Research Article
Parallel kd-Tree Based Approach for Computing the Prediction Horizon Using Wolf’s Method
Algorithm 1
Wolf’s method by computing
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Program fet1(, , , ) | Input: | : data record of scalar quantities; | : embedding delay; | : minimal embedding dimension; | : fixed evolution time; | Output: | For each replacement step : (1) : maximal Lyapunov exponent estimation; (2) : evolving step; | (3) : initial separation between points; (4) : final separation between points. | (1) begin | / Initialization. / | (2) Set as the useful size of ; | (3) Set as the number of replacement steps; | (4) Build using (2) as the set of delay vectors; | (5) Compute as the standard deviation of ; | (6) Set scalmn = 0.0125σ as the noise scale; | (7) Set scalmx = 0.05σ as an estimation of the useful length scale; | (8) Set ; | / Computing maximal Lyapunox exponent. / | (9) Select as the fiducial point; | (10) Search such as ; | (11) for to do | (12) Set as the initial separation; | (13) Set as the final separation; | (14) Set ; | (15) Print ; | (16) repeat | (17) Search such as ; | (18) until was a minimum; | (19) if a replacement point was found then else ; | (20) Set ; | (21) end |
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