def get_param(par, args, m1, m2, s1z, s2z):
"""
Helper function
Parameters
----------
par : string
Name of parameter to calculate
args : Namespace object returned from ArgumentParser instance
Calling code command line options, used for f_lower value
m1 : float or array of floats
First binary component mass (etc.)
Returns
-------
parvals : float or array of floats
Calculated parameter values
"""
if par == 'mchirp':
parvals, _ = pnutils.mass1_mass2_to_mchirp_eta(m1, m2)
elif par == 'mtotal':
parvals = m1 + m2
elif par == 'template_duration':
# default to SEOBNRv4 duration function
parvals = pnutils.get_imr_duration(m1, m2, s1z, s2z, args.f_lower,
args.approximant or "SEOBNRv4")
if args.min_duration:
parvals += args.min_duration
elif par in pnutils.named_frequency_cutoffs.keys():
parvals = pnutils.frequency_cutoff_from_name(par, m1, m2, s1z, s2z)
else:
# try asking for a LALSimulation frequency function
parvals = pnutils.get_freq(par, m1, m2, s1z, s2z)
return parvals
def get_param(par, args, m1, m2, s1z, s2z):
"""
Helper function
Parameters
----------
par : string
Name of parameter to calculate
args : Namespace object returned from ArgumentParser instance
Calling code command line options, used for f_lower value
m1 : float or array of floats
First binary component mass (etc.)
Returns
-------
parvals : float or array of floats
Calculated parameter values
"""
if par == 'mchirp':
parvals, _ = pnutils.mass1_mass2_to_mchirp_eta(m1, m2)
elif par == 'mtotal':
parvals = m1 + m2
elif par == 'template_duration':
# default to SEOBNRv4 duration function
parvals = pnutils.get_imr_duration(m1, m2, s1z, s2z, args.f_lower,
args.approximant or "SEOBNRv4")
if args.min_duration:
parvals += args.min_duration
elif par in pnutils.named_frequency_cutoffs.keys():
parvals = pnutils.frequency_cutoff_from_name(par, m1, m2, s1z, s2z)
else:
# try asking for a LALSimulation frequency function
parvals = pnutils.get_freq(par, m1, m2, s1z, s2z)
return parvals
def get_param(par, args, m1, m2, s1z, s2z):
"""
Helper function
Parameters
----------
par : string
Name of parameter to calculate
args : Namespace object returned from ArgumentParser instance
Calling code command line options, used for f_lower value
m1 : float or array of floats
First binary component mass (etc.)
Returns
-------
parvals : float or array of floats
Calculated parameter values
"""
if par == 'mchirp':
parvals = conversions.mchirp_from_mass1_mass2(m1, m2)
elif par == 'mtotal':
parvals = m1 + m2
elif par == 'eta':
parvals = conversions.eta_from_mass1_mass2(m1, m2)
elif par in ['chi_eff', 'effective_spin']:
parvals = conversions.chi_eff(m1, m2, s1z, s2z)
elif par == 'template_duration':
# default to SEOBNRv4 duration function
if not hasattr(args, 'approximant') or args.approximant is None:
args.approximant = "SEOBNRv4"
parvals = pnutils.get_imr_duration(m1, m2, s1z, s2z, args.f_lower,
args.approximant)
if args.min_duration:
parvals += args.min_duration
elif par == 'tau0':
parvals = conversions.tau0_from_mass1_mass2(m1, m2, args.f_lower)
elif par == 'tau3':
parvals = conversions.tau3_from_mass1_mass2(m1, m2, args.f_lower)
elif par in pnutils.named_frequency_cutoffs.keys():
parvals = pnutils.frequency_cutoff_from_name(par, m1, m2, s1z, s2z)
else:
# try asking for a LALSimulation frequency function
parvals = pnutils.get_freq(par, m1, m2, s1z, s2z)
return parvals
def output_sngl_inspiral_table(outputFile,
tempBank,
metricParams,
ethincaParams,
programName="",
optDict=None,
outdoc=None,
**kwargs):
"""
Function that converts the information produced by the various pyCBC bank
generation codes into a valid LIGOLW xml file containing a sngl_inspiral
table and outputs to file.
Parameters
-----------
outputFile : string
Name of the file that the bank will be written to
tempBank : iterable
Each entry in the tempBank iterable should be a sequence of
[mass1,mass2,spin1z,spin2z] in that order.
metricParams : metricParameters instance
Structure holding all the options for construction of the metric
and the eigenvalues, eigenvectors and covariance matrix
needed to manipulate the space.
ethincaParams: {ethincaParameters instance, None}
Structure holding options relevant to the ethinca metric computation
including the upper frequency cutoff to be used for filtering.
