def process_mock_densdata(options):
print("Using mock Pal 5 data from %s" % options.mockfilename)
# Read and prep data for mocks
xvid= numpy.loadtxt(options.mockfilename)
xv= xvid[:,:6]
xv= xv[numpy.argsort(xvid[:,6])]
XYZ= bovy_coords.galcenrect_to_XYZ(xv[:,0],xv[:,1],xv[:,2],
Xsun=R0,Zsun=0.025)
lbd= bovy_coords.XYZ_to_lbd(XYZ[0],XYZ[1],XYZ[2],degree=True)
radec= bovy_coords.lb_to_radec(lbd[:,0],lbd[:,1],degree=True)
xieta= pal5_util.radec_to_pal5xieta(radec[:,0],radec[:,1],degree=True)
# make sure the progenitor is at (0,0)
xieta[:,0]-= numpy.median(xieta[:,0])
xieta[:,1]-= numpy.median(xieta[:,1])
h,e= numpy.histogram(xieta[:,0],range=[0.2,14.3],bins=141)
xdata= numpy.arange(0.25,14.35,0.1)
# Compute power spectrum
tdata= h-0.
pp= Polynomial.fit(xdata,tdata,deg=options.polydeg,w=1./numpy.sqrt(h+1.))
tdata/= pp(xdata)
ll= xdata
py= signal.csd(tdata,tdata,fs=1./(ll[1]-ll[0]),scaling='spectrum',
nperseg=len(ll))[1]
py= py.real
# Also compute the bispectrum
Bspec, Bpx= bispectrum.bispectrum(numpy.vstack((tdata,tdata)).T,
nfft=len(tdata),wind=7,nsamp=1,overlap=0)
ppyr= numpy.fabs(Bspec[len(Bspec)//2+_BISPECIND,len(Bspec)//2:].real)
ppyi= numpy.fabs(Bspec[len(Bspec)//2+_BISPECIND,len(Bspec)//2:].imag)
return (numpy.sqrt(py*(ll[-1]-ll[0])),numpy.sqrt(h+1.)/pp(xdata),
ppyr,ppyi)
def process_pal5_densdata(options):
# Read and prep data
backg= 400.
data= numpy.loadtxt('data/ibata_fig7b_raw.dat',delimiter=',')
sindx= numpy.argsort(data[:,0])
data= data[sindx]
data_lowerr= numpy.loadtxt('data/ibata_fig7b_rawlowerr.dat',delimiter=',')
sindx= numpy.argsort(data_lowerr[:,0])
data_lowerr= data_lowerr[sindx]
data_uperr= numpy.loadtxt('data/ibata_fig7b_rawuperr.dat',delimiter=',')
sindx= numpy.argsort(data_uperr[:,0])
data_uperr= data_uperr[sindx]
data_err= 0.5*(data_uperr-data_lowerr)
# CUTS
indx= (data[:,0] > options.minxi-0.05)*(data[:,0] < options.maxxi)
data= data[indx]
data_lowerr= data_lowerr[indx]
data_uperr= data_uperr[indx]
data_err= data_err[indx]
# Compute power spectrum
tdata= data[:,1]-backg
pp= Polynomial.fit(data[:,0],tdata,deg=options.polydeg,w=1./data_err[:,1])
tdata/= pp(data[:,0])
ll= data[:,0]
py= signal.csd(tdata,tdata,fs=1./(ll[1]-ll[0]),scaling='spectrum',
nperseg=len(ll))[1]
py= py.real
# Also compute the bispectrum
Bspec, Bpx= bispectrum.bispectrum(numpy.vstack((tdata,tdata)).T,
nfft=len(tdata),wind=7,nsamp=1,overlap=0)
ppyr= numpy.fabs(Bspec[len(Bspec)//2+_BISPECIND,len(Bspec)//2:].real)
ppyi= numpy.fabs(Bspec[len(Bspec)//2+_BISPECIND,len(Bspec)//2:].imag)
return (numpy.sqrt(py*(ll[-1]-ll[0])),data_err[:,1]/pp(data[:,0]),
ppyr,ppyi)
def process_mock_densdata(options):
print ("Using mock Pal 5 data from %s" % options.mockfilename)
# Read and prep data for mocks
xvid = numpy.loadtxt(options.mockfilename)
xv = xvid[:, :6]
xv = xv[numpy.argsort(xvid[:, 6])]
XYZ = bovy_coords.galcenrect_to_XYZ(xv[:, 0], xv[:, 1], xv[:, 2], Xsun=R0, Zsun=0.025)
lbd = bovy_coords.XYZ_to_lbd(XYZ[0], XYZ[1], XYZ[2], degree=True)
