def compute_exact_solution(outdir='./_output',frame=0):
#------------------------------------
from scipy.integrate import fixed_quad, quad
from pyclaw.plotters.data import ClawPlotData
plotdata = ClawPlotData()
plotdata.outdir=outdir
#Read in the solution
dat = plotdata.getframe(frame)
ap=ac.AcousticsProblem('setprob.data','sharpclaw.data')
t = dat.t
print t
grid = dat.grids[0]
xc = dat.center[0]
dx=dat.d
xe = dat.edge[0]
print "Computing exact solution for mx = ",dat.n
qq=zeros([2,size(xc)])
for ii in range(size(xc)):
qq[0,ii],dummy = fixed_quad(ap.pvec,xe[ii],xe[ii+1],args=(t,))
qq[1,ii],dummy = fixed_quad(ap.uvec,xe[ii],xe[ii+1],args=(t,))
#qq[0,ii],dummy= quad(ap.pvec,xe[ii],xe[ii+1],args=(t,),epsabs=1.e-11,epsrel=1.e-11)
#qq[1,ii],dummy= quad(ap.uvec,xe[ii],xe[ii+1],args=(t,),epsabs=1.e-11,epsrel=1.e-11)
qq/=dx
return qq
def FM(self,m,Q,M,alpha,r2bar): if self.presentation==True: #for the presentation period # self consistent equation for m if self.fam==True: #familiar stimuli fun=lambda x:self.distRates(x)*r2bar(x,m,Q,M,alpha) if self.adap_quad==True: var,err=integrate.quad(fun,0.,self.rmax) else: var,err=integrate.fixed_quad(fun,0.,self.rmax,n=self.nquad) return var else: # novel stimuli fun=lambda x:self.distRates(x)*r2bar(x,Q,M,alpha) if self.adap_quad==True: var,err=integrate.quad(fun,0.,self.rmax) else: var,err=integrate.fixed_quad(fun,0.,self.rmax,n=self.nquad) return var else: #for the delay period if self.fam==True: #familiar stimuli fun=lambda x:self.distRates(x)*r2bar(x,m,M,alpha) if self.adap_quad==True: var,err=integrate.quad(fun,0.,self.rmax) else: var,err=integrate.fixed_quad(fun,0.,self.rmax,n=self.nquad) return var else: #novel stimuli fun=lambda x:self.distRates(x)*r2bar(x,M,alpha) if self.adap_quad==True: var,err=integrate.quad(fun,0.,self.rmax) else: var,err=integrate.fixed_quad(fun,0.,self.rmax,n=self.nquad) return var
def _calc_or(self,Rmean,rperi,rap,E,L,fixed_quad,**kwargs):
Tr= 0.
if Rmean > rperi and not fixed_quad:
Tr+= nu.array(integrate.quadrature(_TrSphericalIntegrandSmall,
0.,m.sqrt(Rmean-rperi),
args=(E,L,self._2dpot,
rperi),
**kwargs))[0]
elif Rmean > rperi and fixed_quad:
Tr+= integrate.fixed_quad(_TrSphericalIntegrandSmall,
0.,m.sqrt(Rmean-rperi),
args=(E,L,self._2dpot,
rperi),
n=10,**kwargs)[0]
if Rmean < rap and not fixed_quad:
Tr+= nu.array(integrate.quadrature(_TrSphericalIntegrandLarge,
0.,m.sqrt(rap-Rmean),
args=(E,L,self._2dpot,
rap),
**kwargs))[0]
elif Rmean < rap and fixed_quad:
Tr+= integrate.fixed_quad(_TrSphericalIntegrandLarge,
0.,m.sqrt(rap-Rmean),
args=(E,L,self._2dpot,
rap),
n=10,**kwargs)[0]
Tr= 2.*Tr
return 2.*nu.pi/Tr
def f_dmags(self, dmag, s):
"""Calculates the joint probability density of dMag and projected
separation
Args:
dmag (float):
Value of dMag
s (float):
Value of projected separation (AU)
Returns:
f (float):
Value of joint probability density
"""
if (dmag < self.mindmag(s)) or (dmag > self.maxdmag(s)):
f = 0.0
else:
ztest = (s/self.x)**2*10.**(-0.4*dmag)/self.val
if ztest >= self.zmax:
f = 0.0
elif (self.pconst & self.Rconst):
f = self.f_dmagsz(self.zmin,dmag,s)
else:
if ztest < self.zmin:
f = integrate.fixed_quad(self.f_dmagsz, self.zmin, self.zmax, args=(dmag, s), n=61)[0]
else:
f = integrate.fixed_quad(self.f_dmagsz, ztest, self.zmax, args=(dmag, s), n=61)[0]
return f
def get_FO(self,x,y,z,Q2,qT2,muR2,muF2,charge,ps='dxdQ2dzdqT2',method='gauss'):
D=self.D
D['A1']=1+(2/y-1)**2
D['A2']=-2
w2=qT2/Q2*x*z
w=w2**0.5
xia_=lambda xib: w2/(xib-z)+x
xib_=lambda xia: w2/(xia-x)+z
integrand_xia=lambda xia: self.get_M(xia,xib_(xia),x/xia,z/xib_(xia),Q2,muF2,qT2,charge)
integrand_xib=lambda xib: self.get_M(xia_(xib),xib,x/xia_(xib),z/xib,Q2,muF2,qT2,charge)
if method=='quad':
FO = quad(integrand_xia,x+w,1)[0] + quad(integrand_xib,z+w,1)[0]
elif method=='gauss':
integrand_xia=np.vectorize(integrand_xia)
integrand_xib=np.vectorize(integrand_xib)
FO = fixed_quad(integrand_xia,x+w,1,n=40)[0] + fixed_quad(integrand_xib,z+w,1,n=40)[0]
if ps=='dxdQ2dzdqT2':
s=x*y*Q2
prefactor = D['alphaEM']**2 * self.SC.get_alphaS(muR2)
prefactor/= 2*s**2*Q2*x**2
prefactor*= D['GeV**-2 -> nb']
return prefactor * FO
else:
print 'ps not inplemented'
return None
def _calc_op(self,Or,Rmean,rperi,rap,E,L,fixed_quad,**kwargs):
#Azimuthal period
I= 0.
