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Reduce memory usage when applying supertranslations by a factor of 6 #82

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Reduce memory usage when applying supertranslations by a factor of 6 #82

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151 changes: 117 additions & 34 deletions scri/asymptotic_bondi_data/transformations.py
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Original file line number Diff line number Diff line change
Expand Up @@ -336,11 +336,24 @@ def transform(self, **kwargs):
# σ(u, θ', ϕ') exp(2iλ)
σ = sf.Grid(self.sigma.evaluate(distorted_grid_rotors), spin_weight=2)

# Determine the new time slices. The set timeprime is chosen so that on each slice of constant
# u'_i, the average value of u=(u'/k)+α is precisely <u>=u'γ+<α>=u_i. But then, we have to
# narrow that set down, so that every grid point on all the u'_i' slices correspond to data in
# the range of input data.
timeprime = (u - sf.constant_from_ell_0_mode(supertranslation[0]).real) / γ
timeprime_of_initialtime_directionprime = k * (u[0] - α)
timeprime_of_finaltime_directionprime = k * (u[-1] - α)
earliest_complete_timeprime = np.max(timeprime_of_initialtime_directionprime.view(np.ndarray))
latest_complete_timeprime = np.min(timeprime_of_finaltime_directionprime.view(np.ndarray))
timeprime = timeprime[(timeprime >= earliest_complete_timeprime) & (timeprime <= latest_complete_timeprime)]
abdprime = type(self)(timeprime, output_ell_max)

### The following calculations are done using in-place Horner form. I suspect this will be the
### most efficient form of this calculation, within reason. Note that the factors of exp(isλ)
### were computed automatically by evaluating in terms of quaternions.
#
fprime_of_timenaught_directionprime = np.empty((6, self.n_times, n_theta, n_phi), dtype=complex)
fprime_of_timenaught_directionprime = np.empty((1, self.n_times, n_theta, n_phi), dtype=complex)

# ψ0'(u, θ', ϕ')
fprime_temp = ψ4.copy()
fprime_temp *= ðuprime_over_k
Expand All @@ -352,7 +365,27 @@ def transform(self, **kwargs):
fprime_temp *= ðuprime_over_k
fprime_temp += ψ0
fprime_temp *= one_over_k_cubed
# This will store the values of f'(u', θ', ϕ') for the various functions `f`
fprime_of_timenaught_directionprime[0] = fprime_temp
fprime_of_timeprime_directionprime = np.zeros((1,timeprime.size, n_theta, n_phi), dtype=complex)
# Interpolate the various transformed function values on the transformed grid from the original
# time coordinate to the new set of time coordinates, independently for each direction.
for i in range(n_theta):
for j in range(n_phi):
k_i_j = k[0, i, j]
α_i_j = α[0, i, j]
# u'(u, θ', ϕ')
timeprime_of_timenaught_directionprime_i_j = k_i_j * (u - α_i_j)
# f'(u', θ', ϕ')
fprime_of_timeprime_directionprime[:, :, i, j] = CubicSpline(
timeprime_of_timenaught_directionprime_i_j, fprime_of_timenaught_directionprime[:, :, i, j], axis=1
)(timeprime)
# Transform back from the distorted grid to the SWSH mode weights as measured in that
# grid. I'll abuse notation slightly here by indicating those "distorted" mode weights with
# primes, so that f'(u')_{ℓ', m'} = ∫ f'(u', θ', ϕ') sȲ_{ℓ', m'}(θ', ϕ') sin(θ') dθ' dϕ'
# ψ0'(u')_{ℓ', m'}
abdprime.psi0 = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], 2, output_ell_max)

