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Merge branch 'develop' of ariadne.geophysik.ruhr-uni-bochum.de:/data/git/pylot into develop

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Marcel Paffrath 2016-07-12 14:09:50 +02:00
commit 546dfad722
2 changed files with 120 additions and 59 deletions
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170
pylot/core/util/pdf.py
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@ -3,6 +3,7 @@
import warnings
import numpy as np
import scipy.optimize
from obspy import UTCDateTime
from pylot.core.util.utils import find_nearest, clims
from pylot.core.util.version import get_git_version as _getVersionString
@ -34,7 +35,7 @@ def gauss_parameter(te, tm, tl, eta):
a1 = 2 / (1 + sig2 / sig1)
a2 = 2 / (1 + sig1 / sig2)
return sig1, sig2, a1, a2
return tm, sig1, sig2, a1, a2
def exp_parameter(te, tm, tl, eta):
@ -53,10 +54,10 @@ def exp_parameter(te, tm, tl, eta):
sig2 = np.log(eta) / (tm - tl)
a = 1 / (1 / sig1 + 1 / sig2)
return sig1, sig2, a
return tm, sig1, sig2, a
def gauss_branches(x, mu, sig1, sig2, a1, a2):
def gauss_branches(k, mu, sig1, sig2, a1, a2):
'''
function gauss_branches takes an axes x, a center value mu, two sigma
values sig1 and sig2 and two scaling factors a1 and a2 and return a
@ -75,16 +76,22 @@ def gauss_branches(x, mu, sig1, sig2, a1, a2):
:param a2:
:returns fun_vals: list with function values along axes x
'''
fun_vals = []
for k in x:
def _func(k, mu, sig1, sig2, a1, a2):
if k < mu:
fun_vals.append(a1 * 1 / (np.sqrt(2 * np.pi) * sig1) * np.exp(-((k - mu) / sig1) ** 2 / 2))
rval = a1 * 1 / (np.sqrt(2 * np.pi) * sig1) * np.exp(-((k - mu) / sig1) ** 2 / 2)
else:
fun_vals.append(a2 * 1 / (np.sqrt(2 * np.pi) * sig2) * np.exp(-((k - mu) / sig2) ** 2 / 2))
return np.array(fun_vals)
rval = a2 * 1 / (np.sqrt(2 * np.pi) * sig2) * np.exp(-((k - mu) /
sig2) ** 2 / 2)
return rval
try:
return [_func(x, mu, sig1, sig2, a1, a2) for x in iter(k)]
except TypeError:
return _func(k, mu, sig1, sig2, a1, a2)
def exp_branches(x, mu, sig1, sig2, a):
def exp_branches(k, mu, sig1, sig2, a):
'''
function exp_branches takes an axes x, a center value mu, two sigma
values sig1 and sig2 and a scaling factor a and return a
@ -97,13 +104,19 @@ def exp_branches(x, mu, sig1, sig2, a):
:param a:
:returns fun_vals: list with function values along axes x:
'''
fun_vals = []
for k in x:
def _func(k, mu, sig1, sig2, a):
if k < mu:
fun_vals.append(a * np.exp(sig1 * (k - mu)))
rval = a * np.exp(sig1 * (k - mu))
else:
fun_vals.append(a * np.exp(-sig2 * (k - mu)))
return np.array(fun_vals)
rval = a * np.exp(-sig2 * (k - mu))
return rval
try:
return [_func(x, mu, sig1, sig2, a) for x in iter(k)]
except TypeError:
return _func(k, mu, sig1, sig2, a)
# define container dictionaries for different types of pdfs
parameter = dict(gauss=gauss_parameter, exp=exp_parameter)
@ -117,62 +130,89 @@ class ProbabilityDensityFunction(object):
version = __version__
def __init__(self, x0, incr, npts, pdf):
def __init__(self, x0, incr, npts, pdf, mu, params):
self.x0 = x0
self.incr = incr
self.npts = npts
self.axis = create_axis(x0, incr, npts)
self.data = pdf
self.mu = mu
self._pdf = pdf
self.params = params
def __add__(self, other):
assert isinstance(other, ProbabilityDensityFunction), \
'both operands must be of type ProbabilityDensityFunction'
x0, incr, npts, pdf_self, pdf_other = self.rearrange(other)
x0, incr, npts = self.commonparameter(other)
axis = create_axis(x0, incr, npts)
pdf_self = np.array([self.data(x) for x in axis])
pdf_other = np.array([other.data(x) for x in axis])
