def MaxTimeDelayLine(ifos, ra, dec, gpstime=None, n=3):
"""
Return the n-point SkyPositionTable describing the line perpendicular to
the line of constant time delay through the given ra and dec for the
2-tuple ifos.
"""
# construct sky point
p = SkyPosition()
p.longitude = ra
p.latitude = dec
p.system = 'equatorial'
# remove duplicate site references
ifos = parse_sites(ifos)
assert len(ifos)==2, "More than two sites in given list of detectors"
# get light travel time
ltt = inject.light_travel_time(ifos[0], ifos[1])
# get number of points
dt = ltt/n
return TwoSiteSkyGrid(ifos, gpstime, dt=dt, point=p, sky='full')
def MaxTimeDelayLine(ifos, ra, dec, gpstime=None, n=3):
"""
Return the n-point SkyPositionTable describing the line perpendicular to
the line of constant time delay through the given ra and dec for the
2-tuple ifos.
"""
# construct sky point
p = SkyPosition()
p.longitude = ra
p.latitude = dec
p.system = 'equatorial'
# remove duplicate site references
ifos = parse_sites(ifos)
assert len(ifos) == 2, "More than two sites in given list of detectors"
# get light travel time
ltt = inject.light_travel_time(ifos[0], ifos[1])
# get number of points
dt = ltt / n
return TwoSiteSkyGrid(ifos, gpstime, dt=dt, point=p, sky='full')
def ThreeSiteSkyGrid(ifos, gpstime, dt=0.0005, tiling='square', sky='half'):
"""
Generates a SkyPositionTable for a three-site all-sky grid, covering either
a hemisphere (sky='half') or full sphere (sky='full'), using either
'square' or 'hexagonal tiling.
"""
# remove duplicate site references
pop = []
for i,ifo in enumerate(ifos):
if i==0: continue
site = ifo[0]
if site in [x[0] for x in ifos[0:i]]:
sys.stderr.write("Duplicate site reference, ignoring %s.\n" % ifo)
pop.append(i)
for p in pop[::-1]:
ifos.pop(p)
assert len(ifos)==3
detectors = []
T = []
baseline = []
# load detectors
for i,ifo in enumerate(ifos):
detectors.append(inject.cached_detector.get(inject.prefix_to_name[ifo]))
# get light travel time and baseline for other detectors to first
if i>=1:
T.append(inject.light_travel_time(ifos[0], ifos[i]))
baseline.append(detectors[i].location - detectors[0].location)
baseline[i-1] /= np.linalg.norm(baseline[i-1])
# get angle between baselines
angle = np.arccos(np.dot(baseline[0], baseline[1]))
#
# construct tiling vectors
#
tiling = tiling.lower()
t = np.zeros(len(baseline))
tdgrid = []
# square grid
dx = np.array([1,0])
dy = np.array([0,1])
nx = int(np.floor(T[0]/dt))
ny = int(np.floor(T[1]/dt))
# hexagonal grid
if tiling == 'square':
dm = dx
dn = dy
nm = nx
nn = ny
x = np.linspace(-nx, nx, 2*nx+1)
y = np.linspace(-ny, ny, 2*ny+1)
grid = np.array([[i,j] for i in x for j in y])
# hexagonal grid
elif re.match('hex', tiling):
dm = (2*dx+dy)
dn = (-dx+dy)
dx = dm - dn
# tile grid so that origin gets tiled
grid = []
orig = np.array([0,0])
# find bottom left point on grid
while orig[1] >= -ny: orig -= dn
# loop over y
for y in xrange(-ny,ny+1):
orig[0] = orig[0] % dx[0]
# work out minimal x value
minx = -nx
while minx % 3 != orig[0]: minx+=1
# tile x
x = np.arange(minx, nx+1, dx[0])
# append to grid
grid.extend([[i,y] for i in x])
orig += dn
orig[0] = orig[0] % dx[0]
grid = np.asarray(grid)
#
# Following Rabaste, Chassande-Motin, Piran (2009), construct an ellipse
# of physical values in 2D time-delay space for 3 detectors
#
#
# (theta, phi) coordinate system is as follows:
# detector 1 is origin
# z-axis joins positively to detector 2
# x-axis is orthogonal to z-axis in plane joining D1, D2, and D3
# y-axis forms a right-handed coordinate system
#
# so need to rotate from Rabaste network coordinates into
# earth-fixed coordinates at the end
# set z-axis in Rabaste frame
zaxis = baseline[0]
# work out y-axis in Rabaste frame
yaxis = np.cross(zaxis, baseline[1])
yaxis /= np.linalg.norm(yaxis)
