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Each diagonal value is a cosine evaluated at a coordinate index divided by 10.6. The body uses indices i+1 from one through sixteen. Because those values vary by position, this diagonal matrix generally does not share eigenvectors with the cyclic neighbor matrix.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| k | Coordinate index in the diagonal |
| D_16 | Sixteen-entry diagonal matrix |
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Original context
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public:
explicit IntraStrandBlock(const CouplingParams& p = {}) : params_(p) {
build_matrix();
}
// Matrix form (Section 11.1):
// M_intra = -2α·I₁₆ + α·T₁₆ + κ_intra·D₁₆(10.6)
// where D₁₆(10.6) = diag[cos(2π·k/10.6)]
void build_matrix() {
// Initialize to zero
for (auto& row : M_) row.fill(0.0);
for (int i = 0; i < NUM_STRANDS; ++i) {
// Diagonal: -2α + κ_intra·cos(2π(i+1)/10.6)
double cos_term = std::cos(2.0 * M_PI * (i + 1) / BASE_PAIRS_PER_TURN);
M_[i][i] = -2.0 * params_.alpha + params_.kappa_intra * cos_term;
// Off-diagonal tridiagonal (ring): αExact original notation
where D₁₆(10.6) = diag[cos(2π·k/10.6)]