutputDescription
(inputDescription)Accessor to the description of the output vector. setParameter
(parameter)Accessor to the parameter values. setParameterDescription
(description)Accessor to the parameter description. __call__ -
__init__
(*args)¶ Initialize self. See help(type(self)) for accurate signature.
-
draw
(*args)¶ Draw the output of function as a
Graph
.- Available usages:
draw(inputMarg, outputMarg, CP, xiMin, xiMax, ptNb)
draw(firstInputMarg, secondInputMarg, outputMarg, CP, xiMin_xjMin, xiMax_xjMax, ptNbs)
draw(xiMin, xiMax, ptNb)
draw(xiMin_xjMin, xiMax_xjMax, ptNbs)
Parameters: - outputMarg, inputMarg : int,
outputMarg is the index of the marginal to draw as a function of the marginal with index inputMarg.
- firstInputMarg, secondInputMarg : int,
In the 2D case, the marginal outputMarg is drawn as a function of the two marginals with indexes firstInputMarg and secondInputMarg.
- CP : sequence of float
Central point.
- xiMin, xiMax : float
Define the interval where the curve is plotted.
- xiMin_xjMin, xiMax_xjMax : sequence of float of dimension 2.
In the 2D case, define the intervals where the curves are plotted.
- ptNb : int
or list of ints of dimension 2
The number of points to draw the curves.
Notes
We note
where
and
, with
and
.
- In the first usage:
Draws graph of the given 1D outputMarg marginal
as a function of the given 1D inputMarg marginal with respect to the variation of
in the interval
, when all the other components of
are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph:
.
- In the second usage:
Draws the iso-curves of the given outputMarg marginal
as a function of the given 2D firstInputMarg and secondInputMarg marginals with respect to the variation of
in the interval
, when all the other components of
are fixed to the corresponding ones of the central point CP. Then OpenTURNS draws the graph:
.
- In the third usage:
The same as the first usage but only for function
.
- In the fourth usage:
The same as the second usage but only for function
.
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()
-
getCallsNumber
()¶ Accessor to the number of times the function has been called.
Returns: - calls_number : int
Integer that counts the number of times the function has been called since its creation.
-
getClassName
()¶ Accessor to the object’s name.
Returns: - class_name : str
The object class name (object.__class__.__name__).
-
getDescription
()¶ Accessor to the description of the inputs and outputs.
Returns: - description :
Description
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]
- description :
-
getEvaluation
()¶ Accessor to the evaluation function.
Returns: - function :
EvaluationImplementation
The evaluation function.
Examples
>>> import openturns as ot >>> f = ot.SymbolicFunction(['x1', 'x2'], ... ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6']) >>> print(f.getEvaluation()) [x1,x2]->[2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6]
- function :
-
getEvaluationCallsNumber
()¶ Accessor to the number of times the function has been called.
Returns: - evaluation_calls_number : int
Integer that counts the number of times the function has been called since its creation.
-
getGradient
()¶ Accessor to the gradient function.
Returns: - gradient :
GradientImplementation
The gradient function.
- gradient :
-
getGradientCallsNumber
()¶ Accessor to the number of times the gradient of the function has been called.
Returns: - gradient_calls_number : int
Integer that counts the number of times the gradient of the Function has been called since its creation. Note that if the gradient is implemented by a finite difference method, the gradient calls number is equal to 0 and the different calls are counted in the evaluation calls number.
-
getHessian
()¶ Accessor to the hessian function.
Returns: - hessian :
HessianImplementation
The hessian function.
- hessian :
-
getHessianCallsNumber
()¶ Accessor to the number of times the hessian of the function has been called.
Returns: - hessian_calls_number : int
Integer that counts the number of times the hessian of the Function has been called since its creation. Note that if the hessian is implemented by a finite difference method, the hessian calls number is equal to 0 and the different calls are counted in the evaluation calls number.
-
getId
()¶ Accessor to the object’s id.
Returns: - id : int
Internal unique identifier.
-
getImplementation
(*args)¶ Accessor to the underlying implementation.
Returns: - impl : Implementation
The implementation class.
-
getInputDescription
()¶ Accessor to the description of the input vector.
Returns: - description :
Description
Description of the input vector.
