UniVariatePolynomial

class UniVariatePolynomial(*args)

Base class for univariate polynomials.

Parameters:

coefficients : sequence of float

Polynomial coefficients in increasing polynomial order.

Examples

>>> import openturns as ot

Create a univariate polynomial from a list of coefficients:

>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P)
1 + 2 * X + 3 * X^2

Univariate polynomials are of course callable:

>>> print(P(1.0))
6.0

Addition, subtraction and multiplication of univariate polynomials:

>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> Q = ot.UniVariatePolynomial([1.0, 2.0])
>>> print('(%s) + (%s) = %s' % (P, Q, P + Q))
(1 + 2 * X + 3 * X^2) + (1 + 2 * X) = 2 + 4 * X + 3 * X^2
>>> print('(%s) - (%s) = %s' % (P, Q, P - Q))
(1 + 2 * X + 3 * X^2) - (1 + 2 * X) = 3 * X^2
>>> print('(%s) * (%s) = %s' % (P, Q, P * Q))
(1 + 2 * X + 3 * X^2) * (1 + 2 * X) = 1 + 4 * X + 7 * X^2 + 6 * X^3

Methods

__call__(*args)
derivate() Build the first-order derivative polynomial.
draw(xMin, xMax, pointNumber) Draw the function.
getClassName() Accessor to the object’s name.
getCoefficients() Accessor to the polynomials’s coefficients.
getDegree() Accessor to the polynomials’s degree.
getId() Accessor to the object’s id.
getImplementation(*args) Accessor to the underlying implementation.
getName() Accessor to the object’s name.
getRoots() Compute the roots of the polynomial.
gradient(x) Compute the gradient at point x.
hessian(x) Compute the hessian at point x.
incrementDegree([degree]) Multiply the polynomial by x^k.
setCoefficients(coefficients) Accessor to the polynomials’s coefficients.
setName(name) Accessor to the object’s name.
__init__(*args)
derivate()

Build the first-order derivative polynomial.

Returns:

derivated_polynomial : Univariate

The first-order derivated polynomial.

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P.derivate())
2 + 6 * X
draw(xMin, xMax, pointNumber)

Draw the function.

Parameters:

x_min : float, optional

The starting value that is used for meshing the x-axis.

x_max : float, optional, x_{\max} > x_{\min}

The ending value that is used for meshing the x-axis.

n_points : int, optional

The number of points that is used for meshing the x-axis.

Examples

>>> import openturns as ot
>>> from openturns.viewer import View
>>> f = ot.UniVariatePolynomial([1.0, 2.0, -3.0, 5.0])
>>> View(f.draw(-10.0, 10.0, 100)).show()
getClassName()

Accessor to the object’s name.

Returns:

class_name : str

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

getCoefficients()

Accessor to the polynomials’s coefficients.

Returns:

coefficients : Point

Polynomial coefficients in increasing polynomial order.

See also

setCoefficients

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P.getCoefficients())
[1,2,3]
getDegree()

Accessor to the polynomials’s degree.

Returns:

degree : int

Polynomial’s degree.

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P.getDegree())
2
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.

getName()

Accessor to the object’s name.

Returns:

name : str

The name of the object.

getRoots()

Compute the roots of the polynomial.

Returns:

roots : list of complex values

Polynomial’s roots.

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P.getRoots())
[(-0.333333,0.471405),(-0.333333,-0.471405)]
gradient(x)

Compute the gradient at point x.

Returns:

gradient : float

The value of the function’s first-order derivative at point x.

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P.gradient(1.0))
8.0
hessian(x)

Compute the hessian at point x.

Parameters:

x : float

Input value.

Returns:

hessian : float

The value of the function’s second-order derivative at point x.

incrementDegree(degree=1)

Multiply the polynomial by x^k.

Parameters:

degree : int, optional

The incremented degree k. Default uses k = 1.

Returns:

incremented_degree_polynomial : UniVariatePolynomial

Polynomial with incremented degree.

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> print(P.incrementDegree())
X + 2 * X^2 + 3 * X^3
>>> print(P.incrementDegree(2))
X^2 + 2 * X^3 + 3 * X^4
setCoefficients(coefficients)

Accessor to the polynomials’s coefficients.

Parameters:

coefficients : sequence of float

Polynomial coefficients in increasing polynomial order.

See also

getCoefficients

Examples

>>> import openturns as ot
>>> P = ot.UniVariatePolynomial([1.0, 2.0, 3.0])
>>> P.setCoefficients([4.0, 2.0, 1.0])
>>> print(P)
4 + 2 * X + X^2
setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.