Bounded Principal Component Workbench

How to use Bounded Principal Component Workbench

Origin-shift centering reduces cancellation before a sample covariance matrix is formed. A scaled symmetric Jacobi iteration finds its eigenvectors. Components are sorted by decreasing variance and checked against the original covariance; scores retain every transformed row.

1. Enter numeric observation matrix json.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• 3–500 rows and 1–8 numeric columns; finite magnitudes at most 1e9 and nonzero magnitudes at least 1e-12. Standardization uses sample SD and refuses a constant column. Center-only mode may retain zero-variance columns but refuses a completely constant matrix. At most 10000 rotations; failed residual/orthogonality checks are refused. Tiny negative roundoff eigenvalues may be clamped to zero and are marked. Repeated or close eigenvalues can rotate their basis; signs and individual loadings are not unique. No missing-data imputation, automatic component choice or causal feature-importance claim.
• Local calculation only; no input persistence or external lookup. Text/JSON is limited to 30000 characters and output to 1000000 characters. Numeric model inputs and precision/work limits are stated on this page. Approximate JSON numbers retain full stored values; exact arithmetic outputs retain decimal or fraction strings. Unsupported states fail explicitly.