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_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 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_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())))