radec = bovy_coords.lb_to_radec(lbd[:, 0], lbd[:, 1], degree=True)
xieta = pal5_util.radec_to_pal5xieta(radec[:, 0], radec[:, 1], degree=True)
# make sure the progenitor is at (0,0)
xieta[:, 0] -= numpy.median(xieta[:, 0])
xieta[:, 1] -= numpy.median(xieta[:, 1])
h, e = numpy.histogram(xieta[:, 0], range=[0.2, 14.3], bins=141)
xdata = numpy.arange(0.25, 14.35, 0.1)
# Compute power spectrum
tdata = h - 0.0
pp = Polynomial.fit(xdata, tdata, deg=options.polydeg, w=1.0 / numpy.sqrt(h + 1.0))
tdata /= pp(xdata)
ll = xdata
py = signal.csd(tdata, tdata, fs=1.0 / (ll[1] - ll[0]), scaling="spectrum", nperseg=len(ll))[1]
py = py.real
# Also compute the bispectrum
Bspec, Bpx = bispectrum.bispectrum(numpy.vstack((tdata, tdata)).T, nfft=len(tdata), wind=7, nsamp=1, overlap=0)
ppyr = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2 :].real)
ppyi = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2 :].imag)
return (numpy.sqrt(py * (ll[-1] - ll[0])), numpy.sqrt(h + 1.0) / pp(xdata), ppyr, ppyi)
def process_pal5_densdata(options):
# Read and prep data
backg = 400.0
data = numpy.loadtxt("data/ibata_fig7b_raw.dat", delimiter=",")
sindx = numpy.argsort(data[:, 0])
data = data[sindx]
data_lowerr = numpy.loadtxt("data/ibata_fig7b_rawlowerr.dat", delimiter=",")
sindx = numpy.argsort(data_lowerr[:, 0])
data_lowerr = data_lowerr[sindx]
data_uperr = numpy.loadtxt("data/ibata_fig7b_rawuperr.dat", delimiter=",")
sindx = numpy.argsort(data_uperr[:, 0])
data_uperr = data_uperr[sindx]
data_err = 0.5 * (data_uperr - data_lowerr)
# CUTS
indx = (data[:, 0] > options.minxi - 0.05) * (data[:, 0] < options.maxxi)
data = data[indx]
data_lowerr = data_lowerr[indx]
data_uperr = data_uperr[indx]
data_err = data_err[indx]
# Compute power spectrum
tdata = data[:, 1] - backg
pp = Polynomial.fit(data[:, 0], tdata, deg=options.polydeg, w=1.0 / data_err[:, 1])
tdata /= pp(data[:, 0])
ll = data[:, 0]
py = signal.csd(tdata, tdata, fs=1.0 / (ll[1] - ll[0]), scaling="spectrum", nperseg=len(ll))[1]
py = py.real
# Also compute the bispectrum
Bspec, Bpx = bispectrum.bispectrum(numpy.vstack((tdata, tdata)).T, nfft=len(tdata), wind=7, nsamp=1, overlap=0)
ppyr = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2 :].real)
ppyi = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2 :].imag)
return (numpy.sqrt(py * (ll[-1] - ll[0])), data_err[:, 1] / pp(data[:, 0]), ppyr, ppyi)
def process_mock_densdata(options):
print("Using mock Pal 5 data from %s" % options.mockfilename)
simn = 2
dat = np.loadtxt(
'/Users/hendel/projects/streamgaps/streampepper/data/fakeobs/' +
options.mockfilename,
delimiter=',')
#fix seed for testing
if 0:
print('warning: Poisson seed fixed')
np.random.seed(42)
h = dat[simn] + np.random.poisson(options.nbg, size=len(dat[simn]))
h = np.maximum(h - options.nbg, np.zeros_like(h))
#h,e= np.histogram(xieta[:,0],range=[0.2,14.3],bins=141)
bins = np.linspace(options.ximin, options.ximax, options.nxi)
xdata = (bins[1:] + bins[:-1]) / 2.
