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bpl.py
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bpl.py
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#Power law binned module
import math
import numpy
from scipy import optimize
def bplfit(h, boundaries, **kwargs):
rngal = []
limit = []
bminb = []
# ---------------------------------------------------------------
# ---------------Parsing command-line arguments------------------
# ---------------------------------------------------------------
i=1
for key, value in kwargs.iteritems():
if key == 'range':
rngal = value
elif key == 'limit':
limit = value
elif key == 'bmin':
bminb = value
else:
print "Ignoring invalid argument %s" % (key)
# ---------------------------------------------------------------
# ------------------------Checking input-------------------------
# ---------------------------------------------------------------
# 1. h must have integer counts.
if all(type(x) is int for x in h) == False:
print "(BPLFIT) Error: Vector h should be an integer vector"
alpha = float('nan')
bmin = boundaries[0]
L = float('nan')
return
# 2. h must be non-negative
if len(filter(lambda x: x < 0, h)):
print "(BPLFIT) Error: Vector h should be non-negative"
alpha = float('nan')
bmin = boundaries[0]
L = float('nan')
return
# 3. boundaries must have number of elements as one more than the number in h
if len(boundaries) != len(h) + 1:
print "(BPLFIT) Error: Incorrect number of elements in either boundaries or h"
alpha = float('nan')
bmin = boundaries[0]
L = float('nan')
return
# 4. Need atleast 2 bins to work with.
if len(h) < 2:
print "(BPLFIT) Error: I need atleast 2 bins to make this work"
alpha = float('nan')
bmin = boundaries[0]
L = float('nan')
return
# 5. Checking range vector
if rngal and (not isinstance(rngal, list) or min(rngal or [0]) < 1):
print "(BPLFIT) Error: 'range' argument must contain a valid vector; using default"
rngal = numpy.arange(1.5, 3.51, 0.01) #rngal = 1.5:0.01:3.5;
return
# 6. Checking limit option
if limit and (not isinstance(limit, int) or limit < min(boundaries)):
print "(BPLPVA) Error: 'limit' argument must be a positive value >= boundaries(1); using default."
limit = boundaries[-2] #limit = boundaries(end-2);
return
# 7. Checking bmin option
if bminb and (not isinstance(bminb, int) or bminb >= boundaries[-1]):
print "(BPLPVA) Error: 'bmin' argument must be a positive value < boundaries(end-1); using default."
bminb = boundaries[0]
return
# Reshape the input vectors
h = numpy.reshape(h, (len(h), 1))
boundaries = numpy.reshape(boundaries, (len(boundaries), 1))
# Need a minimum of 2 bins.
bmins = boundaries[1:-2]
if not bminb:
bmins = bmins[(bmins <= bminb)[::-1].argmax()]
if not limit:
bmins[bmins>limit] = []
dat = zeros((bmins.shape[0], bmins.shape[1]))
for xm in range(1, len(bmins)):
bmin = bmins[xm]
# Truncate the data below bmin
ind = (boundaries >= bminq)
z = h[ind:-1]
n = sum(z)
b = boundaries[ind:-1]
# estimate alpha using specified range or using
# numerical maximization
l = b[1:-2]
