From 8575add66c4ecd493b3655f877d4b905af23d740 Mon Sep 17 00:00:00 2001
From: Chad Hanna <chad.hanna@ligo.org>
Date: Tue, 5 Feb 2019 15:38:34 -0500
Subject: [PATCH] remove dead modules
---
.../python/coherent_inspiral_metric.py | 5547 -----------------
...herent_inspiral_metric_detector_details.py | 275 -
.../python/coherent_inspiral_metric_plots.py | 1045 ----
3 files changed, 6867 deletions(-)
delete mode 100644 gstlal-ugly/python/coherent_inspiral_metric.py
delete mode 100644 gstlal-ugly/python/coherent_inspiral_metric_detector_details.py
delete mode 100644 gstlal-ugly/python/coherent_inspiral_metric_plots.py
diff --git a/gstlal-ugly/python/coherent_inspiral_metric.py b/gstlal-ugly/python/coherent_inspiral_metric.py
deleted file mode 100644
index 4e4d6b74ae..0000000000
--- a/gstlal-ugly/python/coherent_inspiral_metric.py
+++ /dev/null
@@ -1,5547 +0,0 @@
-# Copyright (C) 2012 Drew Keppel
-#
-# This program is free software; you can redistribute it and/or modify it
-# under the terms of the GNU General Public License as published by the
-# Free Software Foundation; either version 2 of the License, or (at your
-# option) any later version.
-#
-# This program is distributed in the hope that it will be useful, but
-# WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
-# Public License for more details.
-#
-# You should have received a copy of the GNU General Public License along
-# with this program; if not, write to the Free Software Foundation, Inc.,
-# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
-
-
-#
-# ============================================================================
-#
-# Preamble
-#
-# ============================================================================
-#
-
-
-"""
-This module provides functions for computing different metrics associated with
-the signal manifold based on the coherent statistic for inspiral signals. The
-main assumption made for this calculation is that the detectors are stationary
-for the duration of the signal. The longest signals considered here are
-1M_sun-1M_sun binaries starting at 10Hz for aLIGO. These signals would last for
-30 minutes, and thus approximately satifisy this assumption.
-
-The derivation of the contents of this module is very close to that for
-continuous wave signals. It follows the examples of Prix arXiv:gr-qc/0606088
-although uses some of the notation of Harry and Fairhurst arXiv:1012.4939 for
-coherent inspiral signals.
-
-Some of this code should be moved to c code in LAL in order to speed up calculations
-"""
-
-import sys
-import numpy
-import scipy
-from scipy import log,exp,sin,cos,arccos,arctan2,pi
-from scipy import linalg
-import copy
-from lal import LAL_REARTH_SI as R_earth, LAL_MTSUN_SI as M_sun, \
- LAL_C_SI as c_speed, LAL_PC_SI as pc2m, LAL_GAMMA as gamma
-
-__author__ = "Drew Keppel <drew.keppel@ligo.org>"
-
-pc2s = pc2m / c_speed # par secs in seconds
-
-def A_plus(cosi, distance):
- """
- The plus amplitude.
- """
- Ap = (1.+cosi**2)/(2.*distance)
- return Ap
-
-def A_cross(cosi, distance):
- """
- The cross amplitude.
- """
- Ax = cosi/distance
- return Ax
-
-def A_1(cosi, distance, phi0, psi):
- """
- 1st amplitude parameter for a coherent signal.
- """
- Ap = A_plus(cosi, distance)
- Ax = A_cross(cosi, distance)
- A1 = Ap*cos(phi0)*cos(2.*psi) - Ax*sin(phi0)*sin(2.*psi)
- return A1
-
-def A_2(cosi, distance, phi0, psi):
- """
- 2nd amplitude parameter for a coherent signal.
- """
- Ap = A_plus(cosi, distance)
- Ax = A_cross(cosi, distance)
- A2 = Ap*cos(phi0)*sin(2.*psi) + Ax*sin(phi0)*cos(2.*psi)
- return A2
-
-def A_3(cosi, distance, phi0, psi):
- """
- 3rd amplitude parameter for a coherent signal.
- """
- Ap = A_plus(cosi, distance)
- Ax = A_cross(cosi, distance)
- A3 = -Ap*sin(phi0)*cos(2.*psi) - Ax*cos(phi0)*sin(2.*psi)
- return A3
-
-def A_4(cosi, distance, phi0, psi):
- """
- 4th amplitude parameter for a coherent signal.
- """
- Ap = A_plus(cosi, distance)
- Ax = A_cross(cosi, distance)
- A4 = -Ap*sin(phi0)*sin(2.*psi) + Ax*cos(phi0)*cos(2.*psi)
- return A4
-
-def coherent_signal(cosi, distance, phi0, psi, RA, dec, detector_list, hcos, hsin, f):
- """
- Generates a coherent signal in the frequency domain given an inclination,
- a distance, a reference phase, a polarization angle, a sky location, a
- list of detectors, the cos and sin pieces of the signal, and a frequency vector.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- s = []
- for detector in detector_list:
- fp = Fp(RA,dec,detector)
- fx = Fx(RA,dec,detector)
- dt = -rn(RA,dec,detector)
- phasor = exp(2j*pi*f*dt)
-
- h1 = fp*hcos
- h2 = fx*hcos
- h3 = fp*hsin
- h4 = fx*hsin
-
- h = (A1*h1 + A2*h2 + A3*h3 + A4*h4)*phasor
-
- s.append(h)
- return s
-
-def maximum_likelihood_matrix(RA, dec, detector_list):
- """
- Computes the elements associated with the matrix used for computing
- the maximum likelihood SNR^2 for a coherent analysis of data from the
- given detectors at the given sky location.
- """
- A = scipy.zeros(scipy.shape(RA))
- B = scipy.zeros(scipy.shape(RA))
- C = scipy.zeros(scipy.shape(RA))
- for detector in detector_list:
- fp = Fp(RA,dec,detector)
- fx = Fx(RA,dec,detector)
-
- A += fp*fp*detector.I_n['-7']
- B += fx*fx*detector.I_n['-7']
- C += fp*fx*detector.I_n['-7']
- D = A*B - C**2
-
- return A,B,C,D
-
-def average_snr(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25):
- """
- Computes the average SNR^2 for a signal at a given sky location
- given a list of detectors.
- """
- for detector in detector_list:
- detector.update_I_n(mchirp, eta)
-
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- return 2./5. * (A + B)
-
-def expected_coherent_snr(cosi, distance, phi0, psi, RA, dec, detector_list):
- """
- Computes the expected coherent SNR^2 for a coherent signal given an
- inclination, a distance, a reference phase, a polarization angle, a sky
- location and a list of detectors.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- rhocoh = 0.
- rhocoh += (A1*A1 + A3*A3)*A
- rhocoh += (A2*A2 + A4*A4)*B
- rhocoh += 2.*(A1*A2 + A3*A4)*C
-
- return rhocoh
-
-def coherent_match(s1, s2, detector_list, f):
- """
- Computes the match between two signals given the observed waveforms in
- a set of detectors, the list of detectors, and a frequency vector.
- """
- rho1 = 0.
- rho2 = 0.
- rho12 = 0.
- for s1_x,s2_x,detector in zip(s1,s2,detector_list):
- rho1 += 2*scipy.real(sum(s1_x*scipy.conj(s1_x)/detector.psd))
- rho2 += 2*scipy.real(sum(s2_x*scipy.conj(s2_x)/detector.psd))
- rho12 += 2*scipy.real(sum(s1_x*scipy.conj(s2_x)/detector.psd))
-
- return rho12/(rho1*rho2)**.5
-
-def coherent_filter(s, RA, dec, detector_list, hcos, hsin, f):
- """
- Computes the coherent SNR^2 time series for a template given the
- data observed in different detectors, the sky location, the list of detectors,
- the cos and sin parts of the template waveform (N.B., the template waveform should
- not include the detectors PSDs as the same waveform is used for all detectors and
- the inner product is scaled by the appropriate PSD internally), and a frequency
- vector.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- deltaF = f[1]-f[0]
-
- rhocos = []
- rhosin = []
- fps = []
- fxs = []
- for s_x,detector in zip(s,detector_list):
- dt = -rn(RA,dec,detector)
- rc = scipy.real(scipy.ifft(s_x*scipy.conj(hcos*exp(2j*pi*f*dt))/detector.psd))*deltaF*len(hcos)
- rs = scipy.real(scipy.ifft(s_x*scipy.conj(hsin*exp(2j*pi*f*dt))/detector.psd))*deltaF*len(hsin)
- rhocos.append(rc)
- rhosin.append(rs)
- fps.append(Fp(RA,dec,detector))
- fxs.append(Fx(RA,dec,detector))
-
- rhocoh = scipy.zeros(len(f), dtype='float')
- for rhocos1,rhosin1,fp1,fx1 in zip(rhocos,rhosin,fps,fxs):
- for rhocos2,rhosin2,fp2,fx2 in zip(rhocos,rhosin,fps,fxs):
- rhocoh += B*fp1*fp2*rhocos1*rhocos2
- rhocoh -= C*fp1*fx2*rhocos1*rhocos2
- rhocoh += A*fx1*fx2*rhocos1*rhocos2
- rhocoh -= C*fx1*fp2*rhocos1*rhocos2
- rhocoh += B*fp1*fp2*rhosin1*rhosin2
- rhocoh -= C*fp1*fx2*rhosin1*rhosin2
- rhocoh += A*fx1*fx2*rhosin1*rhosin2
- rhocoh -= C*fx1*fp2*rhosin1*rhosin2
- rhocoh /= D
- return rhocoh
-
-def moments(f, PSD, n, l=0):
- """
- Compute the integral log(f)**l * f**(n/3.) / PSD.
- """
- df = f[1]-f[0]
- psd_moment = scipy.log(f)**l * f**(float(n)/3.) / PSD * df
- return psd_moment.cumsum()
-
-def moments_required():
- """
- These moments over 3 are required in the metric calculation.
- The number of l's in the string denotes to power of log(f) to include.
- """
- return ['-1', '-2', '-3', '-4', '-5', '-6', '-7', '-8', '-9',
- '-10', '-11', '-12', '-13', '-14', '-15', '-17',
- '-3l', '-4l', '-5l', '-6l', '-7l',
- '-8l', '-9l', '-10l', '-11l', '-12l',
- '-5ll', '-6ll', '-7ll']
-
-class Detector:
- """
- A class to store the necessary information associated with a given
- detector for the coherent inspiral metric calculation.
- """
- def __init__(self, name, xarm, yarm, vertex, f=None, psd=None):
- self.xarm = xarm
- self.yarm = yarm
- self.vertex = vertex
- self.response = 0.5*(scipy.outer(xarm,xarm) - scipy.outer(yarm,yarm))
- self.f = f
- self.psd = psd
- self.deltaf = None
- self.one_sided_f = None
- self.one_sided_psd = None
- self.I_n_vec = {}
- self.I_n = {}
- self.name = name
-
- def add_moment(self, n, A=1):
- if self.psd is None:
- print >> sys.stderr, "No psd for this detector!"
- sys.exit()
- self.I_n_vec[n] = moments(self.one_sided_f, self.one_sided_psd, int(str(n).strip('l')), str(n).count('l'))
- self.I_n_vec[n] *= A
- self.I_n[n] = self.I_n_vec[n][-1]
-
- def set_psd(self, f, psd):
- self.f = f
- self.psd = psd
-
- def set_required_moments(self, A=1):
- if None not in [self.f, self.psd]:
- if sum(self.f < 0):
- self.one_sided_f = self.f[1:len(self.f)/2+1]
- self.one_sided_psd = self.psd[1:len(self.psd)/2+1]/2.
- else:
- self.one_sided_f = self.f
- self.one_sided_psd = self.psd
- self.deltaf = self.one_sided_f[1] - self.one_sided_f[0]
-
- for n in moments_required():
- if self.psd is None:
- print >> sys.stderr, "No psd for this detector!"
- sys.exit()
- self.add_moment(n, A)
-
- def update_I_n(self, mchirp, eta):
- f_isco = 1. / (6.**1.5 * pi * mchirp * eta**(-3./5.))
- fidx = min(int(f_isco / self.deltaf), len(self.one_sided_psd)-1)
- for key in self.I_n.keys():
- self.I_n[key] = self.I_n_vec[key][fidx]
-
- def update_I_n_Nyquist(self):
- for key in self.I_n.keys():
- self.I_n[key] = self.I_n_vec[key][-1]
-
-def dx_n2(y,dx):
- """
- Compute the first derivative of y with a second order stencil.
- """
- out = y*0.
- for idx in range(len(y)):
- if idx == 0:
- out[idx] = -3.*y[idx] + 4.*y[idx + 1] - y[idx + 2]
- out[idx] /= 2.*dx
- elif idx == len(y) - 1:
- out[idx] = 3.*y[idx] - 4.*y[idx - 1] + y[idx - 2]
- out[idx] /= 2.*dx
- else:
- out[idx] = y[idx + 1] - y[idx - 1]
- out[idx] /= 2.*dx
-
- return out
-
-def eps_plus(RA, dec):
- """
- The plus response tensor for an interferometric GW detector for a
- given sky location.
- FIXME: Get this from LAL.
- """
- s1 = sin(RA)
- c1 = cos(RA)
- s2 = sin(dec)
- c2 = cos(dec)
-
- e00 = s1**2 - (c1*s2)**2
- e01 = -s1*c1*(1+s2**2)
- e02 = c1*s2*c2
- e11 = c1**2 - (s1*s2)**2
- e12 = s1*s2*c2
- e22 = -c2**2
-
- return scipy.array([
- [e00, e01, e02],
- [e01, e11, e12],
- [e02, e12, e22]
- ])
-
-def Fp(RA, dec, detector):
- """
- Compute the plus-polarization antenna factor.
- FIXME: Get this from LAL.
- """
- d00 = detector.response[0,0]
- d01 = detector.response[0,1]
- d02 = detector.response[0,2]
- d11 = detector.response[1,1]
- d12 = detector.response[1,2]
- d22 = detector.response[2,2]
-
- eps = eps_plus(RA, dec)
- e00 = eps[0,0]
- e01 = eps[0,1]
- e02 = eps[0,2]
- e11 = eps[1,1]
- e12 = eps[1,2]
- e22 = eps[2,2]
-
- return d00*e00 + d11*e11 + d22*e22 + 2*(d01*e01 + d02*e02 + d12*e12)
-
-def deps_plus_dRA(RA, dec):
- """
- The derivative of the plus response tensor for an interferometric GW detector for a
- given sky location with respect to the Right Ascension.
- FIXME: Move this to LAL.
- """
- s1 = sin(RA)
- c1 = cos(RA)
- s2 = sin(dec)
- c2 = cos(dec)
-
- e00 = 2*s1*c1*(1 + s2**2)
- e01 = (s1**2 - c1**2)*(1 + s2**2)
- e02 = -s1*s2*c2
- e11 = -2*s1*c1*(1 + s2**2)
- e12 = c1*s2*c2
- e22 = 0
-
- return scipy.array([
- [e00, e01, e02],
- [e01, e11, e12],
- [e02, e12, e22]
- ])
-
-def dFp_dRA(RA, dec, detector):
- """
- Compute the partial derivate of the plus-polarization antenna factor
- with respect to RA, the right ascension.
- FIXME: Move this to LAL.
- """
- d00 = detector.response[0,0]
- d01 = detector.response[0,1]
- d02 = detector.response[0,2]
- d11 = detector.response[1,1]
- d12 = detector.response[1,2]
- d22 = detector.response[2,2]
-
- eps = deps_plus_dRA(RA, dec)
- e00 = eps[0,0]
- e01 = eps[0,1]
- e02 = eps[0,2]
- e11 = eps[1,1]
- e12 = eps[1,2]
- e22 = eps[2,2]
-
- return d00*e00 + d11*e11 + d22*e22 + 2*(d01*e01 + d02*e02 + d12*e12)
-
-def deps_plus_ddec(RA, dec):
- """
- The derivative of the plus response tensor for an interferometric GW detector for a
- given sky location with respect to the declination.
- FIXME: Move this to LAL.
- """
- s1 = sin(RA)
- c1 = cos(RA)
- s2 = sin(dec)
- c2 = cos(dec)
-
- e00 = -2*c1**2*s2*c2
- e01 = -2*s1*c1*s2*c2
- e02 = c1*(c2**2 - s2**2)
- e11 = -2*s1**2*s2*c2
- e12 = s1*(c2**2 - s2**2)
- e22 = 2*s2*c2
-
- return scipy.array([
- [e00, e01, e02],
- [e01, e11, e12],
- [e02, e12, e22]
- ])
-
-def dFp_ddec(RA, dec, detector):
- """
- Compute the partial derivate of the plus-polarization antenna factor
- with respect to dec, the declination.
- FIXME: Move this to LAL.
- """
- d00 = detector.response[0,0]
- d01 = detector.response[0,1]
- d02 = detector.response[0,2]
- d11 = detector.response[1,1]
- d12 = detector.response[1,2]
- d22 = detector.response[2,2]
-
- eps = deps_plus_ddec(RA, dec)
- e00 = eps[0,0]
- e01 = eps[0,1]
- e02 = eps[0,2]
- e11 = eps[1,1]
- e12 = eps[1,2]
- e22 = eps[2,2]
-
- return d00*e00 + d11*e11 + d22*e22 + 2*(d01*e01 + d02*e02 + d12*e12)
-
-def eps_cross(RA, dec):
- """
- The cross response tensor for an interferometric GW detector for a
- given sky location.
