# CenteredFiniteDifferenceHessian¶

class CenteredFiniteDifferenceHessian(*args)

Second order centered finite-difference scheme.

Available constructors:

CenteredFiniteDifferenceHessian(epsilon, evalImpl)

CenteredFiniteDifferenceHessian(step, evalImpl)

Parameters: evalImpl : EvaluationImplementation Implementation of the evaluation of a function. epsilon : float, sequence of float Finite difference steps for each dimension. step : FiniteDifferenceStep Defines how finite difference steps values are computed.

Notes

CenteredFiniteDifferenceHessian provides a second order centered finite- difference scheme:

Examples

>>> import openturns as ot
>>> formulas = ['x1 * sin(x2)', 'cos(x1 + x2)', '(x2 + 1) * exp(x1 - 2 * x2)']
>>> myFunc = ot.SymbolicFunction(['x1', 'x2'], formulas)
>>> epsilon = [0.01]*2
>>> myHessian = ot.CenteredFiniteDifferenceHessian(epsilon, myFunc.getEvaluation())
>>> inPoint = [1.0]*2
>>> print(myHessian.hessian(inPoint))
sheet #0
[[  0         0.540293 ]
[  0.540293 -0.841443 ]]
sheet #1
[[  0.416133  0.416133 ]
[  0.416133  0.416133 ]]
sheet #2
[[  0.735783 -1.10368  ]
[ -1.10368   1.47152  ]]

Methods

 getCallsNumber() Accessor to the number of times the hessian has been called. getClassName() Accessor to the object’s name. getEpsilon() Get the finite difference steps. getEvaluation() Get the implementation of the evaluation of the function. getFiniteDifferenceStep() Get the finite difference step. getId() Accessor to the object’s id. getInputDimension() Get the input dimension. getMarginal(*args) Accessor to the hessian implementation of a specific output. getName() Accessor to the object’s name. getOutputDimension() Get the output dimension. getParameter() Accessor to the parameter values. getShadowedId() Accessor to the object’s shadowed id. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. hessian(inP) Get the hessian at some point. isActualImplementation() Accessor to the validity flag. setFiniteDifferenceStep(finiteDifferenceStep) Set the finite difference step. setName(name) Accessor to the object’s name. setParameter(parameter) Accessor to the parameter values. setShadowedId(id) Accessor to the object’s shadowed id. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

getCallsNumber()

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

Returns: calls_number : int Integer that counts the number of times the hessian has been called since its creation.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getEpsilon()

Get the finite difference steps.

Returns: epsilon : Point Finite difference steps for each dimension.
getEvaluation()

Get the implementation of the evaluation of the function.

Returns: evalImpl : EvaluationImplementation Implementation of the evaluation of a function.
getFiniteDifferenceStep()

Get the finite difference step.

Returns: step : FiniteDifferenceStep Defines how finite difference steps values are computed.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getInputDimension()

Get the input dimension.

Returns: dimension : int Input dimension.
getMarginal(*args)

Accessor to the hessian implementation of a specific output.

Parameters: i : integer Integer corresponding to the output (Care: it starts at 0). indices : sequence of integer The set of indices for which the outputs are extracted. hessianImplementation : HessianImplementation A hessian implementation restricted to its compenents functions which indices are i or indices.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getOutputDimension()

Get the output dimension.

Returns: dimension : int Output dimension.
getParameter()

Accessor to the parameter values.

Returns: parameter : Point The parameter values.

Accessor to the object’s shadowed id.

Returns: id : int Internal unique identifier.
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.
hessian(inP)

Get the hessian at some point.

Parameters: point : sequence of float Point where the hessian is computed. hessian : SymmetricTensor Hessian evaluated at point.
isActualImplementation()

Accessor to the validity flag.

Returns: is_impl : bool Whether the implementation is valid.
setFiniteDifferenceStep(finiteDifferenceStep)

Set the finite difference step.

Parameters: step : FiniteDifferenceStep Defines how finite difference steps values are computed.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setParameter(parameter)

Accessor to the parameter values.

Parameters: parameter : sequence of float The parameter values.