NOTE: The computation is currently only valid for non-spinning systems
and uses the TaylorF2 approximant.
programName (key-word-argument) : string
Name of the executable that has been run
optDict (key-word argument) : dictionary
Dictionary of the command line arguments passed to the program
outdoc (key-word argument) : ligolw xml document
If given add template bank to this representation of a xml document and
write to disk. If not given create a new document.
kwargs : key-word arguments
All other key word arguments will be passed directly to
ligolw_process.register_to_xmldoc
"""
if optDict is None:
optDict = {}
if outdoc is None:
outdoc = ligolw.Document()
outdoc.appendChild(ligolw.LIGO_LW())
# get IFO to put in search summary table
ifos = []
if 'channel_name' in optDict.keys():
if optDict['channel_name'] is not None:
ifos = [optDict['channel_name'][0:2]]
proc_id = ligolw_process.register_to_xmldoc(outdoc,
programName,
optDict,
ifos=ifos,
**kwargs).process_id
sngl_inspiral_table = convert_to_sngl_inspiral_table(tempBank, proc_id)
# Calculate Gamma components if needed
if ethincaParams is not None:
if ethincaParams.doEthinca:
for sngl in sngl_inspiral_table:
# Set tau_0 and tau_3 values needed for the calculation of
# ethinca metric distances
(sngl.tau0, sngl.tau3) = pnutils.mass1_mass2_to_tau0_tau3(
sngl.mass1, sngl.mass2, metricParams.f0)
fMax_theor, GammaVals = calculate_ethinca_metric_comps(
metricParams,
ethincaParams,
sngl.mass1,
sngl.mass2,
spin1z=sngl.spin1z,
spin2z=sngl.spin2z,
full_ethinca=ethincaParams.full_ethinca)
# assign the upper frequency cutoff and Gamma0-5 values
sngl.f_final = fMax_theor
for i in xrange(len(GammaVals)):
setattr(sngl, "Gamma" + str(i), GammaVals[i])
# If Gamma metric components are not wanted, assign f_final from an
# upper frequency cutoff specified in ethincaParams
elif ethincaParams.cutoff is not None:
for sngl in sngl_inspiral_table:
sngl.f_final = pnutils.frequency_cutoff_from_name(
ethincaParams.cutoff, sngl.mass1, sngl.mass2, sngl.spin1z,
sngl.spin2z)
# set per-template low-frequency cutoff
if 'f_low_column' in optDict and 'f_low' in optDict and \
optDict['f_low_column'] is not None:
for sngl in sngl_inspiral_table:
setattr(sngl, optDict['f_low_column'], optDict['f_low'])
outdoc.childNodes[0].appendChild(sngl_inspiral_table)
# get times to put in search summary table
start_time = 0
end_time = 0
if 'gps_start_time' in optDict.keys() and 'gps_end_time' in optDict.keys():
start_time = optDict['gps_start_time']
end_time = optDict['gps_end_time']
# make search summary table
search_summary_table = lsctables.New(lsctables.SearchSummaryTable)
search_summary = return_search_summary(start_time, end_time,
len(sngl_inspiral_table), ifos,
**kwargs)
search_summary_table.append(search_summary)
outdoc.childNodes[0].appendChild(search_summary_table)
# write the xml doc to disk
proctable = table.get_table(outdoc, lsctables.ProcessTable.tableName)
ligolw_utils.write_filename(outdoc,
outputFile,
gz=outputFile.endswith('.gz'))
def calculate_ethinca_metric_comps(metricParams,
ethincaParams,
mass1,
mass2,
spin1z=0.,
spin2z=0.,
full_ethinca=True):
"""
Calculate the Gamma components needed to use the ethinca metric.
At present this outputs the standard TaylorF2 metric over the end time
and chirp times \tau_0 and \tau_3.
A desirable upgrade might be to use the \chi coordinates [defined WHERE?]
for metric distance instead of \tau_0 and \tau_3.
The lower frequency cutoff is currently hard-coded to be the same as the
bank layout options fLow and f0 (which must be the same as each other).
