def test_mutate(self):
"""Probs mutate should return correct vector from input vector"""
a = Alphabet('abc')**2
m = Probs([0.5, 0.25, 0.25, 0.1, 0.8, 0.1, 0.3, 0.6, 0.1], a)
#because of fp math in accumulate, can't predict boundaries exactly
#so add/subtract eps to get the result we expect
eps = 1e-6
# a b b a c c a b c
seq = array([0, 1, 1, 0, 2, 2, 0, 1, 2])
random_vec = array([0, .01, .8 - eps, 1, 1, .3, .05, .9 + eps, .95])
self.assertEqual(m.mutate(seq, random_vec), \
# a a b c c a a c c
array([0,0,1,2,2,0,0,2,2]))
#check that freq. distribution is about right
seqs = array([m.mutate(seq) for i in range(1000)])
#WARNING: bool operators return byte arrays, whose sums wrap at 256!
zero_count = asarray(seqs == 0, 'int32')
sums = sum(zero_count, axis=0)
#expect: 500, 100, 100, 500, 300, 300, 500, 100, 300
#std dev = sqrt(npq), which is sqrt(250), sqrt(90), sqrt(210)
means = array([500, 100, 100, 500, 300, 300, 500, 100, 300])
var = array([250, 90, 90, 250, 210, 210, 250, 90, 210])
three_sd = 3 * sqrt(var)
for obs, exp, sd in zip(sums, means, three_sd):
assert exp - 2 * sd < obs < exp + 2 * sd
def test_mutate(self):
"""Probs mutate should return correct vector from input vector"""
a = Alphabet('abc')**2
m = Probs([0.5,0.25,0.25,0.1,0.8,0.1,0.3,0.6,0.1], a)
#because of fp math in accumulate, can't predict boundaries exactly
#so add/subtract eps to get the result we expect
eps = 1e-6
# a b b a c c a b c
seq = array([0,1,1,0,2,2,0,1,2])
random_vec = array([0,.01,.8-eps,1,1,.3,.05,.9+eps,.95])
self.assertEqual(m.mutate(seq, random_vec), \
# a a b c c a a c c
array([0,0,1,2,2,0,0,2,2]))
#check that freq. distribution is about right
seqs = array([m.mutate(seq) for i in range(1000)])
#WARNING: bool operators return byte arrays, whose sums wrap at 256!
zero_count = asarray(seqs == 0, 'int32')
sums = sum(zero_count, axis=0)
#expect: 500, 100, 100, 500, 300, 300, 500, 100, 300
#std dev = sqrt(npq), which is sqrt(250), sqrt(90), sqrt(210)
means = array([500, 100, 100, 500, 300, 300, 500, 100, 300])
var = array([250, 90, 90, 250, 210, 210, 250, 90, 210])
three_sd = 3 * sqrt(var)
for obs, exp, sd in zip(sums, means, three_sd):
assert exp - 2*sd < obs < exp + 2*sd
def test_makeModel(self):
"""Probs makeModel should return correct substitution pattern"""
a = Alphabet('abc')**2
m = Probs([0.5,0.25,0.25,0.1,0.8,0.1,0.3,0.6,0.1], a)
obs = m.makeModel(array([0,1,1,0,2,2]))
exp = array([[0.5,0.25,0.25],[0.1,0.8,0.1],[0.1,0.8,0.1],\
[0.5,0.25,0.25],[0.3,0.6,0.1],[0.3,0.6,0.1]])
self.assertEqual(obs, exp)
def test_toCounts(self):
"""Probs toCounts should return counts object w/ right numbers"""
a = Alphabet('abc')**2
m = Probs([0.5,0.25,0.25,0.1,0.8,0.1,0.3,0.6,0.1], a)
obs = m.toCounts(30)
assert isinstance(obs, Counts)
exp = Counts([[5.,2.5,2.5,1,8,1,3,6,1]], a)
self.assertEqual(obs, exp)
def test_toCounts(self):
"""Probs toCounts should return counts object w/ right numbers"""
a = Alphabet('abc')**2
m = Probs([0.5, 0.25, 0.25, 0.1, 0.8, 0.1, 0.3, 0.6, 0.1], a)
obs = m.toCounts(30)
assert isinstance(obs, Counts)
exp = Counts([[5., 2.5, 2.5, 1, 8, 1, 3, 6, 1]], a)
self.assertEqual(obs, exp)