# work out x-axis in Rabaste frame
xaxis = np.cross(yaxis, zaxis)
xaxis /= np.linalg.norm(xaxis)
# work out lines of nodes
north = np.array([0, 0, 1])
lineofnodes = np.cross(baseline[0], north)
lineofnodes /= np.linalg.norm(lineofnodes)
# work out Euler angles
alpha = np.arccos(np.dot(xaxis, lineofnodes))
beta = np.arccos(np.dot(baseline[0], north))
gamma = np.arccos(np.dot(lineofnodes, [1,0,0]))
# construct rotation
R = _rotation_euler(alpha, beta, gamma)
#
# construct sky position table
#
l = SkyPositionTable()
# loop over time-delay between D1 and D2
k = 0
for i in grid:
t = dt*i
# construct coefficients of elliptical equation in quadratic form
A = -T[1]/T[0] * t[0] * np.cos(angle)
B = T[1]**2 * ((t[0]/T[0])**2 - np.sin(angle)**2)
# test condition for inside ellipse and place point
condition = t[1]**2 + 2*A*t[1] + B
if condition <= 0:
ntheta = np.arccos(-t[0]/T[0])
nphi = np.arccos(-(T[0]*t[1]-T[1]*t[0]*np.cos(angle))/\
(T[1]*np.sqrt(T[0]**2-t[0]**2)*np.sin(angle)))
p = SkyPosition()
p.system = 'geographic'
p.longitude = nphi
p.latitude = lal.PI_2 - ntheta
p.probability = None
p.solid_angle = None
p.normalize()
p = p.rotate(R)
p = GeographicToEquatorial(p, LIGOTimeGPS(gpstime))
l.append(p)
if sky=='full':
p2 = SkyPosition()
p2.longitude = p.longitude
p2.latitude = p.latitude + lal.PI
p2.system = 'equatorial'
p2.normalize()
l.append(p2)
return l
def TwoSiteSkyGrid(ifos, gpstime, dt=0.0005, sky='half', point=None):
"""
Generates a SkyPositionTable for a two-site all-sky grid, covering either
a hemisphere (sky='half') or full sphere (sky='full').
The grid can be forced to pass through the given SkyPosition point if
required.
"""
# remove duplicate site references
ifos = parse_sites(ifos)
assert len(ifos)==2, "More than two sites in given list of detectors"
# get detectors
detectors = [inject.cached_detector.get(inject.prefix_to_name[ifo])\
for ifo in ifos]
# get light travel time
ltt = inject.light_travel_time(ifos[0], ifos[1])
# get number of points
max = int(np.floor(ltt/dt))
# get baseline
baseline = detectors[1].location - detectors[0].location
baseline /= np.linalg.norm(baseline)
#
# construct rotation
#
# xaxis points overhead of detector 1 or given point
# zaxis is baseline, or something else
if point:
xaxis = SphericalToCartesian(point)
xaxis /= np.linalg.norm(xaxis)
zaxis = np.cross(xaxis, baseline)
zaxis /= np.linalg.norm(zaxis)
else:
xaxis = detectors[0].location
xaxis /= np.linalg.norm(xaxis)
zaxis = baseline
yaxis = np.cross(zaxis, xaxis)
yaxis /= np.linalg.norm(yaxis)
yaxis = np.cross(xaxis, zaxis)
yaxis /= np.linalg.norm(yaxis)
# construct Euler rotation
lineofnodes = np.cross([0,0,1], zaxis)
lineofnodes /= np.linalg.norm(lineofnodes)
# work out Euler angles
alpha = np.arccos(np.dot([1,0,0], lineofnodes))
beta = np.arccos(np.dot([0,0,1], zaxis))
gamma = np.arccos(np.dot(lineofnodes, xaxis))
# get rotation
R = _rotation_euler(alpha, beta, gamma)
# construct sky table
l = SkyPositionTable()
if sky=='half': longs = [0]
elif sky=='full': longs = [0,lal.PI]
else: raise AttributeError("Sky type \"%s\" not recognised, please use "
"'half' or 'full'" % sky)
for long in longs:
for i in xrange(-max, max+1):
# get time-delay
t = i * dt
# if time-delay greater that light travel time, skip
if abs(t) >= ltt: continue
# construct object
e = SkyPosition()
e.system = 'geographic'
# project time-delay onto prime meridian
e.longitude = long
e.latitude = lal.PI_2-np.arccos(-t/ltt)
e.probability = None
e.solid_angle = None
e.normalize()
e = e.rotate(R)
e = GeographicToEquatorial(e, LIGOTimeGPS(gpstime))
if e not in l:
l.append(e)
return l
def SkyPatch(ifos, ra, dec, radius, gpstime, dt=0.0005, sigma=1.65,\
grid='circular'):
"""
Returns a SkyPositionTable of circular rings emanating from a given
central ra and dec. out to the maximal radius.
