def ID(integrand, T, n, i):
maxn = 1 / (sigma**3 * np.pi / 6)
# maxx = 1
# if maxx*n > maxn:
# maxx = maxn/n
maxx = np.minimum(np.ones_like(n), maxn / n)
return integrate.midpoint(lambda x: integrand_ID(T, n, x, i), 0, maxx, 100)
def ID_ref(integrand,T,n,i):
maxn = 1/(sigma**3*np.pi/6)
#maxx = 1
maxx = np.minimum(np.ones_like(n),maxn/n)
# if maxx*n > maxn:
# maxx = maxn/n
return integrate.midpoint(lambda x: integrand_ID_ref(T,n,x,i),0,maxx,100)
def ID(integrand,T,n,i):
maxn = 1/(sigma**3*np.pi/6)
# maxx = 1
# if maxx*n > maxn:
# maxx = maxn/n
maxx = np.minimum(np.ones_like(n),maxn/(n+1e-100)-1)
return integrate.midpoint(lambda x: integrand_ID(T,n,x,i),0,maxx,1000)*n
def ID_ref(integrand,T,n,i):
maxn = 1/(sigma**3*np.pi/6)
#maxx = 1
#print "N inside IDREF: ",n
maxx = np.minimum(np.ones_like(n),maxn/(n+1e-100)-1)
# if maxx*n > maxn:
# maxx = maxn/n
return integrate.midpoint(lambda x: integrand_ID_ref(T,n,x,i),0,maxx,1000)*n
def ID2star(n, maxx):
maxpower = -1e99
dx = maxx/num_init
xpoints = np.arange(dx/2,maxx, dx)
kmax=0
for k in range(len(xpoints)):
if maxpower<onlyPowerStar(n,xpoints[k],fn):
maxpower = onlyPowerStar(n,xpoints[k],fn)
kmax=k
#########FIND LEFT SIDE
x_left = xpoints[kmax]
k_left = kmax
while k_left>0 and integrand_ID2star(n,maxpower,x_left)>0.1:
k_left -= 1
x_left = xpoints[k_left]
#########FIND RIGHT SIDE
x_right = xpoints[kmax]
k_right = kmax
while k_right<len(xpoints)-1 and integrand_ID2star(n,maxpower,x_right)>0.1:
k_right += 1
x_right = xpoints[k_right]
integral_left = 0
dx_left = x_left/num_left
xpoints_left = np.arange(dx_left/2,x_left,dx_left)
max_power_left = -1e99
for k in range(len(xpoints_left)):
max_power_left = max(max_power_left,onlyPowerStar(n,xpoints_left[k],fn))
integral_right = 0
dx_right = (maxx-x_right)/num_right
xpoints_right = np.arange(x_right+dx_right/2,maxx,dx_right)
max_power_right = -1e99
for k in range(len(xpoints_right)):
max_power_right = max(max_power_right,onlyPowerStar(n,xpoints_right[k],fn))
integral_mid = 0
dx_mid = (x_right-x_left)/num_mid
xpoints_mid = np.arange(x_left+dx_mid/2,x_right,dx_mid)
max_power_mid = -1e99
for k in range(len(xpoints_mid)):
max_power_mid = max(max_power_mid,onlyPowerStar(n,xpoints_mid[k],fn))
if max_power_left > max_power_mid:
x_left = 0
integral_left = 0
else:
integral_left += integrate.midpoint(lambda x: integrand_ID2star(n,max_power_left,x),0,x_left,num_left)*n
if max_power_right > max_power_mid:
x_right = maxx
integral_right = 0
else:
integral_right += integrate.midpoint(lambda x: integrand_ID2star(n,max_power_right,x),x_right,maxx,num_right)*n
if x_left != 0 and x_right != maxx:
integral_mid += integrate.midpoint(lambda x: integrand_ID2star(n,max_power_mid,x),x_left,x_right,num_mid)*n
else:
dx_mid = (x_right-x_left)/num_mid
xpoints_mid = np.arange(x_left+dx_mid/2,x_right,dx_mid)
max_power_mid = -1e99
for k in range(len(xpoints_mid)):
max_power_mid = max(max_power_mid,onlyPowerStar(n,xpoints_mid[k],fn))
integral_mid += integrate.midpoint(lambda x: integrand_ID2star(n,max_power_mid,x),x_left,x_right,num_mid)*n
if integral_left == 0 and integral_right == 0:
#print "TTm=%.2E \r"%(max_power_mid),
return np.log(integral_mid)+max_power_mid
if integral_left != 0 and integral_right == 0:
#print "FTlm=%.2E \r"%(max_power_left-max_power_mid),
return np.log(integral_left*np.exp(max_power_left-max_power_mid)+integral_mid)+max_power_mid
if integral_left == 0 and integral_right != 0:
#print "TFrm=%.2E \r"%(max_power_right-max_power_mid),
return np.log(integral_right*np.exp(max_power_right-max_power_mid)+integral_mid)+max_power_mid
#print "FFlm=%.2E FFrm=%.2E \r"%(max_power_left-max_power_mid,max_power_right-max_power_mid),
return np.log(integral_left*np.exp(max_power_left-max_power_mid)+integral_right*np.exp(max_power_right-max_power_mid)+integral_mid)+max_power_mid
def ID(integrand,T,n,i):
maxn = 1/(sigma**3*np.pi/6)
maxx = np.minimum(np.ones_like(n),maxn/n - 1)
return integrate.midpoint(lambda x: integrand_ID(T,n,x,i),0,maxx,100)
def ID_ref(integrand,T,n,i):
value = integrate.midpoint(lambda x: integrand_ID_ref(T,x,i),0,1,1000)
return value
def ID_ref(integrand, T, n, i):
maxn = 1 / (sigma**3 * np.pi / 6)
maxx = np.minimum(np.ones_like(n), maxn / n - 1)
return integrate.midpoint(lambda x: integrand_ID_ref(T, n, x, i), 0, maxx,
100)