mt op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.spc_mt_distance(data, mean=None, std=None, inv_corr=None, threshold=3.0) (to call the implementation directly, import spc; spc.spc_mt_distance(data, mean=None, std=None, inv_corr=None, threshold=3.0); from the registry, opsspc.get("spc_mt_distance"))
Score observations against an MT-method unit space.
`data is a 2-D array of shape (m, p). Pass the mean, std` and
`inv_corr from :func:spc_mt_unit_space` to score new product against a
stored unit space; omit all three and the unit space is built from `data`
itself, which is the training case and makes `md_sq_mean` land on
`(m-1)/m`.
Each row's distance is `MD_i = sqrt(z_i' R^-1 z_i / p)` with
`z_i = (x_i - mean) / std. Rows with MD > threshold` are reported in
`flagged; the rest in inside. Dividing the quadratic form by p` is
what puts the unit space at 1 regardless of how many features are used, so a
threshold carries over when features are added or removed.
Returns a dict with the per-row `md and md_sq arrays, flagged`,
`inside, the threshold, md_sq_mean, and n/p`.
Relationship to :func:spc_hotelling_t2 (used as the oracle in the tests):
on the standardised matrix the covariance *is* the correlation, so
`md**2 == t2 / p` exactly for the same data.
Raises `ValueError`: a non-2-D / empty *data*, a non-positive
`threshold, a unit space given only in part, a mean / std` /
`inv_corr whose shape disagrees with p`, a non-positive entry in
`std`, or non-finite input.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_mt_hidden_fault — py -3.11 examples/poc_mt_hidden_fault.py
• poc_spc — py -3.11 examples/poc_spc.py
table as input)msa_anova_table · msa_gauge_rr · msa_bias_linearity · msa_attribute_agreement · gum_standard_uncertainty · gum_propagate · gum_expanded · gum_monte_carlo
mt)spc_mt_unit_space · spc_mt_sn_ratio
*Provenance: spc.py — SPC operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.