# control.flatsys.BSplineFamily¶

class control.flatsys.BSplineFamily(breakpoints, degree, smoothness=None, vars=None)[source]

Bases: `BasisFamily`

B-spline basis functions.

This class represents a B-spline basis for piecewise polynomials defined across a set of breakpoints with given degree and smoothness. On each interval between two breakpoints, we have a polynomial of a given degree and the spline is continuous up to a given smoothness at interior breakpoints.

Parameters
• breakpoints (1D array or 2D array of float) – The breakpoints for the spline(s).

• degree (int or list of ints) – For each spline variable, the degree of the polynomial between breakpoints. If a single number is given and more than one spline variable is specified, the same degree is used for each spline variable.

• smoothness (int or list of ints) – For each spline variable, the smoothness at breakpoints (number of derivatives that should match).

• vars (None or int, optional) – The number of spline variables. If specified as None (default), then the spline basis describes a single variable, with no indexing. If the number of spine variables is > 0, then the spline basis is index using the var keyword.

Methods

 `eval` Compute function values given the coefficients and time points. `eval_deriv` Evaluate the kth derivative of the ith basis function at time t. `var_ncoefs` Get the number of coefficients for a variable
__call__(i, t, var=None)[source]

Evaluate the ith basis function at a point in time

eval(coeffs, tlist, var=None)[source]

Compute function values given the coefficients and time points.

eval_deriv(i, k, t, var=None)[source]

Evaluate the kth derivative of the ith basis function at time t.

var_ncoefs(var)[source]

Get the number of coefficients for a variable