Rust Analysis Engine -- 22 Modules, 597 Tests¶

Pure Rust implementations of all 22 spike_stats analysis modules, exposed to Python via PyO3 bindings. Zero NumPy or SciPy dependency on the Rust side -- all linear algebra (eigendecomposition, matrix inversion, Gaussian elimination), FFT (via rustfft), and stochastic processes (via rand_distr) are implemented natively.

Architecture¶

Text Only

engine/src/analysis/
  mod.rs              -- 22 pub mod declarations
  basic.rs            -- spike_times, isi, firing_rate, spike_count, bin_spike_train
  rate.rs             -- instantaneous_rate, psth, population_rate
  variability.rs      -- cv_isi, cv2, local_variation, fano_factor, entropies, Hurst
  correlation.rs      -- cross_correlation, STTC, coherence, covariance
  distance.rs         -- van_rossum, victor_purpura, ISI/SPIKE distances
  information.rs      -- mutual_information, transfer_entropy, KL MI
  causality.rs        -- pairwise/conditional/spectral Granger, PDC, DTF
  decoding.rs         -- population_vector, Bayesian, MLE, LDA, naive Bayes
  network.rs          -- functional_connectivity, unitary_events, assemblies
  surrogates.rs       -- ISI shuffle, dither, Poisson, gamma, compound Poisson
  temporal.rs         -- burst_detection, latency, onset, change points
  patterns.rs         -- spike_directionality, spike_train_order, C3
  spectral.rs         -- power_spectrum (FFT via rustfft)
  waveform.rs         -- width, amplitude, slopes, halfwidth, PT ratio
  point_process.rs    -- conditional_intensity, hazard, survivor, renewal
  statistics.rs       -- significance_bootstrap (Rust-only, takes fn pointer)
  stimulus.rs         -- STA, STC, spatial_information, place fields, tuning
  lfp.rs              -- phase_locking_value, spike_field_coherence, phase histogram
  sorting_quality.rs  -- isolation_distance, L-ratio, silhouette, d', SNR, drift
  dimensionality.rs   -- PCA, demixed PCA, factor analysis (Jacobi eigendecomp)
  gpfa.rs             -- GPFA via EM with squared-exponential GP priors
  spade.rs            -- SPADE: Apriori itemset mining + surrogate significance

Dependency Map¶

External crates used by analysis modules:

Crate	Version	Used by
`rustfft`	6.2	`spectral.rs`, `lfp.rs`, `correlation.rs`
`rand_distr`	0.6	`surrogates.rs`

All other computation (eigendecomposition, matrix inversion, complex arithmetic, Hilbert transforms, histogram binning) is self-contained.

Custom Linear Algebra¶

Several modules implement their own numerical primitives to avoid external LAPACK/BLAS dependencies:

Jacobi eigendecomposition (dimensionality.rs): symmetric eigenvalues + eigenvectors via iterative rotations, O(n^3) per sweep.
Gauss-Jordan inverse (sorting_quality.rs, gpfa.rs, dimensionality.rs, causality.rs): partial-pivot elimination on augmented [A|I] matrix.
Gaussian elimination solver (gpfa.rs, causality.rs, decoding.rs): solves Ax = b with partial pivoting.
Complex matrix ops (causality.rs): C64 type with inverse, determinant, multiply for spectral Granger.

PyO3 Bindings¶

96 functions are exposed to Python via #[pyfunction] wrappers in engine/src/lib.rs. The sole exception is significance_bootstrap in statistics.rs which takes a Fn(&[f64], &[f64]) -> f64 pointer and cannot cross the PyO3 boundary.

Functions NOT exposed via PyO3¶

Function	Reason
`significance_bootstrap`	Takes `Fn` pointer
`generalized_victor_purpura`	Takes `fn(f64) -> f64`
`time_rescaling_ks_test`	Takes `fn(f64) -> f64`
`inhomogeneous_poisson`	Takes `fn(f64) -> f64`
`surrogate_trial_shuffle`	Returns permutation indices only

These are callable from Rust code and tests but require Python-side wrappers with closures.

Module Reference¶

basic¶

Core spike train operations used by most other modules.