- FIXME: Get this from LAL.
- """
- s1 = sin(RA)
- c1 = cos(RA)
- s2 = sin(dec)
- c2 = cos(dec)
-
- e00 = -2*s1*c1*s2
- e01 = s2*(c1**2 - s1**2)
- e02 = s1*c2
- e11 = 2*s1*c1*s2
- e12 = -c1*c2
- e22 = 0
-
- return scipy.array([
- [e00, e01, e02],
- [e01, e11, e12],
- [e02, e12, e22]
- ])
-
-def Fx(RA, dec, detector):
- """
- Compute the cross-polarization antenna factor.
- FIXME: Get this from LAL.
- """
- d00 = detector.response[0,0]
- d01 = detector.response[0,1]
- d02 = detector.response[0,2]
- d11 = detector.response[1,1]
- d12 = detector.response[1,2]
- d22 = detector.response[2,2]
-
- eps = eps_cross(RA, dec)
- e00 = eps[0,0]
- e01 = eps[0,1]
- e02 = eps[0,2]
- e11 = eps[1,1]
- e12 = eps[1,2]
- e22 = eps[2,2]
-
- return d00*e00 + d11*e11 + d22*e22 + 2*(d01*e01 + d02*e02 + d12*e12)
-
-def deps_cross_dRA(RA, dec):
- """
- The derivative of the cross response tensor for an interferometric GW detector for a
- given sky location with respect to the Rigth Ascension.
- FIXME: Move this to LAL.
- """
- s1 = sin(RA)
- c1 = cos(RA)
- s2 = sin(dec)
- c2 = cos(dec)
-
- e00 = 2*(s1**2 - c1**2)*s2
- e01 = -4*s1*c1*s2
- e02 = c1*c2
- e11 = 2*(c1**2 - s1**2)*s2
- e12 = s1*c2
- e22 = 0
-
- return scipy.array([
- [e00, e01, e02],
- [e01, e11, e12],
- [e02, e12, e22]
- ])
-
-def dFx_dRA(RA, dec, detector):
- """
- Compute the partial derivate of the cross-polarization antenna factor
- with respect to RA, the right ascension.
- FIXME: Move this to LAL.
- """
- d00 = detector.response[0,0]
- d01 = detector.response[0,1]
- d02 = detector.response[0,2]
- d11 = detector.response[1,1]
- d12 = detector.response[1,2]
- d22 = detector.response[2,2]
-
- eps = deps_cross_dRA(RA, dec)
- e00 = eps[0,0]
- e01 = eps[0,1]
- e02 = eps[0,2]
- e11 = eps[1,1]
- e12 = eps[1,2]
- e22 = eps[2,2]
-
- return d00*e00 + d11*e11 + d22*e22 + 2*(d01*e01 + d02*e02 + d12*e12)
-
-def deps_cross_ddec(RA, dec):
- """
- The derivative of the cross response tensor for an interferometric GW detector for a
- given sky location with respect to the declination.
- FIXME: Move this to LAL.
- """
- s1 = sin(RA)
- c1 = cos(RA)
- s2 = sin(dec)
- c2 = cos(dec)
-
- e00 = -2*s1*c1*c2
- e01 = (c1**2 - s1**2)*c2
- e02 = -s1*s2
- e11 = 2*s1*c1*c2
- e12 = c1*s2
- e22 = 0
-
- return scipy.array([
- [e00, e01, e02],
- [e01, e11, e12],
- [e02, e12, e22]
- ])
-
-def dFx_ddec(RA, dec, detector):
- """
- Compute the partial derivate of the cross-polarization antenna factor
- with respect to dec, the declination.
- FIXME: Move this to LAL.
- """
- d00 = detector.response[0,0]
- d01 = detector.response[0,1]
- d02 = detector.response[0,2]
- d11 = detector.response[1,1]
- d12 = detector.response[1,2]
- d22 = detector.response[2,2]
-
- eps = deps_cross_ddec(RA, dec)
- e00 = eps[0,0]
- e01 = eps[0,1]
- e02 = eps[0,2]
- e11 = eps[1,1]
- e12 = eps[1,2]
- e22 = eps[2,2]
-
- return d00*e00 + d11*e11 + d22*e22 + 2*(d01*e01 + d02*e02 + d12*e12)
-
-def dlnA_dmchirp_dict(mchirp, eta):
- """
- Computes the derivative of an inspiral signal's Ln[amplitude] with
- respect to the chirp mass. Returns as a dictionary for use in the
- metric calculation.
- """
- dlnA_dmchirp = {}
- dlnA_dmchirp['0'] = 5./(6.*mchirp)
-
- return dlnA_dmchirp
-
-def dlnA_dh0_dict():
- """
- Computes the derivative of an inspiral signal's Ln[amplitude] with
- respect to the unknown amplitude parameter. Returns as a dictionary for use in the
- metric calculation. Used in the single detector metric.
- """
- dlnA_dh0 = {}
- dlnA_dh0['0'] = 1.
-
- return dlnA_dh0
-
-def Phase_dict(mchirp, eta, PNorder=7):
- """
- Computes an inspiral signal's phase. Returns as a dictionary for use in the metric
- calculation.
- """
- Phase = {}
- # 0.0PN
- Phase['-5'] = 3./(128.*pi**(5./3.)*mchirp**(5./3.))
- # 1.0PN
- if PNorder >= 2:
- Phase['-3'] = 5./(384.*pi*mchirp*eta**(2./5.))*(743./84. + 11.*eta)
- # 1.5PN
- if PNorder >= 3:
- Phase['-2'] = -3.*pi**(1./3.)/(8.*mchirp**(2./3.)*eta**(3./5.))
- # 2.0PN
- if PNorder >= 4:
- Phase['-1'] = 5./(3072.*pi**(1./3.)*mchirp**(1./3.)*eta**(4./5.))*(3058673./7056. + 5429./7.*eta + 617.*eta**2)
- # 2.5PN
- if PNorder >= 5:
- Phase['0'] = 5.*pi/(384.*eta)*(7729./84. - 13.*eta)*(1. + log(6.**1.5*pi*mchirp*eta**(-3./5.)))
- Phase['0l'] = 5.*pi/(384.*eta)*(7729./84. - 13.*eta)
- # 3.0PN
- if PNorder >= 6:
- Phase['1'] = pi**(1./3.)*mchirp**(1./3.)/(128.*eta**(6./5.))*(11583231236531./1564738560. - 640.*pi**2 - 6848./7.*(gamma + log(4.*(pi*mchirp)**(1./3.)*eta**(-1./5.))) + 5./4.*(-3147553127./254016. + 451.*pi**2)*eta + 76055./576.*eta**2 - 127825./432.*eta**3)
- Phase['1l'] = -107.*pi**(1./3.)*mchirp**(1./3.)/(42.*eta**(6./5.))
- # 3.5PN
- if PNorder >= 7:
- Phase['2'] = 5.*pi**(5./3.)*mchirp**(2./3.)/(32256.*eta**(7./5.))*(15419335./336. + 75703./2.*eta - 14809.*eta**2)
-
- return Phase
-
-def dPhase_dmchirp_dict(mchirp, eta, PNorder=7):
- """
- Computes the derivative of an inspiral signal's phase with respect to
- the chirp mass. Returns as a dictionary for use in the metric
- calculation.
- """
- dPhase_dmchirp = {}
- # 0.0PN
- dPhase_dmchirp['-5'] = -5./(128.*pi**(5./3.)*mchirp**(8./3.))
- # 1.0PN
- if PNorder >= 2:
- dPhase_dmchirp['-3'] = -5./(384.*pi*mchirp**2.*eta**(2./5.))*(743./84. + 11.*eta)
- # 1.5PN
- if PNorder >= 3:
- dPhase_dmchirp['-2'] = pi**(1./3.)/(4.*mchirp**(5./3.)*eta**(3./5.))
- # 2.0PN
- if PNorder >= 4:
- dPhase_dmchirp['-1'] = -5./(9216.*pi**(1./3.)*mchirp**(4./3.)*eta**(4./5.))*(3058673./7056. + 5429./7.*eta + 617.*eta**2)
- # 2.5PN
- if PNorder >= 5:
- dPhase_dmchirp['0'] = 5.*pi/(384.*eta*mchirp)*(7729./84. - 13.*eta)
- # 3.0PN
- if PNorder >= 6:
- dPhase_dmchirp['1'] = pi**(1./3.)/(384.*eta**(6./5.)*mchirp**(2./3.))*(10052469856691./1564738560. - 640.*pi**2 - 6848./7.*(gamma + log(4.*(pi*mchirp)**(1./3.)*eta**(-1./5.))) + 5./4.*(-3147553127./254016. + 451.*pi**2)*eta + 76055./576.*eta**2 - 127825./432.*eta**3)
- dPhase_dmchirp['1l'] = -107.*pi**(1./3.)/(126.*eta**(6./5.)*mchirp**(2./3.))
- # 3.5PN
- if PNorder >= 7:
- dPhase_dmchirp['2'] = 5.*pi**(5./3.)/(48384.*mchirp**(1./3.)*eta**(7./5.))*(15419335./336. + 75703./2.*eta - 14809.*eta**2)
-
- return dPhase_dmchirp
-
-def dPhase_deta_dict(mchirp, eta, PNorder=7):
- """
- Computes the derivative of an inspiral signal's phase with respect to
- the symmetric mass ratio. Returns as a dictionary for use in the
- metric calculation.
- """
- dPhase_deta = {}
- # 1.0PN
- if PNorder >= 2:
- dPhase_deta['-3'] = -1./(384.*pi*mchirp*eta**(7./5.))*(743./42. - 33.*eta)
- # 1.5PN
- if PNorder >= 3:
- dPhase_deta['-2'] = 9.*pi**(1./3.)/(40.*mchirp**(2./3.)*eta**(8./5.))
- # 2.0PN
- if PNorder >= 4:
- dPhase_deta['-1'] = -3./(3072.*(pi*mchirp)**(1./3.)*eta**(9./5.))*(3058673./5292. - 5429./21.*eta - 1234.*eta**2.)
- # 2.5PN
- if PNorder >= 5:
- dPhase_deta['0'] = -pi/(384.*eta**2.)*(7729./84.*(8. + 5.*log(6**(3./2.)*pi*mchirp*eta**(-3./5.))) - 39.*eta)
- dPhase_deta['0l'] = -38645.*pi/(32256.*eta**2.)
- # 3.0PN
- if PNorder >= 6:
- dPhase_deta['1'] = (pi*mchirp)**(1./3.)/(640.*eta**(11./5.))*(-11328104339891./260789760. + 3840.*pi**2 + 41088./7.*(gamma + log(4*(pi*mchirp)**(1./3.)*eta**(-1./5.))) - 5./4.*(-3147553127./254016. + 451*pi**2)*eta + 76055./144.*eta**2. - 127825./48.*eta**3.)
- dPhase_deta['1l'] = 107.*(pi*mchirp)**(1./3.)/(35.*eta**(11./5.))
- # 3.5PN
- if PNorder >= 7:
- dPhase_deta['2'] = -pi**(5./3.)*mchirp**(2./3.)/(32256.*eta**(12./5.))*(15419335./48. + 75703.*eta + 44427.*eta**2.)
-
- return dPhase_deta
-
-def dPhase_dt_dict():
- """
- Computes the derivative of an inspiral signal's phase with respect to
- the end time. Returns as a dictionary for use in the metric
- calculation.
- """
- dPhase_dt = {}
- dPhase_dt['3'] = 2*pi
-
- return dPhase_dt
-
-def dPhase_dphi_dict():
- """
- Computes the derivative of an inspiral signal's phase with respect to
- the end phase. Returns as a dictionary for use in the metric
- calculation. Used in the single detector metric.
- """
- dPhase_dphi = {}
- dPhase_dphi['0'] = -1.
-
- return dPhase_dphi
-
-# FIXME: should be rotating with time
-def rn(RA, dec, detector):
- """
- The inner product of n(RA,dec) and r_X for detector X.
- """
- dx,dy,dz = detector.vertex
- tmp = dx*cos(RA)*cos(dec) + dy*sin(RA)*cos(dec) + dz*sin(dec)
- return tmp / c_speed
-
-def drn_dRA(RA, dec, detector):
- """
- The derivative of the inner product of n(RA,dec) and r_X for
- detector X with respect to the Right Ascension.
- """
- dx,dy,dz = detector.vertex
- tmp = -dx*sin(RA)*cos(dec) + dy*cos(RA)*cos(dec)
- return tmp / c_speed
-
-def drn_ddec(RA, dec, detector):
- """
- The derivative of the inner product of n(RA,dec) and r_X for
- detector X with respect to the declination.
- """
- dx,dy,dz = detector.vertex
- tmp = -dx*cos(RA)*sin(dec) - dy*sin(RA)*sin(dec) + dz*cos(dec)
- return tmp / c_speed
-
-def mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs=True):
- """
- Computes the first mismatch component associated with the derivatives
- with respect to parameters lambda_i and lambda_j. Take as input the
- list of detectors, the components of the maximum likelihood matrix,
- the plus and cross antenna responses for these detectors, derivatives
- of the plus and cross antenna responses with respect to lambda_i and
- lambda_j, the derivatives of the inspiral waveform phase with respect
- to lambda_i and lambda_j, the derivatives of the inspiral waveform
- Ln[amplitude] with respect to lambda_i and lambda_j, and a flag saying
- whether to include derivatives of the antenna responses in the
- calculation.
- """
- h11ij = scipy.zeros(scipy.shape(A))
- R11i = scipy.zeros(scipy.shape(A))
- R11j = scipy.zeros(scipy.shape(A))
- R21i = scipy.zeros(scipy.shape(A))
- R21j = scipy.zeros(scipy.shape(A))
- R31i = scipy.zeros(scipy.shape(A))
- R31j = scipy.zeros(scipy.shape(A))
- R41i = scipy.zeros(scipy.shape(A))
- R41j = scipy.zeros(scipy.shape(A))
- for detector in detector_list:
- I_n = detector.I_n
- I_dLnAmp_dLnAmp = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- for key2 in dLnAmpj[detector.name].keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmp_dLnAmp += dLnAmpi[detector.name][key1]*dLnAmpj[detector.name][key2]*I_n[psd_key]
- I_dPhase_dPhase = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- for key2 in dPhasej[detector.name].keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhase_dPhase += dPhasei[detector.name][key1]*dPhasej[detector.name][key2]*I_n[psd_key]
- h11ij += fp[detector.name]*fp[detector.name] * (I_dLnAmp_dLnAmp + I_dPhase_dPhase)
- I_dLnAmpi = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpi += dLnAmpi[detector.name][key1]*I_n[psd_key]
- I_dLnAmpj = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpj[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpj += dLnAmpj[detector.name][key1]*I_n[psd_key]
- R11i += fp[detector.name]*fp[detector.name] * I_dLnAmpi
- R11j += fp[detector.name]*fp[detector.name] * I_dLnAmpj
- R21i += fx[detector.name]*fp[detector.name] * I_dLnAmpi
- R21j += fx[detector.name]*fp[detector.name] * I_dLnAmpj
- if Fderivs:
- h11ij += dfpi[detector.name]*fp[detector.name] * I_dLnAmpj
- h11ij += fp[detector.name]*dfpj[detector.name] * I_dLnAmpi
- I_dPhasei = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasei += dPhasei[detector.name][key1]*I_n[psd_key]
- I_dPhasej = scipy.zeros(scipy.shape(A))
- for key1 in dPhasej[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasej += dPhasej[detector.name][key1]*I_n[psd_key]
- R31i -= fp[detector.name]*fp[detector.name] * I_dPhasei
- R31j -= fp[detector.name]*fp[detector.name] * I_dPhasej
- R41i -= fx[detector.name]*fp[detector.name] * I_dPhasei
- R41j -= fx[detector.name]*fp[detector.name] * I_dPhasej
- if Fderivs:
- psd_key = '-7'
- h11ij += dfpi[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R11i += fp[detector.name]*dfpi[detector.name] * I_n[psd_key]
- R11j += fp[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R21i += fx[detector.name]*dfpi[detector.name] * I_n[psd_key]
- R21j += fx[detector.name]*dfpj[detector.name] * I_n[psd_key]
-
- p = h11ij
- q = B*(R11i*R11j + R31i*R31j) + A*(R21i*R21j + R41i*R41j)\
- - C*(R11i*R21j + R21i*R11j + R31i*R41j + R41i*R31j)
- m1 = p - q/D
-
- return m1
-
-def mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs=True):
- """
- Computes the second mismatch component associated with the derivatives
- with respect to parameters lambda_i and lambda_j. Take as input the
- list of detectors, the components of the maximum likelihood matrix,
- the plus and cross antenna responses for these detectors, derivatives
- of the plus and cross antenna responses with respect to lambda_i and
- lambda_j, the derivatives of the inspiral waveform phase with respect
- to lambda_i and lambda_j, the derivatives of the inspiral waveform
- Ln[amplitude] with respect to lambda_i and lambda_j, and a flag saying
- whether to include derivatives of the antenna responses in the
- calculation.
