HaarWaveletFactory

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../../_images/openturns-HaarWaveletFactory-1.png
class HaarWaveletFactory(*args)

Haar wavelet function factory.

Generates the Haar basis defined as follows:

\begin{array}{lcl} \psi_0(x) & = & \fcar{[0, 1]}{x} \\ \psi_n(x) & = & \frac{1}{2^{j/2}}\left[\fcar{[\frac{k}{2^j},\frac{k+1/2}{2^j}]}{x}-\fcar{[\frac{k+1/2}{2^j},\frac{k+1}{2^j}]}{x}\right] \end{array}

where n = 2^j + k, 0 \leq k < 2^j, 0 \leq j.

See also

OrthogonalUniVariatePolynomialFunctionFactory

Methods

build(order)

Build the n-th order orthogonal univariate function.

getClassName()

Accessor to the object's name.

getId()

Accessor to the object's id.

getMeasure()

Accessor to the associated probability measure.

getName()

Accessor to the object's name.

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.

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)
build(order)

Build the n-th order orthogonal univariate function.

Parameters
nint, 0 \leq n

Function order.

Returns
functionUniVariateFunction

Requested orthogonal univariate function.

getClassName()

Accessor to the object’s name.

Returns
class_namestr

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

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getMeasure()

Accessor to the associated probability measure.

Returns
measureDistribution

The associated probability measure (according to which the functions are orthogonal).

Notes

Two functions P and Q are orthogonal with respect to the probability measure w(x) \di{x} if and only if their scalar product:

\langle P, Q \rangle = \int_{\alpha}^{\beta} P(x) Q(x) w(x) \di{x} = 0

where \alpha \in \Rset \cup \{-\infty\} and \beta \in \Rset \cup \{+\infty\}.

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

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.

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.