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C++ API

Function File: output = endtoend (S)
Function File: output = endtoend (…, 'verbose', …)
Function File: output = endtoend (…, weigth_jump, …)

Determine the effect of an end-to-end mismatch on the autocorrelation structure for various sub-sequence lengths.

It is important to avoid jumps and phase slips that occur when the data is periodically continued when making Fourier based surrogates, e.g. with surrogates.

The mismatch in value is measured by: 

          /           \ 2
          |x(1)-x(N) |
          \           /
d     = __________________
 jump     __
         \   /      _ \ 2
          | |x(n)-x |
         /__ \        /

And the phase slip by: 

         /                           \ 2
         |(x(2)-x(1))-(x(N)-x(N-1)) |
         \                           /
d     = _________________________________
 slip        __
            \   /      _ \ 2
             | |x(n)-x |
            /__ \        /

The weighted mismatch is then: 

      weight*d     + (1-weight)*d
              jump               slip

In the multivariate case, the values are computed for each channel separately and then averaged.

Inputs

S

This function always assumes that each time series is along the longer dimension of matrix S. It also assumes that every dimension (counting along the shorter dimension) of S is considered a component of the time series.

weight_jump

The weight used [default = 0.5].

Switch

verbose

If this switch is set the output will be displayed on the screen in readible format.

Output

output

The output is a struct array that contains the following fields:

  • length - the length of the series used in calculating the mismatch
  • offset - the offset (counting from the first element) of the subseries used to calculate the mismatch
  • lost - percent of the of the original series that was lost (not used)
  • jump - the mismatch in value (given as percentage)
  • slip - the phase slip (given as percentage)
  • weigthed - the weigthed mismatch (given as percentage)

Each consecutive structure in this array has an increasingly lower weighted mismatch

See also: surrogates.

Algorithms

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

Package: tisean