- """
- h22ij = scipy.zeros(scipy.shape(A))
- R12i = scipy.zeros(scipy.shape(A))
- R12j = scipy.zeros(scipy.shape(A))
- R14i = scipy.zeros(scipy.shape(A))
- R14j = scipy.zeros(scipy.shape(A))
- R22i = scipy.zeros(scipy.shape(A))
- R22j = scipy.zeros(scipy.shape(A))
- R24i = scipy.zeros(scipy.shape(A))
- R24j = scipy.zeros(scipy.shape(A))
- for detector in detector_list:
- I_n = detector.I_n
- I_dLnAmp_dLnAmp = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- for key2 in dLnAmpj[detector.name].keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmp_dLnAmp += dLnAmpi[detector.name][key1]*dLnAmpj[detector.name][key2]*I_n[psd_key]
- I_dPhase_dPhase = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- for key2 in dPhasej[detector.name].keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhase_dPhase += dPhasei[detector.name][key1]*dPhasej[detector.name][key2]*I_n[psd_key]
- h22ij += fx[detector.name]*fx[detector.name] * (I_dLnAmp_dLnAmp + I_dPhase_dPhase)
- I_dLnAmpi = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpi += dLnAmpi[detector.name][key1]*I_n[psd_key]
- I_dLnAmpj = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpj[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpj += dLnAmpj[detector.name][key1]*I_n[psd_key]
- R12i += fp[detector.name]*fx[detector.name] * I_dLnAmpi
- R12j += fp[detector.name]*fx[detector.name] * I_dLnAmpj
- R22i += fx[detector.name]*fx[detector.name] * I_dLnAmpi
- R22j += fx[detector.name]*fx[detector.name] * I_dLnAmpj
- if Fderivs:
- h22ij += dfxi[detector.name]*fx[detector.name] * I_dLnAmpj
- h22ij += fx[detector.name]*dfxj[detector.name] * I_dLnAmpi
- I_dPhasei = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasei += dPhasei[detector.name][key1]*I_n[psd_key]
- I_dPhasej = scipy.zeros(scipy.shape(A))
- for key1 in dPhasej[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasej += dPhasej[detector.name][key1]*I_n[psd_key]
- R14i += fp[detector.name]*fx[detector.name] * I_dPhasei
- R14j += fp[detector.name]*fx[detector.name] * I_dPhasej
- R24i += fx[detector.name]*fx[detector.name] * I_dPhasei
- R24j += fx[detector.name]*fx[detector.name] * I_dPhasej
- if Fderivs:
- psd_key = '-7'
- h22ij += dfxi[detector.name]*dfxj[detector.name] * I_n[psd_key]
- R12i += fp[detector.name]*dfxi[detector.name] * I_n[psd_key]
- R12j += fp[detector.name]*dfxj[detector.name] * I_n[psd_key]
- R22i += fx[detector.name]*dfxi[detector.name] * I_n[psd_key]
- R22j += fx[detector.name]*dfxj[detector.name] * I_n[psd_key]
-
- p = h22ij
- q = B*(R12i*R12j + R14i*R14j) + A*(R22i*R22j + R24i*R24j)\
- - C*(R12i*R22j + R22i*R12j + R14i*R24j + R24i*R14j)
- m2 = p - q/D
-
- return m2
-
-def mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs=True):
- """
- Computes the third mismatch component associated with the derivatives
- with respect to parameters lambda_i and lambda_j. Take as input the
- list of detectors, the components of the maximum likelihood matrix,
- the plus and cross antenna responses for these detectors, derivatives
- of the plus and cross antenna responses with respect to lambda_i and
- lambda_j, the derivatives of the inspiral waveform phase with respect
- to lambda_i and lambda_j, the derivatives of the inspiral waveform
- Ln[amplitude] with respect to lambda_i and lambda_j, and a flag saying
- whether to include derivatives of the antenna responses in the
- calculation.
- """
- h12ij = scipy.zeros(scipy.shape(A))
- h21ij = scipy.zeros(scipy.shape(A))
- R11i = scipy.zeros(scipy.shape(A))
- R11j = scipy.zeros(scipy.shape(A))
- R12i = scipy.zeros(scipy.shape(A))
- R12j = scipy.zeros(scipy.shape(A))
- R13i = scipy.zeros(scipy.shape(A))
- R13j = scipy.zeros(scipy.shape(A))
- R14i = scipy.zeros(scipy.shape(A))
- R14j = scipy.zeros(scipy.shape(A))
- R21i = scipy.zeros(scipy.shape(A))
- R21j = scipy.zeros(scipy.shape(A))
- R22i = scipy.zeros(scipy.shape(A))
- R22j = scipy.zeros(scipy.shape(A))
- R24i = scipy.zeros(scipy.shape(A))
- R24j = scipy.zeros(scipy.shape(A))
- for detector in detector_list:
- I_n = detector.I_n
- I_dLnAmp_dLnAmp = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- for key2 in dLnAmpj[detector.name].keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmp_dLnAmp += dLnAmpi[detector.name][key1]*dLnAmpj[detector.name][key2]*I_n[psd_key]
- I_dPhase_dPhase = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- for key2 in dPhasej[detector.name].keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhase_dPhase += dPhasei[detector.name][key1]*dPhasej[detector.name][key2]*I_n[psd_key]
- h12ij += fp[detector.name]*fx[detector.name] * (I_dLnAmp_dLnAmp + I_dPhase_dPhase)
- h21ij += fx[detector.name]*fp[detector.name] * (I_dLnAmp_dLnAmp + I_dPhase_dPhase)
- I_dLnAmpi = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpi += dLnAmpi[detector.name][key1]*I_n[psd_key]
- I_dLnAmpj = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpj[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpj += dLnAmpj[detector.name][key1]*I_n[psd_key]
- R11i += fp[detector.name]*fp[detector.name] * I_dLnAmpi
- R11j += fp[detector.name]*fp[detector.name] * I_dLnAmpj
- R12i += fp[detector.name]*fx[detector.name] * I_dLnAmpi
- R12j += fp[detector.name]*fx[detector.name] * I_dLnAmpj
- R21i += fx[detector.name]*fp[detector.name] * I_dLnAmpi
- R21j += fx[detector.name]*fp[detector.name] * I_dLnAmpj
- R22i += fx[detector.name]*fx[detector.name] * I_dLnAmpi
- R22j += fx[detector.name]*fx[detector.name] * I_dLnAmpj
- if Fderivs:
- h12ij += dfpi[detector.name]*fx[detector.name] * I_dLnAmpj
- h12ij += fp[detector.name]*dfxj[detector.name] * I_dLnAmpi
- h21ij += dfxi[detector.name]*fp[detector.name] * I_dLnAmpj
- h21ij += fx[detector.name]*dfpj[detector.name] * I_dLnAmpi
- I_dPhasei = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasei += dPhasei[detector.name][key1]*I_n[psd_key]
- I_dPhasej = scipy.zeros(scipy.shape(A))
- for key1 in dPhasej[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasej += dPhasej[detector.name][key1]*I_n[psd_key]
- R13i += fp[detector.name]*fp[detector.name] * I_dPhasei
- R13j += fp[detector.name]*fp[detector.name] * I_dPhasej
- R14i += fx[detector.name]*fp[detector.name] * I_dPhasei
- R14j += fx[detector.name]*fp[detector.name] * I_dPhasej
- R24i += fx[detector.name]*fx[detector.name] * I_dPhasei
- R24j += fx[detector.name]*fx[detector.name] * I_dPhasej
- if Fderivs:
- psd_key = '-7'
- h12ij += dfpi[detector.name]*dfxj[detector.name] * I_n[psd_key]
- h21ij += dfxi[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R11i += fp[detector.name]*dfpi[detector.name] * I_n[psd_key]
- R11j += fp[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R12i += fp[detector.name]*dfxi[detector.name] * I_n[psd_key]
- R12j += fp[detector.name]*dfxj[detector.name] * I_n[psd_key]
- R21i += fx[detector.name]*dfpi[detector.name] * I_n[psd_key]
- R21j += fx[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R22i += fx[detector.name]*dfxi[detector.name] * I_n[psd_key]
- R22j += fx[detector.name]*dfxj[detector.name] * I_n[psd_key]
-
- p = h12ij + h21ij
- q = B*(R11i*R12j + R13i*R14j) + A*(R21i*R22j + R14i*R24j)\
- - C*(R11i*R22j + R21i*R12j + R13i*R24j + R14i*R14j)
- q += B*(R12i*R11j + R14i*R13j) + A*(R22i*R21j + R24i*R14j)\
- - C*(R12i*R21j + R22i*R11j + R14i*R14j + R24i*R13j)
- m3 = p - q/D
- m3 /= 2.
-
- return m3
-
-def mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs=True):
- """
- Computes the fourth mismatch component associated with the derivatives
- with respect to parameters lambda_i and lambda_j. Take as input the
- list of detectors, the components of the maximum likelihood matrix,
- the plus and cross antenna responses for these detectors, derivatives
- of the plus and cross antenna responses with respect to lambda_i and
- lambda_j, the derivatives of the inspiral waveform phase with respect
- to lambda_i and lambda_j, the derivatives of the inspiral waveform
- Ln[amplitude] with respect to lambda_i and lambda_j, and a flag saying
- whether to include derivatives of the antenna responses in the
- calculation.
- """
- h14ij = scipy.zeros(scipy.shape(A))
- h41ij = scipy.zeros(scipy.shape(A))
- R11i = scipy.zeros(scipy.shape(A))
- R11j = scipy.zeros(scipy.shape(A))
- R12i = scipy.zeros(scipy.shape(A))
- R12j = scipy.zeros(scipy.shape(A))
- R13i = scipy.zeros(scipy.shape(A))
- R13j = scipy.zeros(scipy.shape(A))
- R14i = scipy.zeros(scipy.shape(A))
- R14j = scipy.zeros(scipy.shape(A))
- R21i = scipy.zeros(scipy.shape(A))
- R21j = scipy.zeros(scipy.shape(A))
- R22i = scipy.zeros(scipy.shape(A))
- R22j = scipy.zeros(scipy.shape(A))
- R24i = scipy.zeros(scipy.shape(A))
- R24j = scipy.zeros(scipy.shape(A))
- for detector in detector_list:
- I_n = detector.I_n
- I_dLnAmpi = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpi[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpi += dLnAmpi[detector.name][key1]*I_n[psd_key]
- I_dLnAmpj = scipy.zeros(scipy.shape(A))
- for key1 in dLnAmpj[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmpj += dLnAmpj[detector.name][key1]*I_n[psd_key]
- R11i += fp[detector.name]*fp[detector.name] * I_dLnAmpi
- R11j += fp[detector.name]*fp[detector.name] * I_dLnAmpj
- R12i += fp[detector.name]*fx[detector.name] * I_dLnAmpi
- R12j += fp[detector.name]*fx[detector.name] * I_dLnAmpj
- R21i += fx[detector.name]*fp[detector.name] * I_dLnAmpi
- R21j += fx[detector.name]*fp[detector.name] * I_dLnAmpj
- R22i += fx[detector.name]*fx[detector.name] * I_dLnAmpi
- R22j += fx[detector.name]*fx[detector.name] * I_dLnAmpj
- I_dPhasei = scipy.zeros(scipy.shape(A))
- for key1 in dPhasei[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasei += dPhasei[detector.name][key1]*I_n[psd_key]
- I_dPhasej = scipy.zeros(scipy.shape(A))
- for key1 in dPhasej[detector.name].keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhasej += dPhasej[detector.name][key1]*I_n[psd_key]
- R14i += fp[detector.name]*fx[detector.name] * I_dPhasei
- R14j += fp[detector.name]*fx[detector.name] * I_dPhasej
- R24i += fx[detector.name]*fx[detector.name] * I_dPhasei
- R24j += fx[detector.name]*fx[detector.name] * I_dPhasej
- R13i += fp[detector.name]*fp[detector.name] * I_dPhasei
- R13j += fp[detector.name]*fp[detector.name] * I_dPhasej
- if Fderivs:
- h14ij += (dfpi[detector.name]*fx[detector.name] - dfxi[detector.name]*fp[detector.name]) * I_dPhasej
- h41ij += (fx[detector.name]*dfpj[detector.name] - fp[detector.name]*dfxj[detector.name]) * I_dPhasei
- psd_key = '-7'
- R11i += fp[detector.name]*dfpi[detector.name] * I_n[psd_key]
- R11j += fp[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R12i += fp[detector.name]*dfxi[detector.name] * I_n[psd_key]
- R12j += fp[detector.name]*dfxj[detector.name] * I_n[psd_key]
- R21i += fx[detector.name]*dfpi[detector.name] * I_n[psd_key]
- R21j += fx[detector.name]*dfpj[detector.name] * I_n[psd_key]
- R22i += fx[detector.name]*dfxi[detector.name] * I_n[psd_key]
- R22j += fx[detector.name]*dfxj[detector.name] * I_n[psd_key]
-
- p = h14ij + h41ij
- q = B*(R11i*R14j - R13i*R12j) + A*(R21i*R24j - R14i*R22j)\
- - C*(R11i*R24j + R21i*R14j - R13i*R22j - R14i*R12j)
- q += B*(R14i*R11j - R12i*R13j) + A*(R24i*R21j - R22i*R14j)\
- - C*(R24i*R11j + R14i*R21j - R22i*R13j - R12i*R14j)
- m4 = p - q/D
- m4 /= 2.
-
- return m4
-
-def g_A1_A1(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st amplitude parameter.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- z = A*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A1_A2(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st and 2nd amplitude
- parameters.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- z = C*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A1_A3(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st and 3rd amplitude
- parameters.
- """
- z = 0.*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A1_A4(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st and 4th amplitude
- parameters.
- """
- z = 0.*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A2_A2(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd amplitude parameters.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- z = B*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A2_A3(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd and 3rd amplitude
- parameters.
- """
- z = 0.*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A2_A4(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd and 4th amplitude
- parameters.
- """
- z = 0.*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A3_A3(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd amplitude parameter.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- z = A*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A3_A4(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd and 4th amplitude
- parameters.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- z = C*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A4_A4(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 4th amplitude parameter.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- z = B*scipy.ones(scipy.shape(RA))
- return z
-
-def g_A1_RA(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st amplitude parameter
- and the Right Ascension.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*I_n1[psd_key]
- z += (A3*fp1*fp1 + A4*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z += (A1*fp1*dfp_dRA1 + A2*fp1*dfx_dRA1) * I_n1['-7']
- return z
-
-def g_A2_RA(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd amplitude parameter
- and the Right Ascension.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*I_n1[psd_key]
- z += (A3*fx1*fp1 + A4*fx1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z += (A1*fx1*dfp_dRA1 + A2*fx1*dfx_dRA1) * I_n1['-7']
- return z
-
-def g_A3_RA(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd amplitude parameter
- and the Right Ascension.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*I_n1[psd_key]
- z += (-A1*fp1*fp1 + -A2*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z += (A3*fp1*dfp_dRA1 + A4*fp1*dfx_dRA1) * I_n1['-7']
- return z
-
-def g_A4_RA(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 4th amplitude parameter
- and the Right Ascension.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*I_n1[psd_key]
- z += (-A1*fx1*fp1 - A2*fx1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z += (A3*fx1*dfp_dRA1 + A4*fx1*dfx_dRA1) * I_n1['-7']
- return z
-
-def g_A1_dec(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st amplitude parameter
- and the declination.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*I_n1[psd_key]
- z += (A3*fp1*fp1 + A4*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z += (A1*fp1*dfp_ddec1 + A2*fp1*dfx_ddec1) * I_n1['-7']
- return z
-
-def g_A2_dec(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd amplitude parameter
- and the declination.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*I_n1[psd_key]
- z += (A3*fx1*fp1 + A4*fx1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z += (A1*fx1*dfp_ddec1 + A2*fx1*dfx_ddec1) * I_n1['-7']
- return z
-
-def g_A3_dec(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd amplitude parameter
- and the declination.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*I_n1[psd_key]
- z += (-A1*fp1*fp1 - A2*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z += (A3*fp1*dfp_ddec1 + A4*fp1*dfx_ddec1) * I_n1['-7']
- return z
-
-def g_A4_dec(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 4th amplitude parameter
- and the declination.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*I_n1[psd_key]
- z += (-A1*fx1*fp1 - A2*fx1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z += (A3*fx1*dfp_ddec1 + A4*fx1*dfx_ddec1) * I_n1['-7']
- return z
-
-def g_A1_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st amplitude parameter
- and the end time.
- """
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*I_n1[psd_key]
- z += (A3*fp1*fp1 + A4*fp1*fx1) * z_deriv
- return z
-
-def g_A2_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd amplitude parameter
- and the end time.
