# Hidden Markov Models – Utility functions¶

AUTHOR:

• William Stein, 2010-03
class sage.stats.hmm.util.HMM_Util

Bases: object

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

initial_probs_to_TimeSeries(pi, normalize)

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]

normalize_probability_TimeSeries(T, i, j)

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

state_matrix_to_TimeSeries(A, N, normalize)

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]


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