Chebyshev2Basis - GTSAM Docs

Overview¶

Chebyshev2Basis provides the second-kind Chebyshev polynomial basis $U_n(x)$ on $[-1, 1]$ . It is related to derivatives of first-kind polynomials and is useful when expressing functions directly in a basis of $U_n(x)$ polynomials.

Authors: Frank Dellaert, et al. (see THANKS for the full author list)

See LICENSE for the license information

# Install GTSAM from pip if running in Google Colab
try:
    import google.colab
    %pip install --quiet gtsam-develop
except ImportError:
    pass  # Not in Colab

Key Functionality / API¶

CalculateWeights(N, x, a=-1, b=1) returns basis weights.
DerivativeWeights(N, x, a=-1, b=1) returns derivative weights.
WeightMatrix(N, X) stacks weights for a vector of sample points.

Usage Example¶

Evaluate second-kind Chebyshev weights and build a weight matrix for multiple sample points.

import numpy as np
import gtsam

np.set_printoptions(precision=3, suppress=True)

N = 6
x = -0.3
weights = gtsam.Chebyshev2Basis.CalculateWeights(N, x)
print("Weights at x=-0.3:", np.asarray(weights).ravel())

X = np.linspace(-1.0, 1.0, 5)
W = gtsam.Chebyshev2Basis.WeightMatrix(N, X)
print("WeightMatrix shape:", np.asarray(W).shape)
print("Row for x=0:", np.asarray(W)[2])

Weights at x=-0.3: [ 1.    -0.6   -0.64   0.984  0.05  -1.014]
WeightMatrix shape: (5, 6)
Row for x=0: [ 1.  0. -1. -0.  1.  0.]

Source¶

Chebyshev.h