- """
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*I_n1[psd_key]
- z += (A3*fx1*fp1 + A4*fx1*fx1) * z_deriv
- return z
-
-def g_A3_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd amplitude parameter
- and the end time.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*I_n1[psd_key]
- z += (-A1*fp1*fp1 - A2*fp1*fx1) * z_deriv
- return z
-
-def g_A4_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 4th amplitude parameter
- and the end time.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*I_n1[psd_key]
- z += (-A1*fx1*fp1 - A2*fx1*fx1) * z_deriv
- return z
-
-def g_A1_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st amplitude parameter
- and the chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*I_n1[psd_key]
- z += (A1*fp1*fp1 + A2*fp1*fx1) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*I_n1[psd_key]
- z += (A3*fp1*fp1 + A4*fp1*fx1) * z_deriv
- return z
-
-def g_A2_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd amplitude parameter
- and the chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*I_n1[psd_key]
- z += (A1*fx1*fp1 + A2*fx1*fx1) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*I_n1[psd_key]
- z += (A3*fx1*fp1 + A4*fx1*fx1) * z_deriv
- return z
-
-def g_A3_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd amplitude parameter
- and the chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*I_n1[psd_key]
- z += (A3*fp1*fp1 + A4*fp1*fx1) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*I_n1[psd_key]
- z += (-A1*fp1*fp1 - A2*fp1*fx1) * z_deriv
- return z
-
-def g_A4_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 4th amplitude parameter
- and the chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*I_n1[psd_key]
- z += (A3*fx1*fp1 + A4*fx1*fx1) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*I_n1[psd_key]
- z += (-A1*fx1*fp1 - A2*fx1*fx1) * z_deriv
- return z
-
-def g_A1_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 1st amplitude parameter
- and the symmetric mass ratio.
- """
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*I_n1[psd_key]
- z += (A3*fp1*fp1 + A4*fp1*fx1) * z_deriv
- return z
-
-def g_A2_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 2nd amplitude parameter
- and the symmetric mass ratio.
- """
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*I_n1[psd_key]
- z += (A3*fx1*fp1 + A4*fx1*fx1) * z_deriv
- return z
-
-def g_A3_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 3rd amplitude parameter
- and the symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*I_n1[psd_key]
- z += (-A1*fp1*fp1 - A2*fp1*fx1) * z_deriv
- return z
-
-def g_A4_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the 4th amplitude parameter
- and the symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*I_n1[psd_key]
- z += (-A1*fx1*fp1 - A2*fx1*fx1) * z_deriv
- return z
-
-def g_RA_RA(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the Right Ascension.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- for key2 in dPhase_dRA1.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*dPhase_dRA1[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*I_n1[psd_key]
- z += 2*(A1*A4 - A2*A3)*(fx1*dfp_dRA1 - fp1*dfx_dRA1) * z_deriv
- z += ((A1*A1 + A3*A3)*dfp_dRA1*dfp_dRA1 + (A2*A2 + A4*A4)*dfx_dRA1*dfx_dRA1 \
- + (A1*A2 + A3*A4)*(dfp_dRA1*dfx_dRA1 + dfx_dRA1*dfp_dRA1)) \
- *I_n1['-7']
- return z
-
-def m1_RA_RA(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the Right Ascension.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_dRA(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_dRA(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_RA_RA(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the Right Ascension.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_dRA(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_dRA(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_RA_RA(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the Right Ascension.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_dRA(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_dRA(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_RA_RA(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the Right Ascension.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_dRA(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_dRA(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_RA_RA(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the Right Ascension.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_RA(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_RA(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_RA(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_RA_RA(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the Right Ascension.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_RA(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_RA(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_RA_dec(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the Right Ascension and
- declination.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- for key2 in dPhase_ddec1.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*dPhase_ddec1[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_ddec1 - fp1*dfx_ddec1) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_dRA1 - fp1*dfx_dRA1) * z_deriv
- z += ((A1*A1 + A3*A3)*dfp_dRA1*dfp_ddec1 + (A2*A2 + A4*A4)*dfx_dRA1*dfx_ddec1 \
- + (A1*A2 + A3*A4)*(dfp_dRA1*dfx_ddec1 + dfx_dRA1*dfp_ddec1)) \
- *I_n1['-7']
- return z
-
-def m1_RA_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the Right Ascension and declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_RA_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the Right Ascension and declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_RA_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the Right Ascension and declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_RA_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the Right Ascension and declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_RA_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the Right Ascension and declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_RA_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the Right Ascension and declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_dec_dec(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the declination.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- for key2 in dPhase_ddec1.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*dPhase_ddec1[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*I_n1[psd_key]
- z += 2*(A1*A4 - A2*A3)*(fx1*dfp_ddec1 - fp1*dfx_ddec1) * z_deriv
- z += ((A1*A1 + A3*A3)*dfp_ddec1*dfp_ddec1 + (A2*A2 + A4*A4)*dfx_ddec1*dfx_ddec1 \
- + (A1*A2 + A3*A4)*(dfp_ddec1*dfx_ddec1 + dfx_ddec1*dfp_ddec1)) \
- *I_n1['-7']
- return z
-
-def m1_dec_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_dec_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_dec_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_dec_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = dFp_ddec(RA, dec, detector)
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = dFx_ddec(RA, dec, detector)
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = {}
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- drnj = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
- dPhasej[detector.name]['3'] = -2*pi*drnj
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_dec_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_dec_dec(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the declination.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_dec(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_RA_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the Right Ascension and the
- end time.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- for key2 in dPhase_dt.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*dPhase_dt[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_dRA1 - fp1*dfx_dRA1) * z_deriv
- return z
-
-def m1_RA_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the Right Ascension and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_RA_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the Right Ascension and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_RA_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the Right Ascension and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_RA_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the Right Ascension and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_RA_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the Right Ascension and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_RA_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the Right Ascension and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_dec_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the declination and the
- end time.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- for key2 in dPhase_dt.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*dPhase_dt[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_ddec1 - fp1*dfx_ddec1) * z_deriv
- return z
-
-def m1_dec_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the declination and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_dec_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the declination and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_dec_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the declination and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_dec_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the declination and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_dec_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the declination and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_dec_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the declination and the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_RA_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the Right Ascension and the
- chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- for key2 in dPhase_dmchirp.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*dPhase_dmchirp[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*dfp_dRA1 + (A2*A2 + A4*A4)*fx1*dfx_dRA1 \
- + (A1*A2 + A3*A4)*(fp1*dfx_dRA1 + fx1*dfp_dRA1)) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_dRA1 - fp1*dfx_dRA1) * z_deriv
- return z
-
-def m1_RA_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the Right Ascension and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_RA_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the Right Ascension and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_RA_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the Right Ascension and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_RA_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the Right Ascension and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_RA_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the Right Ascension and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_RA_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the Right Ascension and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_dec_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the declination and the
- chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- for key2 in dPhase_dmchirp.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*dPhase_dmchirp[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*dfp_ddec1 + (A2*A2 + A4*A4)*fx1*dfx_ddec1 \
- + (A1*A2 + A3*A4)*(fp1*dfx_ddec1 + fx1*dfp_ddec1)) * z_deriv
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_ddec1 - fp1*dfx_ddec1) * z_deriv
- return z
-
-def m1_dec_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the declination and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_dec_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the declination and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_dec_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the declination and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_dec_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the declination and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_dec_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the declination and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_dec_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the declination and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_RA_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the Right Ascension and the
- symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_dRA1 = drn_dRA(RA, dec, detector1)
- dPhase_dRA1 = {}
- dPhase_dRA1['3'] = -2*pi*drn_dRA1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dRA1.keys():
- for key2 in dPhase_deta.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dRA1[key1]*dPhase_deta[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_dRA1 = dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = dFx_dRA(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_dRA1 - fp1*dfx_dRA1) * z_deriv
- return z
-
-def m1_RA_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the Right Ascension and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_RA_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the Right Ascension and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_RA_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the Right Ascension and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_RA_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the Right Ascension and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_dRA(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_dRA(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_dRA(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_RA_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the Right Ascension and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_RA_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the Right Ascension and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_RA_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_dec_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the declination and the
- symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- drn_ddec1 = drn_ddec(RA, dec, detector1)
- dPhase_ddec1 = {}
- dPhase_ddec1['3'] = -2*pi*drn_ddec1
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_ddec1.keys():
- for key2 in dPhase_deta.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_ddec1[key1]*dPhase_deta[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- if Fderivs:
- dfp_ddec1 = dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = dFx_ddec(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- ls = key1.count('l')
- n = -7 + int(key1.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*I_n1[psd_key]
- z += (A1*A4 - A2*A3)*(fx1*dfp_ddec1 - fp1*dfx_ddec1) * z_deriv
- return z
-
-def m1_dec_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the declination and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_dec_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the declination and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_dec_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the declination and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_dec_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the declination and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = dFp_ddec(RA, dec, detector)
- dfpj[detector.name] = 0.
- dfxi[detector.name] = dFx_ddec(RA, dec, detector)
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = {}
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
- drni = drn_ddec(RA, dec, detector)
- dPhasei[detector.name]['3'] = -2*pi*drni
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_dec_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the declination and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_dec_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the declination and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_dec_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_t_t(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the end time.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- for key2 in dPhase_dt.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*dPhase_dt[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- return z
-
-def m1_t_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_t_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_t_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_t_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dt
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_t_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_t_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_t_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_t_t(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the end time.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_t_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_t(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_t_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the end time and the
- chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- for key2 in dPhase_dmchirp.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*dPhase_dmchirp[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- return z
-
-def m1_t_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the end time and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_t_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the end time and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_t_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the end time and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_t_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the end time and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_t_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the end time and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_t_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_t_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_t_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the end time and the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_t_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_t_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the end time and the
- symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_dt = dPhase_dt_dict()
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dt.keys():
- for key2 in dPhase_deta.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dt[key1]*dPhase_deta[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- return z
-
-def m1_t_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the end time and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_t_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the end time and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_t_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the end time and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_t_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the end time and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_dt = dPhase_dt_dict()
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dt
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_t_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the end time and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_t_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_t_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_t_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the end time and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_t_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_mchirp_mchirp(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the chirp mass.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dlnA_dmchirp.keys():
- for key2 in dlnA_dmchirp.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dlnA_dmchirp[key1]*dlnA_dmchirp[key2]*I_n1[psd_key]
- for key1 in dPhase_dmchirp.keys():
- for key2 in dPhase_dmchirp.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*dPhase_dmchirp[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- return z
-
-def m1_mchirp_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_mchirp_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_mchirp_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_mchirp_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_dmchirp
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = dlnA_dmchirp
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_mchirp_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_mchirp_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_mchirp_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_mchirp_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_mchirp_mchirp(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the chirp mass.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_mchirp_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_mchirp_mchirp(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_mchirp_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the chirp mass and the
- symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_dmchirp.keys():
- for key2 in dPhase_deta.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_dmchirp[key1]*dPhase_deta[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- return z
-
-def m1_mchirp_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the chirp mass and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = {}
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_mchirp_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the chirp mass and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = {}
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_mchirp_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the chirp mass and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = {}
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_mchirp_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the chirp mass and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dlnA_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_dmchirp
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = dlnA_dmchirp
- dLnAmpj[detector.name] = {}
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_mchirp_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the chirp mass and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_mchirp_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_mchirp_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_mchirp_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_mchirp_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the chirp mass and the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_mchirp_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_mchirp_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= A + B
-
- return gbar
-
-def g_eta_eta(cosi, distance, phi0, psi, RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full metric component associated with the symmetric mass ratio.
- """
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
-
- z = scipy.zeros(scipy.shape(RA))
- for detector1 in detector_list:
- I_n1 = detector1.I_n
- fp1 = Fp(RA, dec, detector1)
- fx1 = Fx(RA, dec, detector1)
- z_deriv = scipy.zeros(scipy.shape(RA))
- for key1 in dPhase_deta.keys():
- for key2 in dPhase_deta.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- z_deriv += dPhase_deta[key1]*dPhase_deta[key2]*I_n1[psd_key]
- z += ((A1*A1 + A3*A3)*fp1*fp1 + (A2*A2 + A4*A4)*fx1*fx1 \
- + 2*(A1*A2 + A3*A4)*fp1*fx1) * z_deriv
- return z
-
-def m1_eta_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 1st mismatch component associated
- with the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_deta
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch1(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m2_eta_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 2nd mismatch component associated
- with the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_deta
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch2(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m3_eta_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 3rd mismatch component associated
- with the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_deta
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch3(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def m4_eta_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized metric's 4th mismatch component associated
- with the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dPhasei = {}
- dPhasej = {}
- dLnAmpi = {}
- dLnAmpj = {}
- fp = {}
- fx = {}
- dfpi = {}
- dfpj = {}
- dfxi = {}
- dfxj = {}
- for detector in detector_list:
- fp[detector.name] = Fp(RA, dec, detector)
- fx[detector.name] = Fx(RA, dec, detector)
- dfpi[detector.name] = 0.
- dfpj[detector.name] = 0.
- dfxi[detector.name] = 0.
- dfxj[detector.name] = 0.
- dPhasei[detector.name] = dPhase_deta
- dPhasej[detector.name] = dPhase_deta
- dLnAmpi[detector.name] = {}
- dLnAmpj[detector.name] = {}
-
- return mismatch4(detector_list, A, B, C, D, fp, fx, dfpi, dfpj, dfxi, dfxj, dPhasei, dPhasej, dLnAmpi, dLnAmpj, Fderivs)
-
-def gbar_eta_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged metric component
- associated with the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_eta_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_eta_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m3 = m3_eta_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = B*m1 + A*m2 - 2.*C*m3
- gbar /= 2.*D
-
- return gbar
-
-def snr2_gbar_eta_eta(RA, dec, detector_list, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged metric component associated
- with the symmetric mass ratio.
- """
- A,B,C,D = maximum_likelihood_matrix(RA, dec, detector_list)
-
- m1 = m1_eta_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
- m2 = m2_eta_eta(RA, dec, detector_list, mchirp, eta, Fderivs, PNorder)
-
- gbar = m1 + m2
- gbar /= (A + B)
-
- return gbar
-
-def full_metric(cosi, distance, phi0, psi, RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The full amplitude-sky-mass-time metric is symmetric and is defined
- with the following signature:
- 0 1 2 3 4 5 6 7 8
- A1 A2 A3 A4 RA dec t mchirp eta
- 0 A1 / A J K L M N O P Q \
- 1 A2 | - B R S T U V W X |
- 2 A3 | - - C Y Z AA AB AC AD |
- 3 A4 | - - - D AE AF AG AH AI |
- g = 4 RA | - - - - E AJ AK AL AM |
- 5 dec | - - - - - F AN AO AP |
- 6 t | - - - - - - G AQ AR |
- 7 mchirp | - - - - - - - H AS |
- 8 eta \ - - - - - - - - I /
- """
- for detector in detectors:
- detector.update_I_n(mchirp, eta)
-
- g = scipy.zeros((9,9))
- # the amplitude-amplitude block
- g[0,0] = g_A1_A1(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,1] = g[1,0] = g_A1_A2(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,2] = g[2,0] = g_A1_A3(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,3] = g[3,0] = g_A1_A4(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,1] = g_A2_A2(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,2] = g[2,1] = g_A2_A3(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,3] = g[3,1] = g_A2_A4(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,2] = g_A3_A3(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,3] = g[3,2] = g_A3_A4(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,3] = g_A4_A4(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
-
- # the amplitude-phase block
- g[0,4] = g[4,0] = g_A1_RA (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,5] = g[5,0] = g_A1_dec (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,6] = g[6,0] = g_A1_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,7] = g[7,0] = g_A1_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,8] = g[8,0] = g_A1_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,4] = g[4,1] = g_A2_RA (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,5] = g[5,1] = g_A2_dec (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,6] = g[6,1] = g_A2_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,7] = g[7,1] = g_A2_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,8] = g[8,1] = g_A2_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,4] = g[4,2] = g_A3_RA (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,5] = g[5,2] = g_A3_dec (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,6] = g[6,2] = g_A3_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,7] = g[7,2] = g_A3_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,8] = g[8,2] = g_A3_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,4] = g[4,3] = g_A4_RA (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,5] = g[5,3] = g_A4_dec (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,6] = g[6,3] = g_A4_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,7] = g[7,3] = g_A4_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,8] = g[8,3] = g_A4_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
-
-
- # the phase-phase block
- g[4,4] = g_RA_RA (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,5] = g[5,4] = g_RA_dec (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,6] = g[6,4] = g_RA_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,7] = g[7,4] = g_RA_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,8] = g[8,4] = g_RA_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[5,5] = g_dec_dec (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[5,6] = g[6,5] = g_dec_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[5,7] = g[7,5] = g_dec_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[5,8] = g[8,5] = g_dec_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[6,6] = g_t_t (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[6,7] = g[7,6] = g_t_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[6,8] = g[8,6] = g_t_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[7,7] = g_mchirp_mchirp (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[7,8] = g[8,7] = g_mchirp_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[8,8] = g_eta_eta (cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
-
- rho2 = expected_coherent_snr(cosi,distance,phi0,psi,RA,dec,detectors)
-
- return g/rho2
-
-def amplitude_dependent_fstat_metric_check(cosi, distance, phi0, psi, RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude dependent sky-mass-time metric is symmetric and is defined
- with the following signature:
- 0 1 2 3 4
- RA dec t mchirp eta
- 0 RA / A F J M P \
- 1 dec | - B G K N |
- g = 2 t | - - C H L |
- 3 mchirp | - - - D I |
- 4 eta \ - - - - E /
-
- Explicit calculation to be compared with calculation based on mismatches in amplitude_dependent_fstat_metric().
