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C++ API

Function File: output = c2t (d2_c1_out)

This program calculates the maximum likelihood estimator (the Takens’ estimator) from correlation sums of the output of d2 (the ’c2’ field of the d2 output) or c1 (the ’c1’ field of c1 output).

The estimator is calculated using the following equation (the integral is computed for the discrete values of C(r) by assuming an exact power law between the available points): 

            C(r)
D (r) = ------------
 T       /r    C(x)
         | dx ----
         /0     x

Input

The input needs to be the output of d2 or c1.

Output

The output is a struct array of the same length as the input. It contains the following fiels:

dim

The dimension for each matrix t.

t

Matrix with two columns. The first contains epsilon (the first column of field ’c2’ from d2 output or field ’c1’ from c1 output) and the second is the maximum likelihood estimator (Takens’ estimator).

See also: demo c2t, d2, c1, c2g, av_d2.

Algorithms

The algorithms for this functions have been taken from the TISEAN package.

Demonstration 1

The following code

 vals          = d2 (henon (1000), 'd', 1, 't', 50, 'm', 5);
 takens        = c2t (vals);
 do_plot_slope = @(x) semilogx (x{1}(:,1),x{1}(:,2),'r');
 hold on
 arrayfun (do_plot_slope, {takens.t});
 hold off
 axis tight
 ylim ([0 3]);
 xlabel ("Epsilon")
 title ("Takens' Estimator");

Produces the following figure

Figure 1

Package: tisean