Chebyshev1Basis - GTSAM Docs

Overview¶

Chebyshev1Basis provides the first-kind Chebyshev polynomial basis $T_n(x)$ on the interval $[-1, 1]$ . Parameters are coefficients of the basis functions, making this a classic orthogonal polynomial expansion for smooth function approximation.

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

Usage Example¶

Evaluate first-kind Chebyshev weights at a point 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 = 0.25
weights = gtsam.Chebyshev1Basis.CalculateWeights(N, x)
print("Weights at x=0.25:", np.asarray(weights).ravel())

X = np.linspace(-1.0, 1.0, 5)
W = gtsam.Chebyshev1Basis.WeightMatrix(N, X)
print("WeightMatrix shape:", np.asarray(W).shape)
print("Row for x=0:", np.asarray(W)[2])

Weights at x=0.25: [ 1.     0.25  -0.875 -0.688  0.531  0.953]
WeightMatrix shape: (5, 6)
Row for x=0: [ 1.  0. -1. -0.  1.  0.]

Source¶

Chebyshev.h