Module data_analysis

Filter data along one-dimension with an IIR or FIR filter.

Description

  Filter a data sequence, x, using a digital filter.  This works for many
  fundamental data types (including Object type).  The filter is a direct
  form II transposed implementation of the standard difference equation
  (see "Algorithm").

Inputs:

  b -- The numerator coefficient vector in a 1-D sequence.
  a -- The denominator coefficient vector in a 1-D sequence.  If a[0]
       is not 1, then both a and b are normalized by a[0].
  x -- An N-dimensional input array.
  axis -- The axis of the input data array along which to apply the
          linear filter. The filter is applied to each subarray along
          this axis (*Default* = -1)
  zi -- Initial conditions for the filter delays.  It is a vector
        (or array of vectors for an N-dimensional input) of length
        max(len(a),len(b)).  If zi=None or is not given then initial
        rest is assumed.  SEE signal.lfiltic for more information.

Outputs: (y, {zf})

  y -- The output of the digital filter.
  zf -- If zi is None, this is not returned, otherwise, zf holds the
        final filter delay values.

Algorithm:

  The filter function is implemented as a direct II transposed structure.
  This means that the filter implements

  a[0]*y[n] = b[0]*x[n] + b[1]*x[n-1] + ... + b[nb]*x[n-nb]
                        - a[1]*y[n-1] - ... - a[na]*y[n-na]

  using the following difference equations:

  y[m] = b[0]*x[m] + z[0,m-1]
  z[0,m] = b[1]*x[m] + z[1,m-1] - a[1]*y[m]
  ...
  z[n-3,m] = b[n-2]*x[m] + z[n-2,m-1] - a[n-2]*y[m]
  z[n-2,m] = b[n-1]*x[m] - a[n-1]*y[m]

  where m is the output sample number and n=max(len(a),len(b)) is the
  model order.

  The rational transfer function describing this filter in the
  z-transform domain is
                              -1               -nb
                  b[0] + b[1]z  + ... + b[nb] z
          Y(z) = ---------------------------------- X(z)
                              -1               -na
                  a[0] + a[1]z  + ... + a[na] z

  

Butterworth digital and analog filter design.

Description:

  Design an Nth order lowpass digital or analog Butterworth filter
  and return the filter coefficients in (B,A) or (Z,P,K) form.

See also buttord.

Log distances (L2-norm) of data points from a reference point (sampleix).

For multiple calls to this function on the same data, it's faster to pass logv precomputed.

return_ixs=True also returns the point indices from the sort to be returned in this argument in a third return value.

Log distances (L2-norm) of data points from a reference point (sampleix). Additionally, it returns a list of the inter-point distances, relative to the reference point, and the inverse of this mapping.

For multiple calls to this function on the same data, it's faster to pass logv precomputed.

return_ixs=True returns the point indices from the sort in a fifth return value. This identifies the points in the returned list of inter-point distances and its inverse.

Half-wave (default) or full-wave signal rectification: specify using optional full Boolean flag. xa must be an array

fitline takes the position of low and high fit limits and returns the slope. Integer indices in the x data set can be specified for the low and high limits, otherwise use a fraction between 0 and 1.

In application to fractal dimension estimation, if x = log d (radius, a.k.a. inter-point distance) and y = log v (index, a.k.a. estimate of volume at a given radius) then the slope is the dimension estimate of the data set.

Also see scipy.stat.linregress for a more sophisticated version

Find the index of a point closest to the 'centre' of a data set. The centre is defined to be where the mean of the points' position vectors relative to the centre is minimized in each direction.

Find recurrences of a trajectory in a ball of radius r centred at the
reference point given by refix in data.

If recurrence times are desired, pass an associated time array corresponding
to the points in the data.

If ignore_small > 0, recurrences of fewer than this number of data points
   will be treated as anomalous and ignored completely.

Returns a structure (class common.args) having attributes:
    partitions -- pairs of entry and exit indices for each recurrence in
            the ball
    ball_ixs -- all consecutive indices into data for each recurrence
    partitions_lengths -- number of indices in each partition
    rec_times -- times to next recurrence in the set from previous

Find approximate diameter of data set, up to tolerance defined by eps > 0.

Data assumed to be a rank-2 array.

Find one or more 'knees' in data, according to high second derivatives.

inlog option finds knees in the logs of the data entries. tol=1. works well if inlog=False tol=0.3 works well if inlog=True