if Rmean > rperi and not fixed_quad:
I+= nu.array(integrate.quadrature(_ISphericalIntegrandSmall,
0.,m.sqrt(Rmean-rperi),
args=(E,L,self._2dpot,
rperi),
**kwargs))[0]
elif Rmean > rperi and fixed_quad:
I+= integrate.fixed_quad(_ISphericalIntegrandSmall,
0.,m.sqrt(Rmean-rperi),
args=(E,L,self._2dpot,rperi),
n=10,**kwargs)[0]
if Rmean < rap and not fixed_quad:
I+= nu.array(integrate.quadrature(_ISphericalIntegrandLarge,
0.,m.sqrt(rap-Rmean),
args=(E,L,self._2dpot,
rap),
**kwargs))[0]
elif Rmean < rap and fixed_quad:
I+= integrate.fixed_quad(_ISphericalIntegrandLarge,
0.,m.sqrt(rap-Rmean),
args=(E,L,self._2dpot,rap),
n=10,**kwargs)[0]
I*= 2*L
return I*Or/2./nu.pi
def compute_errors(odir='.',frame=0):
#------------------------------------
from scipy.integrate import fixed_quad
# change to output directory and read in solution from fort.q000N
# for frame N.
# read in clawpack solution for this frame:
ap=ac.AcousticsProblem('setprob.data','claw.data')
os.chdir(odir)
clawframe = read_clawframe(frame)
t = clawframe.t
# Assume there is only one grid (AMR not used):
grid = clawframe.grids[0]
print "Computing errors for mx = ",grid.mx
xc = grid.xcenter
qq=zeros([2,size(xc)])
for ii in range(size(xc)):
qq[0,ii],dummy = fixed_quad(ap.pvec,grid.xedge[ii],grid.xedge[ii+1],args=(t,))
qq[1,ii],dummy = fixed_quad(ap.uvec,grid.xedge[ii],grid.xedge[ii+1],args=(t,))
dx=grid.xedge[1]-grid.xedge[0]
qq/=dx
errors = qq[0,:] - grid.q[:,0]
ion()
clf()
plot(xc,qq[0,:],'k',xc,grid.q[:,0],'+b')
draw()
ioff()
return errors
def Gamma(view, sun, arch, refl, trans):
'''The one angle Area Scattering Phase Function based on
Myneni V.18 and Shultis (17) isotropic scattering assumption.
This is the phase function of the scattering in a particular
direction based also on the amount of interception in the direction.
-------------------------------------------------------------
Input: view - view zenith angle, sun - the solar zenith angle,
arch - archetype, see gl function for description,
refl - fraction reflected, trans - fraction transmitted.
Output: Area Scattering Phase function value.
'''
'''
# uncomment/comment the code below for bi-lambetian Gamma.
B = sun - view # uncomment these lines to run test plot
gam = (refl + trans)/np.pi/3.*(np.sin(B) - B*np.cos(B)) +\
trans/np.pi*np.cos(B) # Myneni V.15
'''
func = lambda leaf, view, sun, arch, refl, trans: gl(leaf, arch)\
*(refl*Big_psi(view,sun,leaf,'r') + (trans*Big_psi(view,sun,leaf,'t')))
# the integral as defined in Myneni V.18.
if isinstance(sun, np.ndarray):
# to remove singularity at sun==0.
sun = np.where(sun==0.,1.0e-10,sun)
gam = np.zeros_like(sun)
for j,s in enumerate(sun):
gam[j] = fixed_quad(func, 0., np.pi/2.,\
args=(view,s,arch,refl,trans),n=16)[0]
else:
if sun==0.:
sun = 1.0e-10 # to remove singularity at sun==0.
gam = fixed_quad(func, 0., np.pi/2.,\
args=(view,sun,arch,refl,trans),n=16)[0]
# integrate leaf angles between 0 to pi/2.
return gam
def G(view, arch):
'''The Geometry factor for a specific view or solar
direction based on Myneni III.16. The projection of 1 unit
area of leaves within a unit volume onto the plane perpen-
dicular to the view or solar direction.
------------------------------------------------------------
Input: view - the view or solar zenith angle in radians,
arch - archetype, see gl function for description of each.
Output: The integral of the Geometry function (G).
'''
g = lambda angle, view, arch: gl(angle, arch)\
*psi(angle,view) # the G function as defined in Myneni III.16.
if isinstance(view, np.ndarray):
if arch == 's': # avoid integration in case of isometric distr.
G = np.ones_like(view) * 0.5
return G
view = np.where(view > np.pi, 2.*np.pi - view, view)
G = np.zeros_like(view)
for j,v in enumerate(view):
G[j] = fixed_quad(g, 0., np.pi/2., args=(v, arch),n=16)[0]
else:
if arch == 's': # avoid integration, see above...
G = 0.5
return G
if view > np.pi: # symmetry of distribution about z axis
view = np.pi - view
G = fixed_quad(g, 0., np.pi/2., args=(view, arch),n=16)[0]
# integrate g function between 0 to pi/2.
return G
def _calc_angler(self,Or,r,Rmean,rperi,rap,E,L,vr,fixed_quad,**kwargs):
if r < Rmean:
if r > rperi and not fixed_quad:
wr= Or*integrate.quadrature(_TrSphericalIntegrandSmall,
0.,m.sqrt(r-rperi),
args=(E,L,self._2dpot,rperi),
**kwargs)[0]
elif r > rperi and fixed_quad:
wr= Or*integrate.fixed_quad(_TrSphericalIntegrandSmall,
0.,m.sqrt(r-rperi),
args=(E,L,self._2dpot,rperi),
n=10,**kwargs)[0]
else:
wr= 0.