# Compute power spectrum
tdata = h - 0.
pp = Polynomial.fit(xdata,
tdata,
deg=options.polydeg,
w=1. / np.sqrt(h + 1.))
tdata = tdata / pp(xdata)
ll = xdata
px, py = signal.csd(tdata,
tdata,
fs=1. / (ll[1] - ll[0]),
scaling='spectrum',
nperseg=len(ll))
px = 1. / px
py = py.real
py = np.sqrt(py * (ll[-1] - ll[0]))
#get ps error level
nerrsim = 1000
ppy_err = np.empty((nerrsim, len(px)))
terr = np.sqrt(h + 1. + options.nbg) / pp(xdata)
for ii in range(nerrsim):
tmock = terr * np.random.normal(size=len(ll))
ppy_err[ii] = signal.csd(tmock,
tmock,
fs=1. / (ll[1] - ll[0]),
scaling='spectrum',
nperseg=len(ll))[1].real
py_err = np.sqrt(np.median(ppy_err, axis=0) * (ll[-1] - ll[0]))
np.save('/Users/hendel/Desktop/pscrosscheck_abc.npy',
(dat[simn], bins, h, tdata, terr, px, py, py_err))
# Also compute the bispectrum
Bspec, Bpx = bispectrum.bispectrum(np.vstack((tdata, tdata)).T,
nfft=len(tdata),
wind=7,
nsamp=1,
overlap=0)
ppyr = np.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2:].real)
ppyi = np.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2:].imag)
return (py, terr, ppyr, ppyi, py_err)
def pal5_abc(sdf_pepper, options):
"""
"""
# Setup apar grid
bins = np.linspace(options.ximin, options.ximax, options.nxi)
if options.recompute:
# Load density and omega from file
outsamp = options.outsamp
if not options.batch is None:
outsamp = outsamp.replace('.dat', '.%i.dat' % options.batch)
sampdata = np.genfromtxt(outsamp, delimiter=',', skip_header=1)
nd = 0
else:
# Setup saving
if os.path.exists(options.outsamp):
# First read the file to check apar
print('does ' + options.outsamp + ' exist?',
os.path.exists(options.outsamp))
bins_file = np.genfromtxt(options.outsamp,
delimiter=',',
max_rows=1)
print(np.amax(np.fabs(bins_file - bins)))
assert np.amax(
np.fabs(bins_file - bins)
) < 10.**-5., 'bins according to options does not correspond to bins already in outsamp'
csvsamp = open(options.outsamp, 'a')
sampwriter = csv.writer(csvsamp, delimiter=',')
else:
csvsamp = open(options.outsamp, 'w')
sampwriter = csv.writer(csvsamp, delimiter=',')
# First write bins
sampwriter.writerow([b for b in bins])
csvsamp.flush()
# Setup sampling
massrange = simulate_streampepper.parse_mass(options.mass)
rs = simulate_streampepper.rs
sample_GM= lambda: (10.**((-0.5)*massrange[0])\
+(10.**((-0.5)*massrange[1])\
-10.**((-0.5)*massrange[0]))\
*np.random.uniform())**(1./(-0.5))\
/bovy_conversion.mass_in_msol(V0,R0)
sample_rs = lambda x: rs(x * bovy_conversion.mass_in_1010msol(V0, R0) *
10.**10.,
plummer=options.plummer)
rate_range = np.arange(massrange[0] + 0.5, massrange[1] + 0.5, 1)
cdmrate= np.sum([simulate_streampepper.\
dNencdm(sdf_pepper,10.**r,Xrs=options.Xrs,
plummer=options.plummer,
rsfac=options.rsfac)
for r in rate_range])
print("Using an overall CDM rate of %f" % cdmrate)
# Load Pal 5 data to compare to
if options.mockfilename is None:
power_data, data_err, data_ppyr, data_ppyi=\
process_pal5_densdata(options)
else:
power_data, data_err, data_ppyr, data_ppyi, data_py_err=\
process_mock_densdata(options)
# Run ABC
while True:
if not options.recompute:
# Simulate a rate
l10rate = (np.random.uniform() *
(options.ratemax - options.ratemin) + options.ratemin)
#### fix to CDM for testing
if options.fixcdmrate:
print('warning: using only CDM rate')
l10rate = 0.