def test_makeModel(self):
"""Probs makeModel should return correct substitution pattern"""
a = Alphabet('abc')**2
m = Probs([0.5, 0.25, 0.25, 0.1, 0.8, 0.1, 0.3, 0.6, 0.1], a)
obs = m.makeModel(array([0, 1, 1, 0, 2, 2]))
exp = array([[0.5,0.25,0.25],[0.1,0.8,0.1],[0.1,0.8,0.1],\
[0.5,0.25,0.25],[0.3,0.6,0.1],[0.3,0.6,0.1]])
self.assertEqual(obs, exp)
def test_toRates(self):
"""Probs toRates should return log of probs, optionally normalized"""
a = Alphabet('abc')**2
p = Probs([0.9,0.05,0.05,0.1,0.85,0.05,0.02,0.02,0.96], a)
assert p.isValid()
r = p.toRates()
assert isinstance(r, Rates)
assert r.isValid()
assert not r.isComplex()
self.assertEqual(r._data, logm(p._data))
r_norm = p.toRates(normalize=True)
self.assertFloatEqual(trace(r_norm._data), -1.0)
def test_toRates(self):
"""Probs toRates should return log of probs, optionally normalized"""
a = Alphabet('abc')**2
p = Probs([0.9, 0.05, 0.05, 0.1, 0.85, 0.05, 0.02, 0.02, 0.96], a)
assert p.isValid()
r = p.toRates()
assert isinstance(r, Rates)
assert r.isValid()
assert not r.isComplex()
self.assertEqual(r._data, logm(p._data))
r_norm = p.toRates(normalize=True)
self.assertFloatEqual(trace(r_norm._data), -1.0)
def test_timeForSimilarity(self):
"""Rates timeToSimilarity should return correct time"""
a = self.abc_pairs
p = Probs([0.75, 0.1, 0.15, 0.2, 0.7, 0.1, 0.05, 0.15, 0.8], a)
q = p.toRates()
d = 0.5
t = q.timeForSimilarity(d)
x = expm(q._data)(t)
self.assertFloatEqual(average(diagonal(x), axis=0), d)
t = q.timeForSimilarity(d, array([1 / 3.0] * 3))
x = expm(q._data)(t)
self.assertFloatEqual(average(diagonal(x), axis=0), d)
self.assertEqual(q.timeForSimilarity(1), 0)
def test_timeForSimilarity(self):
"""Rates timeToSimilarity should return correct time"""
a = self.abc_pairs
p = Probs([0.75, 0.1, 0.15, 0.2, 0.7, 0.1, 0.05, 0.15, 0.8], a)
q = p.toRates()
d = 0.5
t = q.timeForSimilarity(d)
x = expm(q._data)(t)
self.assertFloatEqual(average(diagonal(x), axis=0), d)
t = q.timeForSimilarity(d, array([1/3.0]*3))
x = expm(q._data)(t)
self.assertFloatEqual(average(diagonal(x), axis=0), d)
self.assertEqual(q.timeForSimilarity(1), 0)
def test_isValid(self):
"""Probs isValid should return True if it's a prob matrix"""
a = self.ab_pairs
m = Probs([0.5, 0.5, 1, 0], a)
self.assertEqual(m.isValid(), True)
#fails if don't sum to 1
m = Probs([0.5, 0, 1, 0], a)
self.assertEqual(m.isValid(), False)
#fails if negative elements
m = Probs([1, -1, 0, 1], a)
self.assertEqual(m.isValid(), False)
def test_toSimilarProbs(self):
"""Rates toSimilarProbs should match individual steps"""
a = self.abc_pairs
p = Probs([0.75, 0.1, 0.15, 0.2, 0.7, 0.1, 0.05, 0.15, 0.8], a)
q = p.toRates()
self.assertEqual(q.toSimilarProbs(0.5), \
q.toProbs(q.timeForSimilarity(0.5)))
#test a case that didn't work for DNA
q = Rates(array(
[[-0.64098451, 0.0217681 , 0.35576469, 0.26345171],
[ 0.31144238, -0.90915091, 0.25825858, 0.33944995],
[ 0.01578521, 0.43162879, -0.99257581, 0.54516182],
[ 0.13229986, 0.04027147, 0.05817791, -0.23074925]]),
DnaPairs)
p = q.toSimilarProbs(0.66)
self.assertFloatEqual(average(diagonal(p._data), axis=0), 0.66)
def test_toProbs(self):