if vr < 0.: wr= 2*m.pi-wr
else:
if r < rap and not fixed_quad:
wr= Or*integrate.quadrature(_TrSphericalIntegrandLarge,
0.,m.sqrt(rap-r),
args=(E,L,self._2dpot,rap),
**kwargs)[0]
elif r < rap and fixed_quad:
wr= Or*integrate.fixed_quad(_TrSphericalIntegrandLarge,
0.,m.sqrt(rap-r),
args=(E,L,self._2dpot,rap),
n=10,**kwargs)[0]
else:
wr= m.pi
if vr < 0.:
wr= m.pi+wr
else:
wr= m.pi-wr
return wr
def onef_dmags(dmag, s, ranges, val, pdfs, funcs, x):
"""Returns joint probability density of s and dmag
Args:
dmag (float):
Value of difference in brightness magnitude
s (float):
Value of planet-star separation
ranges (tuple):
pmin (float): minimum value of geometric albedo
pmax (float): maximum value of geometric albedo
Rmin (float): minimum value of planetary radius (km)
Rmax (float): maximum value of planetary radius (km)
rmin (float): minimum value of orbital radius (AU)
rmax (float): maximum value of orbital radius (AU)
zmin (float): minimum value of pR^2 (km^2)
zmax (float): maximum value of pR^2 (km^2)
val (float):
Value of sin(bstar)**2*Phi(bstar)
pdfs (tuple):
Probability density functions for pR^2 and orbital radius
funcs (tuple):
Inverse functions of sin(b)**2*Phi(b)
x (float):
Conversion factor between AU and km
Returns:
f (float):
Joint probability density of s and dmag
"""
pmin, pmax, Rmin, Rmax, rmin, rmax, zmin, zmax = ranges
minrange = (pmax, Rmax, rmin, rmax)
maxrange = (pmin, Rmin, rmax)
pconst = pmin == pmax
Rconst = Rmin == Rmax
if (dmag < util.mindmag(s, minrange, x)) or (dmag > util.maxdmag(s, maxrange, x)):
f = 0.0
elif (pconst & Rconst):
ranges2 = (rmin, rmax)
f = onef_dmagsz(pmin*Rmin**2, dmag, s, val, pdfs, ranges2, funcs, x)
else:
ztest = (s/x)**2*10.0**(-0.4*dmag)/val
ranges2 = (rmin, rmax)
if ztest >= zmax:
f = 0.0
else:
if ztest < zmin:
f = integrate.fixed_quad(onef_dmagsz, zmin, zmax, args=(dmag, s, val, pdfs, ranges2, funcs, x), n=61)[0]
else:
f = integrate.fixed_quad(onef_dmagsz, ztest, zmax, args=(dmag, s, val, pdfs, ranges2, funcs, x), n=61)[0]
return f
def calc_stream(k, nk, beta, sigma, flag):
stream = k*0.0+1.0
if(flag=='exp'):
for cc in range(0,nk):
tempi = integrate.fixed_quad(pmu_exp,-1,1,args=(k[cc],sigma,beta),n=8)
stream[cc] = 0.5*tempi[0] #0.5* to normalize Legendre L_0
elif(flag=='Gauss'):
for cc in range(0,nk):
tempi = integrate.fixed_quad(pmu_gauss,-1,1,args=(k[cc],sigma,beta),n=8)
stream[cc] = 0.5*tempi[0] #0.5* to normalize Legendre L_0
return stream
def Expectation(model,dist,distparam1,distparam2,Aproj,distparamextra = 0):
from scipy import integrate
import numpy as np
# this routine takes in the name of the roof model desired, the distibution of mass to be integrated with respect to,
# and parameters needed to define the distribution
#fwood,fsteel,fconcrete,fcomposite,flightMetal,ftile= getModel()
functions = getModel()
if model.lower()=='all':
# HERE COMES AN ASSUMPTION TO GIVE ROOF CASUALTY AREA TO ROOF TYPES FOR WHICH DATA IS NOT AVAILABLE:
# assuming that all roof of similar types have the same casualty areas. e.g all wood roofs are the same
# the order of models is assumed to be as follows
# Wood Roof, Wood 1st, Wood 2nd, Steel Roof, Steel 1st, Steel 2nd, Concrete, Concrete 1st, Concrete 2nd, Composite
# Light Metal, Tile Roof, Tile 1st, Tile 2nd, Car, Open
if dist.lower() =='uniform':
lowbound = distparam1
highbound = distparam2
denc = highbound-lowbound
if denc>0.:
c = 1./denc
elif denc<0.:
print 'Check bounds in upper and lower bound. roofPenetration.Expectation'
exit(1)
elif dist.lower() =='gaussian' or dist.lower() == 'normal' or dist.lower()=='gauss':
mu = distparam1
sigma = distparam2
lowbound = max(-1e3,mu-5.*sigma)
highbound = min(1e6,mu+5.*sigma)
fgauss = lambda x: np.exp(-.5*((x-mu)/sigma)**2)/(sigma*(2.*np.pi)**.5)
EretMain = np.zeros((len(functions)))
for index in range(len(functions)):
froof = functions[index]
if dist.lower() =='uniform':
if denc ==0.0:
retval = froof(lowbound)
else:
invals = integrate.fixed_quad(froof,lowbound,highbound,n=50)
retval = invals[0]*c
elif dist.lower() =='gaussian' or dist.lower() == 'normal' or dist.lower()=='gauss':
fvals = lambda x: fgauss(x)*froof(x)
invals = integrate.fixed_quad(fvals,lowbound,highbound,n=50)
retval = invals[0]
EretMain[index] = retval
Eret = np.zeros((16))
Eret = np.concatenate((3*[EretMain[0]],3*[EretMain[1]],3*[EretMain[2]],[EretMain[3]],[EretMain[4]],3*[EretMain[5]],[EretMain[4]],[Aproj]),1)
return Eret
def _calc_anglez(self,Or,Op,ar,z,r,Rmean,rperi,rap,E,L,Lz,vr,axivz,
fixed_quad,**kwargs):
#First calculate psi
i= nu.arccos(Lz/L)
sinpsi= z/r/nu.sin(i)
if sinpsi > 1. and sinpsi < (1.+10.**-7.):
sinpsi= 1.
if sinpsi < -1. and sinpsi > (-1.-10.**-7.):
sinpsi= -1.
psi= nu.arcsin(sinpsi)
if axivz > 0.: psi= nu.pi-psi
psi= psi % (2.*nu.pi)
#Calculate dSr/dL
dpsi= Op/Or*2.*nu.pi #this is the full I integral
if r < Rmean:
if not fixed_quad:
wz= L*integrate.quadrature(_ISphericalIntegrandSmall,
0.,m.sqrt(r-rperi),
args=(E,L,self._2dpot,
rperi),
**kwargs)[0]
elif fixed_quad:
wz= L*integrate.fixed_quad(_ISphericalIntegrandSmall,
0.,m.sqrt(r-rperi),
args=(E,L,self._2dpot,
rperi),
n=10,**kwargs)[0]
if vr < 0.: wz= dpsi-wz
else:
if not fixed_quad:
wz= L*integrate.quadrature(_ISphericalIntegrandLarge,
0.,m.sqrt(rap-r),
args=(E,L,self._2dpot,
rap),
**kwargs)[0]
elif fixed_quad:
wz= L*integrate.fixed_quad(_ISphericalIntegrandLarge,
0.,m.sqrt(rap-r),
args=(E,L,self._2dpot,
rap),
n=10,**kwargs)[0]
if vr < 0.:
wz= dpsi/2.+wz
else:
wz= dpsi/2.-wz
#Add everything
wz= -wz+psi+Op/Or*ar
return wz
def comp_s(self, smin, smax, dMag):
"""Calculates completeness by first integrating over dMag and then
projected separation.
