Hidden Markov Models – Utility functions#

AUTHOR:

  • William Stein, 2010-03

class sage.stats.hmm.util.HMM_Util[source]#

Bases: object

A class used in order to share cdef’s methods between different files.

initial_probs_to_TimeSeries(pi, normalize)[source]#

This function is used internally by the __init__ methods of various Hidden Markov Models.

INPUT:

  • pi – vector, list, or TimeSeries

  • normalize – if True, replace negative entries by 0 and rescale to ensure that the sum of the entries in each row is equal to 1. If the sum of the entries in a row is 0, replace them all by \(1/N\).

OUTPUT:

  • a TimeSeries of length \(N\)

EXAMPLES:

sage: import sage.stats.hmm.util
sage: u = sage.stats.hmm.util.HMM_Util()
sage: u.initial_probs_to_TimeSeries([0.1,0.2,0.9], True)
[0.0833, 0.1667, 0.7500]
sage: u.initial_probs_to_TimeSeries([0.1,0.2,0.9], False)
[0.1000, 0.2000, 0.9000]

>>> from sage.all import *
>>> import sage.stats.hmm.util
>>> u = sage.stats.hmm.util.HMM_Util()
>>> u.initial_probs_to_TimeSeries([RealNumber('0.1'),RealNumber('0.2'),RealNumber('0.9')], True)
[0.0833, 0.1667, 0.7500]
>>> u.initial_probs_to_TimeSeries([RealNumber('0.1'),RealNumber('0.2'),RealNumber('0.9')], False)
[0.1000, 0.2000, 0.9000]
normalize_probability_TimeSeries(T, i, j)[source]#

This function is used internally by the Hidden Markov Models code.

Replace entries of T[i:j] in place so that they are all nonnegative and sum to 1. Negative entries are replaced by 0 and T[i:j] is then rescaled to ensure that the sum of the entries in each row is equal to 1. If all entries are 0, replace them by 1/(j-i).

INPUT:

  • T – a TimeSeries

  • i – nonnegative integer

  • j – nonnegative integer

OUTPUT:

  • T is modified

EXAMPLES:

sage: import sage.stats.hmm.util
sage: T = stats.TimeSeries([.1, .3, .7, .5])
sage: u = sage.stats.hmm.util.HMM_Util()
sage: u.normalize_probability_TimeSeries(T,0,3)
sage: T
[0.0909, 0.2727, 0.6364, 0.5000]
sage: u.normalize_probability_TimeSeries(T,0,4)
sage: T
[0.0606, 0.1818, 0.4242, 0.3333]
sage: abs(T.sum()-1) < 1e-8    # might not exactly equal 1 due to rounding
True

>>> from sage.all import *
>>> import sage.stats.hmm.util
>>> T = stats.TimeSeries([RealNumber('.1'), RealNumber('.3'), RealNumber('.7'), RealNumber('.5')])
>>> u = sage.stats.hmm.util.HMM_Util()
>>> u.normalize_probability_TimeSeries(T,Integer(0),Integer(3))
>>> T
[0.0909, 0.2727, 0.6364, 0.5000]
>>> u.normalize_probability_TimeSeries(T,Integer(0),Integer(4))
>>> T
[0.0606, 0.1818, 0.4242, 0.3333]
>>> abs(T.sum()-Integer(1)) < RealNumber('1e-8')    # might not exactly equal 1 due to rounding
True
state_matrix_to_TimeSeries(A, N, normalize)[source]#

This function is used internally by the __init__ methods of Hidden Markov Models to make a transition matrix from A.

INPUT:

  • A – matrix, list, list of lists, or TimeSeries

  • N – number of states

  • normalize – if True, replace negative entries by 0 and rescale to ensure that the sum of the entries in each row is equal to 1. If the sum of the entries in a row is 0, replace them all by \(1/N\).

OUTPUT:

  • a TimeSeries

EXAMPLES:

sage: import sage.stats.hmm.util
sage: u = sage.stats.hmm.util.HMM_Util()
sage: u.state_matrix_to_TimeSeries([[.1,.7],[3/7,4/7]], 2, True)
[0.1250, 0.8750, 0.4286, 0.5714]
sage: u.state_matrix_to_TimeSeries([[.1,.7],[3/7,4/7]], 2, False)
[0.1000, 0.7000, 0.4286, 0.5714]

>>> from sage.all import *
>>> import sage.stats.hmm.util
>>> u = sage.stats.hmm.util.HMM_Util()
>>> u.state_matrix_to_TimeSeries([[RealNumber('.1'),RealNumber('.7')],[Integer(3)/Integer(7),Integer(4)/Integer(7)]], Integer(2), True)
[0.1250, 0.8750, 0.4286, 0.5714]
>>> u.state_matrix_to_TimeSeries([[RealNumber('.1'),RealNumber('.7')],[Integer(3)/Integer(7),Integer(4)/Integer(7)]], Integer(2), False)
[0.1000, 0.7000, 0.4286, 0.5714]