u = b[2:-1]
if not rngal
H = kron(ones((1, size(rngal))), z) #repmat(z, 1, numel(rngal))
LOWER_EDGE = kron(ones((1, size(rngal))), l) #repmat(l, 1, numel(rngal));
UPPER_EDGE = kron(ones((1, size(rngal))), u) #repmat(u, 1, numel(rngal));
ALPHA_EST = kron(ones((size(b) - 1, 1)), rngal) #repmat(rngal, numel(b)-1, 1);
temp = H * ( math.log(numpy.power(LOWER_EDGE, 1 - ALPHA_EST) - numpy.power(UPPER_EDGE, 1 - ALPHA_EST)) + (ALPHA_EST - 1) * math.log(bmin)) #H .* (log(LOWER_EDGE.^(1-ALPHA_EST) - UPPER_EDGE.^(1-ALPHA_EST)) + (ALPHA_EST-1) .* log(bmin));
sum_ = sum(temp, axis = 1) #sum(temp, 1);
I = sum_.index(max(sum_)) #[~,I] = max(sum_);
al = rngal[I]
else
hnd = lambda alpha: (alpha) -sum( z*( numpy.log((l)**(1-alpha) - (u)**(1-alpha)) + (alpha-1)*numpy.log(bmin) ) );
al = optimize.fmin(func=hnd, x0=1) #fminsearch(hnd, 1);
# compute KS statistic
temp = z[::-1].cumsum(axis=0) #cumsum(z(end:-1:1));
cx = 1 - temp[::-1]/n #1 - temp(end:-1:1)./n;
cf = 1 - numpy.power((l/bmin),(1-al)) #1 - (l./bmin).^(1-al);
dat[xm] = numpy.concatenate(abs(cf - cx)).max() #max(abs(cf-cx));
# Choose bmin which minimizes the KS-statistic
D = min(dat)
bmin = bmins[(dat <= D).argmax()] #bmins(find(dat<=D, 1, 'first'));
# Truncate data below bmin and recompute alpha
ind = (boundaries >= bmin) #find(boundaries>=bmin, 1);
z = h[ind:-1] #h(ind:end);
b = boundaries[ind:-1] #boundaries(ind:end);
n = sum(z)
l = b[1:2] #b(1:end-1);
u = b[2:-1] #b(2:end);
# recompute alpha using specified range or using
# numerical maximization
if not rngal:
H = kron(ones((1, size(rngal))), z) #repmat(z, 1, numel(rngal))
LOWER_EDGE = kron(ones((1, size(rngal))), l) #repmat(l, 1, numel(rngal));
UPPER_EDGE = kron(ones((1, size(rngal))), u) #repmat(u, 1, numel(rngal));
ALPHA_EST = kron(ones((size(b) - 1, 1)), rngal) #repmat(rngal, numel(b)-1, 1);
temp = H * ( math.log(numpy.power(LOWER_EDGE, 1 - ALPHA_EST) - numpy.power(UPPER_EDGE, 1 - ALPHA_EST)) + (ALPHA_EST - 1) * math.log(bmin)) #H .* (log(LOWER_EDGE.^(1-ALPHA_EST) - UPPER_EDGE.^(1-ALPHA_EST)) + (ALPHA_EST-1) .* log(bmin));
sum_ = sum(temp, axis = 1) #sum(temp, 1);
I = sum_.index(max(sum_)) #[~,I] = max(sum_);
al = rngal[I]
else:
hnd = lambda alpha: (alpha) -sum( z*( numpy.log((l)**(1-alpha) - (u)**(1-alpha)) + (alpha-1)*numpy.log(bmin) ) );
alpha = optimize.fmin(func=hnd, x0=1) #fminsearch(hnd, 1);
# Computing likelihood under fitted model (alpha, bmin)
L = (alpha - 1) * math.log(bmin) * sum(z) + sum(z*math.log(l**(1-alpha)) - u**(1-alpha)) #(alpha-1)*log(bmin)*sum(z) + sum(z.*log(l.^(1-alpha) - u.^(1-alpha)));
return [alpha, bmin, L]
#PValue
def bplpva(h, boundaries, bmin, **kwargs):
rngal = []
limit = []
bminb = []
reps = 1000
silent = 0
# Parsing arguments
for key, value in kwargs.iteritems():
if key == 'range':
rngal = value
elif key == 'bminb':
bminb = value
elif key == 'limit':
limit = value
elif key == 'reps':
reps = value
elif key == 'silent':
silent = 1
else:
print "Ignoring invalid argument %s" % (key)
