k = np.arange(0., 1., 0.1)
yp1, yp2 = mp.ellke(k)
yc1, yc2 = mc.ellke(k)
if sum(abs(yp1 - yc1)) < 1e-10 and sum(abs(yp2 - yc2)) < 1e-10:
print("Ellke: PASS")
else:
print("Ellke: FAIL", sum(abs(yp1 - yc1)), sum(abs(yp2 - yc2)))
### ellpic_bulirsch()
n = np.ones(9)
k = np.arange(0.1, 1., 0.1)
yp = mp.ellpic_bulirsch(k, k)
yc = mc.ellpic_bulirsch(k, k)
if np.allclose(yp, yc):
print("E_bulirsch: PASS")
else:
print("E_bulirsch: FAIL", np.np.nansum(abs(yp - yc) / yp))
### chisq()
model = np.ones(1000)
data = np.random.normal(1, 0.1, 1000)
sigma = np.ones(1000) * 0.1
yp = np.sum(((model - data) / sigma)**2)
yc = mc.chisq(model, data, sigma)
def occultquad(z, u1, u2, rprs, lenz):
'''
'''
from models import ellke, ellpic_bulirsch
nz = size(z)
lambdad = zeros(nz)
etad = zeros(nz)
lambdae = zeros(nz)
omega=1.-u1/3.-u2/6.
## tolerance for double precision equalities
## special case integrations
tol = 1e-14
rprs = abs(rprs)
z = where(abs(rprs-z) < tol,rprs,z)
z = where(abs((rprs-1)-z) < tol,rprs-1.,z)
z = where(abs((1-rprs)-z) < tol,1.-rprs,z)
z = where(z < tol,0.,z)
x1=(rprs-z)**2.
x2=(rprs+z)**2.
x3=rprs**2.-z**2.
## trivial case of no planet
if rprs <= 0.:
muo1 = zeros(nz) + 1.
mu0 = zeros(nz) + 1.
#return [muo1,mu0]
return muo1
#return muo1*flux
## Case 1 - the star is unocculted:
## only consider points with z lt 1+rprs
notusedyet = where( z < (1. + rprs) )
notusedyet = notusedyet[0]
if size(notusedyet) == 0:
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*(lambdad+2./3.*(rprs > z))+ \
u2*etad)/omega
mu0=1.-lambdae
#return [muo1,mu0]
return muo1
#return muo1*flux
# Case 11 - the source is completely occulted:
if rprs >= 1.:
occulted = where(z[notusedyet] <= rprs-1.)#,complement=notused2)
if size(occulted) != 0:
ndxuse = notusedyet[occulted]
etad[ndxuse] = 0.5 # corrected typo in paper
lambdae[ndxuse] = 1.
# lambdad = 0 already
notused2 = where(z[notusedyet] > rprs-1)
if size(notused2) == 0:
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*(lambdad+2./3.* \
(rprs > z))+u2*etad)/omega
mu0=1.-lambdae
#return [muo1,mu0]
return muo1
#return muo1*flux
notusedyet = notusedyet[notused2]
# Case 2, 7, 8 - ingress/egress (uniform disk only)
inegressuni = where((z[notusedyet] >= abs(1.-rprs)) & (z[notusedyet] < 1.+rprs))
if size(inegressuni) != 0:
ndxuse = notusedyet[inegressuni]
tmp = (1.-rprs**2.+z[ndxuse]**2.)/2./z[ndxuse]
tmp = where(tmp > 1.,1.,tmp)
tmp = where(tmp < -1.,-1.,tmp)
kap1 = arccos(tmp)
tmp = (rprs**2.+z[ndxuse]**2-1.)/2./rprs/z[ndxuse]
tmp = where(tmp > 1.,1.,tmp)
tmp = where(tmp < -1.,-1.,tmp)
kap0 = arccos(tmp)
tmp = 4.*z[ndxuse]**2-(1.+z[ndxuse]**2-rprs**2)**2
tmp = where(tmp < 0,0,tmp)
lambdae[ndxuse] = (rprs**2*kap0+kap1 - 0.5*sqrt(tmp))/pi
# eta_1
etad[ndxuse] = 1./2./pi*(kap1+rprs**2*(rprs**2+2.*z[ndxuse]**2)*kap0- \
(1.+5.*rprs**2+z[ndxuse]**2)/4.*sqrt((1.-x1[ndxuse])*(x2[ndxuse]-1.)))
# Case 5, 6, 7 - the edge of planet lies at origin of star
ocltor = where(z[notusedyet] == rprs)#, complement=notused3)
t = where(z[notusedyet] == rprs)
if size(ocltor) != 0:
ndxuse = notusedyet[ocltor]
if rprs < 0.5:
# Case 5
q=2.*rprs # corrected typo in paper (2k -> 2rprs)
Ek,Kk = ellke(q)
# lambda_4
lambdad[ndxuse] = 1./3.+2./9./pi*(4.*(2.*rprs**2-1.)*Ek+\
(1.-4.*rprs**2)*Kk)
# eta_2
etad[ndxuse] = rprs**2/2.*(rprs**2+2.*z[ndxuse]**2)
lambdae[ndxuse] = rprs**2 # uniform disk
elif rprs > 0.5:
# Case 7
q=0.5/rprs # corrected typo in paper (1/2k -> 1/2rprs)
Ek,Kk = ellke(q)
# lambda_3
lambdad[ndxuse] = 1./3.+16.*rprs/9./pi*(2.*rprs**2-1.)*Ek-\
(32.*rprs**4-20.*rprs**2+3.)/9./pi/rprs*Kk
# etad = eta_1 already
else:
# Case 6
lambdad[ndxuse] = 1./3.-4./pi/9.