"""Rates toProbs should return correct probability matrix"""
a = self.abc_pairs
p = Probs([0.75, 0.1, 0.15, 0.2, 0.7, 0.1, 0.05, 0.1, 0.85], a)
q = p.toRates()
self.assertEqual(q._data, logm(p._data))
p2 = q.toProbs()
self.assertFloatEqual(p2._data, p._data)
#test a case that didn't work for DNA
q = Rates(
array([[-0.64098451, 0.0217681, 0.35576469, 0.26345171],
[0.31144238, -0.90915091, 0.25825858, 0.33944995],
[0.01578521, 0.43162879, -0.99257581, 0.54516182],
[0.13229986, 0.04027147, 0.05817791, -0.23074925]]),
DnaPairs)
self.assertFloatEqual(q.toProbs(0.5)._data, expm(q._data)(t=0.5))
def test_random_p_matrix_diag_vector(self):
"""Probs random should work with a vector diagonal"""
for i in range(NUM_TESTS):
diag = [0, 0.2, 0.6, 1.0]
p = Probs.random(RnaPairs, diag)._data
for i, d, row in zip(range(4), diag, p):
self.assertFloatEqual(sum(row), 1.0)
self.assertEqual(row[i], diag[i])
def test_toSimilarProbs(self):
"""Rates toSimilarProbs should match individual steps"""
a = self.abc_pairs
p = Probs([0.75, 0.1, 0.15, 0.2, 0.7, 0.1, 0.05, 0.15, 0.8], a)
q = p.toRates()
self.assertEqual(q.toSimilarProbs(0.5), \
q.toProbs(q.timeForSimilarity(0.5)))
#test a case that didn't work for DNA
q = Rates(
array([[-0.64098451, 0.0217681, 0.35576469, 0.26345171],
[0.31144238, -0.90915091, 0.25825858, 0.33944995],
[0.01578521, 0.43162879, -0.99257581, 0.54516182],
[0.13229986, 0.04027147, 0.05817791, -0.23074925]]),
DnaPairs)
p = q.toSimilarProbs(0.66)
self.assertFloatEqual(average(diagonal(p._data), axis=0), 0.66)
def test_toProbs(self):
"""Rates toProbs should return correct probability matrix"""
a = self.abc_pairs
p = Probs([0.75, 0.1, 0.15, 0.2, 0.7, 0.1, 0.05, 0.1, 0.85], a)
q = p.toRates()
self.assertEqual(q._data, logm(p._data))
p2 = q.toProbs()
self.assertFloatEqual(p2._data, p._data)
#test a case that didn't work for DNA
q = Rates(array(
[[-0.64098451, 0.0217681 , 0.35576469, 0.26345171],
[ 0.31144238, -0.90915091, 0.25825858, 0.33944995],
[ 0.01578521, 0.43162879, -0.99257581, 0.54516182],
[ 0.13229986, 0.04027147, 0.05817791, -0.23074925]]),
DnaPairs)
self.assertFloatEqual(q.toProbs(0.5)._data, expm(q._data)(t=0.5))
def test_random_p_matrix_diag_vector(self):
"""Probs random should work with a vector diagonal"""
for i in range(NUM_TESTS):
diag = [0, 0.2, 0.6, 1.0]
p = Probs.random(RnaPairs, diag)._data
for i, d, row in zip(range(4), diag, p):
self.assertFloatEqual(sum(row), 1.0)
self.assertEqual(row[i], diag[i])
def test_random_p_matrix(self):
"""Probs random should return random Probsrows that sum to 1"""
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs)._data
for i in p:
self.assertFloatEqual(sum(i), 1.0)
#length should be 4 by default
self.assertEqual(len(p), 4)
self.assertEqual(len(p[0]), 4)
def test_random_p_matrix(self):
"""Probs random should return random Probsrows that sum to 1"""
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs)._data
for i in p:
self.assertFloatEqual(sum(i), 1.0)
#length should be 4 by default
self.assertEqual(len(p), 4)
self.assertEqual(len(p[0]), 4)
def test_toProbs(self):
"""Counts toProbs should return valid prob matrix."""