- """
- for detector in detectors:
- detector.update_I_n(mchirp, eta)
-
- g = full_metric(cosi, distance, phi0, psi, RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g,rootdiag = extract_diagonal(g)
- g,rootdiag = project_out_dimension(g,rootdiag,3)
- g,rootdiag = project_out_dimension(g,rootdiag,2)
- g,rootdiag = project_out_dimension(g,rootdiag,1)
- g,rootdiag = project_out_dimension(g,rootdiag,0)
- g = restore_diagonal(g,rootdiag)
-
- return g
-
-def amplitude_dependent_fstat_metric(cosi, distance, phi0, psi, RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude dependent sky-mass-time metric is symmetric and is defined
- with the following signature:
- 0 1 2 3 4
- RA dec t mchirp eta
- 0 RA / A F J M P \
- 1 dec | - B G K N |
- g = 2 t | - - C H L |
- 3 mchirp | - - - D I |
- 4 eta \ - - - - E /
-
- Calculation based on mismatches to be compared with explicit calculation in amplitude_dependent_fstat_metric_check().
- """
- for detector in detectors:
- detector.update_I_n(mchirp, eta)
-
- A1 = A_1(cosi, distance, phi0, psi)
- A2 = A_2(cosi, distance, phi0, psi)
- A3 = A_3(cosi, distance, phi0, psi)
- A4 = A_4(cosi, distance, phi0, psi)
-
- g = scipy.zeros((5,5))
-
- m1 = m1_RA_RA(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_RA(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_RA(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_RA_RA(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,0] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_RA_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_RA_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,1] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_RA_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_RA_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,2] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_RA_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_RA_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,3] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_RA_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_RA_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_RA_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_RA_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,4] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_dec_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_dec_dec(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,1] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_dec_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_dec_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,2] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_dec_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_dec_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,3] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_dec_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_dec_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_dec_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_dec_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,4] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_t_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_t_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_t_t(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,2] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_t_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_t_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_t_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,3] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_t_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_t_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_t_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_t_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,4] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_mchirp_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_mchirp_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_mchirp_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_mchirp_mchirp(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,3] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_mchirp_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_mchirp_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_mchirp_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_mchirp_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,4] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- m1 = m1_eta_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m2 = m2_eta_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m3 = m3_eta_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- m4 = m4_eta_eta(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,4] = (A1*A1 + A3*A3)*m1 + (A2*A2 + A4*A4)*m2 + 2.*(A1*A2 + A3*A4)*m3 + 2.*(A1*A4 - A2*A3)*m4
-
- g[1,0] = g[0,1]
- g[2,0] = g[0,2]
- g[3,0] = g[0,3]
- g[4,0] = g[0,4]
- g[2,1] = g[1,2]
- g[3,1] = g[1,3]
- g[4,1] = g[1,4]
- g[3,2] = g[2,3]
- g[4,2] = g[2,4]
- g[4,3] = g[3,4]
-
- rho2 = expected_coherent_snr(cosi,distance,phi0,psi,RA,dec,detectors)
-
- return g/rho2
-
-def average_metric(RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized amplitude-parameter-averaged sky-mass-time
- metric is symmetric and is defined with the following signature:
- 0 1 2 3 4
- RA dec t mchirp eta
- 0 RA / A F J M P \
- 1 dec | - B G K N |
- g = 2 t | - - C H L |
- 3 mchirp | - - - D I |
- 4 eta \ - - - - E /
- """
- for detector in detectors:
- detector.update_I_n(mchirp, eta)
-
- g = scipy.zeros((5,5))
- g[0,0] = gbar_RA_RA (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,1] = gbar_RA_dec (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,2] = gbar_RA_t (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,3] = gbar_RA_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,4] = gbar_RA_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,1] = gbar_dec_dec (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,2] = gbar_dec_t (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,3] = gbar_dec_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,4] = gbar_dec_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,2] = gbar_t_t (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,3] = gbar_t_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,4] = gbar_t_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,3] = gbar_mchirp_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,4] = gbar_mchirp_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,4] = gbar_eta_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
-
- g[1,0] = g[0,1]
- g[2,0] = g[0,2]
- g[3,0] = g[0,3]
- g[4,0] = g[0,4]
- g[2,1] = g[1,2]
- g[3,1] = g[1,3]
- g[4,1] = g[1,4]
- g[3,2] = g[2,3]
- g[4,2] = g[2,4]
- g[4,3] = g[3,4]
-
- return g
-
-def average_sky_metric(RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- g = average_metric(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g,rootdiag = extract_diagonal(g)
- g,rootdiag = project_out_dimension(g,rootdiag,4)
- g,rootdiag = project_out_dimension(g,rootdiag,3)
- g,rootdiag = project_out_dimension(g,rootdiag,2)
- g = restore_diagonal(g,rootdiag)
-
- return g
-
-def average_mass_metric(RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- g = average_metric(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g,rootdiag = extract_diagonal(g)
- g,rootdiag = project_out_dimension(g,rootdiag,2)
- g,rootdiag = project_out_dimension(g,rootdiag,1)
- g,rootdiag = project_out_dimension(g,rootdiag,0)
- g = restore_diagonal(g,rootdiag)
-
- return g
-
-def snr2average_metric(RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- """
- The amplitude maximized SNR^2-averaged sky-mass-time metric is
- symmetric and is defined with the following signature:
- 0 1 2 3 4
- RA dec t mchirp eta
- 0 RA / A F J M P \
- 1 dec | - B G K N |
- g = 2 t | - - C H L |
- 3 mchirp | - - - D I |
- 4 eta \ - - - - E /
- """
- for detector in detectors:
- detector.update_I_n(mchirp, eta)
-
- g = scipy.zeros((5,5))
- g[0,0] = snr2_gbar_RA_RA (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,1] = snr2_gbar_RA_dec (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,2] = snr2_gbar_RA_t (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,3] = snr2_gbar_RA_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[0,4] = snr2_gbar_RA_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,1] = snr2_gbar_dec_dec (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,2] = snr2_gbar_dec_t (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,3] = snr2_gbar_dec_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[1,4] = snr2_gbar_dec_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,2] = snr2_gbar_t_t (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,3] = snr2_gbar_t_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[2,4] = snr2_gbar_t_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,3] = snr2_gbar_mchirp_mchirp (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[3,4] = snr2_gbar_mchirp_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g[4,4] = snr2_gbar_eta_eta (RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
-
- g[1,0] = g[0,1]
- g[2,0] = g[0,2]
- g[3,0] = g[0,3]
- g[4,0] = g[0,4]
- g[2,1] = g[1,2]
- g[3,1] = g[1,3]
- g[4,1] = g[1,4]
- g[3,2] = g[2,3]
- g[4,2] = g[2,4]
- g[4,3] = g[3,4]
-
- return g
-
-def snr2average_sky_metric(RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- g = snr2average_metric(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g,rootdiag = extract_diagonal(g)
- g,rootdiag = project_out_dimension(g,rootdiag,4)
- g,rootdiag = project_out_dimension(g,rootdiag,3)
- g,rootdiag = project_out_dimension(g,rootdiag,2)
- g = restore_diagonal(g,rootdiag)
-
- return g
-
-def snr2average_mass_metric(RA, dec, detectors, mchirp=2.*.25**.6*M_sun, eta=0.25, Fderivs=True, PNorder=7):
- g = snr2average_metric(RA, dec, detectors, mchirp, eta, Fderivs, PNorder)
- g,rootdiag = extract_diagonal(g)
- g,rootdiag = project_out_dimension(g,rootdiag,2)
- g,rootdiag = project_out_dimension(g,rootdiag,1)
- g,rootdiag = project_out_dimension(g,rootdiag,0)
- g = restore_diagonal(g,rootdiag)
-
- return g
-
-def single_g_ij(detector, dPhasei, dPhasej, dLnAmpi, dLnAmpj):
- I_n = detector.I_n
- I_dLnAmp_dLnAmp = 0.
- for key1 in dLnAmpi.keys():
- for key2 in dLnAmpj.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dLnAmp_dLnAmp += dLnAmpi[key1]*dLnAmpj[key2]*I_n[psd_key]
- I_dPhase_dPhase = 0.
- for key1 in dPhasei.keys():
- for key2 in dPhasej.keys():
- ls = key1.count('l') + key2.count('l')
- n = -7 + int(key1.strip('l')) + int(key2.strip('l'))
- psd_key = str(n) + 'l'*ls
- I_dPhase_dPhase += dPhasei[key1]*dPhasej[key2]*I_n[psd_key]
- return I_dLnAmp_dLnAmp + I_dPhase_dPhase
-
-def single_g_h0_h0(detector, mchirp, eta, PNorder=7):
- dPhase_dh0 = {}
- dLnAmp_dh0 = dlnA_dh0_dict()
-
- g = single_g_ij(detector, dPhase_dh0, dPhase_dh0, dLnAmp_dh0, dLnAmp_dh0)
- return g / detector.I_n['-7']
-
-def single_g_h0_phi(detector, mchirp, eta, PNorder=7):
- dPhase_dh0 = {}
- dLnAmp_dh0 = dlnA_dh0_dict()
- dPhase_dphi = dPhase_dphi_dict()
- dLnAmp_dphi = {}
-
- g = single_g_ij(detector, dPhase_dh0, dPhase_dphi, dLnAmp_dh0, dLnAmp_dphi)
- return g / detector.I_n['-7']
-
-def single_g_h0_t(detector, mchirp, eta, PNorder=7):
- dPhase_dh0 = {}
- dLnAmp_dh0 = dlnA_dh0_dict()
- dPhase_dt = dPhase_dt_dict()
- dLnAmp_dt = {}
-
- g = single_g_ij(detector, dPhase_dh0, dPhase_dt, dLnAmp_dh0, dLnAmp_dt)
- return g / detector.I_n['-7']
-
-def single_g_h0_mchirp(detector, mchirp, eta, PNorder=7):
- dPhase_dh0 = {}
- dLnAmp_dh0 = dlnA_dh0_dict()
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dLnAmp_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
-
- g = single_g_ij(detector, dPhase_dh0, dPhase_dmchirp, dLnAmp_dh0, dLnAmp_dmchirp)
- return g / detector.I_n['-7']
-
-def single_g_h0_eta(detector, mchirp, eta, PNorder=7):
- dPhase_dh0 = {}
- dLnAmp_dh0 = dlnA_dh0_dict()
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dLnAmp_deta = {}
-
- g = single_g_ij(detector, dPhase_dh0, dPhase_deta, dLnAmp_dh0, dLnAmp_deta)
- return g / detector.I_n['-7']
-
-def single_g_phi_phi(detector, mchirp, eta, PNorder=7):
- dPhase_dphi = dPhase_dphi_dict()
- dLnAmp_dphi = {}
-
- g = single_g_ij(detector, dPhase_dphi, dPhase_dphi, dLnAmp_dphi, dLnAmp_dphi)
- return g / detector.I_n['-7']
-
-def single_g_phi_t(detector, mchirp, eta, PNorder=7):
- dPhase_dphi = dPhase_dphi_dict()
- dLnAmp_dphi = {}
- dPhase_dt = dPhase_dt_dict()
- dLnAmp_dt = {}
-
- g = single_g_ij(detector, dPhase_dphi, dPhase_dt, dLnAmp_dphi, dLnAmp_dt)
- return g / detector.I_n['-7']
-
-def single_g_phi_mchirp(detector, mchirp, eta, PNorder=7):
- dPhase_dphi = dPhase_dphi_dict()
- dLnAmp_dphi = {}
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dLnAmp_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
-
- g = single_g_ij(detector, dPhase_dphi, dPhase_dmchirp, dLnAmp_dphi, dLnAmp_dmchirp)
- return g / detector.I_n['-7']
-
-def single_g_phi_eta(detector, mchirp, eta, PNorder=7):
- dPhase_dphi = dPhase_dphi_dict()
- dLnAmp_dphi = {}
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dLnAmp_deta = {}
-
- g = single_g_ij(detector, dPhase_dphi, dPhase_deta, dLnAmp_dphi, dLnAmp_deta)
- return g / detector.I_n['-7']
-
-def single_g_t_t(detector, mchirp, eta, PNorder=7):
- dPhase_dt = dPhase_dt_dict()
- dLnAmp_dt = {}
-
- g = single_g_ij(detector, dPhase_dt, dPhase_dt, dLnAmp_dt, dLnAmp_dt)
- return g / detector.I_n['-7']
-
-def single_g_t_mchirp(detector, mchirp, eta, PNorder=7):
- dPhase_dt = dPhase_dt_dict()
- dLnAmp_dt = {}
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dLnAmp_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
-
- g = single_g_ij(detector, dPhase_dt, dPhase_dmchirp, dLnAmp_dt, dLnAmp_dmchirp)
- return g / detector.I_n['-7']
-
-def single_g_t_eta(detector, mchirp, eta, PNorder=7):
- dPhase_dt = dPhase_dt_dict()
- dLnAmp_dt = {}
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dLnAmp_deta = {}
-
- g = single_g_ij(detector, dPhase_dt, dPhase_deta, dLnAmp_dt, dLnAmp_deta)
- return g / detector.I_n['-7']
-
-def single_g_mchirp_mchirp(detector, mchirp, eta, PNorder=7):
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dLnAmp_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
-
- g = single_g_ij(detector, dPhase_dmchirp, dPhase_dmchirp, dLnAmp_dmchirp, dLnAmp_dmchirp)
- return g / detector.I_n['-7']
-
-def single_g_mchirp_eta(detector, mchirp, eta, PNorder=7):
- dPhase_dmchirp = dPhase_dmchirp_dict(mchirp, eta, PNorder)
- dLnAmp_dmchirp = dlnA_dmchirp_dict(mchirp, eta)
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dLnAmp_deta = {}
-
- g = single_g_ij(detector, dPhase_dmchirp, dPhase_deta, dLnAmp_dmchirp, dLnAmp_deta)
- return g / detector.I_n['-7']
-
-def single_g_eta_eta(detector, mchirp, eta, PNorder=7):
- dPhase_deta = dPhase_deta_dict(mchirp, eta, PNorder)
- dLnAmp_deta = {}
-
- g = single_g_ij(detector, dPhase_deta, dPhase_deta, dLnAmp_deta, dLnAmp_deta)
- return g / detector.I_n['-7']
-
-def single_detector_metric(detector, mchirp=2.*.25**.6*M_sun, eta=0.25, PNorder=7):
- """
- The single detector metric is symmetric and is defined with the
- following signature:
- 0 1 2 3 4
- h0 phi t mchirp eta
- 0 h0 / A F J M O \
- 1 phi | - B G K N |
- g = 2 t | - - C H L |
- 3 mchirp | - - - D I |
- 4 eta \ - - - - E /
- """
- detector.update_I_n(mchirp, eta)
-
- g = scipy.zeros((5,5))
- g[0,0] = single_g_h0_h0 (detector, mchirp, eta, PNorder)
- g[1,0] = single_g_h0_phi (detector, mchirp, eta, PNorder)
- g[2,0] = single_g_h0_t (detector, mchirp, eta, PNorder)
- g[3,0] = single_g_h0_mchirp (detector, mchirp, eta, PNorder)
- g[4,0] = single_g_h0_eta (detector, mchirp, eta, PNorder)
- g[1,1] = single_g_phi_phi (detector, mchirp, eta, PNorder)
- g[2,1] = single_g_phi_t (detector, mchirp, eta, PNorder)
- g[3,1] = single_g_phi_mchirp (detector, mchirp, eta, PNorder)
- g[4,1] = single_g_phi_eta (detector, mchirp, eta, PNorder)
- g[2,2] = single_g_t_t (detector, mchirp, eta, PNorder)
- g[3,2] = single_g_t_mchirp (detector, mchirp, eta, PNorder)
- g[4,2] = single_g_t_eta (detector, mchirp, eta, PNorder)
- g[3,3] = single_g_mchirp_mchirp (detector, mchirp, eta, PNorder)
- g[4,3] = single_g_mchirp_eta (detector, mchirp, eta, PNorder)
- g[4,4] = single_g_eta_eta (detector, mchirp, eta, PNorder)
- g[0,1] = g[1,0]
- g[0,2] = g[2,0]
- g[0,3] = g[3,0]
- g[0,4] = g[4,0]
- g[1,2] = g[2,1]
- g[1,3] = g[3,1]
- g[1,4] = g[4,1]
- g[2,3] = g[3,2]
- g[2,4] = g[4,2]
- g[3,4] = g[4,3]
-
- return g
-
-def single_detector_mass_metric(detector, mchirp=2.*.25**.6*M_sun, eta=0.25, PNorder=7):
- g = single_detector_metric(detector, mchirp, eta, PNorder)
- g,rootdiag = extract_diagonal(g)
- g,rootdiag = project_out_dimension(g,rootdiag,2)
- g,rootdiag = project_out_dimension(g,rootdiag,1)
- g,rootdiag = project_out_dimension(g,rootdiag,0)
- g = restore_diagonal(g,rootdiag)
-
- return g
-
-def extract_diagonal(g):
- """
- This transforms the metric into the following form:
- 0 1 2 3 4
- RA dec t mchirp eta
- 0 RA / 1 f j m p \
- 1 dec | - 1 g k n |
- g = 2 t | - - 1 h l |
- 3 mchirp | - - - 1 i |
- 4 eta \ - - - - 1 /
-
- where g'_ij := g_ij / (g_ii * g_jj)**.5 and returns this along with
- the square root of the diagonal. This operation is applied in order to
- scale the matrix such that the matrix norm is more nearly equal to the
- eigenvalues.
