QuadraticTaylor

class QuadraticTaylor(*args)

Second-order Taylor expansion.

Parameters:
centersequence of float

Point \ux_0.

functionFunction

Function h to be approximated at the point \ux_0.

See also

LinearTaylor, LinearLeastSquares, QuadraticLeastSquares

Notes

The response surface is the second-order Taylor expansion of the function h at the point \ux_0. Refer to Taylor Expansion for details.

Examples

>>> import openturns as ot
>>> formulas = ['x1 * sin(x2)', 'cos(x1 + x2)', '(x2 + 1) * exp(x1 - 2 * x2)']
>>> myFunc = ot.SymbolicFunction(['x1', 'x2'], formulas)
>>> myTaylor = ot.QuadraticTaylor([1, 2], myFunc)
>>> myTaylor.run()
>>> responseSurface = myTaylor.getMetaModel()
>>> print(responseSurface([1.2,1.9]))
[1.13655,-0.999155,0.214084]

Methods

getCenter()

Get the center.

getClassName()

Accessor to the object's name.

getConstant()

Get the constant vector of the approximation.

getId()

Accessor to the object's id.

getInputFunction()

Get the function.

getLinear()

Get the gradient of the function at \ux_0.

getMetaModel()

Get the polynomial approximation of the function.

getName()

Accessor to the object's name.

getQuadratic()

Get the hessian of the function at \ux_0.

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.

run()

Perform the second-order Taylor expansion around \ux_0.

setName(name)

Accessor to the object's name.

setShadowedId(id)

Accessor to the object's shadowed id.

setVisibility(visible)

Accessor to the object's visibility state.
__init__(*args)
getCenter()

Get the center.

Returns:
centerPoint

Point \ux_0 where the Taylor expansion of the function is performed.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getConstant()

Get the constant vector of the approximation.

Returns:
constantVectorPoint

Point h(\ux_0).

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getInputFunction()

Get the function.

Returns:
functionFunction

Function h to be approximated.

getLinear()

Get the gradient of the function at \ux_0.

Returns:
gradientMatrix

The matrix \mat{L}.

getMetaModel()

Get the polynomial approximation of the function.

Returns:
approximationFunction

The second-order Taylor expansion of h at \ux_0.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getQuadratic()

Get the hessian of the function at \ux_0.

Returns:
tensorSymmetricTensor

The tensor \mat{Q}.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

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.

run()

Perform the second-order Taylor expansion around \ux_0.

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.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:
visiblebool

Visibility flag.

Examples using the class

Taylor approximations

Taylor approximations

Using the FORM - SORM algorithms on a nonlinear function

Using the FORM - SORM algorithms on a nonlinear function