Args:
smin (ndarray):
Values of minimum projected separation (AU) from instrument
smax (ndarray):
Value of maximum projected separation (AU) from instrument
dMag (ndarray):
Planet delta magnitude
Returns:
comp (ndarray):
Completeness values
"""
# cast to arrays
smin = np.array(smin, ndmin=1, copy=False)
smax = np.array(smax, ndmin=1, copy=False)
dMag = np.array(dMag, ndmin=1, copy=False)
comp = np.zeros(smin.shape)
for i in xrange(len(smin)):
comp[i] = integrate.fixed_quad(self.f_sv, smin[i], smax[i], args=(dMag[i],), n=50)[0]
# ensure completeness values are between 0 and 1
comp = np.clip(comp, 0., 1.)
return comp
def res_wage_operator(self, phi):
"""
Updates the reservation wage function guess phi via the operator
Q.
Parameters
----------
phi : array_like(float, ndim=1, length=len(pi_grid))
This is reservation wage guess
Returns
-------
new_phi : array_like(float, ndim=1, length=len(pi_grid))
The updated reservation wage guess.
"""
# == Simplify names == #
beta, c, f, g, q = self.beta, self.c, self.f, self.g, self.q
# == Turn phi into a function == #
phi_f = lambda p: interp(p, self.pi_grid, phi)
new_phi = np.empty(len(phi))
for i, pi in enumerate(self.pi_grid):
def integrand(x):
"Integral expression on right-hand side of operator"
return npmax(x, phi_f(q(x,pi))) * (pi*f(x) + (1 - pi)*g(x))
integral, error = fixed_quad(integrand, 0, self.w_max)
new_phi[i] = (1 - beta) * c + beta * integral
return new_phi
def get_greedy(self, v):
"""
Compute optimal actions taking v as the value function.
Parameters
----------
v : array_like(float, ndim=1, length=len(pi_grid))
An approximate value function represented as a
one-dimensional array.
Returns
-------
policy : array_like(float, ndim=1, length=len(pi_grid))
The decision to accept or reject an offer where 1 indicates
accept and 0 indicates reject
"""
# == Simplify names == #
f, g, beta, c, q = self.f, self.g, self.beta, self.c, self.q
vf = LinearNDInterpolator(self.grid_points, v)
N = len(v)
policy = np.zeros(N, dtype=int)
for i in range(N):
w, pi = self.grid_points[i,:]
v1 = w / (1 - beta)
integrand = lambda m: vf(m, q(m, pi)) * (pi * f(m) + \
(1 - pi) * g(m))
integral, error = fixed_quad(integrand, 0, self.w_max)
v2 = c + beta * integral
policy[i] = v1 > v2 # Evaluates to 1 or 0
return policy
def test_scalar(self):
n = 4
func = lambda x: x**(2*n - 1)
expected = 1/(2*n)
got, _ = fixed_quad(func, 0, 1, n=n)
# quadrature exact for this input
assert_allclose(got, expected, rtol=1e-12)
def test_vector(self):
n = 4
p = np.arange(1, 2*n)
func = lambda x: x**p[:,None]
expected = 1/(p + 1)
got, _ = fixed_quad(func, 0, 1, n=n)
assert_allclose(got, expected, rtol=1e-12)
def Ef2(self):# mean of f**2 fun=lambda x:self.distRates(x)*self.f(x)*self.f(x) if self.adap_quad==True: var,err=integrate.quad(fun,0.,self.rmax) else: var,err=integrate.fixed_quad(fun,0.,self.rmax,n=self.nquad) return var
def get_A(self,x,mub2,zetaD,bT2,flav):
# Eqs. A10 & A11 of PRD83 114042
D=self.D
factor1 = 0.5*np.log(4/(mub2*bT2))-D['gamma']
factor2 =-0.5*(np.log(bT2*mub2)-2*(np.log(2)-D['gamma']))**2\
-(np.log(bT2*mub2) - 2*(np.log(2)-D['gamma'])) * np.log(zetaD/mub2)
if flav.startswith('g'):
C0 = 0
C1 = lambda z: 0
C2 = lambda z: D['TF']*(2*(1-2*z*(1-z))*factor1 + 2*z*(1-z))
C3 = factor2
else:
C0 = 1
C1 = lambda z: D['CF']*2*factor1*2
C2 = lambda z: D['CF']*(2*factor1*(-1-z) + 1-z)
C3 = factor2
# get alpha strong
alphaS=self.SC.get_alphaS(mub2)
D['DI'] = lambda z: C0 +alphaS/(2*np.pi)*(-(1-x)*C1(z)/z**2/(1-z)\
+ C1(1)*np.log(1-x) + C3)
D['DII'] = lambda z: alphaS/(2*np.pi)*(1-x)*(C1(z)/z**2/(1-z) + C2(z)/z**2)
D['ff'] = lambda x: self.CFF.get_FF(x,D['muF2'],flav,D['charge'])
D['x'] = x
func=np.vectorize(self.integrand4A)
return fixed_quad(func,0,1,n=40)[0]
def grand2(a, r, emin, emax, f_e, f_a):
"""Returns second integrand for determining probability density of orbital
radius
Args:
a (float):
Value of semi-major axis (AU)
r (float):
Value of orbital radius (AU)
emin (float):
Minimum eccentricity
emax (float):
Maximum eccentricity
f_e (callable(e)):
Probability density function for eccentricity
f_a (callable(a)):
Probability density function for semi-major axis
"""
emin1 = np.abs(1.0 - r/a)
if emin1 < emin:
emin1 = emin
if emin1 > emax:
f = 0.0
else:
f = integrate.fixed_quad(grand1, emin1, emax, args=(a,r,f_e,f_a), n=100)[0]
return f
def bellman_operator(self, v):
"""
The Bellman operator. Including for comparison. Value function
iteration is not recommended for this problem. See the reservation
wage operator below.
Parameters
==============
v : An approximate value function represented as a
one-dimensional array.