etad[ndxuse] = 3./32.
notused3 = where(z[notusedyet] != rprs)
if size(notused3) == 0:
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*\
(lambdad+2./3.*(rprs > z))+u2*etad)/omega
mu0=1.-lambdae
#return [muo1,mu0]
return muo1
#return muo1*flux
notusedyet = notusedyet[notused3]
# Case 2, Case 8 - ingress/egress (with limb darkening)
inegress = where( ((z[notusedyet] > 0.5+abs(rprs-0.5)) & \
(z[notusedyet] < 1.+rprs)) | \
( (rprs > 0.5) & (z[notusedyet] > abs(1.-rprs)) & \
(z[notusedyet] < rprs)) )#, complement=notused4)
if size(inegress) != 0:
ndxuse = notusedyet[inegress]
q=sqrt((1.-x1[ndxuse])/(x2[ndxuse]-x1[ndxuse]))
Ek,Kk = ellke(q)
n=1./x1[ndxuse]-1.
# lambda_1:
lambdad[ndxuse]=2./9./pi/sqrt(x2[ndxuse]-x1[ndxuse])*\
(((1.-x2[ndxuse])*(2.*x2[ndxuse]+x1[ndxuse]-3.)-\
3.*x3[ndxuse]*(x2[ndxuse]-2.))*Kk+(x2[ndxuse]-\
x1[ndxuse])*(z[ndxuse]**2+7.*rprs**2-4.)*Ek-\
3.*x3[ndxuse]/x1[ndxuse]*ellpic_bulirsch(n,q))
notused4 = where( ( (z[notusedyet] <= 0.5+abs(rprs-0.5)) | \
(z[notusedyet] >= 1.+rprs) ) & ( (rprs <= 0.5) | \
(z[notusedyet] <= abs(1.-rprs)) | \
(z[notusedyet] >= rprs) ))
if size(notused4) == 0:
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*(lambdad+2./3.*\
(rprs > z))+u2*etad)/omega
mu0=1.-lambdae
#return [muo1,mu0]
return muo1
#return muo1*flux
notusedyet = notusedyet[notused4]
# Case 3, 4, 9, 10 - planet completely inside star
if rprs < 1.:
inside = where(z[notusedyet] <= (1.-rprs))#, complement=notused5)
if size(inside) != 0:
ndxuse = notusedyet[inside]
## eta_2
etad[ndxuse] = rprs**2/2.*(rprs**2+2.*z[ndxuse]**2)
## uniform disk
lambdae[ndxuse] = rprs**2
## Case 4 - edge of planet hits edge of star
edge = where(z[ndxuse] == 1.-rprs)#, complement=notused6)
if size(edge[0]) != 0:
## lambda_5
lambdad[ndxuse[edge]] = 2./3./pi*arccos(1.-2.*rprs)-\
4./9./pi*sqrt(rprs*(1.-rprs))*(3.+2.*rprs-8.*rprs**2)
if rprs > 0.5:
lambdad[ndxuse[edge]] -= 2./3.
notused6 = where(z[ndxuse] != 1.-rprs)
if size(notused6) == 0:
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*\
(lambdad+2./3.*(rprs > z))+u2*etad)/omega
mu0=1.-lambdae
#return [muo1,mu0]
return muo1
#return muo1*flux
ndxuse = ndxuse[notused6[0]]
## Case 10 - origin of planet hits origin of star
origin = where(z[ndxuse] == 0)#, complement=notused7)
if size(origin) != 0:
## lambda_6
lambdad[ndxuse[origin]] = -2./3.*(1.-rprs**2)**1.5
notused7 = where(z[ndxuse] != 0)
if size(notused7) == 0:
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*\
(lambdad+2./3.*(rprs > z))+u2*etad)/omega
mu0=1.-lambdae
#return [muo1,mu0]
#return muo1*flux
return muo1
ndxuse = ndxuse[notused7[0]]
q=sqrt((x2[ndxuse]-x1[ndxuse])/(1.-x1[ndxuse]))
n=x2[ndxuse]/x1[ndxuse]-1.
Ek,Kk = ellke(q)
## Case 3, Case 9 - anywhere in between
## lambda_2
lambdad[ndxuse] = 2./9./pi/sqrt(1.-x1[ndxuse])*\
((1.-5.*z[ndxuse]**2+rprs**2+x3[ndxuse]**2)*Kk+\
(1.-x1[ndxuse])*(z[ndxuse]**2+7.*rprs**2-4.)*Ek-\
3.*x3[ndxuse]/x1[ndxuse]*ellpic_bulirsch(n,q))
## if there are still unused elements, there's a bug in the code
## (please report it)
notused5 = where(z[notusedyet] > (1.-rprs))
if notused5[0] != 0:
print("ERROR: the following values of z didn't fit into a case:")
return [-1,-1]
muo1 =1.-((1.-u1-2.*u2)*lambdae+(u1+2.*u2)*(lambdad+2./3.*(rprs > z))+\
u2*etad)/omega
mu0=1.-lambdae
return muo1