QuadraturePoints

class QuadraturePoints(points_per_axis=None, num_axes=None)[source]

Bases: object

Helper class that defines quadrature points.

Notes

This implements the Probabilist’s version of the Gauss-Hermite quadrature points. This consists of the Hermite polynomial

\[H_{e_n}(x) = (-1)^n \exp{\frac{x^2}{2}} \frac{\partial^n}{\partial x^n} \exp{-\frac{x^2}{2}}\]

and its associated weights. For details see [17], [8] and for a multi-variate extension [11].

points_per_axis

Number of points to use per axis

num_axes

Number of axis in each point. This can be set manually, but will be updated when update_points() is called to match the supplied mean.

weights

Weight of each quadrature point

points

Each row corresponds to a quadrature point and the total number of rows is the total number of points.

Methods

`__init__`
`plot_points`	Plots the weighted points.
`update_points`	Updates the quadrature points given some initial point and scale.

Attributes

`cov`	Covariance of the points, accounting for the weights.
`mean`	Mean of the points, accounting for the weights.
`num_points`	Read only expected number of points.

plot_points(inds, x_lbl='X Position', y_lbl='Y Position', ttl='Weighted Positions', size_factor=10000, **kwargs)[source]

Plots the weighted points.

Keywrod arguments are processed with gncpy.plotting.init_plotting_opts(). This function implements

f_hndl

Any title/axis/text options

Parameters:

inds (list or int) – Indices of the point vector to plot. Can be a list of at most 2 elements. If only 1 is given a bar chart is created.
x_lbl (string, optional) – Label for the x-axis. The default is ‘X Position’.
y_lbl (string, optional) – Label for the y-axis. The default is ‘Y Position’.
ttl (string, optional) – Title of the plot. The default is ‘Weighted positions’.
size_factor (int, optional) – Factor to multiply the weight by when determining the marker size. Only used if plotting 2 indices. The default is 100**2.
**kwargs (dict) – Additional standard plotting options.

Returns:

fig – Handle to the figure used.

Return type:

matplotlib figure handle

update_points(mean, scale, have_sqrt=False)[source]

Updates the quadrature points given some initial point and scale.

Parameters:

mean (N x 1 numpy array) – Point to represent by quadrature points.
scale (N x N numpy array) – Covariance or square root of the covariance matrix of the given point.
have_sqrt (bool) – Optional flag indicating if the square root of the matrix was supplied. The default is False.

Return type:

None.