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]
- description :
-
getInputDimension
()¶ Accessor to the dimension of the input vector.
Returns: - inputDim : int
Dimension of the input vector
.
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: - indices : int or list of ints
Set of indices for which the marginal is extracted.
Returns: - marginal :
Function
Function corresponding to either
or
, with
and
.
-
getName
()¶ Accessor to the object’s name.
Returns: - name : str
The name of the object.
-
getOutputDescription
()¶ Accessor to the description of the output vector.
Returns: - description :
Description
Description of the output vector.
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]
- description :
-
getOutputDimension
()¶ Accessor to the number of the outputs.
Returns: - number_outputs : int
Dimension of the output vector
.
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
-
getParameterDescription
()¶ Accessor to the parameter description.
Returns: - parameter :
Description
The parameter description.
- parameter :
-
getParameterDimension
()¶ Accessor to the dimension of the parameter.
Returns: - parameterDimension : int
Dimension of the parameter.
-
gradient
(inP)¶ Return the Jacobian transposed matrix of the function at a point.
Parameters: - point : sequence of float
Point where the Jacobian transposed matrix is calculated.
Returns: - gradient :
Matrix
The Jacobian transposed matrix of the function at point.
Examples
>>> import openturns as ot >>> f = ot.SymbolicFunction(['x1', 'x2'], ... ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2']) >>> print(f.gradient([3.14, 4])) [[ 13.5345 1 ] [ 4.00001 1 ]]
-
hessian
(inP)¶ Return the hessian of the function at a point.
Parameters: - point : sequence of float
Point where the hessian of the function is calculated.
Returns: - hessian :
SymmetricTensor
Hessian of the function at point.
Examples
>>> import openturns as ot >>> f = ot.SymbolicFunction(['x1', 'x2'], ... ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6','x1 + x2']) >>> print(f.hessian([3.14, 4])) sheet #0 [[ 20 -0.00637061 ] [ -0.00637061 0 ]] sheet #1 [[ 0 0 ] [ 0 0 ]]
-
parameterGradient
(inP)¶ Accessor to the gradient against the parameter.
Returns: - gradient :
Matrix
The gradient.
- gradient :
-
setDescription
(description)¶ Accessor to the description of the inputs and outputs.
Parameters: - description : sequence 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]
-
setEvaluation
(evaluation)¶ Accessor to the evaluation function.
Parameters: - function :
EvaluationImplementation
The evaluation function.
- function :
-
setGradient
(gradient)¶ Accessor to the gradient function.
Parameters: - gradient_function :
GradientImplementation
The gradient function.
Examples
>>> import openturns as ot >>> f = ot.SymbolicFunction(['x1', 'x2'], ... ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6']) >>> f.setGradient(ot.CenteredFiniteDifferenceGradient( ... ot.ResourceMap.GetAsScalar('CenteredFiniteDifferenceGradient-DefaultEpsilon'), ... f.getEvaluation()))
- gradient_function :
-
setHessian
(hessian)¶ Accessor to the hessian function.
Parameters: - hessian_function :
HessianImplementation
The hessian function.
Examples
>>> import openturns as ot >>> f = ot.SymbolicFunction(['x1', 'x2'], ... ['2 * x1^2 + x1 + 8 * x2 + 4 * cos(x1) * x2 + 6']) >>> f.setHessian(ot.CenteredFiniteDifferenceHessian( ... ot.ResourceMap.GetAsScalar('CenteredFiniteDifferenceHessian-DefaultEpsilon'), ... f.getEvaluation()))
- hessian_function :
-
setInputDescription
(inputDescription)¶ Accessor to the description of the input vector.
Parameters: - description :
Description
Description of the input vector.
- description :
-
setName
(name)¶ Accessor to the object’s name.
Parameters: - name : str
The name of the object.
-
setOutputDescription
(inputDescription)¶ Accessor to the description of the output vector.
Parameters: - description :
Description
Description of the output vector.
- description :
-
setParameter
(parameter)¶ Accessor to the parameter values.
Parameters: - parameter : sequence of float
The parameter values.
-
setParameterDescription
(description)¶ Accessor to the parameter description.
Parameters: - parameter :
Description
The parameter description.
- parameter :
- functionCollection : sequence of