def integrand_trapz(del0,m,M0,R0,z): #2s*f_ESP
# of A7, divided by 2s; this IS f_ESP
s = sig0(m2R(m))
V,r,dmdr = pb.volume_radius_dmdr(m,**cosmo)
s,s0,sx = sig0(r), sig0(R0),SX(r,R0)
gamm = gam(r)
epx,q = epX(m,M0), Q(m,M0)
meanmu = del0/n.sqrt(s)*sx/s0
varmu = Q(m,M0)
varx = 1-gamm**2-gamm**2*(1-epx)**2*(1-q)/q
if varx<0:
print "varx<0, breaking at varx, gamm, epx, q,m,M0="
print varx, gamm, epx, q, m, M0
#!! varx can be negative
b = n.arange(0.00001,3.,0.03)
y = []
for bx in b:
newy = prob(bx)*subgrand_trapz(bx,del0,s,s0,sx,epx,q,meanmu,varmu,varx,gamm,R0,V,z)/2/s
#print 'b,y'
#print bx,y[-1]
if n.isnan(newy):
print 'NAN detected, breaking at: '
print bx,prob(bx),del0,s,s0,sx,epx,q,meanmu,varmu,varx,gamm,R0,V
break
else:
y.append(newy)
return n.trapz(y,b)
def integrand_trapz(del0,m,M0,R0,z): #2s*f_ESP
# of A7, divided by 2s; this IS f_ESP
s = sig0(m2R(m))
V,r,dmdr = pb.volume_radius_dmdr(m,**cosmo)
s,s0,sx = sig0(r), sig0(R0),SX(r,R0)
gamm = gam(r)
epx,q = epX(m,M0), Q(m,M0)
meanmu = del0/n.sqrt(s)*sx/s0
varmu = Q(m,M0)
varx = 1-gamm**2-gamm**2*(1-epx)**2*(1-q)/q
if varx<0:
print "varx<0, breaking at varx, gamm, epx, q,m,M0="
print varx, gamm, epx, q, m, M0
#!! varx can be negative
#b = n.arange(0.00001,30.,0.03) #TUNE
b = n.exp(n.linspace(n.log(0.05),n.log(20.),200))
y = []
for bx in b:
newy = prob(bx)*subgrand_trapz(bx,del0,s,s0,sx,epx,q,meanmu,varmu,varx,gamm,R0,V,z)/2/s
#print 'b,y'
#print bx,y[-1]
if n.isnan(newy):
print 'NAN detected, breaking at: '
print bx,prob(bx),del0,s,s0,sx,epx,q,meanmu,varmu,varx,gamm,R0,V
break
else:
y.append(newy)
#import IPython; IPython.embed()
if y[-1]/n.max(y)>1.E-3: print "Warning: choice of bmax too small"
if y[0]/n.max(y)>1.E-3: print "Warning: choice of bmin too big"
return n.trapz(y,b)
def integrand_trapz(del0, m, M0, R0, z): #2s*f_ESP
# of A7, divided by 2s; this IS f_ESP
s = sig0(m2R(m))
V, r, dmdr = pb.volume_radius_dmdr(m, **cosmo)
s, s0, sx = sig0(r), sig0(R0), SX(r, R0)
gamm = gam(r)
epx, q = epX(m, M0), Q(m, M0)
meanmu = del0 / n.sqrt(s) * sx / s0
varmu = Q(m, M0)
varx = 1 - gamm**2 - gamm**2 * (1 - epx)**2 * (1 - q) / q
if varx < 0:
print "varx<0, breaking at varx, gamm, epx, q,m,M0="
print varx, gamm, epx, q, m, M0
#!! varx can be negative
#b = n.arange(0.00001,30.,0.03) #TUNE
b = n.exp(n.linspace(n.log(0.01), n.log(30.),
1000)) #Wide range from E-21 to E-280, peaking at E-7
y = []
for bx in b:
newy = prob(bx) * subgrand_trapz(bx, del0, s, s0, sx, epx, q, meanmu,
varmu, varx, gamm, R0, V, z) / 2 / s
#print 'b,y'
#print bx,y[-1]
if n.isnan(newy):
print 'NAN detected, breaking at: '