Function	Signature	Description
`spike_times`	`(&[i32], f64) -> Vec<f64>`	Extract spike times (s) from binary array
`isi`	`(&[i32], f64) -> Vec<f64>`	Inter-spike intervals (s)
`firing_rate`	`(&[i32], f64) -> f64`	Mean firing rate (Hz)
`spike_count`	`(&[i32]) -> i64`	Total spike count
`bin_spike_train`	`(&[i32], usize) -> Vec<i64>`	Bin into spike counts

spectral¶

Function	Signature	Description
`power_spectrum`	`(&[i32], f64) -> (Vec<f64>, Vec<f64>)`	PSD via FFT, returns (psd, freqs_hz)

waveform¶

Spike waveform shape analysis. All functions take &[f64] waveform samples and dt (sample interval, default 1/30000 s).

Function	Returns	Reference
`waveform_width`	`f64`	Trough-to-peak width (s). Bartho et al. 2004
`waveform_amplitude`	`f64`	Peak-to-trough amplitude
`waveform_repolarization_slope`	`f64`	Max dV/dt after trough. Bean 2007
`waveform_recovery_slope`	`f64`	Min dV/dt after peak. Bean 2007
`waveform_halfwidth`	`f64`	Duration at half-minimum. Bartho et al. 2004
`waveform_pt_ratio`	`f64`	Post-trough peak / trough amplitude

point_process¶

Point process models and hazard functions.

Function	Returns	Reference
`conditional_intensity`	`Vec<f64>`	Moving-window Poisson rate (Hz). Brown et al. 2004
`isi_hazard_function`	`(Vec<f64>, Vec<f64>)`	h(t) = f(t)/S(t). Tuckwell 1988
`isi_survivor_function`	`(Vec<f64>, Vec<f64>)`	S(t) = P(ISI > t)
`renewal_density`	`(Vec<f64>, Vec<f64>)`	Normalised by mean rate. Cox 1962

statistics¶

Function	Signature	Notes
`significance_bootstrap`	`(F, &[f64], &[f64], usize, u64) -> (f64, f64)`	Rust-only. Permutation test with splitmix64 PRNG

stimulus¶

Spike-triggered analysis and receptive field estimation.

Function	Returns	Reference
`spike_triggered_average`	`Vec<f64>`	Mean pre-spike stimulus snippet
`spike_triggered_covariance`	`Vec<f64>` (flat matrix)	Covariance of pre-spike stimulus. Schwartz et al. 2006
`spatial_information`	`f64` (bits/spike)	Skaggs et al. 1993
`place_field_detection`	`Vec<(f64, f64)>`	Contiguous high-rate bins. O'Keefe & Dostrovsky 1971
`tuning_curve`	`(Vec<f64>, Vec<f64>)`	Rate vs stimulus value. Dayan & Abbott 2001

lfp¶

Spike-LFP coupling via analytic signal (Hilbert transform with rustfft).

Function	Returns	Description
`phase_locking_value`	`f64`	PLV =
`spike_field_coherence`	`(Vec<f64>, Vec<f64>)`	SFC =
`spike_phase_histogram`	`(Vec<i64>, Vec<f64>)`	Phase histogram in [-pi, pi]

sorting_quality¶

Spike sorting quality metrics. Cluster/noise inputs are row-major (n_points, n_features) flat arrays.

Function	Returns	Reference
`isolation_distance`	`f64`	Mahalanobis at rank n_cluster. Harris et al. 2001
`l_ratio`	`f64`	Normalised chi2-approximation. Schmitzer-Torbert et al. 2005
`silhouette_score`	`f64`	Mean (b-a)/max(a,b). Rousseeuw 1987
`d_prime`	`f64`	Projected sensitivity index. Green & Swets 1966
`isi_violation_rate`	`f64`	Fraction below refractory. Hill et al. 2011
`presence_ratio`	`f64`	Fraction of occupied bins. IBL 2019
`amplitude_cutoff`	`f64`	Estimated missing spikes. Hill et al. 2011
`snr`	`f64`	Peak / noise_std. Suner et al. 2005
`nn_hit_rate`	`f64`	k-NN cluster purity. Chung et al. 2017
`drift_metric`	`f64`	Amplitude drift over time. IBL 2019

dimensionality¶

Dimensionality reduction with built-in Jacobi eigendecomposition (no LAPACK required).

