Example usage of NRSur7dq4 surrogate model.¶
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import numpy as np
import matplotlib.pyplot as P
%matplotlib inline
import gwsurrogate
import numpy as np
import matplotlib.pyplot as P
%matplotlib inline
import gwsurrogate
setting __package__ to gwsurrogate.new so relative imports work __name__ = gwsurrogate.new.spline_evaluation __package__= gwsurrogate.new setting __package__ to gwsurrogate.new so relative imports work setting __package__ to gwsurrogate.new so relative imports work
Download surrogate data, this only needs to be done once¶
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# This can take a few minutes
gwsurrogate.catalog.pull('NRSur7dq4')
# This can take a few minutes
gwsurrogate.catalog.pull('NRSur7dq4')
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'/Users/vijay/src/gwsurrogate/gwsurrogate/surrogate_downloadsNRSur7dq4.h5'
Load the surrogate, this only needs to be done once at the start of a script¶
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sur = gwsurrogate.LoadSurrogate('NRSur7dq4')
sur = gwsurrogate.LoadSurrogate('NRSur7dq4')
Loaded NRSur7dq4 model
Read the documentation¶
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help(sur)
help(sur)
Help on NRSur7dq4 in module gwsurrogate.surrogate object:
class NRSur7dq4(SurrogateEvaluator)
| A class for the NRSur7dq4 surrogate model presented in Varma et al. 2019,
| arxiv1905.09300.
|
| Evaluates gravitational waveforms generated by precessing binary black hole
| systems with generic mass ratios and spins.
|
| This model includes the following spin-weighted spherical harmonic modes:
| 2<=ell<=4, -ell<=m<=ell.
|
| The parameter space of validity is:
| q \in [1, 6], and |chi1|,|chi2| \in [-1, 1], with generic directions.
| where q is the mass ratio and chi1/chi2 are the spin vectors of the
| heavier/lighter BH, respectively.
|
| The surrogate has been trained in the range
| q \in [1, 4] and |chi1|/|chi2| \in [-0.8, 0.8], but produces reasonable
| waveforms in the above range and has been tested against existing
| NR waveforms in that range.
|
| See the __call__ method on how to evaluate waveforms.
| In the __call__ method, x must have format x = [q, chi1, chi2].
|
| Method resolution order:
| NRSur7dq4
| SurrogateEvaluator
| __builtin__.object
|
| Methods defined here:
|
| __init__(self, h5filename)
|
| ----------------------------------------------------------------------
| Methods inherited from SurrogateEvaluator:
|
| __call__(self, q, chiA0, chiB0, M=None, dist_mpc=None, f_low=None, f_ref=None, dt=None, df=None, times=None, freqs=None, mode_list=None, ellMax=None, inclination=None, phi_ref=0, precessing_opts=None, tidal_opts=None, par_dict=None, units='dimensionless', skip_param_checks=False, taper_end_duration=None)
| INPUT
| =====
| q : Mass ratio, mA/mB >= 1.
| chiA0: Dimensionless spin vector of the heavier black hole at
| reference epoch.
| chiB0: Dimensionless spin vector of the lighter black hole at
| reference epoch.
|
| This follows the same convention as LAL, where the spin
| components are defined as:
| \chi_z = \chi \cdot \hat{L}, where L is the orbital angular
| momentum vector at the epoch.
| \chi_x = \chi \cdot \hat{n}, where n = body2 -> body1 is the
| separation vector at the epoch. body1 is the heavier body.
| \chi_y = \chi \cdot \hat{L \cross n}.
| These spin components are frame-independent as they are
| defined using vector inner products. This is equivalent to
| specifying the spins in the coorbital frame used in the
| surrogate papers.
|
| M, dist_mpc: Either specify both M and dist_mpc or neither.
| M : Total mass (solar masses). Default: None.
| dist_mpc : Distance to binary system (MegaParsecs). Default: None.
|
| f_low : Instantaneous initial frequency of the (2, 2) mode. In
| practice, this is estimated to be twice the initial orbital
| frequency in the coprecessing frame. Note: the coprecessing
| frame is the minimal rotation frame of arXiv:1110.2965.
|
| f_low should be in cycles/M if units = 'dimensionless',
| should be in Hertz if units = 'mks'.
| If 0, the entire waveform is returned.
| Default: None, must be specified by user.
|
| NOTE: For some models like NRSur7dq4, f_low=0 is recommended.