Parameters
-----------
metricParams : metricParameters instance
Structure holding all the options for construction of the metric
and the eigenvalues, eigenvectors and covariance matrix
needed to manipulate the space.
ethincaParams : ethincaParameters instance
Structure holding options relevant to the ethinca metric computation.
mass1 : float
Mass of the heavier body in the considered template.
mass2 : float
Mass of the lighter body in the considered template.
spin1z : float (optional, default=0)
Spin of the heavier body in the considered template.
spin2z : float (optional, default=0)
Spin of the lighter body in the considered template.
full_ethinca : boolean (optional, default=True)
If True calculate the ethinca components in all 3 directions (mass1,
mass2 and time). If False calculate only the time component (which is
stored in Gamma0).
Returns
--------
fMax_theor : float
Value of the upper frequency cutoff given by the template parameters
and the cutoff formula requested.
gammaVals : numpy_array
Array holding 6 independent metric components in
(end_time, tau_0, tau_3) coordinates to be stored in the Gamma0-5
slots of a SnglInspiral object.
"""
if (float(spin1z) != 0. or float(spin2z) != 0.) and full_ethinca:
raise NotImplementedError("Ethinca cannot at present be calculated "
"for nonzero component spins!")
f0 = metricParams.f0
if f0 != metricParams.fLow:
raise ValueError("If calculating ethinca the bank f0 value must be "
"equal to f-low!")
if ethincaParams.fLow is not None and (ethincaParams.fLow !=
metricParams.fLow):
raise NotImplementedError("An ethinca metric f-low different from the"
" bank metric f-low is not supported!")
twicePNOrder = ethinca_order_from_string(ethincaParams.pnOrder)
piFl = PI * f0
totalMass, eta = pnutils.mass1_mass2_to_mtotal_eta(mass1, mass2)
totalMass = totalMass * MTSUN_SI
v0cube = totalMass * piFl
v0 = v0cube**(1. / 3.)
# Get theoretical cutoff frequency and work out the closest
# frequency for which moments were calculated
fMax_theor = pnutils.frequency_cutoff_from_name(ethincaParams.cutoff,
mass1, mass2, spin1z,
spin2z)
fMaxes = metricParams.moments['J4'].keys()
fMaxIdx = abs(numpy.array(fMaxes, dtype=float) - fMax_theor).argmin()
fMax = fMaxes[fMaxIdx]
# Set the appropriate moments
Js = numpy.zeros([18, 3], dtype=float)
for i in range(18):
Js[i, 0] = metricParams.moments['J%d' % (i)][fMax]
Js[i, 1] = metricParams.moments['log%d' % (i)][fMax]
Js[i, 2] = metricParams.moments['loglog%d' % (i)][fMax]
# Compute the time-dependent metric term.
two_pi_flower_sq = TWOPI * f0 * TWOPI * f0
gammaVals = numpy.zeros([6], dtype=float)
gammaVals[0] = 0.5 * two_pi_flower_sq * \
( Js[(1,0)] - (Js[(4,0)]*Js[(4,0)]) )
# If mass terms not required stop here
if not full_ethinca:
return fMax_theor, gammaVals
# 3pN is a mess, so split it into pieces
a0 = 11583231236531 / 200286535680 - 5 * PI * PI - 107 * GAMMA / 14
a1 = (-15737765635 / 130056192 + 2255 * PI * PI / 512) * eta
a2 = (76055 / 73728) * eta * eta
a3 = (-127825 / 55296) * eta * eta * eta
alog = numpy.log(4 * v0) # Log terms are tricky - be careful
# Get the Psi coefficients
Psi = [{}, {}] #Psi = numpy.zeros([2,8,2],dtype=float)
Psi[0][0, 0] = 3 / 5
Psi[0][2, 0] = (743 / 756 + 11 * eta / 3) * v0 * v0
Psi[0][3, 0] = 0.
Psi[0][4,0] = (-3058673/508032 + 5429*eta/504 + 617*eta*eta/24)\
*v0cube*v0
Psi[0][5, 1] = (-7729 * PI / 126) * v0cube * v0 * v0 / 3
Psi[0][6,0] = (128/15)*(-3*a0 - a1 + a2 + 3*a3 + 107*(1+3*alog)/14)\
*v0cube*v0cube
Psi[0][6, 1] = (6848 / 35) * v0cube * v0cube / 3
Psi[0][7, 0] = (-15419335 / 63504 -
75703 * eta / 756) * PI * v0cube * v0cube * v0
Psi[1][0, 0] = 0.
