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# 6.10 `gendimest` - Estimate generalized dimension spectrum

The Renyi dimension spectrum of a points set can be estimated using information about the distribution of the interpoint distances. Since we are interested in the scaling behaviour of the Renyi information for small distances, we don't need to compute all interpoint distances, the distances to `k` nearest neighbors for each reference point are sufficient [150].

Robust estimation is used instead of mean square error fitting.

Syntax:

- `[dimensions, moments] = gendimest(dists, gammas, kmin_low, kmin_high, kmax)`

Input arguments:

- `dists` - a matrix of size `R` by `k` which contains distances from reference points to their k nearest neighbors, sorted in increasing order. This matrix can be obtained by calling nn_search (cf. Section 6.14) or fnearneigh (cf. Section 6.9) on the point set whose dimension spectrum is to be investigated.
- `gammas` - vector of the moment orders
- `kmin_low` - first `kmin`, 1 `kmin_low`
- `kmin_high` - last `kmin`, `kmin_low` `kmin_high` `kmax`
- `kmax` - highest neigbor order up to which, `kmax` `k`

Output arguments:

- `dimensions` - matrix of size `length(gammas)` by `kmin_upper-kmin_lower+1`, holding the dimension estimates
- `moments` (optional) - matrix of size `k` by `length(gammas)`, storing the computed moments of the neigbor distances

Example:

    x = chaosys(25000, 0.025, [0.1 -0.1 0.02], 0);  % generate data from Lorenz system
    x = x(5001:end,:);      % discard first 5000 samples due to transient
    [nn, dist] = fnearneigh(x, randref(1, 20000, 1000), 128, 0);
    gammas = -5:0.5:5;
    gedims = gendimest(dist, gammas, 8, 8, 128);
    plot(1-gammas./gedims', gedims)
    xlabel('q');ylabel('D_q');title('Renyi dimension')

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