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[edit] implementation of difference of two independent random variable as the correlation of the PDFs completed; summation pending due to unclear axis determination of the resultant PDF

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This commit is contained in:
Sebastian Wehling-Benatelli 2016-02-15 20:13:02 +01:00
parent f2cad2e151
commit 3ee221b8eb
1 changed files with 69 additions and 41 deletions
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110
pylot/core/util/pdf.py
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@ -15,6 +15,9 @@ def create_axis(x0, incr, npts):
ax[i] = x0 + incr * i
return ax
def find_nearest_index(array, value):
return (np.abs(array-value)).argmin()
def gauss_parameter(te, tm, tl, eta):
'''
@ -128,15 +131,16 @@ class ProbabilityDensityFunction(object):
assert isinstance(other, ProbabilityDensityFunction), \
'both operands must be of type ProbabilityDensityFunction'
x0, incr, npts, pdf_self, pdf_other = self.rearrange(other)
pdf = np.convolve(pdf_self, pdf_other, 'same') * incr
# shift axis values for correct plotting
midpoint = int(npts // 2) + 1
x0 += incr * midpoint
return ProbabilityDensityFunction(x0, incr, npts, pdf)
raise NotImplementedError('implementation of resulting axis unclear - feature pending!')
# x0, incr, npts, pdf_self, pdf_other = self.rearrange(other)
#
# pdf = np.convolve(pdf_self, pdf_other, 'same') * incr
#
# # shift axis values for correct plotting
# midpoint = npts / 2
# x0 = incr * midpoint
#
# return ProbabilityDensityFunction(x0, incr, npts, pdf)
def __sub__(self, other):
assert isinstance(other, ProbabilityDensityFunction), \
@ -147,8 +151,8 @@ class ProbabilityDensityFunction(object):
pdf = np.correlate(pdf_self, pdf_other, 'same') * incr
# shift axis values for correct plotting
midpoint = int(npts // 2) + 1
x0 -= incr * midpoint
midpoint = npts / 2
x0 = -incr * midpoint
return ProbabilityDensityFunction(x0, incr, npts, pdf)
@ -172,29 +176,49 @@ class ProbabilityDensityFunction(object):
self._x = np.array(x)
@classmethod
def fromPick(self, incr, lbound, midpoint, rbound, decfact=0.01, type='gauss'):
def fromPick(self, incr, lbound, barycentre, rbound, decfact=0.01, type='gauss'):
'''
Initialize a new ProbabilityDensityFunction object.
Takes incr, lbound, midpoint and rbound to derive x0 and the number
Takes incr, lbound, barycentre and rbound to derive x0 and the number
of points npts for the axis vector.
Maximum density
is given at the midpoint and on the boundaries the function has
is given at the barycentre and on the boundaries the function has
declined to decfact times the maximum value. Integration of the
function over a particular interval gives the probability for the
variable value to be in that interval.
'''
margin = 1.5 * np.max(midpoint - lbound, rbound - midpoint)
x0 = midpoint - margin
npts = int(2 * margin // incr)
params = parameter[type](lbound, midpoint, rbound, decfact)
# derive adequate window of definition
margin = 1.5 * np.max([barycentre - lbound, rbound - barycentre])
# find midpoint accounting also for `~obspy.UTCDateTime` object usage
try:
pdf = branches[type](create_axis(x0, incr, npts), midpoint, *params)
midpoint = (rbound + lbound) / 2
except TypeError:
midpoint = (rbound + float(lbound)) / 2
# find x0 on a grid point and sufficient npts
n = int(np.ceil((barycentre - midpoint) / incr))
m = int(np.ceil((margin / incr)))
midpoint = barycentre - n * incr
margin = m * incr
x0 = midpoint - margin
npts = 2 * m
# 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 as e:
print('Warning:\n' + e.message + '\n' + 'trying timestamp instead')
assert isinstance(midpoint, UTCDateTime), 'object not capable of' \
assert isinstance(barycentre, UTCDateTime), 'object not capable of' \
' timestamp representation'
pdf = branches[type](create_axis(x0, incr, npts),
midpoint.timestamp, *params)
barycentre.timestamp, *params)
# return the object
return ProbabilityDensityFunction(x0, incr, npts, pdf)
def commonlimits(self, incr, other, max_npts=1e5):
@ -209,37 +233,41 @@ class ProbabilityDensityFunction(object):
:param r2:
:param max_npts:
:return:
'''
# >>> manu = ProbabilityDensityFunction.fromPick(0.01, 0.3, 0.5, 0.54)
# >>> auto = ProbabilityDensityFunction.fromPick(0.01, 0.3, 0.34, 0.54)
# >>> manu.commonlimits(0.01, auto)
# (
l1 = self.x0
r1 = np.max(self.axis)
r1 = l1 + self.incr * self.npts
l2 = other.x0
r2 = np.max(other.axis)
r2 = l2 + other.incr * other.npts
if l1 >= l2 and r1 >= r2:
x0 = l2
npts = int(r1 - x0 // incr)
elif l1 < l2 and r1 >= r2:
if l1 < l2:
x0 = l1
npts = int(r1 - x0 // incr)
elif l1 >= l2 and r1 < r2:
x0 = l2
npts = int(r2 - x0 // incr)
elif l1 >= r2:
x0 = l2
npts = int(r1 - x0 // incr)
elif l2 >= r1:
x0 = l1
npts = int(r2 - x0 // incr)
else:
x0 = None
npts = None
x0 = l2
# calculate index for rounding
ri = int(np.ceil(np.abs(np.log10(incr))))
if r1 < r2:
npts = int(round(r2 - x0, ri) // incr)
else:
npts = int(round(r1 - x0, ri) // incr)
if npts > max_npts:
raise ValueError('Maximum number of points exceeded:\n'
'max_npts - %d\n'
'npts - %d\n' % (max_npts, npts))
npts = np.max([npts, self.npts, other.npts])
if npts < self.npts or npts < other.npts:
raise ValueError('new npts is to small')
return x0, npts
@ -268,9 +296,9 @@ class ProbabilityDensityFunction(object):
x = create_axis(x0, incr, npts)
sstart = np.where(x == self.x0)
sstart = find_nearest_index(x, self.x0)
s_end = sstart + self.data.size
ostart = np.where(x == other.x0)
ostart = find_nearest_index(x, other.x0)
o_end = ostart + other.data.size
pdf_self[sstart:s_end] = self.data