Persistence
============


The following example computes the minimum and maximum birth times, as well as the maximum persistence::

  from ripser import ripser
  from teaspoon.TDA.Draw import drawDgm
  from teaspoon.MakeData.PointCloud import Torus
  from teaspoon.TDA.Persistence import maxBirth, minBirth, maxPers

  numPts = 500
  seed = 0

  # Generate Torus
  t = Torus(N=numPts,seed = seed)

  # Compute persistence diagrams
  PD1 = ripser(t,2)['dgms'][1]

  print('Maximum Birth: ', maxBirth(PD1))
  print('Minimum Birth: ', minBirth(PD1))
  print('Max Persistence: ', maxPers(PD1))

The output of this code is::

  Maximum Birth:  1.0100464820861816
  Minimum Birth:  0.17203105986118317
  Max Persistence:  1.3953008949756622


The following example computes the minimum and maximum birth times and the
maximum persistence across all persistence diagrams in the specified column of
the DataFrame::

  from teaspoon.MakeData.PointCloud import testSetManifolds
  from teaspoon.TDA.Persistence import maxBirthSeries, minBirthSeries, maxPersistenceSeries

  df = testSetManifolds(numDgms = 1, numPts = 500, seed=0)

  print('Maximum Birth of all diagrams: ', maxBirthSeries(df['Dgm1']))
  print('Minimum Birth of all diagrams: ', minBirthSeries(df['Dgm1']))
  print('Max Persistence of all diagrams: ', maxPersistenceSeries(df['Dgm1']))

The output of this code is::

  Maximum Birth of all diagrams:  1.2070081233978271
  Minimum Birth of all diagrams:  0.028233738616108894
  Max Persistence of all diagrams:  1.6290252953767776

The following example computes the Betti Curve for a persistence diagram::

  from teaspoon.MakeData.PointCloud import Torus
  from teaspoon.TDA.Persistence import BettiCurve
  from ripser import ripser

  T = Torus(N=300, r=1, R=2, seed=48823)
  Dgm = ripser(T,2)['dgms'][1]
  t, x = BettiCurve(Dgm,3,5)
  print('Betti Curve:', x)
  

The output of this code is::

  Betti Curve: [ 0. 36.  2.  0.  0.]


The following example computes the CROCKER plot for a set of persistence diagrams::

  from teaspoon.MakeData.PointCloud import Torus
  from teaspoon.TDA.Persistence import CROCKER
  from ripser import ripser

  DGMS = []
  for i in range(0, 5):

      T = Torus(N=300, r=i+1, R=i+2, seed=48823)
      Dgm = ripser(T,2)['dgms'][0]
      
      DGMS.append(Dgm)

  Crocker = CROCKER(DGMS, 3, 5, plotting=False)

Functions
---------

.. automodule:: teaspoon.TDA.Persistence
   :members: minPers, maxPers, maxBirth, minBirth, minPersistenceSeries, maxPersistenceSeries, minBirthSeries, maxBirthSeries, removeInfiniteClasses, BettiCurve, CROCKER, CROCKER_Stack