tensor4all-benchmark

Reproducible benchmarks for tensor network algorithms in tensor4all-rs. Inputs use fixed seeds, timed regions exclude preparation, every arm writes JSON, and reports are generated from those records.

Maintained cases

Case	Input and operation	Arms	Scaling axis
elementwise_fourier	Elementwise product of two random one-dimensional Fourier QTTs	naive, zip-up, fit, ACI	measured input χ
gaussian_elementwise	Elementwise product of randomly rotated anisotropic Gaussian QTTs	global fit, patched fit, global ACI, patched ACI	compressed input χ
gaussian_mpo_contraction	MPO-MPO contraction of the same Gaussian input family	global fit, patched fit	compressed input χ

There is no independent R sweep. R is the smallest value that gives at least eight grid cells across the fixed minor-axis standard deviation. Gaussian count N and R are construction metadata, not analysis axes.

Gaussian input

Every Gaussian has an independent positive weight, center, log-uniform aspect ratio, and orientation uniform in [0, pi). Each term is independently constructed by two-dimensional interpolate_multi_scale_nd. Principal-axis unsafe points spaced by half the minor-axis standard deviation keep the narrow ridge refined.

The terms are combined by deterministic balanced pairwise reduction. Every pair is added and immediately compressed with the recorded intermediate relative-L2/SVD tolerance. This gives logarithmic reduction depth and avoids an exact intermediate sum whose bond dimension grows with the number of terms. A final global relative-L2/SVD truncation uses 1e-6.

The expensive raw input pair is cached atomically in .cache/inputs/. The cache key includes the schema version, pinned tensor4all-rs revision, N, R, width, aspect range, spacing, polynomial degree, interpolation tolerance, addition tolerance, and seed. Cases 2 and 3 share the same cache entry. Set BENCH_INPUT_CACHE_REFRESH=1 to rebuild it or BENCH_INPUT_CACHE_DIR to move the cache.

Patching and accuracy

The patch cap is fixed at 128 and has no runtime setting. Gaussian fit arms use relative-L2/SVD truncation. ACI uses its own interpolation residual, which is not identified with an L2 tolerance. Records therefore carry both the internal tolerance metric and a common deterministic holdout sampled relative-L2 error.

Case 2 compares:

• global fit
• patched fit
• global ACI with scale-relative residual
• patched ACI with patch-local absolute residual followed by global L2 budgeting

Case 3 compares global TreeTN fit with patched chain-TreeTN fit. Its reference is the finite left-endpoint quantics grid contraction, evaluated analytically with endpoint corrections.

Input construction, cache I/O, global input compression, format conversion, patch preparation, output conversion, and accuracy evaluation are outside timed regions.

Running

Requirements are Rust, HDF5, and a BLAS/LAPACK implementation. A complete single-core run is:

BENCH_CPU_CORE=0 scripts/run_all.sh linux-epyc-7713p

The script pins Rayon and common BLAS implementations to one thread, runs the three maintained binaries in release mode, writes raw records under result/<profile>/raw/, records machine metadata in run.yaml, and generates report.md.

For a probe run:

RAYON_NUM_THREADS=1 OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 \
MKL_NUM_THREADS=1 VECLIB_MAXIMUM_THREADS=1 \
BENCH_NS=2 OUT_DIR=/tmp/t4a-probe/raw \
taskset -c 0 cargo run --release --locked --bin elementwise_gauss2d_patched

Gaussian knobs shared by Cases 2 and 3:

Variable	Default	Meaning
BENCH_NS	2,8,32,128	Gaussian counts used to produce measured χ points
BENCH_SEED	0	deterministic instance seed
BENCH_RUNS	1	timed repetitions
BENCH_WARMUPS	0	untimed repetitions
BENCH_INPUT_CACHE_DIR	.cache/inputs	shared input cache
BENCH_INPUT_CACHE_REFRESH	0	rebuild cache entry when nonzero
OUT_DIR	result/dev/raw	JSON output directory

Case 2 additionally accepts BENCH_ACI_TOL, default 1e-8. This is an ACI residual threshold, not an L2 truncation tolerance.

Case 1 accepts BENCH_KS, BENCH_R, BENCH_TOL, BENCH_MAX_BOND, BENCH_RUNS, BENCH_WARMUPS, BENCH_SEED, and BENCH_ALGOS. Its report is sorted by measured input χ even though mode count generates the instances.

Validation

cargo fmt --all -- --check
cargo test --release
cargo clippy --locked --all-targets -- -D warnings
cargo check --locked --all-targets
python3 scripts/report.py result/<profile>
git diff --check

The focused tests cover difficult rotated interpolation, balanced pairwise sums, cache round trips, index identity, global and patched fit/ACI accuracy, contraction accuracy, patch caps, parameter accounting, and JSON serialization.