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 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_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'$\partial_\delta F_\times$')