c = Counts([1, 2, 3, 4, 2, 2, 2, 2, 0.2, 0.4, 0.6, 0.8, 1, 0, 0, 0],
RnaPairs)
p = c.toProbs()
assert isinstance(p, Probs)
self.assertEqual(p, Probs([0.1,0.2,0.3,0.4,0.25,0.25,0.25,0.25, \
0.1,0.2,0.3,0.4,1.0,0.0,0.0,0.0], RnaPairs))
self.assertEqual(p['U', 'U'], 0.1)
self.assertEqual(p['G', 'U'], 1.0)
self.assertEqual(p['G', 'G'], 0.0)
def test_random_p_matrix_diag(self):
"""Probs random should work with a scalar diagonal"""
#if diagonal is 1, off-diagonal elements should be 0
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs, 1)._data
self.assertEqual(p, identity(4, 'd'))
#if diagonal is between 0 and 1, rows should sum to 1
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs, 0.5)._data
for i in range(4):
self.assertFloatEqual(sum(p[i]), 1.0)
self.assertEqual(p[i][i], 0.5)
assert min(p[i]) >= 0
assert max(p[i]) <= 1
#if diagonal > 1, rows should still sum to 1
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs, 2)._data
for i in range(4):
self.assertEqual(p[i][i], 2.0)
self.assertFloatEqual(sum(p[i]), 1.0)
assert min(p[i]) < 0
def test_random_p_matrix_diag(self):
"""Probs random should work with a scalar diagonal"""
#if diagonal is 1, off-diagonal elements should be 0
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs, 1)._data
self.assertEqual(p, identity(4, 'd'))
#if diagonal is between 0 and 1, rows should sum to 1
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs, 0.5)._data
for i in range(4):
self.assertFloatEqual(sum(p[i]), 1.0)
self.assertEqual(p[i][i], 0.5)
assert min(p[i]) >= 0
assert max(p[i]) <= 1
#if diagonal > 1, rows should still sum to 1
for i in range(NUM_TESTS):
p = Probs.random(RnaPairs, 2)._data
for i in range(4):
self.assertEqual(p[i][i], 2.0)
self.assertFloatEqual(sum(p[i]), 1.0)
assert min(p[i]) < 0
def test_isValid(self):
"""Probs isValid should return True if it's a prob matrix"""
a = self.ab_pairs
m = Probs([0.5,0.5,1,0], a)
self.assertEqual(m.isValid(), True)
#fails if don't sum to 1
m = Probs([0.5, 0, 1, 0], a)
self.assertEqual(m.isValid(), False)
#fails if negative elements
m = Probs([1, -1, 0, 1], a)
self.assertEqual(m.isValid(), False)
def test_probs_to_rates(self):
"""probs_to_rates converts probs to rates, omitting problem cases"""
probs = dict([(i, Probs.random(DnaPairs)) for i in range(100)])
rates = probs_to_rates(probs)
#check we got at most the same number of items as in probs
assert len(rates) <= len(probs)
#check that we didn't get anything bad
vals = rates.values()
for v in vals:
assert not v.isSignificantlyComplex()
#check that we didn't miss anything good
for key, val in probs.items():
if key not in rates:
try:
r = val.toRates()
print r.isValid()
assert r.isSignificantlyComplex() or (not r.isValid())
except (ZeroDivisionError, OverflowError, ValueError):
pass