rate = 10.**l10rate * cdmrate
print(l10rate, rate)
# Simulate
sdf_pepper.simulate(rate=rate,
sample_GM=sample_GM,
sample_rs=sample_rs,
Xrs=options.Xrs)
# Compute density along stream
try:
samp, binn = np.histogram(get_star_dx(sdf_pepper,
n=options.nsamples,
returnxi=True),
bins=bins)
except:
continue
write_samp = [l10rate]
write_samp.extend(list(samp))
sampwriter.writerow(write_samp)
csvsamp.flush()
else:
if nd >= len(densdata): break
l10rate = densdata[nd, 0]
dens = densdata[nd, 1:]
omega = omegadata[nd, 1:]
nd += 1
# Convert density to observed density
xixi = (bins[1:] + bins[:-1]) / 2.
dens = samp
# Add errors (Rao-Blackwellize...)
for ee in range(options.nerrsim):
tdens = dens + np.random.poisson(options.nbg, size=len(dens))
tdens = np.maximum(tdens - options.nbg, np.zeros_like(tdens))
pp = Polynomial.fit(xixi,
tdens,
deg=options.polydeg,
w=1. / np.sqrt(tdens + 1.))
tdens = tdens / pp(xixi)
# Compute power spectrum
tcsd = signal.csd(tdens,
tdens,
fs=1. / (xixi[1] - xixi[0]),
scaling='spectrum',
nperseg=len(xixi))[1].real
power = np.sqrt(tcsd * (xixi[-1] - xixi[0]))
# Compute bispectrum
Bspec, Bpx = bispectrum.bispectrum(np.vstack((tdens, tdens)).T,
nfft=len(tdens),
wind=7,
nsamp=1,
overlap=0)
ppyr = np.fabs(Bspec[len(Bspec) // 2 + _BISPECIND,
len(Bspec) // 2:].real)
ppyi = np.fabs(Bspec[len(Bspec) // 2 + _BISPECIND,
len(Bspec) // 2:].imag)
yield (
l10rate,
power,
ppyr,
ppyi,
#np.fabs(power[1]-power_data[1]),
#np.fabs(power[2]-power_data[2]),
#np.fabs(power[3]-power_data[3]),
#np.fabs(np.log(np.mean(tdens[7:17])\
# /np.mean(tdens[107:117]))),
#np.fabs(ppyr-data_ppyr)[_BISPECIND],
#np.fabs(ppyi-data_ppyi)[_BISPECIND],
ee)
def pal5_abc(sdf_pepper, sdf_smooth, options):
"""
"""
# Setup apar grid
apar = numpy.arange(options.amin, options.amax, options.dapar)
dens_unp = numpy.array([sdf_smooth._density_par(a) for a in apar])
if options.recompute:
# Load density and omega from file
outdens = options.outdens
outomega = options.outomega
if not options.batch is None:
outdens = outdens.replace('.dat', '.%i.dat' % options.batch)
if not options.batch is None:
outomega = outomega.replace('.dat', '.%i.dat' % options.batch)
densdata = numpy.genfromtxt(outdens, delimiter=',', skip_header=1)
omegadata = numpy.genfromtxt(outomega, delimiter=',', skip_header=1)
nd = 0
else:
# Setup saving of the densities and mean Omegas
denswriter, omegawriter, csvdens, csvomega=\
setup_densOmegaWriter(apar,options)
# Setup sampling
massrange = simulate_streampepper.parse_mass(options.mass)
rs = simulate_streampepper.rs
sample_GM= lambda: (10.**((-0.5)*massrange[0])\
+(10.**((-0.5)*massrange[1])\
-10.**((-0.5)*massrange[0]))\
*numpy.random.uniform())**(1./(-0.5))\
/bovy_conversion.mass_in_msol(V0,R0)
sample_rs = lambda x: rs(x * bovy_conversion.mass_in_1010msol(V0, R0) *
10.**10.,
plummer=options.plummer)
rate_range = numpy.arange(massrange[0] + 0.5, massrange[1] + 0.5, 1)
cdmrate= numpy.sum([simulate_streampepper.\
dNencdm(sdf_pepper,10.**r,Xrs=options.Xrs,
plummer=options.plummer,
rsfac=options.rsfac)
