From 4cfd00e4d766da85803c4f690400625750cbb43e Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Tue, 27 Jan 2026 22:49:02 -0500 Subject: [PATCH 1/2] add GS utils updates changes to fit attempt at restoring older changes attempt at restoring older changes few checks few checks rename changes pyproject fix --- pyproject.toml | 4 +- ringdown/fit.py | 38 +- ringdown/model.py | 148 ++++--- ringdown/utils/matrix.py | 55 +++ uv.lock | 823 ++++++++++++++++++++------------------- 5 files changed, 604 insertions(+), 464 deletions(-) create mode 100644 ringdown/utils/matrix.py diff --git a/pyproject.toml b/pyproject.toml index cd650953..cc4ccea6 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -42,8 +42,8 @@ ringdown_scan = "ringdown.cli.ringdown_scan:main" requires = ["hatchling", "hatch-vcs"] build-backend = "hatchling.build" -[tool.uv] -dev-dependencies = [ +[dependency-groups] +dev = [ "ringdown", ] diff --git a/ringdown/fit.py b/ringdown/fit.py index 9e809951..9e17ff64 100644 --- a/ringdown/fit.py +++ b/ringdown/fit.py @@ -16,7 +16,9 @@ import xarray as xr import lal import logging +import scipy.linalg # Added for AR coefficient calculation from .data import Data, AutoCovariance, PowerSpectrum +import jax from . import utils from .utils import try_parse from .target import Target, TargetCollection @@ -347,7 +349,7 @@ def update_prior(self, *args, **kwargs): @property def run_input(self) -> list: """Arguments to be passed to model function at runtime: - [times, strains, ls, fp, fc]. + [times, strains, ar_coeffs, sigmas, fp, fc]. """ if not self.has_data: raise ValueError("no data loaded") @@ -383,16 +385,40 @@ def run_input(self) -> list: np.array(d.time) - self.start_times[i] for i, d in data_dict.items() ] + # MODIFIED: Convert ACFs to AR Coefficients + Sigma for Gohberg-Semencul + ar_coeffs = [] + sigmas = [] + + for acf_obj in self.acfs.values(): + # Extract relevant ACF slice and normalize by strain scale^2 + # (since strain is scaled by 'scale', Variance is scaled by 'scale^2') + acf_vals = acf_obj.iloc[: self.n_analyze].values / scale**2 + + # Use Levinson-Durbin (via Toeplitz solver) to get AR coeffs + # R * a = -r where R is Toeplitz(acf[:-1]), r is acf[1:] + R = acf_vals[:-1] + r = acf_vals[1:] + + # This solves for [a1, a2, ... ap] + a_coeffs = scipy.linalg.solve_toeplitz((R, R), -r) + + # Prepend 1.0 to get full AR filter [1, a1, ... ap] + full_ar_coeffs = np.concatenate(([1.0], a_coeffs)) + ar_coeffs.append(full_ar_coeffs) + + # Calculate innovation variance (sigma^2) + # sigma^2 = gamma_0 + sum(a_k * gamma_k) + sigma_sq = acf_vals[0] + np.dot(a_coeffs, r) + sigmas.append(np.sqrt(sigma_sq)) + # arguments to be passed to function returned by model_function # make sure this agrees with that function call! - # [times, strains, ls, fp, fc] + # [times, strains, ar_coeffs, sigmas, fp, fc] input = [ times, [s.values / scale for s in data_dict.values()], - [ - (a.iloc[: self.n_analyze] / scale**2).cholesky - for a in self.acfs.values() - ], + ar_coeffs, # New argument for optimized model + sigmas, # New argument for optimized model fp, fc, ] diff --git a/ringdown/model.py b/ringdown/model.py index 277d1b1d..31c75cee 100644 --- a/ringdown/model.py +++ b/ringdown/model.py @@ -14,6 +14,7 @@ from .indexing import ModeIndexList from .result import Result from .utils.swsh import construct_sYlm, calc_YpYc +from utils.matrix import apply_matrix_fft_precomputed, apply_cinv_gs_fast, next_fast_len import arviz as az from arviz.data.base