"""
# form centre point
p = SkyPosition()
p.longitude = ra
p.latitude = dec
# get detectors
ifos.sort()
detectors = []
for ifo in ifos:
if ifo not in inject.prefix_to_name.keys():
raise ValueError("Interferometer '%s' not recognised." % ifo)
detectors.append(inject.cached_detector.get(\
inject.prefix_to_name[ifo]))
alpha = 0
for i in xrange(len(ifos)):
for j in xrange(i+1,len(ifos)):
# get opening angle
baseline = date.XLALArrivalTimeDiff(detectors[i].location,\
detectors[j].location,\
ra, dec, LIGOTimeGPS(gpstime))
ltt = inject.light_travel_time(ifos[i], ifos[j])
angle = np.arccos(baseline/ltt)
# get window
lmin = angle-radius
lmax = angle+radius
if lmin < lal.PI_2 and lmax > lal.PI_2:
l = lal.PI_2
elif np.fabs(lal.PI_2-lmin) <\
np.fabs(lal.PI_2-lmax):
l = lmin
else:
l = lmax
# get alpha
dalpha = ltt * np.sin(l)
if dalpha > alpha:
alpha = dalpha
# get angular resolution
angRes = 2 * dt/alpha
# generate grid
if grid.lower() == 'circular':
grid = CircularGrid(angRes, radius)
else:
raise RuntimeError("Must use grid='circular', others not coded yet")
#
# Need to rotate grid onto (ra, dec)
#
# calculate opening angle from north pole
north = [0, 0, 1]
angle = np.arccos(np.dot(north, SphericalToCartesian(p)))
#angle = north.opening_angle(p)
# get rotation axis
axis = np.cross(north, SphericalToCartesian(p))
axis = axis / np.linalg.norm(axis)
# rotate grid
R = _rotation(axis, angle)
grid = grid.rotate(R)
#
# calculate probability density function
#
# assume Fisher distribution in angle from centre
kappa = (0.66*radius/sigma)**(-2)
# compute probability
for p in grid:
overlap = np.cos(p.opening_angle(grid[0]))
p.probability = np.exp(kappa*(overlap-1))
probs = [p.probability for p in grid]
for p in grid:
p.probability = p.probability/max(probs)
return grid
def dt_binning(instrument1, instrument2): dt = 0.005 + inject.light_travel_time(instrument1, instrument2) # seconds return rate.NDBins((rate.ATanBins(-dt, +dt, 801),))
def ThreeSiteSkyGrid(ifos, gpstime, dt=0.0005, tiling='square', sky='half'):
"""
Generates a SkyPositionTable for a three-site all-sky grid, covering either
a hemisphere (sky='half') or full sphere (sky='full'), using either
'square' or 'hexagonal tiling.
