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.

Methods

getCenter()

Get the center.

getClassName()

Accessor to the object's name.

getConstant()

Get the constant vector of the approximation.

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.

hasName()

Test if the object is named.

run()

Perform the second-order Taylor expansion around \ux_0.

setName(name)

Accessor to the object's name.

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]
__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).

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}.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

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.

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