componentwise-bound

At its defaults it draws two perturbation bounds and the error that was measured, on a 8×8 matrix spread over 8 decades of units. Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 4·10⁷ times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

componentwise-bound is one function in lib/figures/scaling.js — units — the condition number that is a choice of them, and the one that is not. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 4·10⁷ times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 4·10⁷ times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 4120 times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 4·10⁹ times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 2.1 times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

Three curves against the size of an entrywise relative perturbation. The normwise bound κ_∞·ε is a valid bound and sits 3.7·10⁷ times above the componentwise one cond(A, x)·ε, which is also a bound and is nearly attained by the worst of forty random perturbations at each size.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

14 distinct claims across 6 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

It draws a decomposition and prints its residual. It calls solve, condInf, condSkeelAt, and every figure above carries the badge — which residualcheck verifies by looking for it in the emitted SVG rather than by finding the call that builds one. A badge that is constructed and then left out of the body is the failure that check exists for.

Across the library: the rule bites on 90 of 174 generators — 75 print a residual and 15 are exempt with a published reason; 84 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.