import dict_to_dataset @@ -186,10 +187,10 @@ def rd_design_matrix( dm = jnp.concatenate( [ # Yp * Fp * cos + Yc * Fc * sin - Yp_mat * dm[:, :, :nmode] + Yc_mat * dm[:, :, 3 * nmode :], + Yp_mat * dm[:, :, :nmode] + Yc_mat * dm[:, :, 3 * nmode:], # Yp * Fp * sin - Yc * Fc * cos - Yp_mat * dm[:, :, nmode : 2 * nmode] - - Yc_mat * dm[:, :, 2 * nmode : 3 * nmode], + Yp_mat * dm[:, :, nmode: 2 * nmode] + - Yc_mat * dm[:, :, 2 * nmode: 3 * nmode], ], axis=2, ) @@ -272,9 +273,9 @@ def get_quad_derived_quantities( # ellip = 0 and theta = 0,pi/2 for the single polarization model else: apx_unit = quads[:nmodes] - apy_unit = quads[nmodes : 2 * nmodes] - acx_unit = quads[2 * nmodes : 3 * nmodes] - acy_unit = quads[3 * nmodes :] + apy_unit = quads[nmodes: 2 * nmodes] + acx_unit = quads[2 * nmodes: 3 * nmodes] + acy_unit = quads[3 * nmodes:] numpyro.deterministic("apx", apx_unit * a_scale) numpyro.deterministic("apy", apy_unit * a_scale) @@ -525,7 +526,8 @@ def make_model( def model( times, strains, - ls, + ar_coeffs, + sigmas, fps, fcs, predictive: bool = predictive, @@ -543,19 +545,43 @@ def model( strains : array_like The strain data; list of 1D arrays for each IFO, or a 2D array with shape (n_det, n_times). - ls : array_like - The noise covariance matrices; list of 2D arrays for each IFO, or a - 3D array with shape (n_det, n_times, n_times). + ar_coeffs : array_like + The AR coefficients of the noise covariance (used for FFT inversion). + sigmas : array_like + The innovation standard deviation of the noise. fps : array_like The "plus" polarization coefficients for each IFO; length `n_det`. fcs : array_like The "cross" polarization coefficients for each IFO; length `n_det`. """ - times, strains, ls, fps, fcs = map( - jnp.array, (times, strains, ls, fps, fcs) + times, strains, fps, fcs = map( + jnp.array, (times, strains, fps, fcs) ) + ar_coeffs = [jnp.array(a) for a in ar_coeffs] + sigmas = jnp.array(sigmas) n_det = times.shape[0] + n_time = times.shape[1] + + # --------------------------------------------------------------------- + # Precompute FFTs for GS Inversion (Optimization Trick) + # --------------------------------------------------------------------- + # We assume AR coeffs are constant per detector. + # Find optimal FFT size P + N - 1 + P = ar_coeffs[0].shape[0] # Order of AR model + n_fft = next_fast_len(n_time + P - 1) + + fft_as = [] + fft_bs = [] + + for i in range(n_det): + ac = ar_coeffs[i] + # A column: [1, a1, ... ap] padded + fft_as.append(jnp.fft.rfft(ac, n=n_fft)) + + # B column: [0, ap, ... a1] padded (reversed coeffs) + rev_coeffs = jnp.pad(ac[1:][::-1], (1, 0)) + fft_bs.append(jnp.fft.rfft(rev_coeffs, n=n_fft)) # Here is where the particular model choice is made: # @@ -583,7 +609,8 @@ def model( # which, happily, is provided by the composed transformation f_latent = numpyro.sample( "f_latent", - dist.ImproperUniform(dist.constraints.real, (), (n_modes,)), + dist.ImproperUniform( + dist.constraints.real, (), (n_modes,)), ) f_transform = dist.transforms.ComposeTransform( [ @@ -594,7 +621,8 @@ def model( ) f = numpyro.deterministic("f", f_transform(f_latent)) numpyro.factor( - "f_transform", f_transform.log_abs_det_jacobian(f_latent, f) + "f_transform", f_transform.log_abs_det_jacobian( + f_latent, f) ) g = numpyro.sample( @@ -607,7 +635,8 @@ def model( g_latent = numpyro.sample( "g_latent", - dist.ImproperUniform(dist.constraints.real, (), (n_modes,)), + dist.ImproperUniform( + dist.constraints.real, (), (n_modes,)), ) g_transform = dist.transforms.ComposeTransform( [ @@ -618,7 +647,8 @@ def model( ) g = numpyro.deterministic("g", g_transform(g_latent)) numpyro.factor( - "g_transform", g_transform.log_abs_det_jacobian(g_latent, g) + "g_transform", g_transform.log_abs_det_jacobian( + g_latent, g) ) else: f = numpyro.sample("f", dist.Uniform(f_min, f_max)) @@ -726,8 +756,10 @@ def model( # and the strain (y) for the current detector # (ndet, ntime, nquads*nmode) => (i, ntime, nquads*nmode) M = dms[i, :, :] - L = ls[i, :, :] y = strains[i, :] + sigma = sigmas[i] + fft_a = fft_as[i] + fft_b = fft_bs[i] # M acts as a coordinate transformation matrix, taking us # from the space of quadratures to the space of the data , @@ -744,9 +776,18 @@ def model( # likelihood precision (M^T C^-1 M): # A_inv = Lambda_inv + M^T C^-1 M # so that A and A_inv are (nquads*nmode, nquads*nmode) - A_inv = Lambda_inv + jnp.dot( - M.T, jsp.linalg.cho_solve((L, True), M) - ) + + # 1. Compute C^{-1} terms using FFT-GS + # C^{-1} y + Cinv_y = apply_cinv_gs_fast(y, fft_a, fft_b, n_fft, sigma) + + # C^{-1} M (Vectorized over columns) + # Helper closure for vmap + def fast_gs_col(col): return apply_cinv_gs_fast( + col, fft_a, fft_b, n_fft, sigma) + Cinv_M = jax.vmap(fast_gs_col, in_axes=1, out_axes=1)(M) + + A_inv = Lambda_inv + jnp.dot(M.T, Cinv_M) A_inv_chol = jsp.linalg.cholesky(A_inv, lower=True) # we can also compute the marginal-posterior mean (a), @@ -754,11 +795,8 @@ def model( # (mu) and the likelihood mean (M^T C^-1 y): # a = A_inv (Lambda_inv mu + M^T C^-1 y) # so that a is (nquads*nmode,) - a = jsp.linalg.cho_solve( - (A_inv_chol, True), - jnp.dot(Lambda_inv, mu) - + jnp.dot(M.T, jsp.linalg.cho_solve((L, True), y)), - ) + rhs = jnp.dot(Lambda_inv, mu) + jnp.dot(M.T, Cinv_y) + a = jsp.linalg.cho_solve((A_inv_chol, True), rhs) # the mean (b) of the marginal likelihood p(y|b, B), # i.e., the likelihood obtained after integrating out @@ -789,17 +827,14 @@ def model( # ignore the 2pi factor since it introduces a term like # - 0.5*ntime*log(2pi), which is constant r = y - b - Cinv_r = jsp.linalg.cho_solve((L, True), r) - M_A_Mt_Cinv_r = jnp.dot( - M, - jsp.linalg.cho_solve( - (A_inv_chol, True), jnp.dot(M.T, Cinv_r) - ), - ) + # Need C^{-1} r + Cinv_r = apply_cinv_gs_fast(r, fft_a, fft_b, n_fft, sigma) - Cinv_M_A_Mt_Cinv_r = jsp.linalg.cho_solve( - (L, True), M_A_Mt_Cinv_r + Mt_Cinv_r = jnp.dot(M.T, Cinv_r) + woodbury_corr = jnp.dot( + Mt_Cinv_r.T, + jsp.linalg.cho_solve((A_inv_chol, True), Mt_Cinv_r) ) # now all we have left to compute is the log determinant @@ -814,8 +849,13 @@ def model( # writing similarly for |A| and |Lambda|, we thus have # that log_sqrt_det_B = 0.5 log|B| is # (note that |A| = -|A_inv|) + + # Log Determinants + # log|C| approx 2 * N * log(sigma) for AR process + log_det_C = 2.0 * len(y) * jnp.log(sigma) + log_sqrt_det_B = ( - jnp.sum(jnp.log(jnp.diag(L))) + 0.5 * log_det_C - jnp.sum(jnp.log(jnp.diag(Lambda_inv_chol))) + jnp.sum(jnp.log(jnp.diag(A_inv_chol))) ) @@ -823,7 +863,7 @@ def model( # putting it all together we can get the contribution # to the log likelihood from this detector logl = ( - -0.5 * jnp.dot(r, Cinv_r - Cinv_M_A_Mt_Cinv_r) + -0.5 * (jnp.dot(r, Cinv_r) - woodbury_corr) - log_sqrt_det_B ) @@ -952,13 +992,18 @@ def model( if not prior: for i, strain in enumerate(strains): - numpyro.sample( - f"logl_{i}", - dist.MultivariateNormal( - h_det[i, :], scale_tril=ls[i, :, :] - ), - obs=strain, - ) + # Compute log likelihood using GS: -0.5 * r^T