choreo.segm.quad.InterpolateOnSegment

InterpolateOnSegment()

Interpolates a function given its value on quadrature nodes of an interval.

Lagrange interpolation of a function evaluated at quadrature nodes of an interval.

Given the \(n\) function values \(f_i\), the Lagrange interpolating polynomial is the unique polynomial \(L_f\) of degree \(n-1\) such that \(L_f(x_i)=f_i\).

Parameters:

• funvals (numpy.ndarray(shape = (nx, ndim), dtype = np.float64)) – Function values to be interpolated. See also EvalOnNodes().

• x (numpy.ndarray(shape = (nx), dtype = np.float64)) – Array of nodes where the interpolation should be evaluated.

• x_span (tuple (numpy.float64, numpy.float64)) – Lower and upper bound of the evaluation interval.

• quad (QuadTable) – Normalized evaluation nodes.

• eps (numpy.float64) – If \(|x-x_i|<\text{eps}\), then the approximation \(l_i(x)=1.\) is used to avoid division by zero. By default 1e-14.

Returns:

The approximated value of the integral.

Return type:

numpy.ndarray(shape = (ndim), dtype = np.float64)