pdf = np.convolve(pdf_self, pdf_other, 'full') * incr
# shift axis values for correct plotting
npts = pdf.size
x0 *= 2
return ProbabilityDensityFunction(x0, incr, npts, pdf)
axis = create_axis(x0, incr, npts)
params, pcov = scipy.optimize.curve_fit(branches['gauss'], axis, pdf)
mu = axis[np.where(pdf == max(pdf))]
return ProbabilityDensityFunction(x0, incr, npts, branches['gauss'], mu,
params)
def __sub__(self, other):
assert isinstance(other, ProbabilityDensityFunction), \
'both operands must be of type ProbabilityDensityFunction'
x0, incr, npts, pdf_self, pdf_other = self.rearrange(other)
x0, incr, npts = self.commonparameter(other)
axis = create_axis(x0, incr, npts)
pdf_self = np.array([self.data(x) for x in axis])
pdf_other = np.array([other.data(x) for x in axis])
pdf = np.correlate(pdf_self, pdf_other, 'full') * incr
npts = len(pdf)
# shift axis values for correct plotting
npts = len(pdf)
midpoint = npts / 2
x0 = -incr * midpoint
axis = create_axis(x0, incr, npts)
return ProbabilityDensityFunction(x0, incr, npts, pdf)
mu = axis[np.where(pdf == max(pdf))][0]
bounds = ([mu, 0., 0., 0., 0.],[mu, np.inf, np.inf, np.inf, np.inf])
params, pcov = scipy.optimize.curve_fit(branches['gauss'], axis, pdf,
bounds=bounds)
return ProbabilityDensityFunction(x0, incr, npts, branches['gauss'], mu,
params)
def __nonzero__(self):
prec = self.precision(self.incr)
gtzero = np.all(self.data >= 0)
data = np.array([self.data(t) for t in self.axis])
gtzero = np.all(data >= 0)
probone = bool(np.round(self.prob_gt_val(self.axis[0]), prec) == 1.)
return bool(gtzero and probone)
def __str__(self):
return str(self.data)
return str([self.data(val) for val in create_axis(self.x0, self.incr,
self.npts)])
@staticmethod
def precision(incr):
prec = int(np.ceil(np.abs(np.log10(incr)))) - 2
return prec if prec >= 0 else 0
@property
def data(self):
return self._pdf
def data(self, value):
return self._pdf(value, *self.params)
@data.setter
def data(self, pdf):
self._pdf = np.array(pdf)
@property
def mu(self):
return self._mu
@mu.setter
def mu(self, mu):
self._mu = mu
@property
def axis(self):
@ -226,17 +266,12 @@ class ProbabilityDensityFunction(object):
# calculate parameter for pdf representing function
params = parameter[type](lbound, barycentre, rbound, decfact)
# calculate pdf values
try:
pdf = branches[type](create_axis(x0, incr, npts), barycentre, *params)
except TypeError:
assert isinstance(barycentre, UTCDateTime), 'object not capable of' \
' timestamp representation'
pdf = branches[type](create_axis(x0, incr, npts),
barycentre.timestamp, *params)
# select pdf type
pdf = branches[type]
# return the object
return ProbabilityDensityFunction(x0, incr, npts, pdf)
return ProbabilityDensityFunction(x0, incr, npts, pdf, barycentre,
params)
def broadcast(self, pdf, si, ei, data):
try:
@ -259,14 +294,14 @@ class ProbabilityDensityFunction(object):
rval = 0
axis = self.axis - self.x0
for n, x in enumerate(axis):
rval += x * self.data[n]
rval += x * self.data(n)
return rval * self.incr + self.x0
def standard_deviation(self):
mu = self.expectation()
mu = self.mu
rval = 0
for n, x in enumerate(self.axis):
rval += (x - mu) ** 2 * self.data[n]
rval += (x - mu) ** 2 * self.data(n)
return rval * self.incr
def prob_lt_val(self, value):
@ -280,8 +315,8 @@ class ProbabilityDensityFunction(object):
return self.prob_limits((value, self.axis[-1]))
def prob_limits(self, limits):
lim_ind = np.logical_and(limits[0] <= self.axis, self.axis <= limits[1])
data = self.data[lim_ind]
lim = np.arange(limits[0], limits[1], self.incr)
data = [self.data(t) for t in lim]
min_est, max_est = 0., 0.