for r in rate_range])
print "Using an overall CDM rate of %f" % cdmrate
# Load Pal 5 data to compare to
if options.mockfilename is None:
power_data, data_err, data_ppyr, data_ppyi=\
process_pal5_densdata(options)
else:
power_data, data_err, data_ppyr, data_ppyi=\
process_mock_densdata(options)
# Run ABC
while True:
if not options.recompute:
# Simulate a rate
l10rate = (numpy.random.uniform() *
(options.ratemax - options.ratemin) + options.ratemin)
rate = 10.**l10rate * cdmrate
print l10rate, rate
# Simulate
sdf_pepper.simulate(rate=rate,
sample_GM=sample_GM,
sample_rs=sample_rs,
Xrs=options.Xrs)
# Compute density and meanOmega and save
try:
densOmega= numpy.array([\
sdf_pepper._densityAndOmega_par_approx(a) for a in apar]).T
except IndexError: # no hit
dens = numpy.array([sdf_smooth._density_par(a) for a in apar])
omega = numpy.array(
[sdf_smooth.meanOmega(a, oned=True) for a in apar])
else:
dens = densOmega[0]
omega = densOmega[1]
write_dens = [l10rate]
write_omega = [l10rate]
write_dens.extend(list(dens))
write_omega.extend(list(omega))
denswriter.writerow(write_dens)
omegawriter.writerow(write_omega)
csvdens.flush()
csvomega.flush()
else:
if nd >= len(densdata): break
l10rate = densdata[nd, 0]
dens = densdata[nd, 1:]
omega = omegadata[nd, 1:]
nd += 1
# Convert density to observed density
xixi, dens = convert_dens_to_obs(sdf_pepper,
apar,
dens,
omega,
dens_unp,
minxi=options.minxi,
maxxi=options.maxxi)
# Add errors (Rao-Blackwellize...)
for ee in range(options.nerrsim):
tdens = dens + numpy.random.normal(size=len(xixi)) * data_err
# Compute power spectrum
tcsd = signal.csd(tdens,
tdens,
fs=1. / (xixi[1] - xixi[0]),
scaling='spectrum',
nperseg=len(xixi))[1].real
power = numpy.sqrt(tcsd * (xixi[-1] - xixi[0]))
# Compute bispectrum
Bspec, Bpx = bispectrum.bispectrum(numpy.vstack((tdens, tdens)).T,
nfft=len(tdens),
wind=7,
nsamp=1,
overlap=0)
ppyr = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND,
len(Bspec) // 2:].real)
ppyi = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND,
len(Bspec) // 2:].imag)
yield (l10rate,
numpy.fabs(power[1]-power_data[1]),
numpy.fabs(power[2]-power_data[2]),
numpy.fabs(power[3]-power_data[3]),
numpy.fabs(numpy.log(numpy.mean(tdens[7:17])\
/numpy.mean(tdens[107:117]))),
numpy.fabs(ppyr-data_ppyr)[_BISPECIND],
numpy.fabs(ppyi-data_ppyi)[_BISPECIND],
ee)
def pal5_abc(sdf_pepper, sdf_smooth, options):
"""
"""
# Setup apar grid
apar = numpy.arange(options.amin, options.amax, options.dapar)
dens_unp = numpy.array([sdf_smooth._density_par(a) for a in apar])
if options.recompute:
# Load density and omega from file
outdens = options.outdens
outomega = options.outomega
if not options.batch is None:
outdens = outdens.replace(".dat", ".%i.dat" % options.batch)
if not options.batch is None:
outomega = outomega.replace(".dat", ".%i.dat" % options.batch)
densdata = numpy.genfromtxt(outdens, delimiter=",", skip_header=1)
omegadata = numpy.genfromtxt(outomega, delimiter=",", skip_header=1)
nd = 0
else:
# Setup saving of the densities and mean Omegas
denswriter, omegawriter, csvdens, csvomega = setup_densOmegaWriter(apar, options)
# Setup sampling
massrange = simulate_streampepper.parse_mass(options.mass)
rs = simulate_streampepper.rs
sample_GM = lambda: (
10.0 ** ((-0.5) * massrange[0])
+ (10.0 ** ((-0.5) * massrange[1]) - 10.0 ** ((-0.5) * massrange[0])) * numpy.random.uniform()
) ** (1.0 / (-0.5)) / bovy_conversion.mass_in_msol(V0, R0)
sample_rs = lambda x: rs(x * bovy_conversion.mass_in_1010msol(V0, R0) * 10.0 ** 10.0, plummer=options.plummer)
rate_range = numpy.arange(massrange[0] + 0.5, massrange[1] + 0.5, 1)
cdmrate = numpy.sum(
[
simulate_streampepper.dNencdm(
sdf_pepper, 10.0 ** r, Xrs=options.Xrs, plummer=options.plummer, rsfac=options.rsfac
)
for r in rate_range
]
)
print "Using an overall CDM rate of %f" % cdmrate
# Load Pal 5 data to compare to
if options.mockfilename is None:
power_data, data_err, data_ppyr, data_ppyi = process_pal5_densdata(options)
else:
power_data, data_err, data_ppyr, data_ppyi = process_mock_densdata(options)
# Run ABC
while True:
if not options.recompute:
# Simulate a rate
l10rate = numpy.random.uniform() * (options.ratemax - options.ratemin) + options.ratemin
rate = 10.0 ** l10rate * cdmrate
print l10rate, rate
# Simulate
sdf_pepper.simulate(rate=rate, sample_GM=sample_GM, sample_rs=sample_rs, Xrs=options.Xrs)
# Compute density and meanOmega and save
try:
densOmega = numpy.array([sdf_pepper._densityAndOmega_par_approx(a) for a in apar]).T
except IndexError: # no hit
dens = numpy.array([sdf_smooth._density_par(a) for a in apar])
omega = numpy.array([sdf_smooth.meanOmega(a, oned=True) for a in apar])
else:
dens = densOmega[0]
omega = densOmega[1]
write_dens = [l10rate]
write_omega = [l10rate]
write_dens.extend(list(dens))
write_omega.extend(list(omega))
denswriter.writerow(write_dens)
omegawriter.writerow(write_omega)
csvdens.flush()
csvomega.flush()
else:
if nd >= len(densdata):
break
l10rate = densdata[nd, 0]
dens = densdata[nd, 1:]
omega = omegadata[nd, 1:]
nd += 1
# Convert density to observed density
xixi, dens = convert_dens_to_obs(
sdf_pepper, apar, dens, omega, dens_unp, minxi=options.minxi, maxxi=options.maxxi
)
# Add errors (Rao-Blackwellize...)
for ee in range(options.nerrsim):
tdens = dens + numpy.random.normal(size=len(xixi)) * data_err
# Compute power spectrum
tcsd = signal.csd(tdens, tdens, fs=1.0 / (xixi[1] - xixi[0]), scaling="spectrum", nperseg=len(xixi))[1].real
power = numpy.sqrt(tcsd * (xixi[-1] - xixi[0]))
# Compute bispectrum
Bspec, Bpx = bispectrum.bispectrum(
numpy.vstack((tdens, tdens)).T, nfft=len(tdens), wind=7, nsamp=1, overlap=0
)
ppyr = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2 :].real)
ppyi = numpy.fabs(Bspec[len(Bspec) // 2 + _BISPECIND, len(Bspec) // 2 :].imag)
yield (
l10rate,
numpy.fabs(power[1] - power_data[1]),
numpy.fabs(power[2] - power_data[2]),
numpy.fabs(power[3] - power_data[3]),
numpy.fabs(numpy.log(numpy.mean(tdens[7:17]) / numpy.mean(tdens[107:117]))),
numpy.fabs(ppyr - data_ppyr)[_BISPECIND],
numpy.fabs(ppyi - data_ppyi)[_BISPECIND],
ee,
)
