def PlanetPropertiestoLinearModelAmplitudes(T0, P, mass, e, varpi, T10, P1,
mass1, e1, varpi1):
"""
"""
j = get_nearest_firstorder(P / P1)
j_2 = 1.0 / j / j
Delta = (j - 1) * P1 / P / j - 1
Delta_2 = 1.0 / Delta / Delta
ex = e * np.cos(varpi)
ey = e * np.sin(varpi)
ex1 = e1 * np.cos(varpi1)
ey1 = e1 * np.sin(varpi1)
alpha = (P / P1)**(2. / 3.)
alpha_2 = 1.0 / alpha / alpha
fCoeffIn, fCoeffOut = get_fCoeffs(j, alpha)
denom = (fCoeffIn * fCoeffIn + fCoeffOut * fCoeffOut)**(0.5)
Zx = fCoeffIn * ex + fCoeffOut * ex1
Zy = fCoeffIn * ey + fCoeffOut * ey1
Zx /= denom
Zy /= denom
S = mass1 * Zx
C = mass1 * Zy
S1 = mass * Zx
C1 = mass * Zy
return np.array([T0, P, mass1, S, C]), np.array([T10, P1, mass, S1, C1])
def ttv_basis_function_matrix_outer(P,
P1,
T0,
T10,
Ntrans,
IncludeLinearBasis=True):
"""
Compute the transit time basis function matrix, 'M', for a planet subject to an interior perturber.
Args:
P (real): Inner planet period.
P1 (real): Inner planet period.
T (real): Outer planet initial time of transit
T1 (real): Outer planet initial time of transit
Ntrans (int): number of transits
IncludeLinearBasis (bool): Whether basis functions representing a linear transit emphemris is included. Default is True.
Returns:
Array: the resulting basis function matrix is returned an (Ntrans, 5) array or an (Ntrans, 3) array if IncludeLinearBasis=False.
"""
j = get_nearest_firstorder(P / P1)
assert j > 0, "Bad period ratio!!! P,P1 = %.3f \t %.3f" % (P, P1)
superP = get_superperiod(P, P1)
superPhase = 2 * np.pi * (j * (-T10 / P1) - (j - 1) * (-T0 / P))
Times = T10 + np.arange(Ntrans) * P1
# Normalize super-sin/cos so that basis fn amplitude is mu * (Zx/Zy)
#
j_2 = 1.0 / j / j
Delta = (j - 1) * P1 / P / j - 1
Delta_2 = 1.0 / Delta / Delta
alpha = (P / P1)**(2. / 3.)
alpha_2 = 1.0 / alpha / alpha
fCoeffIn, fCoeffOut = get_fCoeffs(j, alpha)
denom = (fCoeffIn * fCoeffIn + fCoeffOut * fCoeffOut)**(0.5)
S1 = 1.5 * (j) * j_2 * Delta_2 * denom * P1 / (np.pi)
C1 = -1.5 * (j) * j_2 * Delta_2 * denom * P1 / (np.pi)
dt0 = dt0_OuterPlanet(P, P1, T0, T10, Ntrans)
superSin = S1 * np.sin(2 * np.pi * Times / superP + superPhase)
superCos = C1 * np.cos(2 * np.pi * Times / superP + superPhase)
if IncludeLinearBasis:
basis_function_matrix = np.vstack(
(np.ones(Ntrans), np.arange(Ntrans), dt0, superSin, superCos)).T
else:
basis_function_matrix = np.vstack((dt0, superSin, superCos)).T
return basis_function_matrix