print bx, prob(
bx), del0, s, s0, sx, epx, q, meanmu, varmu, varx, gamm, R0, V
break
else:
y.append(newy)
#import IPython; IPython.embed()
return n.trapz(y, b)
def All(x,b,m,del0,M0,z): #z,y,x,c,c,c V,r,dmdr = pb.volume_radius_dmdr(m,**cosmo) R0 = m2R(M0) s,s0,sx = sig0(r), sig0(R0),SX(r,R0) Bb = B(z,b,s) gamm = gam(r) epx,q = epX(m,M0), Q(m,M0) #print 'gamm,epx,q =',gamm,epx,q meanmu = del0/n.sqrt(s)*sx/s0 varmu = Q(m,M0) meanx = gamm*((Bb-del0*sx/s0)*(1-epx)/q/n.sqrt(s)+Bb*epx/n.sqrt(s)) varx = 1-gamm**2-gamm**2*(1-epx)**2*(1-q)/q fact = V/Vstar(R0)*pG(Bb/n.sqrt(s),meanmu, varmu) #print b, Bb/n.sqrt(s),meanmu,varmu,pG(Bb/n.sqrt(s),meanmu, varmu) return fact*prob(b)*(x/gamm-b)*F(x)*pG(x,meanx,varx)/2/sig0(m2R(m))*dsdm(m)
def subgrand(b,del0,m,M0,z): V,r,dmdr = pb.volume_radius_dmdr(m,**cosmo) R0 = m2R(M0) s,s0,sx = sig0(r), sig0(R0),SX(r,R0) Bb = B(z,b,s) gamm = gam(r) epx,q = epX(m,M0), Q(m,M0) print 'gamm,epx,q =',gamm,epx,q meanmu = del0/n.sqrt(s)*sx/s0 varmu = Q(m,M0) meanx = gamm*((Bb-del0*sx/s0)*(1-epx)/q/n.sqrt(s)+Bb*epx/n.sqrt(s)) varx = 1-gamm**2-gamm**2*(1-epx)**2*(1-q)/q fact = V/Vstar(R0)*pG(Bb/n.sqrt(s),meanmu, varmu) print b, Bb/n.sqrt(s),meanmu,varmu,pG(Bb/n.sqrt(s),meanmu, varmu) factint = quad(lambda x: (x/gamm-b)*F(x)*pG(x,meanx,varx),b*gamm,100)[0] #print fact, factint return fact*factint
def All(x, b, m, del0, M0, z): #z,y,x,c,c,c
V, r, dmdr = pb.volume_radius_dmdr(m, **cosmo)
R0 = m2R(M0)
s, s0, sx = sig0(r), sig0(R0), SX(r, R0)
Bb = B(z, b, s)
gamm = gam(r)
epx, q = epX(m, M0), Q(m, M0)
#print 'gamm,epx,q =',gamm,epx,q
meanmu = del0 / n.sqrt(s) * sx / s0
varmu = Q(m, M0)
meanx = gamm * ((Bb - del0 * sx / s0) *
(1 - epx) / q / n.sqrt(s) + Bb * epx / n.sqrt(s))
varx = 1 - gamm**2 - gamm**2 * (1 - epx)**2 * (1 - q) / q
fact = V / Vstar(R0) * pG(Bb / n.sqrt(s), meanmu, varmu)
#print b, Bb/n.sqrt(s),meanmu,varmu,pG(Bb/n.sqrt(s),meanmu, varmu)
return fact * prob(b) * (x / gamm - b) * F(x) * pG(
x, meanx, varx) / 2 / sig0(m2R(m)) * dsdm(m)
def subgrand(b, del0, m, M0, z):
V, r, dmdr = pb.volume_radius_dmdr(m, **cosmo)
R0 = m2R(M0)
s, s0, sx = sig0(r), sig0(R0), SX(r, R0)
Bb = B(z, b, s)
gamm = gam(r)
epx, q = epX(m, M0), Q(m, M0)
print 'gamm,epx,q =', gamm, epx, q
meanmu = del0 / n.sqrt(s) * sx / s0
varmu = Q(m, M0)
meanx = gamm * ((Bb - del0 * sx / s0) *
(1 - epx) / q / n.sqrt(s) + Bb * epx / n.sqrt(s))
varx = 1 - gamm**2 - gamm**2 * (1 - epx)**2 * (1 - q) / q
fact = V / Vstar(R0) * pG(Bb / n.sqrt(s), meanmu, varmu)
print b, Bb / n.sqrt(s), meanmu, varmu, pG(Bb / n.sqrt(s), meanmu, varmu)
factint = quad(lambda x: (x / gamm - b) * F(x) * pG(x, meanx, varx),
