Stroud rules

class SpectralToolbox.Stroud.Stroud(weight, params)

Bases: object

Initialization of the Stroud integral points generator.

This method generates an instance of the Stroud class, to be used in order to generate N-dimensional cubature rules with respect to the selected weight. Available weight types can be selected using their string name or by predefined attributes

• ‘Gaussian’ or Stroud.GAUSSIAN
• ‘Beta’ or Stroud.BETA
• ‘Gamma’ or Stroud.GAMMA

Additional parameters are required for some weights.

Weight	Parameters
Gaussian	None
Beta	(alpha,beta)
Gamma	alpha

See [Str57] and [Xiu08] for details.

Parameters:

• weight (Stroud.AVAIL_WEIGHTS) – type of the multidimensional weight for the formula.
• params (object) – The parameters needed by the selected weight

params = []

stroud2(n)

stroud2(): Generates n+1 equally weighted points for the degree 2 Stroud formula.

Syntax:

x = stroud2(n)

Input:

• n = (int) number of dimensions of the integration formula.

Output:

• x = (float, nd-array (n+1,n)) n+1 quadrature nodes.
• w0 = (float) weight (equal for all the points)

stroud3(n)

stroud2(): Generates 2n equally weighted points for the degree 3 Stroud formula.

Syntax:

x = stroud3(n)

Input:

• n = (int) number of dimensions of the integration formula.

Output:

• x = (float, nd-array (n+1,n)) n+1 quadrature nodes.
• w0 = (float) weight (equal for all the points)

Description:

The method is available only for distributions in symmetric regions, thus only for integrals with Gaussian weights and symmetric Beta weights (alpha=beta) in R^n

weight = []