- """
- rootdiag = []
- for idx in range(len(g)):
- rootdiag.append(g[idx,idx]**.5)
- scale = scipy.diag(1./scipy.array(rootdiag))
-
- g_scaled = scipy.dot(g, scale)
- g_scaled = scipy.dot(scale.T, g_scaled)
-
- return g_scaled,rootdiag
-
-def restore_diagonal(g, rootdiag):
- """
- Takes the modified metric and the square root of the diagonal and
- undoes the scaling operation of extract_diagonal(g).
- """
- scale = scipy.diag(rootdiag)
-
- g_scaled = scipy.dot(g, scale)
- g_scaled = scipy.dot(scale.T, g_scaled)
-
- return g_scaled
-
-def project_out_dimension(g, rootdiag, dim):
- """
- Projects out the dim'th dimension from g and rootdiag.
- """
- old_shape = scipy.shape(g)
- new_shape = []
- for d in old_shape:
- new_shape.append(d-1)
- g_projected = scipy.zeros(new_shape)
-
- for idx in range(len(g)):
- out_idx = idx
- if idx == dim:
- continue
- elif idx > dim:
- out_idx -= 1
- for jdx in range(len(g)):
- out_jdx = jdx
- if jdx == dim:
- continue
- elif jdx > dim:
- out_jdx -= 1
- g_projected[out_idx,out_jdx] = g[idx,jdx] - g[idx,dim]*g[dim,jdx]/g[dim,dim]
-
- rootdiag_projected = copy.deepcopy(rootdiag)
- rootdiag_projected.pop(dim)
-
- return g_projected,rootdiag_projected
-
-def metric_distance_on_sphere(test_point, point, metric_at_point):
- """
- Computes the metric distance between two points using the metric
- assuming the points can be wrapped as though on a sphere.
- """
- dRA = test_point[0] - point[0]
- ddec = test_point[1] - point[1]
- if dRA > pi:
- dRA = -2*pi + dRA
- if dRA < -pi:
- dRA = 2*pi + dRA
- dist = metric_at_point[0,0]*dRA**2 \
- + metric_at_point[1,1]*ddec**2 \
- + 2.*metric_at_point[0,1]*dRA*ddec
-
- return dist
-
-def metric_distance(test_point, point, metric_at_point):
- """
- Computes the metric distance between two points using the metric.
- """
- dx = test_point[0] - point[0]
- dy = test_point[1] - point[1]
- dist = metric_at_point[0,0]*dx**2 \
- + metric_at_point[1,1]*dy**2 \
- + 2.*metric_at_point[0,1]*dx*dy
-
- return dist
-
-def mchirpeta2m1m2(mchirp, eta):
- M = mchirp * eta**(-3./5.)
- q = (1. - 2.*eta + (1. - 4.*eta)**.5) / (2.*eta)
-
- m2 = M/(1.+q)
- m1 = M - m2
-
- return m1,m2
-
-def m1m22taus(m1, m2, f0=10.):
- """
- Solve for tau_0 and tau_3 from m1 and m2.
- """
- M = m1 + m2
- eta = m1 * m2 / M**2
- mchirp = M * eta**(3./5.)
- return mchirpeta2taus(mchirp, eta, f0)
-
-def mchirpeta2taus(mchirp, eta, f0=10.):
- """
- Solve for tau_0 and tau_3 from mchirp and eta.
- """
- tau0 = 5./256. * (pi*f0)**(-8./3.) * mchirp**(-5./3.)
- tau3 = pi/8. * (pi*f0)**(-5./3.) * eta**(-3./5.) * mchirp**(-2./3.)
- return tau0, tau3
-
-def taus2mchirpeta(tau0, tau3, f0=10.):
- """
- Solve for mchirp and eta from tau_0 and tau_3.
- """
- mchirp = (256./5.*(pi*f0)**(8./3.) * tau0)**(-3./5.)
- eta = (pi/8./(pi*f0)**(5./3.) / tau3 / mchirp**(2./3.))**(5./3.)
- return mchirp,eta
-
-def taus2m1m2(tau0, tau3, f0=10.):
- mchirp,eta = taus2mchirpeta(tau0, tau3, f0)
- return mchirpeta2m1m2(mchirp, eta)
-
-def dmchirp_dtau0(mchirp, eta, f0=10.):
- return -(768./25.) * (pi * f0 * mchirp)**(8./3.)
-
-def dmchirp_dtau3(mchirp, eta, f0=10.):
- return 0.
-
-def deta_dtau0(mchirp, eta, f0=10.):
- return (512./15.) * (pi * f0)**(8./3.) * eta * mchirp**(5./3.)
-
-def deta_dtau3(mchirp, eta, f0=10.):
- return -(40./(3.*pi)) * (pi * f0)**(5./3.) * eta**(8./5.) * mchirp**(2./3.)
-
-def massmetric2taumetric(g, mchirp, eta, f0=10.):
- dtau = scipy.eye(len(g))
- dtau[-2,-2] = dmchirp_dtau0(mchirp, eta, f0)
- dtau[-1,-2] = dmchirp_dtau3(mchirp, eta, f0)
- dtau[-2,-1] = deta_dtau0(mchirp, eta, f0)
- dtau[-1,-1] = deta_dtau3(mchirp, eta, f0)
-
- g_taus = scipy.dot(g, dtau.T)
- g_taus = scipy.dot(dtau, g_taus)
-
- return g_taus
diff --git a/gstlal-ugly/python/coherent_inspiral_metric_detector_details.py b/gstlal-ugly/python/coherent_inspiral_metric_detector_details.py
deleted file mode 100644
index 8780b42cf8..0000000000
--- a/gstlal-ugly/python/coherent_inspiral_metric_detector_details.py
+++ /dev/null
@@ -1,275 +0,0 @@
-# Copyright (C) 2012,2013 Drew Keppel
-#
-# This program is free software; you can redistribute it and/or modify it
-# under the terms of the GNU General Public License as published by the
-# Free Software Foundation; either version 2 of the License, or (at your
-# option) any later version.
-#
-# This program is distributed in the hope that it will be useful, but
-# WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
-# Public License for more details.
-#
-# You should have received a copy of the GNU General Public License along
-# with this program; if not, write to the Free Software Foundation, Inc.,
-# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
-
-
-#
-# ============================================================================
-#
-# Preamble
-#
-# ============================================================================
-#
-
-
-"""
-This module provides instances for some of the common cases for use with the
-coherent inspiral metric module.
-"""
-
-import pylab
-import scipy
-import numpy
-import lalsimulation
-from gstlal import coherent_inspiral_metric as metric
-from scipy import pi,sin,cos
-
-__author__ = "Drew Keppel <drew.keppel@ligo.org>"
-
-
-def f_for_fft(fLow, fNyq, deltaF):
- f = scipy.arange(2*(fNyq/deltaF))*deltaF
- f[fNyq/deltaF+1:] = -f[fNyq/deltaF-1:0:-1]
- return f
-
-def f_PSD_from_file(filename, fLow, fNyq, deltaF):
- """
- Read a detector ascii ASD file and return the PSD and frequency vector
- for use with ffts.
- """
- f_in,S_in = numpy.loadtxt(filename, unpack=True)
- f = numpy.linspace(fLow,fNyq,scipy.ceil((fNyq-fLow)/deltaF)+1)
- S = pylab.interp(f, f_in, S_in)
- # packing is of the form:
- # [0 deltaF 2*deltaF ... fNyquist-deltaF fNyquist -fNyquist+deltaF ... -2*deltaF -deltaF]
- PSD = scipy.zeros(2*(fNyq/deltaF), dtype='float')+scipy.inf
- PSD[round(fLow/deltaF):fNyq/deltaF+1] = S**2
- if -round(fLow/deltaF) == 0:
- PSD[fNyq/deltaF+1:] = S[-2:0:-1]**2
- else:
- PSD[fNyq/deltaF+1:-round(fLow/deltaF)] = S[-2:0:-1]**2
- f = f_for_fft(fLow, fNyq, deltaF)
- nNyq = round(fNyq/deltaF)
- nLow = round(fLow/deltaF)
- PSD = scipy.zeros(2*nNyq)+scipy.inf
- PSD[nLow:nNyq+1] = S**2
- if -nLow == 0:
- PSD[nNyq+1:] = S[-2:0:-1]**2
- else:
- PSD[nNyq+1:-nLow] = S[-2:0:-1]**2
- return f,PSD
-
-def f_PSD_from_func(psd_func, fLow, fNyq, deltaF):
- """
- Construct a (frequency, PSD) vector for use with FFTs from the specified
- lalsimulation PSD functions.
- """
- f = numpy.linspace(fLow,fNyq,scipy.ceil((fNyq-fLow)/deltaF)+1)
- S = numpy.array([psd_func(x) for x in f])
- # packing is of the form:
- # [0 deltaF 2*deltaF ... fNyquist-deltaF fNyquist -fNyquist+deltaF ... -2*deltaF -deltaF]
- f = f_for_fft(fLow, fNyq, deltaF)
- nNyq = round(fNyq/deltaF)
- nLow = round(fLow/deltaF)
- PSD = scipy.zeros(2*nNyq)+scipy.inf
- PSD[nLow:nNyq+1] = S
- if -nLow == 0:
- PSD[nNyq+1:] = S[-2:0:-1]
- else:
- PSD[nNyq+1:-nLow] = S[-2:0:-1]
- return f,PSD
-
-def DegMinSec2Rad(sign,deg,minutes,seconds):
- """
- A routine to convet from Degrees, Minutes, Seconds to radians.
- """
- return sign*(deg + minutes/60. + seconds/3600.)*(pi/180.)
-
-def lat_lon_2_vertex(lat,lon):
- """
- A routine to return the location of a detector's vertex in 3D
- Cartesean Coordinates given the latitude and longitude of the
- detector. This routine approximates teh Earth as a sphere.
- """
- return (metric.R_earth*cos(lon)*cos(lat), metric.R_earth*sin(lon)*cos(lat), metric.R_earth*sin(lat))
-
-def lat_lon_ori_2_xarm(lat, lon, ori):
- """
- A routine to return the x-arm vector of a detector in 3D
- Cartesean Coordinates given the latitude, longitude, and orientation
- of the detector. This routine approximates the Earth as a sphere.
- """
- ori += pi/4.
- dx0_dRA,dy0_dRA,dz0_dRA = -sin(lon)*cos(lat), cos(lon)*cos(lat), 0
- dx0_ddec,dy0_ddec,dz0_ddec = -cos(lon)*sin(lat), -sin(lon)*sin(lat), cos(lat)
- x = dx0_dRA*sin(ori) + dx0_ddec*cos(ori)
- y = dy0_dRA*sin(ori) + dy0_ddec*cos(ori)
- z = dz0_dRA*sin(ori) + dz0_ddec*cos(ori)
- return (x,y,z)
-
-def lat_lon_ori_2_yarm(lat, lon, ori):
- """
- A routine to return the y-arm vector of a detector in 3D
- Cartesean Coordinates given the latitude, longitude, and orientation
- of the detector. This routine approximates the Earth as a sphere.
- """
- ori -= pi/4.
- dx0_dRA,dy0_dRA,dz0_dRA = -sin(lon)*cos(lat), cos(lon)*cos(lat), 0
- dx0_ddec,dy0_ddec,dz0_ddec = -cos(lon)*sin(lat), -sin(lon)*sin(lat), cos(lat)
- x = dx0_dRA*sin(ori) + dx0_ddec*cos(ori)
- y = dy0_dRA*sin(ori) + dy0_ddec*cos(ori)
- z = dz0_dRA*sin(ori) + dz0_ddec*cos(ori)
- return (x,y,z)
-
-
-# PSDs obtainable from:
-# Adv. LIGO:
-# https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=2974
-
-# Adv. Virgo:
-# https://wwwcascina.virgo.infn.it/advirgo/
-# https://wwwcascina.virgo.infn.it/advirgo/docs/AdV_refsens_100512.txt
-
-# LCGT (detuned):
-# http://gwcenter.icrr.u-tokyo.ac.jp/en/researcher/parameter
-# https://granite.phys.s.u-tokyo.ac.jp/trac/LCGT/browser/trunk/sensitivity/spectrum/BW2009_VRSED.dat
-
-# LCGT (broadband):
-# https://granite.phys.s.u-tokyo.ac.jp/trac/LCGT/browser/trunk/sensitivity/spectrum/BW2009_VRSEB.dat
-
-# detector geometries from LALDetectors.h
-def make_LHO(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDaLIGOZeroDetHighPower, fLow, fNyq, deltaF)
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'H',
- (-0.22389266154,0.79983062746,0.55690487831),
- (-0.91397818574,0.02609403989,-0.40492342125),
- (-2.16141492636e+06,-3.83469517889e+06,4.60035022664e+06),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
-def make_LLO(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDaLIGOZeroDetHighPower, fLow, fNyq, deltaF)
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'L',
- (-0.95457412153,-0.14158077340,-0.26218911324),
- (0.29774156894,-0.48791033647,-0.82054461286),
- (-7.42760447238e+04,-5.49628371971e+06,3.22425701744e+06),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
-def make_Virgo(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDAdvVirgo, fLow, fNyq, deltaF)
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'V',
- (-0.70045821479,0.20848948619,0.68256166277),
- (-0.05379255368,-0.96908180549,0.24080451708),
- (4.54637409900e+06,8.42989697626e+05,4.37857696241e+06),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
-def make_GEO(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- # Adv. LIGO but 10x less sensitive
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDaLIGOZeroDetHighPower, fLow, fNyq, deltaF)
- psd *= 100
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'G',
- (-0.44530676905, 0.86651354130, 0.22551311312),
- (-0.62605756776, -0.55218609524, 0.55058372486),
- (3.85630994926e+06, 6.66598956317e+05, 5.01964141725e+06),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
-# detector geometry from http://gwcenter.icrr.u-tokyo.ac.jp/en/
-def make_KAGRA(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDKAGRA, fLow, fNyq, deltaF)
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'K',
- (-0.3758971922940067, -0.83615832915098853, 0.3994252738835008),
- (0.71644138561445658, 0.011148317434329416, 0.6975582097554448),
- (-3.777336055e+06, 3.484898386e+06, 3.765313690e+06),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
-# detector geometries from arxiv:1102.5421v2
-def make_LCGT(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDKAGRA, fLow, fNyq, deltaF)
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'C',
- lat_lon_ori_2_xarm(DegMinSec2Rad(1,36.,15.,0.),DegMinSec2Rad(1,137.,10.,48.),DegMinSec2Rad(1,20.,0.,0.)),
- lat_lon_ori_2_yarm(DegMinSec2Rad(1,36.,15.,0.),DegMinSec2Rad(1,137.,10.,48.),DegMinSec2Rad(1,20.,0.,0.)),
- lat_lon_2_vertex(DegMinSec2Rad(1,36.,15.,0.),DegMinSec2Rad(1,137.,10.,48.)),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
-def make_IndIGO(fLow=10., fNyq=2048., deltaF=0.1, psd_filename=None):
- if psd_filename is None:
- f, psd = f_PSD_from_func(
- lalsimulation.SimNoisePSDaLIGOZeroDetHighPower, fLow, fNyq, deltaF)
- else:
- f, psd = f_PSD_from_file(psd_filename,fLow,fNyq,deltaF)
- detector = metric.Detector(
- 'I',
- lat_lon_ori_2_xarm(DegMinSec2Rad(1,19.,5.,47.),DegMinSec2Rad(1,74.,2.,51.),DegMinSec2Rad(1,270.,0.,0.)),
- lat_lon_ori_2_yarm(DegMinSec2Rad(1,19.,5.,47.),DegMinSec2Rad(1,74.,2.,51.),DegMinSec2Rad(1,270.,0.,0.)),
- lat_lon_2_vertex(DegMinSec2Rad(1,19.,5.,47.),DegMinSec2Rad(1,74.,2.,51.)),
- f=f,
- psd=psd
- )
- detector.set_required_moments()
- return detector
-
diff --git a/gstlal-ugly/python/coherent_inspiral_metric_plots.py b/gstlal-ugly/python/coherent_inspiral_metric_plots.py
deleted file mode 100644
index d8d1a9ad30..0000000000
--- a/gstlal-ugly/python/coherent_inspiral_metric_plots.py
+++ /dev/null
@@ -1,1045 +0,0 @@
-# Copyright (C) 2012 Drew Keppel
-#
-# This program is free software; you can redistribute it and/or modify it
-# under the terms of the GNU General Public License as published by the
-# Free Software Foundation; either version 2 of the License, or (at your
-# option) any later version.
-#
-# This program is distributed in the hope that it will be useful, but
-# WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
-# Public License for more details.
-#
-# You should have received a copy of the GNU General Public License along
-# with this program; if not, write to the Free Software Foundation, Inc.,
-# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
-
-
-#
-# ============================================================================
-#
-# Preamble
-#
-# ============================================================================
-#
-
-
-"""
-This module provides tools for plotting different results associated with the
-coheerent inspiral metric module.
-"""
-
-import matplotlib
-from gstlal import coherent_inspiral_metric as metric
-import numpy
-import scipy
-from scipy import pi,log,exp,sin,cos,log10
-import pylab
-import math
-import sys
-from mpl_toolkits.basemap import Basemap
-pylab.rc('text', usetex=True)
-
-__author__ = "Drew Keppel <drew.keppel@ligo.org>"
-
-def plotErrorEllipse(xy,g,d,ax,edge='b',face='none', style='solid', **kwargs):
- """
- Computes error ellipses for points in a two dimensional space given a
- position and the 2D metric.