#Check input
# 1. h must have integer counts.
if all(type(x) is int for x in h) == False:
print "(BPLPVA) Error: Vector h should be an integer vector"
return
# 2. h must be non-negative
if len(filter(lambda x: x < 0, h)):
print "(BPLPVA) Error: Vector h should be non-negative"
return
# 3. boundaries must have number of elements as one more than the number in h
if len(boundaries) != len(h) + 1:
print "(BPLPVA) Error: Incorrect number of elements in either boundaries or h"
return
# 4. Need atleast 2 bins to work with.
if len(h) < 2:
print "(BPLPVA) Error: I need atleast 2 bins to make this work"
return
# 5. Checking range vector
if rngal and (not isinstance(rngal, list) or min(rngal or [0]) < 1):
print "(BPLPVA) Error: 'range' argument must contain a valid vector; using default"
rngal = numpy.arange(1.5, 3.51, 0.01) #rngal = 1.5:0.01:3.5;
return
# 6. Checking limit option
if limit and (not isinstance(limit, int) or limit < min(boundaries)):
print "(BPLPVA) Error: 'limit' argument must be a positive value >= boundaries(1); using default."
limit = boundaries[-2] #limit = boundaries(end-2);
return
# 7. Checking bmin option
if bminb and (not isinstance(bminb, int) or bminb >= boundaries[-1]):
print "(BPLPVA) Error: 'bmin' argument must be a positive value < boundaries(end-1); using default."
bminb = boundaries[0]
return
# 8. Checking number of repititons
if reps and (not isinstance(reps, int) or reps < 2):
print "(BPLPVA) Error: ''reps'' argument must be a positive value > 1; using default"
reps = 1000
return
# Reshape the input vectors
h = numpy.reshape(h, (len(h), 1))
boundaries = numpy.reshape(boundaries, (len(boundaries), 1))
N = sum(h)
d = numpy.zeros((reps,1))
if not silent:
print "Power-law distribution, parameter uncertainty calculation"
print "Copyright 2012 Yogesh Virkar";
print "Warning: This can be a slow calculation; please be patient"
print "reps = %i" % len(d);
# ---------------------------------------------------------------
#---------------Compute the empirical distance D*------------------
# ---------------------------------------------------------------
# Data above bmin
ind = (boundaries>=bmin).argmax()
z = h[ind:]
nz = sum(z);
b = boundaries[ind:];
l = b[1:-1];
u = b[2:];
# Data below bmin
y = h[1:ind-1]; #ny = sum(y);
by = boundaries[1:ind];
ly = by[1:-1];
uy = by[2:];
# Compute alpha using numerical maximization
hnd = lambda alpha: (alpha) -sum( z*( numpy.log((l)**(1-alpha) - (u)**(1-alpha)) + (alpha-1)*numpy.log(bmin) ) );
alpha = optimize.fmin(func=hnd, x0=1) #alpha = fminsearch(hnd, 1);
# Compute distance using KS statistic
temp = z[::-1].cumsum(axis=0) #cumsum(z(end:-1:1));
cx = 1 - temp[::-1]/nz #1 - temp(end:-1:1)./nz;
cf = 1 - numpy.power((l/bmin),(1-alpha)) #1 - (l./bmin).^(1-alpha);
Dstar = numpy.concatenate(abs(cf - cx)).max() #max(abs(cf-cx));
# ---------------------------------------------------------------
# Compute the distribution of gofs using semiparametric bootstrap
# ---------------------------------------------------------------
# Probability of choosing value above bmin
pz = nz/N;
for i in range(1,reps + 1):
#semi-parametric bootstrap of data
n1 = sum(numpy.random.random((N,))>pz)
temp = (ly+uy)/2
temp2=[]
for t in range(1, len(y) + 1):
temp2 = numpy.array([temp2,kron(ones((y[t],1)),temp[t])]) #[temp2;repmat(temp(t),y(t),1)];
temp2 = temp2[numpy.random.permutation(len(temp2))] #temp2(randperm(numel(temp2)));
x1 = temp2[ numpy.ceil(temp2.size() * numpy.random.random((1,n1)))] #x1 = temp2(ceil(numel(temp2)*rand(n1,1)));
n2 = N - n1;
x2 = bmin*numpy.power(1 - numpy.random.random((1,n2), (-1/(alpha-1)))) #x2 = bmin.*(1-rand(n2,1)).^(-1/(alpha-1));
x = [x1,x2]
h2 = np.digitize(x, boundaries) #h2 = histc(x, boundaries);
h2 = np.delete(h2, -1) #h2(end) = [];
ind = (h2[::-1] != 0).argmax() - 1 #ind = find(h2(end:-1:1)~=0,1,'first')-1;
if ind == 1:
h2 = np.delete(h2, -1) #h2(end)= [];
else:
if ind > 1:
ind2 = ind - 1
end = h2.size() - 1
h2 = np.delete(h2, range(end - ind2, end)) #h2(end-ind2:end) = [];
boundaries2 = boundaries[1:-1-ind]; #boundaries2 = boundaries(1:end-ind);
