FourierBasis - GTSAM Docs

Overview¶

FourierBasis provides a real Fourier series basis for periodic functions. The basis is ordered as $[1, \cos(x), \sin(x), \cos(2x), \sin(2x), \ldots]$ , making it convenient for truncated Fourier expansions and their derivatives.

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) returns the real Fourier basis weights.
DifferentiationMatrix(N) returns the linear operator for derivatives.
DerivativeWeights(N, x) returns weights that evaluate the derivative at x.

Usage Example¶

Evaluate a real Fourier basis, its derivative weights, and a slice of the differentiation matrix.

import numpy as np
import gtsam

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

N = 7
x = 1.2
weights = gtsam.FourierBasis.CalculateWeights(N, x)
dweights = gtsam.FourierBasis.DerivativeWeights(N, x)
D = gtsam.FourierBasis.DifferentiationMatrix(N)

print("Weights:", np.asarray(weights).ravel())
print("Derivative weights:", np.asarray(dweights).ravel())
print("D[1:3, 1:3]:", np.asarray(D)[1:3, 1:3])

Weights: [ 1.     0.362  0.932 -0.737  0.675 -0.897 -0.443]
Derivative weights: [ 0.    -0.932  0.362 -1.351 -1.475  1.328 -2.69 ]
D[1:3, 1:3]: [[ 0.  1.]
 [-1.  0.]]

Source¶

Fourier.h