- """
- a,b,b,c = g.flatten()
- semimajor = (2./((a+c)-((a-c)**2+4*b**2)**.5))**.5
- semiminor = (2./((a+c)+((a-c)**2+4*b**2)**.5))**.5
-
- U, s, Vh = scipy.linalg.svd(g)
- orient = math.atan2(U[0,0],U[1,0])*180/pi
- ellipsePlot = matplotlib.patches.Ellipse(xy=xy, width=2*d**.5*semimajor,
- height=2*d**.5*semiminor, angle=-orient, facecolor=face, edgecolor=edge, linestyle=style, **kwargs)
- ax.add_patch(ellipsePlot)
-
-def plot_skymetric_from_file(filename,maxmismatch=0.1):
- """
- Plot the position, error ellipses, and square root of the determinant
- of the metric for the template locations on the sky. Takes in the name
- of the ascii file containing the sky locations and metric as well as
- the size of the error ellipses (maxmismatch).
- """
- RAs,decs,gRRs,gRds,gdds = numpy.loadtxt(filename, unpack=True, usecols=(0,1,2,3,4))
- gs = []
- rootdetgs = []
- for gRR,gRd,gdd in zip(gRRs,gRds,gdds):
- g = numpy.array([[gRR,gRd],[gRd,gdd]])
- rootdetgs.append((scipy.linalg.det(g))**.5)
- gs.append(g)
-
- fig = pylab.figure()
- ax = fig.add_axes((.1,.1,.8,.8))
-
- dRA = 2*pi/200
- ddec = pi/200
- RA,dec = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
- z = pylab.griddata(RAs,decs,rootdetgs,RA,dec)
- levels = scipy.linspace(-1.,2.,101)
- CF = ax.contourf(RA, dec, log10(z), levels=levels)
- matplotlib.pyplot.colorbar(CF)
-
- for RA,dec,g in zip(RAs,decs,gs):
- plotErrorEllipse((RA,dec),g,maxmismatch,ax,edge='k')
-
- ax.set_yticks([-pi/2,-pi/4,0,pi/4,pi/2])
- ax.set_yticklabels(['$-\pi/2$','$-\pi/4$','$0$','$\pi/4$','$\pi/2$'])
- ax.set_xticks([-pi,-pi/2,0,pi/2,pi])
- ax.set_xticklabels(['$-\pi$','$-\pi/2$','$0$','$\pi/2$','$\pi$'])
- ax.set_xlim(-pi,pi)
- ax.set_ylim(-pi/2,pi/2)
- ax.set_xlabel(r'$\alpha$')
- ax.set_ylabel(r'$\delta$')
- ax.invert_xaxis()
- ax.set_title('Sky Metric')
-
-def plot_skymetric_averagesnr_from_file(filename, maxmismatch=0.1, detectors=None):
- """
- Plot the position, error ellipses, and average SNR^2 for the template
- locations on the sky. Takes in the name of the ascii file containing
- the sky locations and metric as well as the size of the error ellipses
- (maxmismatch).
- """
- RAs,decs,gRRs,gRds,gdds = numpy.loadtxt(filename, unpack=True, usecols=(0,1,2,3,4))
-
- avesnr = metric.average_snr(RAs, decs, detectors)
-
- gs = []
- for gRR,gRd,gdd in zip(gRRs,gRds,gdds):
- g = numpy.array([[gRR,gRd],[gRd,gdd]])
- gs.append(g)
-
- fig = pylab.figure()
- ax = fig.add_axes((.1,.1,.8,.8))
-
- dRA = 2*pi/200
- ddec = pi/200
- RA,dec = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
- z = pylab.griddata(RAs,decs,avesnr,RA,dec)
- CF = ax.contourf(RA, dec, log(z)/log(10.), 100)
- matplotlib.pyplot.colorbar(CF)
-
- for RA,dec,g in zip(RAs,decs,gs):
- plotErrorEllipse((RA,dec),g,maxmismatch,ax,edge='k')
-
- ax.set_yticks([-pi/2,-pi/4,0,pi/4,pi/2])
- ax.set_yticklabels(['$-\pi/2$','$-\pi/4$','$0$','$\pi/4$','$\pi/2$'])
- ax.set_xticks([-pi,-pi/2,0,pi/2,pi])
- ax.set_xticklabels(['$-\pi$','$-\pi/2$','$0$','$\pi/2$','$\pi$'])
- ax.set_xlim(-pi,pi)
- ax.set_ylim(-pi/2,pi/2)
- ax.set_xlabel(r'$\alpha$')
- ax.set_ylabel(r'$\delta$')
- ax.invert_xaxis()
- ax.set_title('Sky Metric and Average SNR')
-
-def plot_massmetric_on_sky_from_file(filename):
- """
- Plot the position, and square root of the determinant of the mass
- metric for the template locations on the sky. Takes in the name of the
- ascii file containing the locations and metric as well as the size of
- the error ellipses (maxmismatch).
- """
- RAs,decs,gmms,gmes,gees = numpy.loadtxt(filename, unpack=True, usecols=(0,1,5,6,7))
- gs = []
- rootdetgs = []
- for gmm,gme,gee in zip(gmms,gmes,gees):
- g = numpy.array([[gmm,gme],[gme,gee]])
- rootdetgs.append((scipy.linalg.det(g))**.5)
- gs.append(g)
-
- fig = pylab.figure()
- ax = fig.add_axes((.1,.1,.8,.8))
-
- dRA = 2*pi/200
- ddec = pi/200
- RA,dec = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
- z = pylab.griddata(RAs,decs,rootdetgs,RA,dec)
- CF = ax.contourf(RA, dec, log(z), 100)
- ax.plot(RAs, decs, 'kx')
- matplotlib.pyplot.colorbar(CF)
-
- ax.set_yticks([-pi/2,-pi/4,0,pi/4,pi/2])
- ax.set_yticklabels(['$-\pi/2$','$-\pi/4$','$0$','$\pi/4$','$\pi/2$'])
- ax.set_xticks([-pi,-pi/2,0,pi/2,pi])
- ax.set_xticklabels(['$-\pi$','$-\pi/2$','$0$','$\pi/2$','$\pi$'])
- ax.set_xlim(-pi,pi)
- ax.set_ylim(-pi/2,pi/2)
- ax.set_xlabel(r'$\alpha$')
- ax.set_ylabel(r'$\delta$')
- ax.invert_xaxis()
- ax.set_title('Mass Metric')
-
-def plot_massmetric_variations_from_file(filename, maxmismatch=0.1):
- """
- Plot the variations of the mass metric as a function of sky position
- for a single point in the mass space. Read mass metric from ascii
- file and the size of the error ellipses are determined by the
- parameter maxmismatch.
- """
- gmms,gmes,gees = numpy.loadtxt(filename, unpack=True, usecols=(5,6,7))
- gs = []
- rootdetgs = []
- for gmm,gme,gee in zip(gmms,gmes,gees):
- g = numpy.array([[gmm,gme],[gme,gee]])
- rootdetgs.append((scipy.linalg.det(g))**.5)
- gs.append(g)
-
- fig = pylab.figure()
- ax = fig.add_axes((.1,.1,.8,.8))
-
- eta = 0.25
- mchirp = 2. * metric.M_sun * eta**(3./5.)
-
- for g in gs:
- plotErrorEllipse((mchirp,eta),g,maxmismatch,ax,edge='r')
-
- g = numpy.array([[scipy.mean(gmms),scipy.mean(gmes)],[scipy.mean(gmes),scipy.mean(gees)]])
- plotErrorEllipse((mchirp,eta),g,maxmismatch,ax,edge='k')
-
- g = scipy.array([[4.22613677e+18, -2.17901658e+11],
- [ -2.17901658e+11,1.47648365e+04]])
- plotErrorEllipse((mchirp,eta),g,maxmismatch,ax,edge='b')
-
- ax.set_xlim(mchirp/1.0005,mchirp*1.0005)
- ax.set_ylim(0.24,0.26)
-
- ax.set_xlabel(r'$M_c$')
- ax.set_ylabel(r'$\eta$')
- ax.set_title('Mass Metric')
-
-def plot_massmetric_from_file(filename,maxmismatch=0.06):
- """
- Plot the position, error ellipses, and average SNR^2 for the template
- locations in the mass space. Takes in the name of the ascii file
- containing the locations and metric as well as the size of the error
- ellipses (maxmismatch).
- """
- mchirps,etas,gmms,gmes,gees = numpy.loadtxt(filename, unpack=True, usecols=(0,1,2,3,4))
- gs = []
- rootdetgs = []
- for gmm,gme,gee in zip(gmms,gmes,gees):
- g = numpy.array([[gmm,gme],[gme,gee]])
- rootdetgs.append((scipy.linalg.det(g))**.5)
- gs.append(g)
-
- fig = pylab.figure()
- ax = fig.add_axes((.1,.1,.8,.8))
-
- for mchirp,eta,g in zip(mchirps,etas,gs):
- plotErrorEllipse((mchirp,eta),g,maxmismatch,ax,edge='r')
-
- ax.plot(mchirps,etas,'kx')
-
- mmin = 1.0
- mmax = 3.0
-
- m1s = scipy.linspace(mmin,mmax,20)*metric.M_sun
- m2s = scipy.linspace(mmin,mmin,20)*metric.M_sun
- Ms = m1s + m2s
- etas = m1s * m2s / Ms**2
- mchirps = Ms * etas**.6
- ax.plot(mchirps, etas, 'b')
-
- m1s = scipy.linspace(mmax,mmax,20)*metric.M_sun
- m2s = scipy.linspace(mmin,mmax,20)*metric.M_sun
- Ms = m1s + m2s
- etas = m1s * m2s / Ms**2
- mchirps = Ms * etas**.6
- ax.plot(mchirps, etas, 'b')
-
- m1s = scipy.linspace(mmin,mmax,20)*metric.M_sun
- m2s = scipy.linspace(mmin,mmax,20)*metric.M_sun
- Ms = m1s + m2s
- etas = m1s * m2s / Ms**2
- mchirps = Ms * etas**.6
- ax.plot(mchirps, etas, 'b')
-
- ax.set_xlabel(r'$M_c$')
- ax.set_ylabel(r'$\eta$')
- ax.set_title('Mass Metric')
-
-def mollwiede_map(ax):
- """
- Create a mollwiede projection map of the earth for plotting ontop of.
- """
- m = Basemap(projection='moll',lon_0=0,resolution='c', ax=ax)
-
- # draw coastlines, country boundaries, fill continents.
- m.drawcoastlines()
- m.fillcontinents(color='none', lake_color='none')
- m.drawcountries()
- m.drawmapboundary(fill_color='w')
- # draw the edge of the map projection region (the projection limb)
- m.drawmapboundary()
- # draw lat/lon grid lines every 30 degrees.
- m.drawmeridians(scipy.arange(-180, 180, 30))
- m.drawparallels(scipy.arange(-90, 90, 30))
-
- return m
-
-def plot_arms(m, detectors):
- """
- Plot the arm directions of an interferometric GW detector
- at the correct location and with the correct orientation.
- """
- for detector in detectors:
- vertex = scipy.array(detector.vertex)
- vertex /= sum(vertex**2)**.5
-
- for arm in [detector.xarm, detector.yarm]:
- n_arm = scipy.array(arm)
- arm = []
- xs = scipy.linspace(0,.05,10)
- for x in xs:
- point = x*n_arm + vertex
- point /= sum(point**2)**.5
- dec = pi/2 - scipy.arccos(point[2])
- RA = scipy.arctan2(point[1],point[0])
-
- arm.append([RA,dec])
- arm = scipy.array(arm)
-
- x, y = m(arm[:,0]*180./pi, arm[:,1]*180./pi)
- m.plot(x, y, 'k', linewidth=3)
-
-def boundingbox(nrows, ncols, rownum, colnum):
- """
- Create a bounding box for use in plots with many panels.
- Generalized past single digits from matplotlib's subplot
- routine.
- """
- vtextspace = .05
- xspace = (1. - (ncols+1)*vtextspace)/ncols
-
- htextspace = .05
- yspace = (1. - (nrows+1)*htextspace)/nrows
-
- rownum = nrows + 1 - rownum
-
- return (vtextspace*(colnum) + xspace*(colnum-1), htextspace*rownum + yspace*(rownum-1), xspace, yspace)
-
-def plot_detector(detector):
- """
- Plot different detector antenna responses in a new figure.
- """
- fig = pylab.figure()
-
- ax = fig.add_axes(boundingbox(3,1,1,1))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.Fp(RAs, decs, detector)**2
- z += metric.Fx(RAs, decs, detector)**2
- z = z**.5
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(detector.name)
-
- ax = fig.add_axes(boundingbox(3,3,2,1))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.Fp(RAs, decs, detector)
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(r'$F_+$')
-
- ax = fig.add_axes(boundingbox(3,3,2,2))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.dFp_dRA(RAs, decs, detector)
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(r'$\partial_\alpha F_+$')
-
- ax = fig.add_axes(boundingbox(3,3,2,3))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.dFp_ddec(RAs, decs, detector)
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(r'$\partial_\delta F_+$')
-
- ax = fig.add_axes(boundingbox(3,3,3,1))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.Fx(RAs, decs, detector)
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(r'$F_\times$')
-
- ax = fig.add_axes(boundingbox(3,3,3,2))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.dFx_dRA(RAs, decs, detector)
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(r'$\partial_\alpha F_\times$')
-
- ax = fig.add_axes(boundingbox(3,3,3,3))
- m = mollwiede_map(ax)
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- z = metric.dFx_ddec(RAs, decs, detector)
- levels = scipy.linspace(min(0,min(z.flatten())),max(z.flatten()),20)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m,[detector])
- ax.set_title(r'$\partial_\delta F_\times$')
-
-def check_RA_derivatives(detector):
- """
- Create a plot to check the RA directional derivatives.
- """
- pylab.figure()
- dRA = 2*pi/100
- ddec = pi/100
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
- dec0 = pi/3
-
- ax = pylab.subplot(231)
- z = metric.Fp(RAs, decs, detector)
- levels = 100
- CF = ax.contourf(RAs, decs, z, levels)
- CS = ax.contour(RAs, decs, z, levels)
- RAs = scipy.linspace(-pi,pi,100)
- decs = dec0*scipy.ones(len(RAs))
- CF = ax.plot(RAs,decs,'k')
- ax.set_title(r'$F_+$')
-
- ax = pylab.subplot(232)
- z = metric.Fp(RAs, decs, detector)
- CF = ax.plot(RAs, z)
- ax.set_title(r'$F_+$')
-
- ax = pylab.subplot(233)
- z = metric.dx_n2(z,RAs[1]-RAs[0])
- CF = ax.plot(RAs, z, 'r')
- z = metric.dFp_dRA(RAs, decs, detector)
- CF = ax.plot(RAs, z, 'b')
- ax.set_title(r'$\partial_\alpha F_+$')
-
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
-
- ax = pylab.subplot(234)
- z = metric.Fx(RAs, decs, detector)
- levels = 100
- CF = ax.contourf(RAs, decs, z, levels)
- CS = ax.contour(RAs, decs, z, levels)
- RAs = scipy.linspace(-pi,pi,100)
- decs = dec0*scipy.ones(len(RAs))
- CF = ax.plot(RAs,decs,'k')
- ax.set_title(r'$F_\times$')
-
- ax = pylab.subplot(235)
- z = metric.Fx(RAs, decs, detector)
- CF = ax.plot(RAs, z)
- ax.set_title(r'$F_\times$')
-
- ax = pylab.subplot(236)
- z = metric.dx_n2(z,RAs[1]-RAs[0])
- CF = ax.plot(RAs, z, 'r')
- z = metric.dFx_dRA(RAs, decs, detector)
- CF = ax.plot(RAs, z, 'b')
- ax.set_title(r'$\partial_\alpha F_\times$')
-
-def check_dec_derivatives(detector):
- """
- Create a plot to check the dec directional derivatives.
- """
- pylab.figure()
- dRA = 2*pi/100
- ddec = pi/100
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
- RA0 = pi/3
-
- ax = pylab.subplot(231)
- z = metric.Fp(RAs, decs, detector)
- levels = 100
- CF = ax.contourf(RAs, decs, z, levels)
- CS = ax.contour(RAs, decs, z, levels)
- decs = scipy.linspace(-pi/2,pi/2,100)
- RAs = RA0*scipy.ones(len(decs))
- CF = ax.plot(RAs,decs,'k')
- ax.set_title(r'$F_+$')
-
- ax = pylab.subplot(232)
- z = metric.Fp(RAs, decs, detector)
- CF = ax.plot(decs, z)
- ax.set_title(r'$F_+$')
-
- ax = pylab.subplot(233)
- z = metric.dx_n2(z,decs[1]-decs[0])
- CF = ax.plot(decs, z, 'r')
- z = metric.dFp_ddec(RAs, decs, detector)
- CF = ax.plot(decs, z, 'b')
- ax.set_title(r'$\partial_\delta F_+$')
-
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2+ddec:pi/2:ddec]
-
- ax = pylab.subplot(234)
- z = metric.Fx(RAs, decs, detector)
- levels = 100
- CF = ax.contourf(RAs, decs, z, levels)
- CS = ax.contour(RAs, decs, z, levels)
- decs = scipy.linspace(-pi/2,pi/2,100)
- RAs = RA0*scipy.ones(len(decs))
- CF = ax.plot(RAs,decs,'k')
- ax.set_title(r'$F_\times$')
-
- ax = pylab.subplot(235)
- z = metric.Fx(RAs, decs, detector)
- CF = ax.plot(decs, z)
- ax.set_title(r'$F_\times$')
-
- ax = pylab.subplot(236)
- z = metric.dx_n2(z,decs[1]-decs[0])
- CF = ax.plot(decs, z, 'r')
- z = metric.dFx_ddec(RAs, decs, detector)
- CF = ax.plot(decs, z, 'b')
- ax.set_title(r'$\partial_\delta F_\times$')
-
-def plot_metric(detectors, Fderivs):
- """
- Plot the different components of the full metric as a function of sky
- location in different panels of the same figure.