"""
# == Simplify names == #
f, g, beta, c, q = self.f, self.g, self.beta, self.c, self.q
vf = LinearNDInterpolator(self.grid_points, v)
N = len(v)
new_v = np.empty(N)
for i in range(N):
w, pi = self.grid_points[i,:]
v1 = w / (1 - beta)
integrand = lambda m: vf(m, q(m, pi)) * (pi * f(m) \
+ (1 - pi) * g(m))
integral, error = fixed_quad(integrand, 0, self.w_max)
v2 = c + beta * integral
new_v[i] = max(v1, v2)
return new_v
def f_dmag(self, dmag, smin, smax):
"""Calculates probability density of dMag by integrating over projected
separation
Args:
dmag (float):
Planet delta magnitude
smin (float):
Value of minimum projected separation (AU) from instrument
smax (float):
Value of maximum projected separation (AU) from instrument
Returns:
f (float):
Value of probability density
"""
if dmag < self.mindmag(smin):
f = 0.0
else:
su = self.s_bound(dmag, smax)
if su > smax:
su = smax
if su < smin:
f = 0.0
else:
f = integrate.fixed_quad(self.f_sdmagv, smin, su, args=(dmag,), n=50)[0]
return f
def f_s(self, s, dMagMax):
"""Calculates probability density of projected separation marginalized
up to dMagMax
Args:
s (float):
Value of projected separation
dMagMax (float):
Maximum planet delta magnitude
Returns:
f (float):
Probability density
"""
if (s == 0.0) or (s == self.rmax):
f = 0.0
else:
d1 = self.mindmag(s)
d2 = self.maxdmag(s)
if d2 > dMagMax:
d2 = dMagMax
if d1 > d2:
f = 0.0
else:
f = integrate.fixed_quad(self.f_dmagsv, d1, d2, args=(s,), n=50)[0]
return f
def H_element(n, n_prim, problem, step_size, l = 0, j = .5):
p, p_prim = [(x + 1)*step_size for x in (n, n_prim)]
diagonal = p**2 / (2 * problem.mass) * (n == n_prim)
V = problem.potential
integral, _ = fixed_quad(integrand, 0, 10, \
n = 20, args=(p, p_prim, V, l, j))
return diagonal + 2 * p_prim**2 * step_size / sp.pi * integral
def onef_zeta(zetai, pdfs, ranges):
"""Determines probability density for zeta = p*R^2
Args:
zetai (float):
Value of zeta = pR^2
pdfs (tuple):
Probability density functions f_p and f_R
ranges (tuple):
pmin (float): minimum value of geometric albedo
pmax (float): maximum value of geometric albedo
Rmin (float): minimum value of planetary radius (km)
Rmax (float): maximum value of planetary radius (km)
Returns:
f (float):
probability density of given zetai
"""
f_p, f_R = pdfs
pmin, pmax, Rmin, Rmax = ranges
p1 = zetai/Rmax**2
p2 = zetai/Rmin**2
if p1 < pmin:
p1 = pmin
if p2 > pmax:
p2 = pmax
f = integrate.fixed_quad(pgrand,p1,p2,args=(zetai,f_p,f_R),n=200)[0]
return f
def integrate(self, g, int_min=None, int_max=None):
"""
Integrate the function g(z) * self.phi(z) from int_min to
int_max.
Parameters
----------
g : function
The function which to integrate
int_min, int_max : scalar(float), optional
The bounds of integration. If either of these parameters are
`None` (the default), they will be set to 4 standard
deviations above and below the mean.
Returns
-------
result : scalar(float)
The result of the integration
"""
# == Simplify notation == #
phi = self.phi
if int_min is None:
int_min = self._int_min
if int_max is None:
int_max = self._int_max
# == set up integrand and integrate == #
integrand = lambda z: g(z) * phi.pdf(z)
result, error = fixed_quad(integrand, int_min, int_max)
return result
def Eg2(self):# mean of g**2 fun=lambda x:self.distRates2(x)*self.g(x)*self.g(x) if self.adap_quad==True: var,err=integrate.quad(fun,0.,self.rmaxSig) else: var,err=integrate.fixed_quad(fun,0.,self.rmaxSig,n=self.nquad) return var
def Function(self, x, param):
Ktrans, ve = param
#s = quadrature(lambda t: self.Aif(t) * scipy.exp(-Ktrans*(x-t)/ve), 0.0, x, tol=1.0e-03, vec_func=False)
s = fixed_quad(lambda t: self.Aif(t) * scipy.exp(-Ktrans*(x-t)/ve), 0.0, x, n=5)
y = Ktrans * s[0]
return y
def predict_proba(self, X, interval=0.95, *args, **kwargs):
# Expectation and variance in latent space
Ey_t, Vy_t, ql, qu = super().predict_proba(X, interval)
# Save computation if identity transform
if type(self.target_transform) is transforms.Identity:
return Ey_t, Vy_t, ql, qu
# Save computation if standardise transform
elif type(self.target_transform) is transforms.Standardise:
Ey = self.target_transform.itransform(Ey_t)
Vy = Vy_t * self.target_transform.ystd**2
ql, qu = norm.interval(interval, loc=Ey, scale=np.sqrt(Vy))
return Ey, Vy, ql, qu
# All other transforms require quadrature
Ey = np.empty_like(Ey_t)
Vy = np.empty_like(Vy_t)
# Used fixed order quadrature to transform prob. estimates
for i, (Eyi, Vyi) in enumerate(zip(Ey_t, Vy_t)):
# Establish bounds
Syi = np.sqrt(Vyi)
a, b = Eyi - 3 * Syi, Eyi + 3 * Syi # approx 99% bounds
# Quadrature
Ey[i], _ = fixed_quad(self.__expec_int,
a,
b,
n=QUADORDER,
args=(Eyi, Syi))
Vy[i], _ = fixed_quad(self.__var_int,
a,
b,
n=QUADORDER,
args=(Ey[i], Eyi, Syi))
ql, qu = norm.interval(interval, loc=Ey, scale=np.sqrt(Vy))
return Ey, Vy, ql, qu
def piecewise_ramp(step_func,
t_channels,
t_currents,
currents,
n=20,
eps=1e-10):
"""
Computes response from piecewise linear current waveform
with a single pulse. This basically evaluates the convolution
between dI/dt and step-off response.