| The role of f_low is only to truncate the lower frequencies
| before returning the waveform. Since this model is already
| very short, this truncation is not required. On the other hand,
| f_ref is used to set the reference epoch, and can be freely
| specified.
|
| WARNING: Using f_low=0 with a small dt (like 0.1M) can lead to
| very expensive evaluation for hybridized surrogates like
| NRHybSur3dq8.
|
| f_ref: Frequency used to set the reference epoch at which the
| reference frame is defined and the spins are specified.
| See below for definition of the reference frame.
| Should be in cycles/M if units = 'dimensionless', should be
| in Hertz if units = 'mks'.
| Default: If f_ref is not given, we set f_ref = f_low. If
| f_low is 0, this corresponds to the initial index.
|
| For time domain models, f_ref is used to determine a t_ref,
| such that the orbital frequency in the coprecessing frame
| equals f_ref/2 at t=t_ref.
|
| dt, df : Time/Frequency step size, specify at most one of dt/df,
| depending on whether the surrogate is a time/frequency domain
| surrogate.
| Default: None. If None, the internal domain of the surrogate is
| used, which can be nonuniformly sampled.
| dt (df) Should be in M (cycles/M) if units = 'dimensionless',
| should be in seconds (Hertz) if units = 'mks'. Do not specify
| times/freqs if using dt/df.
|
|
| times, freqs:
| Array of time/frequency samples at which to evaluate the
| waveform, depending on whether the surrogate is a
| time/frequency domain surrogate. time (freqs) should be in
| M (cycles/M) if units = 'dimensionless', should be in
| seconds (Hertz) if units = 'mks'. Do not specify dt/df if
| using times/freqs. Default None.
|
| ellMax: Maximum ell index for modes to include. All available m
| indicies for each ell will be included automatically.
| Default: None, in which case all available modes wll be
| included.
|
| mode_list : A list of (ell, m) modes tuples to be included.
| Example: mode_list = [(2,2),(2,1)].
| Default: None, in which case all available modes are included.
| The m<0 modes will automatically be included for nonprecessing
| models. At most one of ellMax and mode_list can be specified.
|
| Note: mode_list is allowed only for nonprecessing models; for
| precessing models use ellMax. For precessing systems, all m
| indices of a given ell index mix with each other, so there is
| no clear hierarchy. To get the individual modes just don't
| specify inclination and a dictionary of modes will be returned.
|
| inclination : Inclination angle between the orbital angular momentum
| direction at the reference epoch and the line-of-sight to the
| observer. If inclination is None, the mode data is returned
| as a dictionary.
| Default: None.
|
| phi_ref : The azimuthal angle on the sky of the source frame following
| the LAL convention.
| Default: 0.
|
| If inclination/phi_ref are specified, the complex strain (h =
| hplus -i hcross) evaluated at (inclination, pi/2 - phi_ref) on
| the sky of the reference frame is returned. This follows the
| same convention as LAL. See below for definition of the
| reference frame.
|
| precessing_opts:
| A dictionary containing optional parameters for a precessing
| surrogate model. Default: None.
| Allowed keys are:
| init_orbphase: The orbital phase in the coprecessing frame
| at the reference epoch.
| Default: 0, in which case the coorbital frame and
| coprecessing frame are the same.
| init_quat: The unit quaternion (length 4 vector) giving the
| rotation from the coprecessing frame to the inertial frame
| at the reference epoch.
| Default: None, in which case the coprecessing frame is the
| same as the inertial frame.
| return_dynamics:
| Return the frame dynamics and spin evolution along with
| the waveform. Default: False.
| Example: precessing_opts = {
| 'init_orbphase': 0,
| 'init_quat': [1,0,0,0],
| 'return_dynamics': True
| }
|
| tidal_opts:
| A dictionary containing optional parameters for a tidal
| surrogate model. Default: None.
| Allowed keys are:
| Lambda1: The tidal deformability parameter for the heavier
| object.
| Lambda2: The tidal deformability parameter for the lighter
| object.
| Example: tidal_opts = {'Lambda1': 200, 'Lambda2': 300}
|
|
| par_dict: A dictionary containing any additional parameters needed for a
| particular surrogate model. Default: None.
|
| units: 'dimensionless' or 'mks'. Default: 'dimensionless'.
| If 'dimensionless': Any of f_low, f_ref, dt, df, times and
| freqs, if specified, must be in dimensionless units. That
| is, dt/times should be in units of M, while f_ref, f_low
| and df/freqs should be in units of cycles/M.