"""
# remove duplicate site references
pop = []
for i, ifo in enumerate(ifos):
if i == 0: continue
site = ifo[0]
if site in [x[0] for x in ifos[0:i]]:
sys.stderr.write("Duplicate site reference, ignoring %s.\n" % ifo)
pop.append(i)
for p in pop[::-1]:
ifos.pop(p)
assert len(ifos) == 3
detectors = []
T = []
baseline = []
# load detectors
for i, ifo in enumerate(ifos):
detectors.append(inject.cached_detector.get(
inject.prefix_to_name[ifo]))
# get light travel time and baseline for other detectors to first
if i >= 1:
T.append(inject.light_travel_time(ifos[0], ifos[i]))
baseline.append(detectors[i].location - detectors[0].location)
baseline[i - 1] /= np.linalg.norm(baseline[i - 1])
# get angle between baselines
angle = np.arccos(np.dot(baseline[0], baseline[1]))
#
# construct tiling vectors
#
tiling = tiling.lower()
t = np.zeros(len(baseline))
tdgrid = []
# square grid
dx = np.array([1, 0])
dy = np.array([0, 1])
nx = int(np.floor(T[0] / dt))
ny = int(np.floor(T[1] / dt))
# hexagonal grid
if tiling == 'square':
dm = dx
dn = dy
nm = nx
nn = ny
x = np.linspace(-nx, nx, 2 * nx + 1)
y = np.linspace(-ny, ny, 2 * ny + 1)
grid = np.array([[i, j] for i in x for j in y])
# hexagonal grid
elif re.match('hex', tiling):
dm = (2 * dx + dy)
dn = (-dx + dy)
dx = dm - dn
# tile grid so that origin gets tiled
grid = []
orig = np.array([0, 0])
# find bottom left point on grid
while orig[1] >= -ny:
orig -= dn
# loop over y
for y in xrange(-ny, ny + 1):
orig[0] = orig[0] % dx[0]
# work out minimal x value
minx = -nx
while minx % 3 != orig[0]:
minx += 1
# tile x
x = np.arange(minx, nx + 1, dx[0])
# append to grid
grid.extend([[i, y] for i in x])
orig += dn
orig[0] = orig[0] % dx[0]
grid = np.asarray(grid)
#
# Following Rabaste, Chassande-Motin, Piran (2009), construct an ellipse
# of physical values in 2D time-delay space for 3 detectors
#
#
# (theta, phi) coordinate system is as follows:
# detector 1 is origin
# z-axis joins positively to detector 2
# x-axis is orthogonal to z-axis in plane joining D1, D2, and D3
# y-axis forms a right-handed coordinate system
#
# so need to rotate from Rabaste network coordinates into
# earth-fixed coordinates at the end
# set z-axis in Rabaste frame
zaxis = baseline[0]
# work out y-axis in Rabaste frame
yaxis = np.cross(zaxis, baseline[1])
yaxis /= np.linalg.norm(yaxis)
# work out x-axis in Rabaste frame
xaxis = np.cross(yaxis, zaxis)
xaxis /= np.linalg.norm(xaxis)
# work out lines of nodes
north = np.array([0, 0, 1])
lineofnodes = np.cross(baseline[0], north)
lineofnodes /= np.linalg.norm(lineofnodes)
# work out Euler angles
alpha = np.arccos(np.dot(xaxis, lineofnodes))
beta = np.arccos(np.dot(baseline[0], north))
gamma = np.arccos(np.dot(lineofnodes, [1, 0, 0]))
# construct rotation
R = _rotation_euler(alpha, beta, gamma)
#
# construct sky position table
#
l = SkyPositionTable()
# loop over time-delay between D1 and D2
k = 0
for i in grid:
t = dt * i
# construct coefficients of elliptical equation in quadratic form
A = -T[1] / T[0] * t[0] * np.cos(angle)
B = T[1]**2 * ((t[0] / T[0])**2 - np.sin(angle)**2)
# test condition for inside ellipse and place point
condition = t[1]**2 + 2 * A * t[1] + B
if condition <= 0:
ntheta = np.arccos(-t[0] / T[0])
nphi = np.arccos(-(T[0]*t[1]-T[1]*t[0]*np.cos(angle))/\
(T[1]*np.sqrt(T[0]**2-t[0]**2)*np.sin(angle)))
p = SkyPosition()
p.system = 'geographic'
p.longitude = nphi
p.latitude = lal.PI_2 - ntheta
p.probability = None
p.solid_angle = None
p.normalize()
p = p.rotate(R)
p = GeographicToEquatorial(p, LIGOTimeGPS(gpstime))
l.append(p)
if sky == 'full':
p2 = SkyPosition()
p2.longitude = p.longitude
p2.latitude = p.latitude + lal.PI
p2.system = 'equatorial'
p2.normalize()
l.append(p2)
return l
def TwoSiteSkyGrid(ifos, gpstime, dt=0.0005, sky='half', point=None):
"""
Generates a SkyPositionTable for a two-site all-sky grid, covering either
a hemisphere (sky='half') or full sphere (sky='full').
The grid can be forced to pass through the given SkyPosition point if
required.
