def get_required_coverage(self, M=0.01):
"""Return the required coverage to ensure the genome is covered
A general question is what should be the coverage to make sure
that e.g. E=99% of the genome is covered by at least a read.
The answer is:
.. math:: \log^{-1/(E-1)}
This equation is correct but have a limitation due to floating precision.
If one provides E=0.99, the answer is 4.6 but we are limited to a
maximum coverage of about 36 when one provides E=0.9999999999999999
after which E is rounded to 1 on most computers. Besides, it is no
convenient to enter all those numbers. A scientific notation would be better but
requires to work with :math:`M=1-E` instead of :math:`E`.
.. math:: \log^{-1/ - M}
So instead of asking the question what is the
requested fold coverage to have 99% of the genome covered, we ask the question what
is the requested fold coverage to have 1% of the genome not covered.
This allows us to use :math:`M` values as low as 1e-300 that is a fold coverage
as high as 690.
:param float M: this is the fraction of the genome not covered by
any reads (e.g. 0.01 for 1%). See note above.
:return: the required fold coverage
.. plot::
import pylab
from sequana import Coverage
cover = Coverage()
misses = np.array([1e-1, 1e-2, 1e-3, 1e-4,1e-5,1e-6])
required_coverage = cover.get_required_coverage(misses)
pylab.semilogx(misses, required_coverage, 'o-')
pylab.ylabel("Required coverage", fontsize=16)
pylab.xlabel("Uncovered genome", fontsize=16)
pylab.grid()
# The inverse equation is required fold coverage = [log(-1/(E - 1))]
"""
# What should be the fold coverage to have 99% of the genome sequenced ?
# It is the same question as equating 1-e^{-(NL/G}) == 0.99, we need NL/G = 4.6
if isinstance(M, float) or isinstance(M, int):
assert M < 1
assert M >= 0
else:
M = np.array(M)
# Here we do not use log(-1/(E-1)) but log(-1/(1-E-1)) to allow
# for using float down to 1e-300 since 0.999999999999999 == 1
return np.log(-1 / (-M))
# source
# http://nbviewer.ipython.org/github/tritemio/notebooks/blob/master/Mixture_Model_Fitting.ipynb
from easydev import DevTools, AttrDict
devtools = DevTools()
from sequana.lazy import numpy as np
from sequana.lazy import pylab
from . import criteria
import numpy as np
half_log_two_pi = 0.5 * np.log(2 * np.pi)
__all__ = ["Fitting", "GaussianMixtureModel", "GaussianMixtureFitting", "EM"]
class GaussianMixtureModel(object):
"""Gaussian Mixture Model
.. plot::
from sequana import mixture
from pylab import plot, linspace
m = mixture.GaussianMixtureModel(k=2)
X = linspace(0,10,100)
plot(X, [m.pdf(x, params=[1, 0.5, 0.2, 4, 0.5, 0.8]) for x in X])
"""
def __init__(self, k=2):