| M and dist_mpc must be None. The waveform and domain are
| returned as dimensionless quantities as well.
| If 'mks': Any of f_low, f_ref, dt, df, times and freqs, if
| specified, must be in MKS units. That is, dt/times should
| be in seconds, while f_ref, f_low and df/freqs should be
| in Hz. M and dist_mpc must be specified. The waveform and
| domain are returned in MKS units as well.
|
|
| skip_param_checks :
| Skip sanity checks for inputs. Use this if you want to
| extrapolate outside allowed range. Default: False.
|
| taper_end_durataion:
| Taper the last TAPER_END_DURATION (M) of a time-domain waveform
| in units of M. For exmple, passing 40 will taper the last 40M.
| When set to None, no taper is applied
| Default: None.
|
| RETURNS
| =====
|
| domain, h, dynamics
|
|
| domain : Array of time/frequency samples corresponding to h and
| dynamics, depending on whether the surrogate is a
| time/frequency domain model. This is the same as times/freqs
| if times/freqs are given as an inputs.
| For time domain models the time is set to 0 at the peak of
| the waveform. The time (frequency) values are in M (cycles/M)
| if units = 'dimensionless', they are in seconds (Hertz) if
| units = 'mks'
|
| h : The waveform.
| If inclination is specified, the complex strain (h = hplus
| -i hcross) evaluated at (inclination, pi/2 - phi_ref) on
| the sky of the reference frame is returned. This follows
| the LAL convention, see below for details. This includes
| all modes given in the ellMax/mode_list argument. For
| nonprecessing systems the m<0 modes are automatically
| deduced from the m>0 modes. To see if a model is precessing
| check self.keywords.
|
| Else, h is a dictionary of available modes with (l, m)
| tuples as keys. For example, h22 = h[(2,2)].
|
| If M and dist_mpc are given, the physical waveform
| at that distance is returned. Else, it is returned in
| code units: r*h/M extrapolated to future null-infinity.
|
| dynamics: A dict containing the frame dynamics and spin evolution. This
| is None for nonprecessing models. This is also None if
| return_dynamics in precessing_opts is False (Default).
|
| The dynamics include (L=len(domain)):
|
| q_copr = dynamics['q_copr']
| The quaternion representing the coprecessing frame with
| shape (4, L)
| orbphase = dynamics['orbphase']
| The orbital phase in the coprecessing frame with length L.
| chiA = dynamics['chiA']
| The inertial frame chiA with shape (L, 3)
| chiB = dynamics['chiB']
| The inertial frame chiB with shape (L, 3)
|
|
| IMPORTANT NOTES:
| ===============
|
| The reference frame (or inertial frame) is defined as follows:
| The +ve z-axis is along the orbital angular momentum at the reference
| epoch. The separation vector from the lighter BH to the heavier BH at
| the reference epoch is along the +ve x-axis. The y-axis completes the
| right-handed triad. The reference epoch is set using f_ref.
|
| Now, if inclination/phi_ref are given, the waveform is evaluated at
| (inclination, pi/2 - phi_ref) in the reference frame. This agrees with
| the LAL convention. See LIGO DCC document T1800226 for the LAL frame
| diagram.