C^{-1} r - log_det + model_strain = h_det[i, :] + r = strain - model_strain + sigma = sigmas[i] + + Cinv_r = apply_cinv_gs_fast( + r, fft_as[i], fft_bs[i], n_fft, sigma) + log_det_C = 2.0 * len(r) * jnp.log(sigma) + + logl = -0.5 * jnp.dot(r, Cinv_r) - 0.5 * log_det_C + + numpyro.factor(f"logl_{i}", logl) return model @@ -1049,7 +1094,8 @@ def get_arviz( if len(modes) != n_mode: raise ValueError(f"expected {n_mode} modes, got {len(modes)}") # get ifo from shape of Fc, assuming it's last argument provided to model - n_ifo = len(sampler._args[-1]) + # NOTE: In new model signature, fcs is at index 5. strains is index 1. + n_ifo = len(sampler._args[1]) if ifos is None: ifos = np.arange(n_ifo, dtype=int) elif len(ifos) != n_ifo: @@ -1073,13 +1119,22 @@ def get_arviz( in_dims = { "time": ["ifo", "time_index"], "strain": ["ifo", "time_index"], - "cholesky_factor": ["ifo", "time_index", "time_index_1"], + "ar_coeffs": ["ifo", "ar_lag"], + "sigma": ["ifo"], "fp": ["ifo"], "fc": ["ifo"], "epoch": ["ifo"], } + # Updated mapping for new model signature + # args: (times, strains, ar_coeffs, sigmas, fps, fcs) + args = sampler._args in_data = { - k: np.array(v) for k, v in zip(in_dims.keys(), sampler._args) + "time": np.array(args[0]), + "strain": np.array(args[1]), + # "ar_coeffs": np.array(args[2]), # Might be list of arrays, skip for simple netcdf + "sigma": np.array(args[3]), + "fp": np.array(args[4]), + "fc": np.array(args[5]), } in_data["epoch"] = np.array(epoch) in_data["scale"] = scale or 1.0 @@ -1087,6 +1142,7 @@ def get_arviz( if injections is not None: in_data["injection"] = np.array(injections) in_dims["injection"] = ["ifo", "time_index"] + dims.update(in_dims) obs_data = {"strain": in_data.pop("strain")} else: diff --git a/ringdown/utils/matrix.py b/ringdown/utils/matrix.py new file mode 100644 index 00000000..53351eec --- /dev/null +++ b/ringdown/utils/matrix.py @@ -0,0 +1,55 @@ +import jax.numpy as jnp + +# ============================================================================= +# OPTIMIZATION HELPERS (FFT / Gohberg-Semencul) +# ============================================================================= + + +def next_fast_len(target): + """Find the next power of 2 for efficient FFT.""" + return 1 << (int(target) - 1).bit_length() + + +def apply_matrix_fft_precomputed(x, filter_fft, N, n_fft): + """ + Computes A @ x using precomputed FFT of the filter. + A is Lower Triangular Toeplitz. + """ + X_f = jnp.fft.rfft(x, n=n_fft) + out_f = X_f * filter_fft + out = jnp.fft.irfft(out_f, n=n_fft) + return out[:N] + + +def apply_cinv_gs_fast(vector, fft_a, fft_b, n_fft, sigma): + """ + Computes x^T C^{-1} y using Gohberg-Semencul with precomputed FFTs. + Returns C^{-1} @ vector. + """ + N = vector.shape[0] + + # Helper to apply A @ v (Lower Triangular Toeplitz) + def apply_A(v): + return apply_matrix_fft_precomputed(v, fft_a, N, n_fft) + + # Helper to apply A.T @ v = Flip( A @ Flip(v) ) + def apply_At(v): + return jnp.flip(apply_A(jnp.flip(v))) + + # Helper to apply B @ v + def apply_B(v): + return apply_matrix_fft_precomputed(v, fft_b, N, n_fft) + + # Helper to apply B.T @ v + def apply_Bt(v): + return jnp.flip(apply_B(jnp.flip(v))) + + # GS Formula: C^{-1} r = (1/sigma^2) * [ A(A.T r) - B(B.T r) ] + + # Term 1: A @ (A.T @ vector) + t1 = apply_A(apply_At(vector)) + + # Term 2: B @ (B.T @ vector) + t2 = apply_B(apply_Bt(vector)) + + return (t1 - t2) / (sigma**2) diff --git a/uv.lock 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