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Avoid half the cosines in IntegrationWeights

release/4.3a0
Frank Dellaert 2025-03-22 16:57:32 -04:00
parent 44e692c3e9
commit 5ffa9c1788
1 changed files with 12 additions and 10 deletions
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22
gtsam/basis/Chebyshev2.cpp
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@ -228,24 +228,26 @@ Chebyshev2::DiffMatrix Chebyshev2::DifferentiationMatrix(size_t N, double a, dou
}
Weights Chebyshev2::IntegrationWeights(size_t N, double a, double b) {
// Allocate space for weights
Weights weights(N);
size_t K = N - 1, // number of intervals between N points
K2 = K * K;
K2 = K * K;
// Compute endpoint weight.
weights(0) = 0.5 * (b - a) / (K2 + K % 2 - 1);
weights(N - 1) = weights(0);
size_t last_k = K / 2 + K % 2 - 1;
for (size_t i = 1; i <= N - 2; ++i) {
// Compute up to the middle; mirror symmetry holds.
size_t mid = (N - 1) / 2;
for (size_t i = 1; i <= mid; ++i) {
double theta = i * M_PI / K;
weights(i) = (K % 2 == 0) ? 1 - cos(K * theta) / (K2 - 1) : 1;
double w = (K % 2 == 0) ? 1 - cos(K * theta) / (K2 - 1) : 1;
size_t last_k = K / 2 + K % 2 - 1;
for (size_t k = 1; k <= last_k; ++k)
weights(i) -= 2 * cos(2 * k * theta) / (4 * k * k - 1);
weights(i) *= (b - a) / K;
w -= 2 * cos(2 * k * theta) / (4 * k * k - 1);
w *= (b - a) / K;
weights(i) = w;
weights(N - 1 - i) = w;
}
return weights;
}