|
| ----------------------------------------------------------------------
| Data descriptors inherited from SurrogateEvaluator:
|
| __dict__
| dictionary for instance variables (if defined)
|
| __weakref__
| list of weak references to the object (if defined)
Evaluate the waveform¶
Evaluate waveform modes in dimensionless units (default)¶
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q = 4
chiA = [-0.2, 0.4, 0.1]
chiB = [-0.5, 0.2, -0.4]
dt = 0.1 # timestep size, Units of M
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low) # dyn stands for dynamics, do dyn.keys() to see contents
q = 4
chiA = [-0.2, 0.4, 0.1]
chiB = [-0.5, 0.2, -0.4]
dt = 0.1 # timestep size, Units of M
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low) # dyn stands for dynamics, do dyn.keys() to see contents
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# Let's see all available modes
print( sorted(h.keys()) )
# Let's see all available modes
print( sorted(h.keys()) )
[(2, -2), (2, -1), (2, 0), (2, 1), (2, 2), (3, -3), (3, -2), (3, -1), (3, 0), (3, 1), (3, 2), (3, 3), (4, -4), (4, -3), (4, -2), (4, -1), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]
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P.plot(t, h[(2,2)].real, label='l2m2 real')
P.plot(t, h[(2,1)].real, label='l2m1 real')
P.plot(t, h[(3,3)].real, label='l3m3 real')
P.ylabel('Re[$h_{lm}$]', fontsize=18)
P.xlabel('t [M]', fontsize=18)
P.legend()
P.plot(t, h[(2,2)].real, label='l2m2 real')
P.plot(t, h[(2,1)].real, label='l2m1 real')
P.plot(t, h[(3,3)].real, label='l3m3 real')
P.ylabel('Re[$h_{lm}$]', fontsize=18)
P.xlabel('t [M]', fontsize=18)
P.legend()
Out[7]:
<matplotlib.legend.Legend at 0x1a1ae55410>
Evaluate waveform modes in physical units¶
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q = 4
chiA = [-0.2, 0.4, 0.1]
chiB = [-0.5, 0.2, -0.4]
f_ref = 20 # Reference frequecny in Hz. The spins are assumed to specified at this frequency
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
M = 70 # Total masss in solar masses
dist_mpc = 100 # distance in megaparsecs
dt = 1./4096 # step size in seconds
ellMax = 4 # Highest ell index for modes to use
# dyn stands for dynamics, do dyn.keys() to see contents
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low, f_ref=f_ref, ellMax=ellMax, M=M, dist_mpc=dist_mpc, units='mks')
P.plot(t, h[(2,2)].real, label='l2m2 real')
P.plot(t, h[(2,1)].real, label='l2m1 real')
P.ylabel('Re[$h_{lm}$]', fontsize=18)
P.xlabel('t [s]', fontsize=18)
P.legend()
q = 4
chiA = [-0.2, 0.4, 0.1]
chiB = [-0.5, 0.2, -0.4]
f_ref = 20 # Reference frequecny in Hz. The spins are assumed to specified at this frequency
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
M = 70 # Total masss in solar masses
dist_mpc = 100 # distance in megaparsecs
dt = 1./4096 # step size in seconds
ellMax = 4 # Highest ell index for modes to use
# dyn stands for dynamics, do dyn.keys() to see contents
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low, f_ref=f_ref, ellMax=ellMax, M=M, dist_mpc=dist_mpc, units='mks')
P.plot(t, h[(2,2)].real, label='l2m2 real')
P.plot(t, h[(2,1)].real, label='l2m1 real')
P.ylabel('Re[$h_{lm}$]', fontsize=18)
P.xlabel('t [s]', fontsize=18)
P.legend()
Out[8]:
<matplotlib.legend.Legend at 0x113ad5ad0>
Evaluate waveform at a point on the sky¶
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q = 4
chiA = [-0.2, 0.4, 0.1]
chiB = [-0.5, 0.2, -0.4]
f_ref = 20 # Reference frequecny in Hz. The spins are assumed to specified at this frequency
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
M = 70 # Total masss in solar masses
dist_mpc = 100 # distance in megaparsecs
dt = 1./4096 # step size in seconds
ellMax = 4 # Highest ell index for modes to use
inclination = np.pi/4
phi_ref = np.pi/5
# Will only include modes ell<=ellMax
# Returns h = h_+ -i h_x at (inclination, phi_ref) in the sky of the source frame
# dyn stands for dynamics, do dyn.keys() to see contents
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low, f_ref=f_ref, ellMax=ellMax, M=M, dist_mpc=dist_mpc,
inclination=inclination, phi_ref=phi_ref, units='mks')
P.plot(t, h.real)
