matlab-data-analysis

MATLAB Data Analysis

Use this skill when the deliverable is a validated number: an integral, a solution vector, a fit, a p-value, an uncertainty, or a figure whose axis is backed by arithmetic. The plot is never the evidence.

Skill Root

The installed directory containing this SKILL.md is the resource root. Add its helper folder for the current MATLAB session only — never through savepath, startup.m, or a global path edit:

skillRoot = '<absolute path to the installed matlab-data-analysis Skill directory>';
addpath(fullfile(skillRoot, 'scripts'));

Resolve references/, tests/, and helper calls from that root, not from the caller's working directory. If a shipped helper or reference is missing, report the exact path and reinstall the Skill; do not scan the disk for a substitute.

Workflow

1. 任务识别 — State the quantity, its units, the tolerance that makes it acceptable, and what independent source could contradict it. A claim without a tolerance has no PASS.
2. 能力选择 — r = mas_route(prompt); confirm this skill is primary, then read the matching tool contract below instead of the whole toolbox.
3. 环境检查 — mas_precheck before toolbox-only APIs (fitlm, Statistics Toolbox). Missing toolbox degrades the method explicitly; it never silently swaps the method.
4. MATLAB 执行 — build a small reproducible subset first; save intermediate arrays so a failing check can be inspected rather than guessed.
5. 独立验收 — grade with the tools below. Every accepted number needs a second route: closed form, hand algebra, a different factorization, resampling, or Monte Carlo.
6. 错误恢复 — a fail/UNDETERMINED is fixed for the named reason (add tolerance, improve the reference, raise precision, extend the record) and re-run; it is never skipped or relabelled.
7. 结果交付 — report value, tolerance, condition/uncertainty, and verdict. SKIP/BLOCKED stays SKIP/BLOCKED.

Verification tools

q = mas_quad_check(@(x) 4./(1+x.^2), 0, 1, struct('value',pi,'tolRel',1e-8, ...
        'method','simpson','n',32,'derivAt',0.5,'derivValue',-2.56));
q.verdict  q.valueErr  q.orders  q.refGap  q.floorI

L = mas_linsolve_check(A, x, b, struct('tolRel',1e-10));
L.verdict  L.backwardError  L.errorBound  L.cond  L.rank  L.routeDiff

c = mas_converge_check(hist, struct('tolFinal',1e-10,'order',2,'rate',0.5));
c.verdict  c.observed.order  c.observed.rate  c.observed.final

r = mas_fit_check(X, y, beta, struct('tolRel',1e-8,'r2',0.98, ...
        'se',se,'holdout',struct('X',Xh,'y',yh)));
r.verdict  r.r2  r.rmse  r.ci  r.betaRef  r.condX

s = mas_stat_check(x, struct('mu0',5,'alpha',0.05,'tail','two-sided'));
s = mas_stat_check(x1, x2, struct('claimDiff',0));          % Welch
s.verdict  s.p  s.ci  s.decision  s.pResample  s.methodAgreement

u = mas_uncert_check(@(p) p(1).*p(2).^2, [2;3], [0.02;0.03], ...
        struct('value',18,'sigma',0.36,'sigmaTolRel',0.05));
u.verdict  u.sigmaLin  u.sigmaMC  u.mcSE  u.sensitivity  u.jacobianMethod

p = mas_repro_check(@() myExperiment(), struct('seed',20261021,'tol',0));
p.verdict  p.sameSeed  p.seedEffect  p.digest  p.diffSameSeed

o = mas_ode_check(@(t,y) [y(2);-y(1)], [0 2*pi], [1;0], struct( ...
        'reference', @(t) [cos(t);-sin(t)], 'refTolRel', 1e-8, ...
        'invariant', @(t,y) y(1)^2+y(2)^2, 'invTolRel', 1e-8, ...
        'finalValue', [1;0], 'finalTolRel', 1e-8));
o.verdict  o.levels  o.error.maxScaled  o.invariant.maxRelDrift  o.stiffness.classified