for n in range(len(data) - 1):
min_est += min(data[n], data[n + 1])
@ -292,13 +327,20 @@ class ProbabilityDensityFunction(object):
if not (self.axis[0] <= value <= self.axis[-1]):
Warning('{0} not on axis'.format(value))
return None
return self.data[find_nearest(self.axis, value)] * self.incr
return self.data(value) * self.incr
def quantile(self, prob_value, eps=0.01):
'''
:param prob_value:
:param eps:
:return:
'''
l = self.axis[0]
r = self.axis[-1]
m = (r + l) / 2
diff = prob_value - self.prob_lt_val(m)
while abs(diff) > eps:
if diff > 0:
l = m
@ -306,7 +348,6 @@ class ProbabilityDensityFunction(object):
r = m
m = (r + l) / 2
diff = prob_value - self.prob_lt_val(m)
print(m, prob_value, self.prob_lt_val(m))
return m
def quantile_distance(self, prob_value):
@ -318,7 +359,9 @@ class ProbabilityDensityFunction(object):
def plot(self, label=None):
import matplotlib.pyplot as plt
plt.plot(self.axis, self.data)
axis = self.axis
plt.plot(axis, self.data(axis))
plt.xlabel('x')
plt.ylabel('f(x)')
plt.autoscale(axis='x', tight=True)
@ -338,6 +381,13 @@ class ProbabilityDensityFunction(object):
return l1, r1
def cincr(self, other):
if not self.incr == other.incr:
raise NotImplementedError(
'Upsampling of the lower sampled PDF not implemented yet!')
else:
return self.incr
def commonlimits(self, incr, other, max_npts=1e5):
'''
Takes an increment incr and two left and two right limits and returns
@ -371,6 +421,15 @@ class ProbabilityDensityFunction(object):
return x0, npts
def commonparameter(self, other):
assert isinstance(other, ProbabilityDensityFunction), \
'both operands must be of type ProbabilityDensityFunction'
incr = self.cincr(other)
x0, npts = self.commonlimits(incr, other)
return x0, incr, npts
def rearrange(self, other):
'''
@ -382,15 +441,10 @@ class ProbabilityDensityFunction(object):
:return:
'''
assert isinstance(other, ProbabilityDensityFunction), \
'both operands must be of type ProbabilityDensityFunction'
if not self.incr == other.incr:
raise NotImplementedError('Upsampling of the lower sampled PDF not implemented yet!')
else:
x0 = self.x0
incr = self.incr
npts = self.npts
x0, npts = self.commonlimits(incr, other)
pdf_self = np.zeros(npts)
pdf_other = np.zeros(npts)

7
pylot/testing/test_pdf.py Normal file
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@ -0,0 +1,7 @@
#!/usr/bin/env python
# -*- coding: utf-8 -*-
from pylot.core.util.pdf import ProbabilityDensityFunction
pdf = ProbabilityDensityFunction.from_pick(0.34, 0.5, 0.54, type='exp')
pdf2 = ProbabilityDensityFunction.from_pick(0.34, 0.5, 0.54, type='exp')
diff = pdf - pdf2