LinearTaylor¶

class LinearTaylor(*args)

First order polynomial response surface by Taylor expansion.

Available constructors:
LinearTaylor(center, function)
Parameters: center : sequence of float Point where the Taylor expansion of the function is performed. function : Function Function to be approximated.

Notes

The approximation of the model response around a specific set of input parameters may be of interest. One may then substitute for its Taylor expansion at point . Hence is replaced with a first or second-order polynomial whose evaluation is inexpensive, allowing the analyst to apply the uncertainty anaysis methods.

We consider here the first order Taylor expansion around .

Introducing a vector notation, the previous equation rewrites:

where:

• is the vector model response evaluated at ;
• is the current set of input parameters;
• is the transposed Jacobian matrix evaluated at .

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.LinearTaylor([1, 2], myFunc)
>>> myTaylor.run()
>>> responseSurface = myTaylor.getResponseSurface()
>>> print(responseSurface([1.2,1.9]))
[1.13277,-1.0041,0.204127]


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 . getName() Accessor to the object’s name. getResponseSurface() Get an approximation of the function. 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 Linear Taylor expansion around . 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)

Initialize self. See help(type(self)) for accurate signature.

getCenter()

Get the center.

Returns: center : Point Point where the Taylor expansion of the function is performed.
getClassName()

Accessor to the object’s name.

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

Get the constant vector of the approximation.

Returns: constantVector : Point Constant vector of the approximation, equal to .
getId()

Accessor to the object’s id.

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

Get the function.

Returns: function : Function Function to be approximated.
getLinear()

Get the gradient of the function at .

Returns: gradient : Matrix Gradient of the function at the point (the transposition of the jacobian matrix).
getName()

Accessor to the object’s name.

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

Get an approximation of the function.

Returns: approximation : Function An approximation of the function by a Linear Taylor expansion at the point .
getShadowedId()

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.
run()

Perform the Linear Taylor expansion around .

setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.