"""
# remove duplicate site references
ifos = parse_sites(ifos)
assert len(ifos) == 2, "More than two sites in given list of detectors"
# get detectors
detectors = [inject.cached_detector.get(inject.prefix_to_name[ifo])\
for ifo in ifos]
# get light travel time
ltt = inject.light_travel_time(ifos[0], ifos[1])
# get number of points
max = int(np.floor(ltt / dt))
# get baseline
baseline = detectors[1].location - detectors[0].location
baseline /= np.linalg.norm(baseline)
#
# construct rotation
#
# xaxis points overhead of detector 1 or given point
# zaxis is baseline, or something else
if point:
xaxis = SphericalToCartesian(point)
xaxis /= np.linalg.norm(xaxis)
zaxis = np.cross(xaxis, baseline)
zaxis /= np.linalg.norm(zaxis)
else:
xaxis = detectors[0].location
xaxis /= np.linalg.norm(xaxis)
zaxis = baseline
yaxis = np.cross(zaxis, xaxis)
yaxis /= np.linalg.norm(yaxis)
yaxis = np.cross(xaxis, zaxis)
yaxis /= np.linalg.norm(yaxis)
# construct Euler rotation
lineofnodes = np.cross([0, 0, 1], zaxis)
lineofnodes /= np.linalg.norm(lineofnodes)
# work out Euler angles
alpha = np.arccos(np.dot([1, 0, 0], lineofnodes))
beta = np.arccos(np.dot([0, 0, 1], zaxis))
gamma = np.arccos(np.dot(lineofnodes, xaxis))
# get rotation
R = _rotation_euler(alpha, beta, gamma)
# construct sky table
l = SkyPositionTable()
if sky == 'half': longs = [0]
elif sky == 'full': longs = [0, lal.PI]
else:
raise AttributeError("Sky type \"%s\" not recognised, please use "
"'half' or 'full'" % sky)
for long in longs:
for i in xrange(-max, max + 1):
# get time-delay
t = i * dt
# if time-delay greater that light travel time, skip
if abs(t) >= ltt: continue
# construct object
e = SkyPosition()
e.system = 'geographic'
# project time-delay onto prime meridian
e.longitude = long
e.latitude = lal.PI_2 - np.arccos(-t / ltt)
e.probability = None
e.solid_angle = None
e.normalize()
e = e.rotate(R)
e = GeographicToEquatorial(e, LIGOTimeGPS(gpstime))
if e not in l:
l.append(e)
return l
def SkyPatch(ifos, ra, dec, radius, gpstime, dt=0.0005, sigma=1.65,\
grid='circular'):
"""
Returns a SkyPositionTable of circular rings emanating from a given
central ra and dec. out to the maximal radius.
"""
# form centre point
p = SkyPosition()
p.longitude = ra
p.latitude = dec
# get detectors
ifos.sort()
detectors = []
for ifo in ifos:
if ifo not in inject.prefix_to_name.keys():
raise ValueError("Interferometer '%s' not recognised." % ifo)
detectors.append(inject.cached_detector.get(\
inject.prefix_to_name[ifo]))
alpha = 0
for i in xrange(len(ifos)):
for j in xrange(i + 1, len(ifos)):
# get opening angle
baseline = date.XLALArrivalTimeDiff(detectors[i].location,\
detectors[j].location,\
ra, dec, LIGOTimeGPS(gpstime))
ltt = inject.light_travel_time(ifos[i], ifos[j])
angle = np.arccos(baseline / ltt)
# get window
lmin = angle - radius
lmax = angle + radius
if lmin < lal.PI_2 and lmax > lal.PI_2:
l = lal.PI_2
elif np.fabs(lal.PI_2-lmin) <\
np.fabs(lal.PI_2-lmax):
l = lmin
else:
l = lmax
# get alpha
dalpha = ltt * np.sin(l)
if dalpha > alpha:
alpha = dalpha
# get angular resolution
angRes = 2 * dt / alpha
# generate grid
if grid.lower() == 'circular':
grid = CircularGrid(angRes, radius)
else:
raise RuntimeError("Must use grid='circular', others not coded yet")
#
# Need to rotate grid onto (ra, dec)
#
# calculate opening angle from north pole
north = [0, 0, 1]
angle = np.arccos(np.dot(north, SphericalToCartesian(p)))
#angle = north.opening_angle(p)
# get rotation axis
axis = np.cross(north, SphericalToCartesian(p))
axis = axis / np.linalg.norm(axis)
# rotate grid
R = _rotation(axis, angle)
grid = grid.rotate(R)
#
# calculate probability density function
#
# assume Fisher distribution in angle from centre
kappa = (0.66 * radius / sigma)**(-2)
# compute probability
for p in grid:
overlap = np.cos(p.opening_angle(grid[0]))
p.probability = np.exp(kappa * (overlap - 1))
probs = [p.probability for p in grid]
for p in grid:
p.probability = p.probability / max(probs)
return grid
def dt_binning(instrument1, instrument2): dt = 0.005 + inject.light_travel_time(instrument1, instrument2) # seconds return rate.NDBins((rate.ATanBins(-dt, +dt, 801),))