- """
- fig = pylab.figure(figsize=(16,9))
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- levels = 20
-
- ax = fig.add_axes(boundingbox(5,5,1,1))
- m = mollwiede_map(ax)
- z = metric.g_RA_RA(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\alpha \alpha}$')
-
- ax = fig.add_axes(boundingbox(5,5,1,2))
- m = mollwiede_map(ax)
- z = metric.g_RA_dec(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\alpha \delta}$')
-
- ax = fig.add_axes(boundingbox(5,5,2,1))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\delta \alpha}$')
-
- ax = fig.add_axes(boundingbox(5,5,1,3))
- m = mollwiede_map(ax)
- z = metric.g_RA_t(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\alpha t}$')
-
- ax = fig.add_axes(boundingbox(5,5,3,1))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{t \alpha}$')
-
- ax = fig.add_axes(boundingbox(5,5,1,4))
- m = mollwiede_map(ax)
- z = metric.g_RA_mchirp(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\alpha M_c}$')
-
- ax = fig.add_axes(boundingbox(5,5,4,1))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{M_c \alpha}$')
-
- ax = fig.add_axes(boundingbox(5,5,1,5))
- m = mollwiede_map(ax)
- z = metric.g_RA_eta(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\alpha \eta}$')
-
- ax = fig.add_axes(boundingbox(5,5,5,1))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\eta \alpha}$')
-
- ax = fig.add_axes(boundingbox(5,5,2,2))
- m = mollwiede_map(ax)
- z = metric.g_dec_dec(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\delta \delta}$')
-
- ax = fig.add_axes(boundingbox(5,5,2,3))
- m = mollwiede_map(ax)
- z = metric.g_dec_t(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\delta t}$')
-
- ax = fig.add_axes(boundingbox(5,5,3,2))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{t \delta}$')
-
- ax = fig.add_axes(boundingbox(5,5,2,4))
- m = mollwiede_map(ax)
- z = metric.g_dec_mchirp(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\delta M_c}$')
-
- ax = fig.add_axes(boundingbox(5,5,4,2))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{M_c \delta}$')
-
- ax = fig.add_axes(boundingbox(5,5,2,5))
- m = mollwiede_map(ax)
- z = metric.g_dec_eta(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\delta \eta}$')
-
- ax = fig.add_axes(boundingbox(5,5,5,2))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\eta \delta}$')
-
- ax = fig.add_axes(boundingbox(5,5,3,3))
- m = mollwiede_map(ax)
- z = metric.g_t_t(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{t t}$')
-
- ax = fig.add_axes(boundingbox(5,5,3,4))
- m = mollwiede_map(ax)
- z = metric.g_t_mchirp(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{t M_c}$')
-
- ax = fig.add_axes(boundingbox(5,5,4,3))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{M_c t}$')
-
- ax = fig.add_axes(boundingbox(5,5,3,5))
- m = mollwiede_map(ax)
- z = metric.g_t_eta(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{t \eta}$')
-
- ax = fig.add_axes(boundingbox(5,5,5,3))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\eta t}$')
-
- ax = fig.add_axes(boundingbox(5,5,4,4))
- m = mollwiede_map(ax)
- z = metric.g_mchirp_mchirp(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{M_c M_c}$')
-
- ax = fig.add_axes(boundingbox(5,5,4,5))
- m = mollwiede_map(ax)
- z = metric.g_mchirp_eta(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{M_c \eta}$')
-
- ax = fig.add_axes(boundingbox(5,5,5,4))
- m = mollwiede_map(ax)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\eta M_c}$')
-
- ax = fig.add_axes(boundingbox(5,5,5,5))
- m = mollwiede_map(ax)
- z = metric.g_eta_eta(RAs, decs, detectors, Fderivs=Fderivs)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, detectors)
- ax.set_title(r'$g_{\eta \eta}$')
-
-def check_toa(detectors):
- """
- Create a figure to plot the times of arrival of a GW signal
- as a function of sky location.
- """
- fig = pylab.figure(figsize=(6,6))
-
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
-
- for idx,detector in enumerate(detectors):
- ax = fig.add_axes(boundingbox(len(detectors),3,idx+1,1))
- m = mollwiede_map(ax)
- levels = 20
- z = metric.rn(RAs, decs, detector)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, [detector])
- ax.set_title(r'$\vec{r_{\rm %s}} \cdot \hat{n}$'%(detector.name))
-
- ax = fig.add_axes(boundingbox(len(detectors),3,idx+1,2))
- m = mollwiede_map(ax)
- levels = 20
- z = metric.drn_dRA(RAs, decs, detector)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, [detector])
- ax.set_title(r'$\partial_\alpha (\vec{r_{\rm %s}} \cdot \hat{n})$'%(detector.name))
-
- ax = fig.add_axes(boundingbox(len(detectors),3,idx+1,3))
- m = mollwiede_map(ax)
- levels = 20
- z = metric.drn_ddec(RAs, decs, detector)
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, z, levels)
- plot_arms(m, [detector])
- ax.set_title(r'$\partial_\delta (\vec{r_{\rm %s}} \cdot \hat{n})$'%(detector.name))
-
-def plot_maximum_likelihood_matrix(detectors):
- """
- Create a figure to plot the components of the maximum likelihood
- matrix as a function of sky location.
- """
- fig = pylab.figure(figsize=(8,4.5))
-
- dRA = 2*pi/200
- ddec = pi/200
- RAs,decs = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
- A,B,C,D = metric.maximum_likelihood_matrix(RAs, decs, detectors)
-
- ax = fig.add_axes(boundingbox(2,2,1,1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, A, levels)
- plot_arms(m, detectors)
- ax.set_title('$A \in [%.2e, %.2e]$'%(min(A.flatten()), max(A.flatten())))
-
- ax = fig.add_axes(boundingbox(2,2,1,2))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, B, levels)
- plot_arms(m, detectors)
- ax.set_title('$B \in [%.2e, %.2e]$'%(min(B.flatten()), max(B.flatten())))
-
- ax = fig.add_axes(boundingbox(2,2,2,1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, C, levels)
- plot_arms(m, detectors)
- ax.set_title('$C \in [%.2e, %.2e]$'%(min(C.flatten()), max(C.flatten())))
-
- ax = fig.add_axes(boundingbox(2,2,2,2))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RAs*180./pi, decs*180./pi)
- CS = m.contour(x, y, scipy.log(D), levels)
- plot_arms(m, detectors)
- ax.set_title('$\log(D) ,\, D \in [%.2e, %.2e]$'%(min(D.flatten()), max(D.flatten())))
-
-def plot_metric_component_pieces(RA, dec, z0, z1, z2, z3):
- """
- Create a figure to plot the different components of a 2D metric as a
- function of sky location.
- """
- Z = scipy.zeros(scipy.shape(RA))
- fig = pylab.figure(figsize=(6,6))
- for idx in range(len(detectors)):
- ax = fig.add_axes(boundingbox(len(detectors),2,idx+1,1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, z0[idx], levels)
- plot_arms(m, detectors)
-
- Z += z0[idx]
-
- ax = fig.add_axes(boundingbox(len(detectors),2,idx+1,2))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, z1[idx], levels)
- plot_arms(m, detectors)
-
- Z += z1[idx]
-
- fig = pylab.figure(figsize=(6,6))
- for idx in range(len(detectors)):
- for jdx in range(len(detectors)):
- ax = fig.add_axes(boundingbox(len(detectors),len(detectors),idx+1,jdx+1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, z2[idx][jdx], levels)
- plot_arms(m, detectors)
-
- Z += z2[idx][jdx]
-
- fig = pylab.figure(figsize=(6,6))
- for idx in range(len(detectors)):
- for jdx in range(len(detectors)):
- ax = fig.add_axes(boundingbox(len(detectors),len(detectors),idx+1,jdx+1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, z3[idx][jdx], levels)
- plot_arms(m, detectors)
-
- Z += z3[idx][jdx]
-
- fig = pylab.figure(figsize=(6,6))
-
- ax = fig.add_axes(boundingbox(3,2,1,1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, sum(z0), levels)
- plot_arms(m, detectors)
-
- ax = fig.add_axes(boundingbox(3,2,1,2))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, sum(z1), levels)
- plot_arms(m, detectors)
-
- ax = fig.add_axes(boundingbox(3,1,2,1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, Z, levels)
- plot_arms(m, detectors)
-
- ax = fig.add_axes(boundingbox(3,2,3,1))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, sum([sum(z) for z in z2]), levels)
- plot_arms(m, detectors)
-
- ax = fig.add_axes(boundingbox(3,2,3,2))
- m = mollwiede_map(ax)
- levels = 20
- x, y = m(RA*180./pi, dec*180./pi)
- CS = m.contour(x, y, sum([sum(z) for z in z3]), levels)
- plot_arms(m, detectors)
-
-def check_g_RA_RA(detectors):
- """
- Create a figure to plot the RA RA component of the amplitude maximized
- metric.
- """
- dRA = 2*pi/200
- ddec = pi/200
- RA,dec = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
-
- A,B,C,D = metric.maximum_likelihood_matrix(RA, dec, detectors)
-
- z0 = []
- z1 = []
- z2 = []
- z3 = []
- Fderivs = True
- for detector1 in detectors:
- I_n1 = detector1.I_n
- fp1 = metric.Fp(RA, dec, detector1)
- fx1 = metric.Fx(RA, dec, detector1)
- if Fderivs:
- dfp_dRA1 = metric.dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = metric.dFx_dRA(RA, dec, detector1)
- drn_dRA1 = metric.drn_dRA(RA, dec, detector1)
- z0.append((B*fp1*fp1+A*fx1*fx1-2*C*fp1*fx1)*(-2*pi*drn_dRA1)**2*I_n1['-1']/D)
- if Fderivs:
- z1.append((B*dfp_dRA1*dfp_dRA1+A*dfx_dRA1*dfx_dRA1-C*dfp_dRA1*dfx_dRA1-C*dfx_dRA1*dfp_dRA1)*I_n1['-7']/D)
- z2.append([])
- z3.append([])
- for detector2 in detectors:
- I_n2 = detector2.I_n
- fp2 = metric.Fp(RA, dec, detector2)
- fx2 = metric.Fx(RA, dec, detector2)
- if Fderivs:
- dfp_dRA2 = metric.dFp_dRA(RA, dec, detector2)
- dfx_dRA2 = metric.dFx_dRA(RA, dec, detector2)
- drn_dRA2 = metric.drn_dRA(RA, dec, detector2)
- pre = B*fp1*fp2+A*fx1*fx2-C*fp1*fx2-C*fx1*fp2
- z2[-1].append(pre*(B*fp1*fp2+A*fx1*fx2-C*fp1*fx2-C*fx1*fp2)/D**2 \
- *I_n1['-4']*I_n2['-4']*(-2*pi*drn_dRA1)*(-2*pi*drn_dRA2))
- if Fderivs:
- z3[-1].append(pre*(B*dfp_dRA1*dfp_dRA2+A*dfx_dRA1*dfx_dRA2-C*dfp_dRA1*dfx_dRA2-C*dfx_dRA1*dfp_dRA2)/D**2 \
- *I_n1['-7']*I_n2['-7'])
-
- plot_metric_component_pieces(RA, dec, z0, z1, z2, z3)
-
-def check_g_RA_dec(detectors):
- """
- Create a figure to plot the RA dec component of the
- amplitude-maximized amplitude-averaged metric.
- """
- dRA = 2*pi/200
- ddec = pi/200
- RA,dec = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
-
- A,B,C,D = metric.maximum_likelihood_matrix(RA, dec, detectors)
-
- z0 = []
- z1 = []
- z2 = []
- z3 = []
- Fderivs = True
- for detector1 in detectors:
- I_n1 = detector1.I_n
- fp1 = metric.Fp(RA, dec, detector1)
- fx1 = metric.Fx(RA, dec, detector1)
- if Fderivs:
- dfp_dRA1 = metric.dFp_dRA(RA, dec, detector1)
- dfx_dRA1 = metric.dFx_dRA(RA, dec, detector1)
- dfp_ddec1 = metric.dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = metric.dFx_ddec(RA, dec, detector1)
- drn_dRA1 = metric.drn_dRA(RA, dec, detector1)
- drn_ddec1 = metric.drn_ddec(RA, dec, detector1)
- z0.append((B*fp1*fp1+A*fx1*fx1-2*C*fp1*fx1)/D*I_n1['-1']*(-2*pi*drn_dRA1)*(-2*pi*drn_ddec1))
- if Fderivs:
- z1.append((B*dfp_dRA1*dfp_ddec1+A*dfx_dRA1*dfx_ddec1-C*dfp_dRA1*dfx_ddec1-C*dfx_dRA1*dfp_ddec1)/D \
- *I_n1['-7'])
- z2.append([])
- z3.append([])
- for detector2 in detectors:
- I_n2 = detector2.I_n
- fp2 = metric.Fp(RA, dec, detector2)
- fx2 = metric.Fx(RA, dec, detector2)
- if Fderivs:
- dfp_ddec2 = metric.dFp_ddec(RA, dec, detector2)
- dfx_ddec2 = metric.dFx_ddec(RA, dec, detector2)
- drn_ddec2 = metric.drn_ddec(RA, dec, detector2)
- pre = B*fp1*fp2+A*fx1*fx2-C*fp1*fx2-C*fx1*fp2
- z2[-1].append(pre*(B*fp1*fp2+A*fx1*fx2-C*fp1*fx2-C*fx1*fp2)/D**2 \
- *I_n1['-4']*I_n2['-4']*(-2*pi*drn_dRA1)*(-2*pi*drn_ddec2))
- if Fderivs:
- z3[-1].append(pre*(B*dfp_dRA1*dfp_ddec2+A*dfx_dRA1*dfx_ddec2-C*dfp_dRA1*dfx_ddec2-C*dfx_dRA1*dfp_ddec2)/D**2 \
- *I_n1['-7']*I_n2['-7'])
-
- plot_metric_component_pieces(RA, dec, z0, z1, z2, z3)
-
-def check_g_dec_dec(detectors):
- """
- Create a figure to plot the dec dec component of the
- amplitude-maximized amplitude-averaged metric.
- """
- dRA = 2*pi/200
- ddec = pi/200
- RA,dec = scipy.mgrid[-pi+dRA:pi:dRA, -pi/2:pi/2+ddec:ddec]
-
- A,B,C,D = metric.maximum_likelihood_matrix(RA, dec, detectors)
-
- z0 = []
- z1 = []
- z2 = []
- z3 = []
- Fderivs = True
- for detector1 in detectors:
- I_n1 = detector1.I_n
- fp1 = metric.Fp(RA, dec, detector1)
- fx1 = metric.Fx(RA, dec, detector1)
- if Fderivs:
- dfp_ddec1 = metric.dFp_ddec(RA, dec, detector1)
- dfx_ddec1 = metric.dFx_ddec(RA, dec, detector1)
- drn_ddec1 = metric.drn_ddec(RA, dec, detector1)
- z0.append((B*fp1*fp1+A*fx1*fx1-2*C*fp1*fx1)/D*I_n1['-1']*(-2*pi*drn_ddec1)**2)
- if Fderivs:
- z1.append((B*dfp_ddec1*dfp_ddec1+A*dfx_ddec1*dfx_ddec1-C*dfp_ddec1*dfx_ddec1-C*dfx_ddec1*dfp_ddec1)/D \
- *I_n1['-7'])
- z2.append([])
- z3.append([])
- for detector2 in detectors:
- I_n2 = detector2.I_n
- fp2 = metric.Fp(RA, dec, detector2)
- fx2 = metric.Fx(RA, dec, detector2)
- if Fderivs:
- dfp_ddec2 = metric.dFp_ddec(RA, dec, detector2)
- dfx_ddec2 = metric.dFx_ddec(RA, dec, detector2)
- drn_ddec2 = metric.drn_ddec(RA, dec, detector2)
- pre = B*fp1*fp2+A*fx1*fx2-C*fp1*fx2-C*fx1*fp2
- z2[-1].append(pre*(B*fp1*fp2+A*fx1*fx2-C*fp1*fx2-C*fx1*fp2)/D**2 \
- *I_n1['-4']*I_n2['-4']*(-2*pi*drn_ddec1)*(-2*pi*drn_ddec2))
- if Fderivs:
- z3[-1].append(pre*(B*dfp_ddec1*dfp_ddec2+A*dfx_ddec1*dfx_ddec2-C*dfp_ddec1*dfx_ddec2-C*dfx_ddec1*dfp_ddec2)/D**2 \
- *I_n1['-7']*I_n2['-7'])
-
- plot_metric_component_pieces(RA, dec, z0, z1, z2, z3)
-
-
-
--
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