# ψ1'(u, θ', ϕ')
fprime_temp = -ψ4
fprime_temp *= ðuprime_over_k
Expand All @@ -362,45 +395,107 @@ def transform(self, **kwargs):
fprime_temp *= ðuprime_over_k
fprime_temp += ψ1
fprime_temp *= one_over_k_cubed
fprime_of_timenaught_directionprime[1] = fprime_temp
# This will store the values of f'(u', θ', ϕ') for the various functions `f`
fprime_of_timenaught_directionprime[0] = fprime_temp
# Interpolate the various transformed function values on the transformed grid from the original
# time coordinate to the new set of time coordinates, independently for each direction.
for i in range(n_theta):
for j in range(n_phi):
k_i_j = k[0, i, j]
α_i_j = α[0, i, j]
# u'(u, θ', ϕ')
timeprime_of_timenaught_directionprime_i_j = k_i_j * (u - α_i_j)
# f'(u', θ', ϕ')
fprime_of_timeprime_directionprime[:, :, i, j] = CubicSpline(
timeprime_of_timenaught_directionprime_i_j, fprime_of_timenaught_directionprime[:, :, i, j], axis=1
)(timeprime)
# Transform back from the distorted grid to the SWSH mode weights as measured in that
# grid. I'll abuse notation slightly here by indicating those "distorted" mode weights with
# primes, so that f'(u')_{ℓ', m'} = ∫ f'(u', θ', ϕ') sȲ_{ℓ', m'}(θ', ϕ') sin(θ') dθ' dϕ'
# ψ1'(u')_{ℓ', m'}
abdprime.psi1 = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], 1, output_ell_max)

# ψ2'(u, θ', ϕ')
fprime_temp = ψ4.copy()
fprime_temp *= ðuprime_over_k
fprime_temp += -2 * ψ3
fprime_temp *= ðuprime_over_k
fprime_temp += ψ2
fprime_temp *= one_over_k_cubed
fprime_of_timenaught_directionprime[2] = fprime_temp
# This will store the values of f'(u', θ', ϕ') for the various functions `f`
fprime_of_timenaught_directionprime[0] = fprime_temp
# Interpolate the various transformed function values on the transformed grid from the original
# time coordinate to the new set of time coordinates, independently for each direction.
for i in range(n_theta):
for j in range(n_phi):
k_i_j = k[0, i, j]
α_i_j = α[0, i, j]
# u'(u, θ', ϕ')
timeprime_of_timenaught_directionprime_i_j = k_i_j * (u - α_i_j)
# f'(u', θ', ϕ')
fprime_of_timeprime_directionprime[:, :, i, j] = CubicSpline(
timeprime_of_timenaught_directionprime_i_j, fprime_of_timenaught_directionprime[:, :, i, j], axis=1
)(timeprime)
# Transform back from the distorted grid to the SWSH mode weights as measured in that
# grid. I'll abuse notation slightly here by indicating those "distorted" mode weights with
# primes, so that f'(u')_{ℓ', m'} = ∫ f'(u', θ', ϕ') sȲ_{ℓ', m'}(θ', ϕ') sin(θ') dθ' dϕ'
# ψ2'(u')_{ℓ', m'}
abdprime.psi2 = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], 0, output_ell_max)

# ψ3'(u, θ', ϕ')
fprime_temp = -ψ4
fprime_temp *= ðuprime_over_k
fprime_temp += ψ3
fprime_temp *= one_over_k_cubed
fprime_of_timenaught_directionprime[3] = fprime_temp
# This will store the values of f'(u', θ', ϕ') for the various functions `f`
fprime_of_timenaught_directionprime[0] = fprime_temp
# Interpolate the various transformed function values on the transformed grid from the original
# time coordinate to the new set of time coordinates, independently for each direction.
for i in range(n_theta):
for j in range(n_phi):
k_i_j = k[0, i, j]
α_i_j = α[0, i, j]
# u'(u, θ', ϕ')
timeprime_of_timenaught_directionprime_i_j = k_i_j * (u - α_i_j)
# f'(u', θ', ϕ')
fprime_of_timeprime_directionprime[:, :, i, j] = CubicSpline(
timeprime_of_timenaught_directionprime_i_j, fprime_of_timenaught_directionprime[:, :, i, j], axis=1
)(timeprime)
# Transform back from the distorted grid to the SWSH mode weights as measured in that
# grid. I'll abuse notation slightly here by indicating those "distorted" mode weights with
# primes, so that f'(u')_{ℓ', m'} = ∫ f'(u', θ', ϕ') sȲ_{ℓ', m'}(θ', ϕ') sin(θ') dθ' dϕ'
# ψ3'(u')_{ℓ', m'}
abdprime.psi3 = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], -1, output_ell_max)

