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