step_func: function handle to evaluate step-off response
t_channels: time channels when the current is on or off
currents: input source currents
n: Gaussian quadrature order
"""
dt = np.diff(t_currents)
dI = np.diff(currents)
dIdt = dI / dt
nt = t_currents.size
response = np.zeros(t_channels.size, dtype=float)
pulse_time = t_currents.max()
for i in range(1, nt):
t_lag = pulse_time - t_currents[i]
time = t_lag + t_channels
t0 = dt[i - 1]
const = -dIdt[i - 1]
if abs(const) > eps:
for j, t in enumerate(time):
# on-time
# TODO: this is only working when we have a single ramp...
if t < 0.:
print(t + t0)
response[j] += (fixed_quad(step_func, 0, t + t0, n=n)[0] *
const)
# off-time
else:
response[j] += (fixed_quad(step_func, t, t + t0, n=n)[0] *
const)
return response
def integ_lens(total ,k1): f1 = interpolate.interp1d(k1, total) def func(x): return f1(x) * (2*x +1) kmin = np.min(k1) kmax = np.max(k1) intf,_ = integrate.fixed_quad(func, kmin, kmax, n = 200) return intf
def arc_length(tfinal, CTRL):
degree = 3
knotvector = bs.Knotvector(CTRL, degree)
length = integrate.fixed_quad(func_to_integrate,
0.0,
tfinal,
args=(CTRL, degree, knotvector),
n=10)
return length[0]
def slope_parameter(self, a):
def kernel(x):
return self.total_likelyhood(a, x)
s = np.log(
integrate.fixed_quad(kernel, self.b_min, self.b_max,
n=self.Nquad)[0])
s = s - np.log(self.Normalization)
s = np.exp(s)
return s
def line_integral(function, p0, p1, singular):
x0, y0, x1, y1 = *p0, *p1
length = np.sqrt((x1 - x0)**2 + (y1 - y0)**2)
def to_quad(t):
return function(
np.array([(x1 + x0) / 2 + t * (x1 - x0) / 2,
(y1 + y0) / 2 + t * (y1 - y0) / 2]))
if singular:
return length * complex_quad(to_quad, -1, 1, points=[0]) / 2
return length * fixed_quad(np.vectorize(to_quad), -1.0, 1.0)[0] / 2
def min_func_local(estimate):
discrimination[ndx] = estimate
_mml_abstract(difficulty[ndx, None], scalar[ndx, None],
discrimination[ndx, None], theta, distribution, options)
estimate_int = _compute_partial_integral(theta, difficulty[ndx, None],
discrimination[ndx, None],
the_sign[ndx, None])
estimate_int *= partial_int
otpt = integrate.fixed_quad(
lambda x: estimate_int, quad_start, quad_stop, n=quad_n)[0]
return -np.log(otpt).dot(counts)
def _local_min_func(estimate):
new_betas = estimate[2:]
new_values = _unfold_partial_integral(theta, estimate[1],
new_betas,
estimate[0], fold_span[item_ndx],
responses[item_ndx])
new_values *= partial_int
otpt = integrate.fixed_quad(
lambda x: new_values, quad_start, quad_stop, n=quad_n)[0]
return -np.log(otpt).sum()
def integ(der1, der2 ,k, kmin, kmax): f1 = interpolate.interp1d(k, der1) f2 = interpolate.interp1d(k, der2) def func(x): return f1(x) * (x**2)* f2(x) intf,_ = integrate.fixed_quad(func, kmin, kmax, n = 200) return intf
def get_exact_moments(distribution, moments_fn):
"""
Get exact moments from given distribution
:param distribution: Distribution object
:param moments_fn: Function for generating moments
:return: Exact moments
"""
integrand = lambda x: moments_fn(x).T * distribution.pdf(x)
a, b = moments_fn.domain
integral = integrate.fixed_quad(integrand, a, b, n=moments_fn.size * 5)[0]
return integral[1:]
def _calc_jr(self,rperi,rap,E,L,fixed_quad,**kwargs):
if fixed_quad:
return integrate.fixed_quad(_JrSphericalIntegrand,
rperi,rap,
args=(E,L,self._2dpot),
n=10,
**kwargs)[0]/nu.pi
else:
return (nu.array(integrate.quad(_JrSphericalIntegrand,
rperi,rap,
args=(E,L,self._2dpot),
**kwargs)))[0]/nu.pi
def MaxEnt(supp, g_X, restrictions):
f = f_X(g_X)
S = lambda v: integrate.fixed_quad(
lambda x, v: f(x, v) * np.log(f(x, v)), supp[0], supp[1], args=(v, ))[0
]
moms = [moment(f, gi_X, supp) for gi_X in g_X]
h = [
lambda v: moms[i](v) - restrictions[i]
for i in range(len(restrictions))
]
v = ALM(S, h, np.zeros(len(restrictions)), 100)
return f, v
def _calc_angler(self, Or, r, Rmean, rperi, rap, E, L, vr, fixed_quad,
**kwargs):
if r < Rmean:
if r > rperi and not fixed_quad:
wr = Or * integrate.quadrature(_TrSphericalIntegrandSmall,
0.,
m.sqrt(r - rperi),
args=(E, L, self._2dpot, rperi),
**kwargs)[0]
elif r > rperi and fixed_quad:
wr = Or * integrate.fixed_quad(_TrSphericalIntegrandSmall,
0.,
m.sqrt(r - rperi),
args=(E, L, self._2dpot, rperi),
n=10,
**kwargs)[0]
else:
wr = 0.