# ψ4'(u, θ', ϕ')
fprime_temp = ψ4.copy()
fprime_temp *= one_over_k_cubed
fprime_of_timenaught_directionprime[4] = fprime_temp
# This will store the values of f'(u', θ', ϕ') for the various functions `f`
fprime_of_timenaught_directionprime[0] = fprime_temp
# Interpolate the various transformed function values on the transformed grid from the original
# time coordinate to the new set of time coordinates, independently for each direction.
for i in range(n_theta):
for j in range(n_phi):
k_i_j = k[0, i, j]
α_i_j = α[0, i, j]
# u'(u, θ', ϕ')
timeprime_of_timenaught_directionprime_i_j = k_i_j * (u - α_i_j)
# f'(u', θ', ϕ')
fprime_of_timeprime_directionprime[:, :, i, j] = CubicSpline(
timeprime_of_timenaught_directionprime_i_j, fprime_of_timenaught_directionprime[:, :, i, j], axis=1
)(timeprime)
# Transform back from the distorted grid to the SWSH mode weights as measured in that
# grid. I'll abuse notation slightly here by indicating those "distorted" mode weights with
# primes, so that f'(u')_{ℓ', m'} = ∫ f'(u', θ', ϕ') sȲ_{ℓ', m'}(θ', ϕ') sin(θ') dθ' dϕ'
# ψ4'(u')_{ℓ', m'}
abdprime.psi4 = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], -2, output_ell_max)

# σ'(u, θ', ϕ')
fprime_temp = σ.copy()
fprime_temp -= ððα
fprime_temp *= one_over_k
fprime_of_timenaught_directionprime[5] = fprime_temp

# Determine the new time slices. The set timeprime is chosen so that on each slice of constant
# u'_i, the average value of u=(u'/k)+α is precisely <u>=u'γ+<α>=u_i. But then, we have to
# narrow that set down, so that every grid point on all the u'_i' slices correspond to data in
# the range of input data.
timeprime = (u - sf.constant_from_ell_0_mode(supertranslation[0]).real) / γ
timeprime_of_initialtime_directionprime = k * (u[0] - α)
timeprime_of_finaltime_directionprime = k * (u[-1] - α)
earliest_complete_timeprime = np.max(timeprime_of_initialtime_directionprime.view(np.ndarray))
latest_complete_timeprime = np.min(timeprime_of_finaltime_directionprime.view(np.ndarray))
timeprime = timeprime[(timeprime >= earliest_complete_timeprime) & (timeprime <= latest_complete_timeprime)]

# This will store the values of f'(u', θ', ϕ') for the various functions `f`
fprime_of_timeprime_directionprime = np.zeros((6, timeprime.size, n_theta, n_phi), dtype=complex)

fprime_of_timenaught_directionprime[0] = fprime_temp
# Interpolate the various transformed function values on the transformed grid from the original
# time coordinate to the new set of time coordinates, independently for each direction.
for i in range(n_theta):
Expand All @@ -413,22 +508,10 @@ def transform(self, **kwargs):
fprime_of_timeprime_directionprime[:, :, i, j] = CubicSpline(
timeprime_of_timenaught_directionprime_i_j, fprime_of_timenaught_directionprime[:, :, i, j], axis=1
)(timeprime)

# Finally, transform back from the distorted grid to the SWSH mode weights as measured in that
# Transform back from the distorted grid to the SWSH mode weights as measured in that
# grid. I'll abuse notation slightly here by indicating those "distorted" mode weights with
# primes, so that f'(u')_{ℓ', m'} = ∫ f'(u', θ', ϕ') sȲ_{ℓ', m'}(θ', ϕ') sin(θ') dθ' dϕ'
abdprime = type(self)(timeprime, output_ell_max)
# ψ0'(u')_{ℓ', m'}
abdprime.psi0 = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], 2, output_ell_max)
# ψ1'(u')_{ℓ', m'}
abdprime.psi1 = spinsfast.map2salm(fprime_of_timeprime_directionprime[1], 1, output_ell_max)
# ψ2'(u')_{ℓ', m'}
abdprime.psi2 = spinsfast.map2salm(fprime_of_timeprime_directionprime[2], 0, output_ell_max)
# ψ3'(u')_{ℓ', m'}
abdprime.psi3 = spinsfast.map2salm(fprime_of_timeprime_directionprime[3], -1, output_ell_max)
# ψ4'(u')_{ℓ', m'}
abdprime.psi4 = spinsfast.map2salm(fprime_of_timeprime_directionprime[4], -2, output_ell_max)
# σ'(u')_{ℓ', m'}
abdprime.sigma = spinsfast.map2salm(fprime_of_timeprime_directionprime[5], 2, output_ell_max)
abdprime.sigma = spinsfast.map2salm(fprime_of_timeprime_directionprime[0], 2, output_ell_max)

return abdprime