P.ylabel('$h_{+}$ $(\iota, \phi_{ref})$', fontsize=18)
P.xlabel('t [s]', fontsize=18)
q = 4
chiA = [-0.2, 0.4, 0.1]
chiB = [-0.5, 0.2, -0.4]
f_ref = 20 # Reference frequecny in Hz. The spins are assumed to specified at this frequency
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
M = 70 # Total masss in solar masses
dist_mpc = 100 # distance in megaparsecs
dt = 1./4096 # step size in seconds
ellMax = 4 # Highest ell index for modes to use
inclination = np.pi/4
phi_ref = np.pi/5
# Will only include modes ell<=ellMax
# Returns h = h_+ -i h_x at (inclination, phi_ref) in the sky of the source frame
# dyn stands for dynamics, do dyn.keys() to see contents
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low, f_ref=f_ref, ellMax=ellMax, M=M, dist_mpc=dist_mpc,
inclination=inclination, phi_ref=phi_ref, units='mks')
P.plot(t, h.real)
P.ylabel('$h_{+}$ $(\iota, \phi_{ref})$', fontsize=18)
P.xlabel('t [s]', fontsize=18)
Out[9]:
Text(0.5,0,'t [s]')
Dynamics Surrogate¶
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q = 4
chiA = [-0.2, 0.4, 0.1] # unless f_ref is given the spins are assumed to be given at the start of the waveform
chiB = [-0.5, 0.2, -0.4]
dt = 0.1 # step size, Units of M
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low, precessing_opts={'return_dynamics': True}) # dyn stands for dynamics, do dyn.keys() to see contents
q = 4
chiA = [-0.2, 0.4, 0.1] # unless f_ref is given the spins are assumed to be given at the start of the waveform
chiB = [-0.5, 0.2, -0.4]
dt = 0.1 # step size, Units of M
f_low = 0 # initial frequency, f_low=0 returns the full surrogate
t, h, dyn = sur(q, chiA, chiB, dt=dt, f_low=f_low, precessing_opts={'return_dynamics': True}) # dyn stands for dynamics, do dyn.keys() to see contents
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# See all available dynamics data
dyn.keys()
# See all available dynamics data
dyn.keys()
Out[11]:
['chiB', 'orbphase', 'chiA', 'q_copr']
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P.figure(1)
P.plot(t, dyn['chiA'][:,0], label='$\chi_{Ax}$')
P.plot(t, dyn['chiA'][:,1], label='$\chi_{Ay}$')
P.plot(t, dyn['chiA'][:,2], label='$\chi_{Az}$')
P.ylabel('$\chi_A$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Spin of heavier BH')
P.legend(fontsize=14)
P.figure(2)
P.plot(t, dyn['chiB'][:,0], label='$\chi_{Bx}$')
P.plot(t, dyn['chiB'][:,1], label='$\chi_{By}$')
P.plot(t, dyn['chiB'][:,2], label='$\chi_{Bz}$')
P.ylabel('$\chi_B$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Spin of lighter BH')
P.legend(fontsize=14)
P.figure(3)
P.plot(t, dyn['orbphase'][:,])
P.ylabel('$\phi_{\mathrm{orb}}$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Orbital phase')
P.figure(4)
P.plot(t, dyn['q_copr'][0,:], label='$\hat{Q}_0$')
P.plot(t, dyn['q_copr'][1,:], label='$\hat{Q}_1$')
P.plot(t, dyn['q_copr'][2,:], label='$\hat{Q}_2$')
P.plot(t, dyn['q_copr'][3,:], label='$\hat{Q}_3$')
P.ylabel('$\hat{Q}$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Coprecessing frame quaternions')
P.legend(fontsize=14)
P.figure(1)
P.plot(t, dyn['chiA'][:,0], label='$\chi_{Ax}$')
P.plot(t, dyn['chiA'][:,1], label='$\chi_{Ay}$')
P.plot(t, dyn['chiA'][:,2], label='$\chi_{Az}$')
P.ylabel('$\chi_A$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Spin of heavier BH')
P.legend(fontsize=14)
P.figure(2)
P.plot(t, dyn['chiB'][:,0], label='$\chi_{Bx}$')
P.plot(t, dyn['chiB'][:,1], label='$\chi_{By}$')
P.plot(t, dyn['chiB'][:,2], label='$\chi_{Bz}$')
P.ylabel('$\chi_B$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Spin of lighter BH')
P.legend(fontsize=14)
P.figure(3)
P.plot(t, dyn['orbphase'][:,])
P.ylabel('$\phi_{\mathrm{orb}}$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Orbital phase')
P.figure(4)
P.plot(t, dyn['q_copr'][0,:], label='$\hat{Q}_0$')
P.plot(t, dyn['q_copr'][1,:], label='$\hat{Q}_1$')
P.plot(t, dyn['q_copr'][2,:], label='$\hat{Q}_2$')
P.plot(t, dyn['q_copr'][3,:], label='$\hat{Q}_3$')
P.ylabel('$\hat{Q}$', fontsize=18)
P.xlabel('t', fontsize=18)
P.title('Coprecessing frame quaternions')
P.legend(fontsize=14)
Out[12]:
<matplotlib.legend.Legend at 0x1a1be28fd0>
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