```#!/usr/bin/env python
"""Test out HMMs using the Occasionally Dishonest Casino.

This uses the ocassionally dishonest casino example from Biological
Sequence Analysis by Durbin et al.

In this example, we are dealing with a casino that has two types of
dice, a fair dice that has 1/6 probability of rolling any number and
a loaded dice that has 1/2 probability to roll a 6, and 1/10 probability
to roll any other number. The probability of switching from the fair to
loaded dice is .05 and the probability of switching from loaded to fair is
.1.
"""

from __future__ import print_function

import os
if os.name == 'java':
from Bio import MissingExternalDependencyError
#This is a slight miss-use of MissingExternalDependencyError,
#but it will do in the short term to skip this unit test on Jython
raise MissingExternalDependencyError("This test can cause a fatal error "
"on Jython with some versions of Java")

# standard modules
import random

# biopython
from Bio import Alphabet
from Bio.Seq import MutableSeq
from Bio.Seq import Seq

# HMM stuff we are testing
from Bio.HMM import MarkovModel
from Bio.HMM import Trainer
from Bio.HMM import Utilities

# whether we should print everything out. Set this to zero for
# regression testing
VERBOSE = 0

# -- set up our alphabets
class DiceRollAlphabet(Alphabet.Alphabet):
letters = ['1', '2', '3', '4', '5', '6']

class DiceTypeAlphabet(Alphabet.Alphabet):
letters = ['F', 'L']

# -- useful functions
"""Generate a loaded dice roll based on the state and a random number
"""
if cur_state == 'F':
if chance_num <= (float(1) / float(6)):
return '1'
elif chance_num <= (float(2) / float(6)):
return '2'
elif chance_num <= (float(3) / float(6)):
return '3'
elif chance_num <= (float(4) / float(6)):
return '4'
elif chance_num <= (float(5) / float(6)):
return '5'
else:
return '6'
elif cur_state == 'L':
if chance_num <= (float(1) / float(10)):
return '1'
elif chance_num <= (float(2) / float(10)):
return '2'
elif chance_num <= (float(3) / float(10)):
return '3'
elif chance_num <= (float(4) / float(10)):
return '4'
elif chance_num <= (float(5) / float(10)):
return '5'
else:
return '6'
else:
raise ValueError("Unexpected cur_state %s" % cur_state)

def generate_rolls(num_rolls):
"""Generate a bunch of rolls corresponding to the casino probabilities.

Returns:

o The generate roll sequence

o The state sequence that generated the roll.
"""
# start off in the fair state
cur_state = 'F'
roll_seq = MutableSeq('', DiceRollAlphabet())
state_seq = MutableSeq('', DiceTypeAlphabet())

# generate the sequence
for roll in range(num_rolls):
state_seq.append(cur_state)
# generate a random number
chance_num = random.random()

# add on a new roll to the sequence
roll_seq.append(new_roll)

# now give us a chance to switch to a new state
chance_num = random.random()
if cur_state == 'F':
if chance_num <= .05:
cur_state = 'L'
elif cur_state == 'L':
if chance_num <= .1:
cur_state = 'F'

return roll_seq.toseq(), state_seq.toseq()

# -- build a MarkovModel
mm_builder = MarkovModel.MarkovModelBuilder(DiceTypeAlphabet(),
DiceRollAlphabet())

mm_builder.allow_all_transitions()
mm_builder.set_random_probabilities()
"""
mm_builder.set_transition_score('F', 'L', .05)
mm_builder.set_transition_score('F', 'F', .95)
mm_builder.set_transition_score('L', 'F', .10)
mm_builder.set_transition_score('L', 'L', .9)
mm_builder.set_emission_score('F', '1', .17)
mm_builder.set_emission_score('F', '2', .17)
mm_builder.set_emission_score('F', '3', .17)
mm_builder.set_emission_score('F', '4', .17)
mm_builder.set_emission_score('F', '5', .17)
mm_builder.set_emission_score('F', '6', .17)
mm_builder.set_emission_score('L', '1', .1)
mm_builder.set_emission_score('L', '2', .1)
mm_builder.set_emission_score('L', '3', .1)
mm_builder.set_emission_score('L', '4', .1)
mm_builder.set_emission_score('L', '5', .1)
mm_builder.set_emission_score('L', '6', .5)
"""

# just get two different Markov Models -- we'll train one using
# Baum Welch, and one using the Standard trainer
baum_welch_mm = mm_builder.get_markov_model()
standard_mm = mm_builder.get_markov_model()

# get a sequence of rolls to train the markov model with
rolls, states = generate_rolls(3000)

# predicted_states, prob = my_mm.viterbi(rolls, DiceTypeAlphabet())
# print("prob: %f" % prob)
# Utilities.pretty_print_prediction(rolls, states, predicted_states)

# -- now train the model
def stop_training(log_likelihood_change, num_iterations):
"""Tell the training model when to stop.
"""
if VERBOSE:
print("ll change: %f" % log_likelihood_change)
if log_likelihood_change < 0.01:
return 1
elif num_iterations >= 10:
return 1
else:
return 0

# -- Standard Training with known states
print("Training with the Standard Trainer...")
known_training_seq = Trainer.TrainingSequence(rolls, states)

trainer = Trainer.KnownStateTrainer(standard_mm)
trained_mm = trainer.train([known_training_seq])

if VERBOSE:
print(trained_mm.transition_prob)
print(trained_mm.emission_prob)

test_rolls, test_states = generate_rolls(300)

predicted_states, prob = trained_mm.viterbi(test_rolls, DiceTypeAlphabet())
if VERBOSE:
print("Prediction probability: %f" % prob)
Utilities.pretty_print_prediction(test_rolls, test_states, predicted_states)

# -- Baum-Welch training without known state sequences
print("Training with Baum-Welch...")
training_seq = Trainer.TrainingSequence(rolls, Seq("", DiceTypeAlphabet()))

trainer = Trainer.BaumWelchTrainer(baum_welch_mm)
trained_mm = trainer.train([training_seq], stop_training)

if VERBOSE:
print(trained_mm.transition_prob)
print(trained_mm.emission_prob)

test_rolls, test_states = generate_rolls(300)

predicted_states, prob = trained_mm.viterbi(test_rolls, DiceTypeAlphabet())
if VERBOSE:
print("Prediction probability: %f" % prob)
Utilities.pretty_print_prediction(test_rolls, test_states, predicted_states)

```