if vr < 0.: wr = 2 * m.pi - wr
else:
if r < rap and not fixed_quad:
wr = Or * integrate.quadrature(_TrSphericalIntegrandLarge,
0.,
m.sqrt(rap - r),
args=(E, L, self._2dpot, rap),
**kwargs)[0]
elif r < rap and fixed_quad:
wr = Or * integrate.fixed_quad(_TrSphericalIntegrandLarge,
0.,
m.sqrt(rap - r),
args=(E, L, self._2dpot, rap),
n=10,
**kwargs)[0]
else:
wr = m.pi
if vr < 0.:
wr = m.pi + wr
else:
wr = m.pi - wr
return wr
def min_local_func(beta_estimate):
difficulty[item_ndx] = beta_estimate
estimate_int = _compute_partial_integral(theta, difficulty[item_ndx, None],
discrimination[item_ndx, None],
the_sign[item_ndx, None])
estimate_int *= partial_int
otpt = integrate.fixed_quad(
lambda x: estimate_int, quad_start, quad_stop, n=quad_n)[0]
return -np.log(otpt).dot(counts)
def intaeE(self, a, e):
"""Returns integral over eccentric anomaly for probability density
function for observed eccentricity"""
# a is a scalar, e is a scalar
if self.pconst and self.Rconst:
intaebv = np.vectorize(self.intaeb)
grand = lambda E: (1.0 - e * np.cos(E)) * intaebv(
E, a, e, self.pop.prange[0] * self.pop.Rrange[0]**2)
else:
grand = lambda E: (1.0 - e * np.cos(E)) * self.intaezv(E, a, e)
f = integrate.fixed_quad(grand, 0.0, 2.0 * np.pi, n=20)[0]
return f
def snr_at_z(z):
logzp1 = np.log(z + 1)
integrand = lambda log_f: [
np.exp(num(log_f + logzp1) + denom(log_f)) for denom in denoms
]
integrals, _ = fixed_quad(integrand,
log_f_lo,
log_f_hi - logzp1,
n=1024)
snr = get_decisive_snr(np.sqrt(4 * integrals))
with np.errstate(divide='ignore'):
snr /= cosmo.angular_diameter_distance(z).to_value(units.Mpc)
return snr
def eulerDiff(self, c, X):
if (np.isscalar(c)):
EuPrime = integrate.fixed_quad(self.EuPrimePart,
self.yMin,
self.yMax,
args=(X, c),
n=self.quad_order)
return self.uPrime(c) - (self.beta * self.R * EuPrime[0])
diff = np.empty(len(c))
for ix, (cVal, XVal) in enumerate(zip(c, X)):
EuPrime = integrate.fixed_quad(self.EuPrimePart,
self.yMin,
self.yMax,
args=(XVal, cVal),
n=self.quad_order)
diff[ix] = self.uPrime(cVal) - (self.beta * self.R * EuPrime[0])
return diff
def get_L2_norm(cell_faces, function):
# Integrate square of function over each cell.
sq_int_parts = np.zeros(cell_faces.shape[0] + 1)
for i in range(0, cell_faces.shape[0] - 1):
sq_int_parts[i] = fixed_quad(func=lambda x_lam: (function(x_lam))**2,
a=cell_faces[i],
b=cell_faces[i + 1],
n=5)[0]
# Sum integrals of individual cells, and take sqrt of sum.
norm = np.sqrt(np.sum(sq_int_parts))
return norm
def theoretical_prediction4(
self, RRp, theta, rbin_min,
rbin_max): # cen-sat_pairs model, no miscentering
lnmparent_true, lnmsat_true, lnmstellar_true, conc_parent, conc_sat, mck = theta
dsigma_sat = DeltaSigmaSatellite(10**lnmsat_true, conc_sat).dsigma(RRp)
dsigma_parent = DeltaSigmaParent(10**lnmparent_true,
conc_parent).dsigma(RRp)
dsigma_stellar = DeltaSigmaStellar(10**lnmstellar_true).dsigma(RRp)
dsigma_thp = dsigma_parent + dsigma_sat + dsigma_stellar
spline_thpredict = interp1d(np.log10(RRp),
dsigma_thp,
fill_value="extrapolate")
storing_delta_sigma1 = np.zeros(len(pairs_plot) - 1)
if not len(RRp) == len(storing_delta_sigma1):
print("You are not plotting with observational axis")
sys.exit()
for i in range(len(pairs_plot) - 1):
a = pairs_plot[i]
b = pairs_plot[i + 1]
integration_numerator = fixed_quad(
lambda x: (10**spline_totalpairs(np.log10(x))
) * spline_thpredict(np.log10(x)),
a,
b,
n=50)[0]
integration_denominator = fixed_quad(
lambda x: (10**spline_totalpairs(np.log10(x))), a, b, n=50)[0]
delta_sigma_a_b = integration_numerator / integration_denominator
storing_delta_sigma1[i] = delta_sigma_a_b
#integration_numerator2=quad(lambda x: spline_thpredict(np.log10(x)),a,b)[0]
#integration_denominator2=b-a
#delta_sigma_a_b2=integration_numerator2/integration_denominator2
#storing_delta_sigma2[i] =delta_sigma_a_b2
#storing_sat_axis[i]=(a+b)/2
#print("delta_sigma averaged,not averaged,observed",delta_sigma_a_b,delta_sigma_a_b2)
return storing_delta_sigma1
def get_x(func_val, n):
if func_val >= 0.5:
return 4.99999
a = 0
b = 5
while True:
num = (fixed_quad(f, 0, (a + b) / 2, n=n)[0] / sqrt(2 * pi))
if num < func_val + 0.00000001 and num > func_val - 0.00000001:
return round((a + b) / 2, 5)
elif num < func_val:
a = (a + b) / 2
elif num > func_val:
b = (a + b) / 2
def direct_estimate_diff_var(self, level_sims, distr, moments_fn):
"""
Used in mlmc_test_run
Calculate variances of level differences using numerical quadrature.
:param moments_fn:
:param domain:
:return:
"""
mom_domain = moments_fn.domain
means = []
vars = []
sim_l = None
for l in range(len(level_sims)):
# TODO: determine integration domain as _sample_fn ^{-1} ( mom_domain )
domain = mom_domain
sim_0 = sim_l
sim_l = lambda x, h=level_sims[l].step: level_sims[l]._sample_fn(
x, h)
if l == 0:
md_fn = lambda x: moments_fn(sim_l(x))
else:
md_fn = lambda x: moments_fn(sim_l(x)) - moments_fn(sim_0(x))
fn = lambda x: (md_fn(x)).T * distr.pdf(x)
moment_means = integrate.fixed_quad(fn,
domain[0],
domain[1],
n=100)[0]
fn2 = lambda x: (
(md_fn(x) - moment_means[None, :])**2).T * distr.pdf(x)
moment_vars = integrate.fixed_quad(fn2,
domain[0],
domain[1],
n=100)[0]
means.append(moment_means)
vars.append(moment_vars)
return means, vars
def rgrand2(self, a, r):
"""Calculates second integrand for determining probability density of
orbital radius
Args:
a (float):
Value of semi-major axis in AU
r (float):
Value of orbital radius in AU
Returns:
f (float):
Value of second integrand
"""
emin1 = np.abs(1.0 - r / a)
emin1 *= (1.0 + 1e-3)
if emin1 < self.emin:
emin1 = self.emin
if emin1 >= self.emax:
f = 0.0
else:
if self.PlanetPopulation.constrainOrbits:
if a <= 0.5 * (self.amin + self.amax):
elim = 1.0 - self.amin / a
else:
elim = self.amax / a - 1.0
if emin1 > elim:
f = 0.0
else:
f = self.dist_sma(a) / a * integrate.fixed_quad(
self.rgrand1, emin1, elim, args=(a, r), n=60)[0]
else:
f = self.dist_sma(a) / a * integrate.fixed_quad(
self.rgrand1, emin1, self.emax, args=(a, r), n=60)[0]
return f
def min_func(estimate):
discrimination[:] = estimate
_mml_abstract(difficulty, scalar, discrimination,
theta, distribution, options)
partial_int = _compute_partial_integral(theta, difficulty,
discrimination, the_sign)
# add distribution
partial_int *= distribution
otpt = integrate.fixed_quad(
lambda x: partial_int, quad_start, quad_stop, n=quad_n)[0]
return -np.log(otpt).dot(counts)
def inner_prod(self, f, i, quad_size=40):
"""
Compute the inner product
\int f(x) h_i(x) \pi(x) dx
where \pi is the standard normal distribution.