Function	Returns	Reference
`spike_train_pca`	`(Vec<f64>, Vec<f64>)`	(projected, explained_variance_ratio)
`demixed_pca`	`(Vec<f64>, Vec<f64>)`	Condition-dependent variance. Kobak et al. 2016
`factor_analysis`	`(Vec<f64>, Vec<f64>)`	(loadings, uniquenesses). Rubin & Thayer 1982

gpfa¶

Gaussian Process Factor Analysis. Full EM implementation with squared-exponential GP kernels, block-structured precision matrices, and approximate log-likelihood monitoring.

Function	Returns	Reference
`gpfa`	`GpfaResult` struct	Trajectories, C, d, R, tau, log-likelihoods. Yu et al. 2009
`gpfa_transform`	`Vec<f64>`	Project new data with learned parameters

GpfaResult fields: trajectories, c, d, r, tau, log_likelihoods, n_latents, n_bins, n_neurons.

spade¶

Spike Pattern Detection and Evaluation. Apriori-style frequent itemset mining extended to spatiotemporal patterns with lag search and surrogate significance testing.

Function	Returns	Reference
`spade_detect`	`Vec<SpadePattern>`	Significant patterns with p-values. Torre et al. 2013

SpadePattern fields: neurons, lags, count, p_value.

Test Coverage¶

597 tests across all modules. Every public function has at least:

Positive case (typical input producing expected output)
Edge case (empty input, single element, degenerate dimensions)
Numerical accuracy check (comparison against known values or bounds)

Run tests:

Bash

export PATH="$HOME/.rustup/toolchains/stable-x86_64-unknown-linux-gnu/bin:$PATH"
cd engine && cargo test --lib

Run a single module's tests:

Bash

cargo test --lib analysis::spectral
cargo test --lib analysis::gpfa

Benchmark Results¶

Measured with Criterion on i5-11600K @ 3.90 GHz, DDR4-3200. Values are median latency. Pure CPU benchmarks.

Last measured: 2026-05-02 (cargo bench --bench analysis_bench)

basic¶

Function	100	10K	100K
spike_times	86 ns	5.4 µs	85.0 µs
isi	106 ns	5.6 µs	86.3 µs
firing_rate	13 ns	1.2 µs	15.3 µs
bin_spike_train	36 ns	2.5 µs	29.0 µs

rate¶

Function	100	10K	100K
instantaneous_rate	4.3 µs	352 µs	3.5 ms

variability¶

Function	100	10K	100K
cv_isi	108 ns	6.5 µs	94.7 µs
fano_factor	76 ns	4.8 µs	50.7 µs
sample_entropy	32.6 µs	3.23 ms	O(n²) — not benchmarked

correlation¶

Function	100	10K
cross_correlation	1.46 µs	213 µs
event_synchronization	142 ns	63.1 µs

distance¶

Function	100	5K
van_rossum	1.07 µs	314 µs
victor_purpura	162 ns	274 µs
isi_distance	165 ns	5.95 µs

information¶

Function	100	10K
mutual_information	714 ns	48.7 µs
transfer_entropy	1.03 µs	60.8 µs

causality¶

Function	100	5K
pairwise_granger	102 ns	81.7 µs

decoding¶

Function	Latency
population_vector_decode	14.9 µs
bayesian_decode	11.0 µs

network¶

Function	Latency
functional_connectivity (10n)	814 µs

surrogates¶

Function	1K	100K
isi_shuffle	865 ns	103 µs
homogeneous_poisson	2.55 µs	242 µs

temporal¶

Function	1K	100K
burst_detection	708 ns	91.4 µs
change_point_detection	296 ns	31.8 µs

patterns¶

Function	Latency
spike_directionality (5K)	3.85 µs
cubic_higher_order (5K)	409 µs

spectral¶

Function	256	10K	100K
power_spectrum	3.81 µs	177 µs	4.91 ms

waveform (50 samples)¶

Function	Latency
waveform_width	64 ns
waveform_amplitude	38 ns
waveform_repolarization_slope	72 ns
waveform_halfwidth	168 ns
waveform_pt_ratio	58 ns