# Need a minimum of 2 bins.
bmins = boundaries2[1:-1-2];
if bminb:
bmins = bmins[(bmins <= bminb)[::-1].argmax()] #bmins(find(bmins<=bminb, 1, 'last'));
if limit:
bmins[(bmins > limit)] = [] #bmins(bmins>limit) = [];
dat = zeros((a.shape[0], a.shape[1])) #zeros(size(bmins));
for xm in range(1,bmins.size() + 1):
bminq = bmins[xm];
# Truncate the data below bmin
indq = (boundaries2 >= bminq) #find(boundaries2>=bminq, 1);
zq = h2[indq:-1];
nq = zq.sum(axis=0) #sum(zq);
bq = boundaries2[indq:-1] #boundaries2(indq:end);
# estimate alpha using specified range or using
# numerical maximization
lq = bq[1:-2] #bq(1:end-1);
uq = bq[2:-1] #bq(2:end);
if rngal:
H = kron(ones((1, size(rngal))), zp) #repmat(zq, 1, numel(rngal));
LOWER_EDGE = kron(ones((1, size(rngal))), lq) #repmat(lq, 1, numel(rngal));
UPPER_EDGE = kron(ones((1, size(rngal))), uq) #repmat(uq, 1, numel(rngal));
ALPHA_EST = kron(ones((size(bq) - 1, 1)), rngal) #repmat(rngal, numel(bq)-1, 1);
tempq = H * ( math.log(numpy.power(LOWER_EDGE, 1 - ALPHA_EST) - numpy.power(UPPER_EDGE, 1 - ALPHA_EST)) + (ALPHA_EST - 1) * math.log(bminq)) #H .* (log(LOWER_EDGE.^(1-ALPHA_EST) - UPPER_EDGE.^(1-ALPHA_EST)) + (ALPHA_EST-1) .* log(bminq));
sum_ = sum(tempq, axis = 1) #sum(tempq, 1);
I = sum_.index(max(sum_)) #[~,I] = max(sum_);
al = rngal[I]
else:
hnd = lambda al2: (al2) -sum( zq*( numpy.log((lq)**(1-al2) - (uq)**(1-al2)) + (al2-1)*numpy.log(bminq) ) ); #TODO
al = optimize.fmin(func=hnd, x0=1) #fminsearch(hnd, 1);
# compute KS statistic
tempq = cumsum(zq[::-1]) #cumsum(zq(end:-1:1));
cxq = 1 - tempq[::-1]/nq #1 - tempq(end:-1:1)./nq;
cfq = 1 - numpy.power(lq/bminq, 1 - al) #1 - (lq./bminq).^(1-al);
dat[xm] = max(abs(cfq - cxq)) #dat(xm) = max(abs(cfq-cxq));
if not silent:
print "iter = {}".format(i)
d[i] = min(dat) #d(i) = min(dat);
p = sum(d >= Dstar)/reps #sum(d>=Dstar)./reps;
return [p,d]