"""
integrand = lambda x: f(x) * self.__call__(i, x) * norm.pdf(
x, loc=self.mu, scale=self.sig)
std_devs = 5 # Integrate out to 5 std deviations in each direction
a = self.mu - self.sig * std_devs
b = self.mu + self.sig * std_devs
return fixed_quad(integrand, a, b, n=quad_size)[0]
def alpha_min_func(alpha_estimate):
discrimination[:] = alpha_estimate
for iteration in range(options['max_iteration']):
previous_difficulty = difficulty.copy()
# Quadrature evaluation for values that do not change
partial_int = _compute_partial_integral(theta, difficulty,
discrimination, the_sign)
partial_int *= distribution
for item_ndx in range(n_items):
# pylint: disable=cell-var-from-loop
# remove contribution from current item
local_int = _compute_partial_integral(theta, difficulty[item_ndx, None],
discrimination[item_ndx, None],
the_sign[item_ndx, None])
partial_int /= local_int
def min_local_func(beta_estimate):
difficulty[item_ndx] = beta_estimate
estimate_int = _compute_partial_integral(theta, difficulty[item_ndx, None],
discrimination[item_ndx, None],
the_sign[item_ndx, None])
estimate_int *= partial_int
otpt = integrate.fixed_quad(
lambda x: estimate_int, quad_start, quad_stop, n=quad_n)[0]
return -np.log(otpt).dot(counts)
fminbound(min_local_func, -4, 4)
# Update the partial integral based on the new found values
estimate_int = _compute_partial_integral(theta, difficulty[item_ndx, None],
discrimination[item_ndx, None],
the_sign[item_ndx, None])
# update partial integral
partial_int *= estimate_int
if(np.abs(previous_difficulty - difficulty).max() < 1e-3):
break
cost = integrate.fixed_quad(
lambda x: partial_int, quad_start, quad_stop, n=quad_n)[0]
return -np.log(cost).dot(counts)
def negObjFunc(self, c, X):
if (np.isscalar(c)):
EV = integrate.fixed_quad(self.EVpart,
self.yMin,
self.yMax,
args=(X, c),
n=self.quad_order)
return -(self.u(c) + (self.beta * EV[0]))
obj = np.empty(len(c))
for ix, (cVal, XVal) in enumerate(zip(c, X)):
EV = integrate.fixed_quad(self.EVpart,
self.yMin,
self.yMax,
args=(XVal, cVal),
n=self.quad_order)
obj[ix] = -(self.u(cVal) + (self.beta * EV[0]))
return obj
def PhotozProbabilities(zmin, zmax, membz, membzerr, fast=True):
if fast:
out = fastGaussianIntegration(membz, membzerr, zmin, zmax)
else:
out = []
for i in range(len(membz)):
aux, err = integrate.fixed_quad(gaussian,
zmin,
zmax,
args=(membz[i], membzerr[i]))
out.append(aux)
out = np.array(out)
return out
def matter_correlation_function(self,
r=None,
rmin=10,
rmax=200,
pk=None,
kh=None,
redshifts=[
0,
],
npoints=200,
bias_f=None):
#print "Estimate Correlation function"
if pk is None:
self.camb_params.WantTransfer = True
self.camb_params.set_matter_power(redshifts=redshifts, kmax=50.0)
self.get_results()
kh, z, pk = self.results.get_matter_power_spectrum(minkh=1.e-4,
maxkh=50.,
npoints=npoints)
#npoints = pk.shape[1]
if r is None:
r = np.linspace(rmin, rmax, npoints)
xi = np.zeros([len(redshifts), r.shape[0]])
k_min = kh.min()
k_max = kh.max()
#lgk_min = np.log10(kh.min())
#lgk_max = np.log10(kh.max())
#pkf = lambda lgk, i: np.interp(lgk, np.log10(kh), pk[i])
#itf = lambda lgk, r, i: 10.**(lgk*3) * np.log(10.) * pkf(lgk, i)\
# * jn(0, (10.**lgk)*r) / 2. / np.pi**2
#xif = np.vectorize(lambda r, i: \
# fixed_quad(itf, lgk_min, lgk_max, args=(r, i), n=10000)[0])
if bias_f is not None:
pkf = lambda k, i: np.interp(k, kh, pk[i]) * bias_f(k, i)
else:
pkf = lambda k, i: np.interp(k, kh, pk[i])
itf = lambda k, r, i: k**2 * pkf(k, i) * jn(0, k * r) / 2. / np.pi**2
xif = np.vectorize(lambda r, i: \
fixed_quad(itf, k_min, k_max, args=(r, i), n=20000)[0])
for i in range(len(redshifts)):
#print "z = %3.1f"%redshifts[i]
xi[i, :] = xif(r, i)
return xi, r
def distance_quadrature(vol, p1, p2, axis, epsabs=1.49e-08, epsrel=1.49e-08):
lb = p1[axis]
ub = p2[axis]
print(p1)
print(p2)
y = None
if axis == 0:
spat_dev = np.array([1,0,0])
y = integrate.fixed_quad(lambda x: integrand(x, p1[1], p1[2], vol, spat_dev), lb, ub, n=2)
elif axis == 1:
spat_dev = np.array([0,1,0])
args = (p1[1], p1[2], vol, spat_dev, axis)
def weighted_Delta_sigma_fixed_parent_final(self, RR):
def integrand(Rsat, R):
return number_density_spline(Rsat) * self.Delta_sigma_parent(
R, Rsat)
if np.isscalar(RR):
RRR = np.array([RR])
else:
RRR = RR
ans = np.zeros(RRR.size)
for i in range(RRR.size):
ans[i] = fixed_quad(integrand, b_min, b_max, args=[RRR[i]])[0]
return ans / factor