Read the equation
The sum includes indices at distance at most three from m, excludes m itself, and clips the range at the ends of the array. It therefore includes fewer neighbors near a boundary than in the interior. This finite-range rule helps explain why row sums vary across the matrix.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| m | Current index |
| m_prime | Neighbor index |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
// η·Σ cos(2π(m-m')/10.6)
double eigenvalue(int m) const {
double decay = std::exp(-4.0 * m * HELIX_RADIUS *
std::sin(M_PI / 8.0) / params_.xi);
double cos_8 = std::cos(8.0 * M_PI * m / BASE_PAIRS_PER_TURN);
double main_term = params_.gamma_0 * decay * cos_8;
// Sum over neighbors |m' - m| ≤ 3
double neighbor_sum = 0.0;
for (int mp = std::max(0, m - 3); mp <= std::min(CROSS_HELIX_BONDS - 1, m + 3); ++mp) {
if (mp != m) {
neighbor_sum += std::cos(2.0 * M_PI * (m - mp) / BASE_PAIRS_PER_TURN);
}
}
return main_term + params_.eta * neighbor_sum;
}
Exact original notation
Sum over neighbors |m' - m| ≤ 3