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optim_hic_curve.py
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__author__ = 'hervemn'
import numpy as np
from scipy.optimize import fmin_slsqp
from scipy.optimize import fsolve
# from scipy.optimize import minimize
from scipy.optimize import leastsq
from leastsqbound import *
def log_residuals(p, y, x):
d0, d1, alpha_0, alpha_1, alpha_2, A = p
hic_c = np.zeros(x.shape)
if d1 > d0:
if d0 > 0:
val_lim_0 = np.log(A) + alpha_0 * np.log(d0) - alpha_1 * np.log(d0)
else:
val_lim_0 = -10**15.
val_lim_1 = val_lim_0 + alpha_1 * np.log(d1) - alpha_2 * np.log(d1)
else:
val_lim_1 = -10**15
val_lim_0 = -10**15
for i in range(0, len(hic_c)):
if x[i] <= 0:
hic_c[i] = 0
elif x[i] <= d0 and x[i] > 0:
hic_c[i] = np.log(A) + alpha_0 * np.log(x[i])
elif x[i] > d0 and x[i] <= d1:
hic_c[i] = val_lim_0 + alpha_1 * np.log(x[i])
elif x[i] > d1:
hic_c[i] = val_lim_1 + alpha_2 * np.log(x[i])
err = y - hic_c
return err
def log_peval(x, param):
d0, d1, alpha_0, alpha_1, alpha_2, A = param
hic_c = np.zeros(x.shape)
if d1 > d0:
if d0 > 0:
val_lim_0 = np.log(A) + alpha_0 * np.log(d0) - alpha_1 * np.log(d0)
else:
val_lim_0 = -10**15.
val_lim_1 = val_lim_0 + alpha_1 * np.log(d1) - alpha_2 * np.log(d1)
else:
val_lim_1 = -10**15
val_lim_0 = -10**15
for i in range(0, len(hic_c)):
if x[i] <= 0:
hic_c[i] = 0
elif x[i] <= d0 and x[i] > 0:
hic_c[i] = np.log(A) + alpha_0 * np.log(x[i])
elif x[i] > d0 and x[i]<= d1:
hic_c[i] = val_lim_0 + alpha_1 * np.log(x[i])
elif x[i] > d1:
hic_c[i] = val_lim_1 + alpha_2 * np.log(x[i])
return hic_c
def peval(x, param):
d0, d1, alpha_0, alpha_1, alpha_2, A = param
hic_c = np.zeros(x.shape)
if d1 > d0:
if d0 > 0:
val_lim_0 = A * np.power(d0, alpha_0) / np.power(d0, alpha_1)
else:
val_lim_0 = -10**15.
val_lim_1 = val_lim_0 * np.power(d1, alpha_1) / np.power(d1, alpha_2)
else:
val_lim_0 = -10**15
val_lim_1 = -10**15
for i in range(0, len(hic_c)):
if x[i] <= 0:
hic_c[i] = 0
elif x[i] <= d0 and x[i] > 0:
hic_c[i] = A * np.power(x[i], alpha_0)
elif x[i] > d0 and x[i] <= d1:
# hic_c[i] = A * np.power(x[i], alpha_1)
hic_c[i] = val_lim_0 * np.power(x[i], alpha_1)
elif x[i] > d1:
hic_c[i] = val_lim_1 * np.power(x[i], alpha_2)
return hic_c
def estimate_param_hic(y_meas, x_bins):
d0 = 20.0
d1 = 300.0
alpha_0 = -1.5
alpha_1 = -1.5
alpha_2 = -1.5
x0 = x_bins.min()
print "x0 = ", x0
A = np.max(y_meas) * (x0 ** (- alpha_0))
p0 = [d0, d1, alpha_0, alpha_1, alpha_2, A]
plsq = leastsq(log_residuals, p0, args=(np.log(y_meas), x_bins))
print plsq
# plsq[0][2] = -0.9
# plsq[0][5] = np.max(y_meas) * (x0 ** (- plsq[0][2]))
y_estim = peval(np.arange(x_bins.min(), x_bins.max(), 5), plsq[0])
return plsq, y_estim
def residual_4_max_dist(x, p):
d0, d1, alpha_0, alpha_1, alpha_2, A, y = p
hic_c = np.zeros(x.shape)
if d1 > d0:
if d0 > 0:
val_lim_0 = A * np.power(d0, alpha_0) / np.power(d0, alpha_1)
else:
val_lim_0 = -10**15.
val_lim_1 = val_lim_0 * np.power(d1, alpha_1) / np.power(d1, alpha_2)
else:
val_lim_0 = -10**15
val_lim_1 = -10**15
for i in range(0, len(hic_c)):
if x[i] <= 0:
hic_c[i] = 0
elif x[i] <= d0 and x[i] > 0:
hic_c[i] = A * np.power(x[i], alpha_0)
elif x[i] > d0 and x[i] <= d1:
# hic_c[i] = A * np.power(x[i], alpha_1)
hic_c[i] = val_lim_0 * np.power(x[i], alpha_1)
elif x[i] > d1:
hic_c[i] = val_lim_1 * np.power(x[i], alpha_2)
err = y - hic_c
return err
def estimate_max_dist_intra(p, val_inter):
print "val_inter = ", val_inter
d0, d1, alpha_0, alpha_1, alpha_2, A = p
p0 = [d0, d1, alpha_0, alpha_1, alpha_2, A, val_inter]
s0 = d1
x = fsolve(residual_4_max_dist, s0, args=(p0))
print "limit inter/intra distance = ", x
print "val model @ dist inter = ", peval(x, p)
# raw_input("alors?")
return x[0]