Psi[1][2, 0] = (3715 / 12096 - 55 * eta / 96) / PI / v0
Psi[1][3, 0] = -3 / 2
Psi[1][4,0] = (15293365/4064256 - 27145*eta/16128 - 3085*eta*eta/384)\
*v0/PI
Psi[1][5, 1] = (193225 / 8064) * v0 * v0 / 3
Psi[1][6,0] = (4/PI)*(2*a0 + a1/3 - 4*a2/3 - 3*a3 -107*(1+6*alog)/42)\
*v0cube
Psi[1][6, 1] = (-428 / PI / 7) * v0cube / 3
Psi[1][7,0] = (77096675/1161216 + 378515*eta/24192 + 74045*eta*eta/8064)\
*v0cube*v0
# Set the appropriate moments
Js = numpy.zeros([18, 3], dtype=float)
for i in range(18):
Js[i, 0] = metricParams.moments['J%d' % (i)][fMax]
Js[i, 1] = metricParams.moments['log%d' % (i)][fMax]
Js[i, 2] = metricParams.moments['loglog%d' % (i)][fMax]
# Calculate the g matrix
PNterms = [(0, 0), (2, 0), (3, 0), (4, 0), (5, 1), (6, 0), (6, 1), (7, 0)]
PNterms = [term for term in PNterms if term[0] <= twicePNOrder]
# Now can compute the mass-dependent gamma values
for m in [0, 1]:
for k in PNterms:
gammaVals[1+m] += 0.5 * two_pi_flower_sq * Psi[m][k] * \
( Js[(9-k[0],k[1])]
- Js[(12-k[0],k[1])] * Js[(4,0)] )
g = numpy.zeros([2, 2], dtype=float)
for (m, n) in [(0, 0), (0, 1), (1, 1)]:
for k in PNterms:
for l in PNterms:
g[m,n] += Psi[m][k] * Psi[n][l] * \
( Js[(17-k[0]-l[0], k[1]+l[1])]
- Js[(12-k[0],k[1])] * Js[(12-l[0],l[1])] )
g[m, n] = 0.5 * two_pi_flower_sq * g[m, n]
g[n, m] = g[m, n]
gammaVals[3] = g[0, 0]
gammaVals[4] = g[0, 1]
gammaVals[5] = g[1, 1]
return fMax_theor, gammaVals
def output_sngl_inspiral_table(outputFile, tempBank, metricParams,
ethincaParams, programName="", optDict = None,
outdoc=None, **kwargs):
"""
Function that converts the information produced by the various pyCBC bank
generation codes into a valid LIGOLW xml file containing a sngl_inspiral
table and outputs to file.
Parameters
-----------
outputFile : string
Name of the file that the bank will be written to
tempBank : iterable
Each entry in the tempBank iterable should be a sequence of
[mass1,mass2,spin1z,spin2z] in that order.
metricParams : metricParameters instance
Structure holding all the options for construction of the metric
and the eigenvalues, eigenvectors and covariance matrix
needed to manipulate the space.
ethincaParams: {ethincaParameters instance, None}
Structure holding options relevant to the ethinca metric computation
including the upper frequency cutoff to be used for filtering.
NOTE: The computation is currently only valid for non-spinning systems
and uses the TaylorF2 approximant.
programName (key-word-argument) : string
Name of the executable that has been run
optDict (key-word argument) : dictionary
Dictionary of the command line arguments passed to the program
outdoc (key-word argument) : ligolw xml document
If given add template bank to this representation of a xml document and
write to disk. If not given create a new document.