b * gamm, 100)[0]
#print fact, factint
return fact * factint
def integrand_trapz(del0,m,M0,R0,z): #2s*f_ESP s = sig0(m2R(m)) V,r,dmdr = pb.volume_radius_dmdr(m,**cosmo) s,s0,sx = sig0(r), sig0(R0),SX(r,R0) gamm = gam(r) epx,q = epX(m,M0), Q(m,M0) meanmu = del0/n.sqrt(s)*sx/s0 varmu = Q(m,M0) varx = 1-gamm**2-gamm**2*(1-epx)**2*(1-q)/q b = n.arange(0.000001,3.,0.03) y = [] for bx in b: y.append(prob(bx)*subgrand_trapz(bx,del0,s,s0,sx,epx,q,meanmu,varmu,varx,gamm,R0,V,z)/2/s) #print 'b,y' #print bx,y[-1] if n.isnan(y[-1]): print 'NAN detected, breaking at: ' print bx,prob(bx),del0,s,s0,sx,epx,q,meanmu,varmu,varx,gamm,R0,V break return n.trapz(y,b,dx=0.05)
def integrand_trapz(del0, m, M0, R0, z): #2s*f_ESP
# of A7, divided by 2s; this IS f_ESP
s = sig0(m2R(m))
V, r, dmdr = pb.volume_radius_dmdr(m, **cosmo)
s, s0, sx = sig0(r), sig0(R0), SX(r, R0)
gamm = gam(r)
epx, q = epX(m, M0), Q(m, M0)
meanmu = del0 / np.sqrt(s) * sx / s0
varmu = q
varx = 1 - gamm**2
#print varmu, varx
if varx < 0:
print "varx<0, breaking at varx, gamm, epx, q,m,M0="
print varx, gamm, epx, q, m, M0
#b = np.arange(0.00001,30.,0.03) #TUNE
b = np.logspace(-6, 3, 100)
y = _integrand_trapz_y(b, del0, s, s0, sx, epx, q, meanmu, varmu, varx,
gamm, R0, V, z)
if (y == 0.).all(): return 0.
blims = _blims(b, y)
while blims[0] == blims[1]:
b = np.logspace(np.log10(blims[0] * 0.99), np.log10(blims[1] * 1.01),
100)
y = _integrand_trapz_y(b, del0, s, s0, sx, epx, q, meanmu, varmu, varx,
gamm, R0, V, z)
blims = _blims(b, y)
b = np.logspace(np.log10(blims[0]), np.log10(blims[1]), 100)
y = _integrand_trapz_y(b, del0, s, s0, sx, epx, q, meanmu, varmu, varx,
gamm, R0, V, z)
if y[-1] / np.max(y) > 1.E-3:
print "Warning: choice of bmax too small"
print y
print blims
import IPython
IPython.embed()
raise (Exception)
if y[0] / np.max(y) > 1.E-3:
print "Warning: choice of bmin too big"
return np.trapz(y, b)
def integrand_trapz(del0, m, M0, R0, z): #2s*f_ESP
s = sig0(m2R(m))
V, r, dmdr = pb.volume_radius_dmdr(m, **cosmo)
s, s0, sx = sig0(r), sig0(R0), SX(r, R0)
gamm = gam(r)
epx, q = epX(m, M0), Q(m, M0)
meanmu = del0 / n.sqrt(s) * sx / s0
varmu = Q(m, M0)
varx = 1 - gamm**2 - gamm**2 * (1 - epx)**2 * (1 - q) / q
b = n.arange(0.000001, 3., 0.03)
y = []
for bx in b:
y.append(
prob(bx) * subgrand_trapz(bx, del0, s, s0, sx, epx, q, meanmu,
varmu, varx, gamm, R0, V, z) / 2 / s)
#print 'b,y'
#print bx,y[-1]
if n.isnan(y[-1]):
print 'NAN detected, breaking at: '
print bx, prob(
bx), del0, s, s0, sx, epx, q, meanmu, varmu, varx, gamm, R0, V
break
return n.trapz(y, b, dx=0.05)