kwargs : key-word arguments
All other key word arguments will be passed directly to
ligolw_process.register_to_xmldoc
"""
if optDict is None:
optDict = {}
if outdoc is None:
outdoc = ligolw.Document()
outdoc.appendChild(ligolw.LIGO_LW())
# get IFO to put in search summary table
ifos = []
if 'channel_name' in optDict.keys():
if optDict['channel_name'] is not None:
ifos = [optDict['channel_name'][0:2]]
proc_id = ligolw_process.register_to_xmldoc(outdoc, programName, optDict,
ifos=ifos, **kwargs).process_id
sngl_inspiral_table = convert_to_sngl_inspiral_table(tempBank, proc_id)
# Calculate Gamma components if needed
if ethincaParams is not None:
if ethincaParams.doEthinca:
for sngl in sngl_inspiral_table:
# Set tau_0 and tau_3 values needed for the calculation of
# ethinca metric distances
(sngl.tau0,sngl.tau3) = pnutils.mass1_mass2_to_tau0_tau3(
sngl.mass1, sngl.mass2, metricParams.f0)
fMax_theor, GammaVals = calculate_ethinca_metric_comps(
metricParams, ethincaParams,
sngl.mass1, sngl.mass2, spin1z=sngl.spin1z,
spin2z=sngl.spin2z, full_ethinca=ethincaParams.full_ethinca)
# assign the upper frequency cutoff and Gamma0-5 values
sngl.f_final = fMax_theor
for i in xrange(len(GammaVals)):
setattr(sngl, "Gamma"+str(i), GammaVals[i])
# If Gamma metric components are not wanted, assign f_final from an
# upper frequency cutoff specified in ethincaParams
elif ethincaParams.cutoff is not None:
for sngl in sngl_inspiral_table:
sngl.f_final = pnutils.frequency_cutoff_from_name(
ethincaParams.cutoff,
sngl.mass1, sngl.mass2, sngl.spin1z, sngl.spin2z)
# set per-template low-frequency cutoff
if 'f_low_column' in optDict and 'f_low' in optDict and \
optDict['f_low_column'] is not None:
for sngl in sngl_inspiral_table:
setattr(sngl, optDict['f_low_column'], optDict['f_low'])
outdoc.childNodes[0].appendChild(sngl_inspiral_table)
# get times to put in search summary table
start_time = 0
end_time = 0
if 'gps_start_time' in optDict.keys() and 'gps_end_time' in optDict.keys():
start_time = optDict['gps_start_time']
end_time = optDict['gps_end_time']
# make search summary table
search_summary_table = lsctables.New(lsctables.SearchSummaryTable)
search_summary = return_search_summary(start_time, end_time,
len(sngl_inspiral_table), ifos, **kwargs)
search_summary_table.append(search_summary)
outdoc.childNodes[0].appendChild(search_summary_table)
# write the xml doc to disk
ligolw_utils.write_filename(outdoc, outputFile,
gz=outputFile.endswith('.gz'))
def calculate_ethinca_metric_comps(metricParams, ethincaParams, mass1, mass2,
spin1z=0., spin2z=0., full_ethinca=True):
"""
Calculate the Gamma components needed to use the ethinca metric.
At present this outputs the standard TaylorF2 metric over the end time
and chirp times \tau_0 and \tau_3.
A desirable upgrade might be to use the \chi coordinates [defined WHERE?]
for metric distance instead of \tau_0 and \tau_3.
The lower frequency cutoff is currently hard-coded to be the same as the
bank layout options fLow and f0 (which must be the same as each other).
Parameters
-----------
metricParams : metricParameters instance
Structure holding all the options for construction of the metric
and the eigenvalues, eigenvectors and covariance matrix
needed to manipulate the space.
ethincaParams : ethincaParameters instance
Structure holding options relevant to the ethinca metric computation.
mass1 : float
Mass of the heavier body in the considered template.
mass2 : float
Mass of the lighter body in the considered template.
spin1z : float (optional, default=0)
Spin of the heavier body in the considered template.
spin2z : float (optional, default=0)
Spin of the lighter body in the considered template.
full_ethinca : boolean (optional, default=True)
If True calculate the ethinca components in all 3 directions (mass1,
mass2 and time). If False calculate only the time component (which is
stored in Gamma0).
Returns
--------
fMax_theor : float
Value of the upper frequency cutoff given by the template parameters
and the cutoff formula requested.
gammaVals : numpy_array
Array holding 6 independent metric components in
(end_time, tau_0, tau_3) coordinates to be stored in the Gamma0-5
slots of a SnglInspiral object.
"""
if (float(spin1z) != 0. or float(spin2z) != 0.) and full_ethinca:
raise NotImplementedError("Ethinca cannot at present be calculated "
"for nonzero component spins!")
f0 = metricParams.f0
if f0 != metricParams.fLow:
raise ValueError("If calculating ethinca the bank f0 value must be "
"equal to f-low!")
if ethincaParams.fLow is not None and (
ethincaParams.fLow != metricParams.fLow):
raise NotImplementedError("An ethinca metric f-low different from the"
" bank metric f-low is not supported!")
twicePNOrder = ethinca_order_from_string(ethincaParams.pnOrder)
piFl = PI * f0
totalMass, eta = pnutils.mass1_mass2_to_mtotal_eta(mass1, mass2)
totalMass = totalMass * MTSUN_SI
v0cube = totalMass*piFl
v0 = v0cube**(1./3.)
# Get theoretical cutoff frequency and work out the closest
# frequency for which moments were calculated
fMax_theor = pnutils.frequency_cutoff_from_name(
ethincaParams.cutoff, mass1, mass2, spin1z, spin2z)
fMaxes = metricParams.moments['J4'].keys()
fMaxIdx = abs(numpy.array(fMaxes,dtype=float) - fMax_theor).argmin()
fMax = fMaxes[fMaxIdx]
# Set the appropriate moments
Js = numpy.zeros([18,3],dtype=float)
for i in range(18):
Js[i,0] = metricParams.moments['J%d'%(i)][fMax]
Js[i,1] = metricParams.moments['log%d'%(i)][fMax]
Js[i,2] = metricParams.moments['loglog%d'%(i)][fMax]
# Compute the time-dependent metric term.
two_pi_flower_sq = TWOPI * f0 * TWOPI * f0
gammaVals = numpy.zeros([6],dtype=float)
gammaVals[0] = 0.5 * two_pi_flower_sq * \
( Js[(1,0)] - (Js[(4,0)]*Js[(4,0)]) )
# If mass terms not required stop here
if not full_ethinca:
return fMax_theor, gammaVals
# 3pN is a mess, so split it into pieces
a0 = 11583231236531/200286535680 - 5*PI*PI - 107*GAMMA/14
a1 = (-15737765635/130056192 + 2255*PI*PI/512)*eta
a2 = (76055/73728)*eta*eta
a3 = (-127825/55296)*eta*eta*eta
alog = numpy.log(4*v0) # Log terms are tricky - be careful
# Get the Psi coefficients
Psi = [{},{}] #Psi = numpy.zeros([2,8,2],dtype=float)
Psi[0][0,0] = 3/5
Psi[0][2,0] = (743/756 + 11*eta/3)*v0*v0
Psi[0][3,0] = 0.
Psi[0][4,0] = (-3058673/508032 + 5429*eta/504 + 617*eta*eta/24)\
*v0cube*v0
Psi[0][5,1] = (-7729*PI/126)*v0cube*v0*v0/3
Psi[0][6,0] = (128/15)*(-3*a0 - a1 + a2 + 3*a3 + 107*(1+3*alog)/14)\
*v0cube*v0cube
Psi[0][6,1] = (6848/35)*v0cube*v0cube/3
Psi[0][7,0] = (-15419335/63504 - 75703*eta/756)*PI*v0cube*v0cube*v0
Psi[1][0,0] = 0.
Psi[1][2,0] = (3715/12096 - 55*eta/96)/PI/v0;
Psi[1][3,0] = -3/2
Psi[1][4,0] = (15293365/4064256 - 27145*eta/16128 - 3085*eta*eta/384)\
*v0/PI
Psi[1][5,1] = (193225/8064)*v0*v0/3
Psi[1][6,0] = (4/PI)*(2*a0 + a1/3 - 4*a2/3 - 3*a3 -107*(1+6*alog)/42)\
*v0cube
Psi[1][6,1] = (-428/PI/7)*v0cube/3
Psi[1][7,0] = (77096675/1161216 + 378515*eta/24192 + 74045*eta*eta/8064)\
*v0cube*v0
# Set the appropriate moments
Js = numpy.zeros([18,3],dtype=float)
for i in range(18):
Js[i,0] = metricParams.moments['J%d'%(i)][fMax]
Js[i,1] = metricParams.moments['log%d'%(i)][fMax]
Js[i,2] = metricParams.moments['loglog%d'%(i)][fMax]
# Calculate the g matrix
PNterms = [(0,0),(2,0),(3,0),(4,0),(5,1),(6,0),(6,1),(7,0)]
PNterms = [term for term in PNterms if term[0] <= twicePNOrder]
# Now can compute the mass-dependent gamma values
for m in [0, 1]:
for k in PNterms:
gammaVals[1+m] += 0.5 * two_pi_flower_sq * Psi[m][k] * \
( Js[(9-k[0],k[1])]
- Js[(12-k[0],k[1])] * Js[(4,0)] )
g = numpy.zeros([2,2],dtype=float)
for (m,n) in [(0,0),(0,1),(1,1)]:
for k in PNterms:
for l in PNterms:
g[m,n] += Psi[m][k] * Psi[n][l] * \
( Js[(17-k[0]-l[0], k[1]+l[1])]
- Js[(12-k[0],k[1])] * Js[(12-l[0],l[1])] )
g[m,n] = 0.5 * two_pi_flower_sq * g[m,n]
g[n,m] = g[m,n]
gammaVals[3] = g[0,0]
gammaVals[4] = g[0,1]
gammaVals[5] = g[1,1]
return fMax_theor, gammaVals