cg-filter-shape

At its defaults it draws the filter 8 conjugate gradient steps apply, measured and predicted. Filter factors against the singular-value index. The factors measured off the iterate and the polynomial predicted from the recurrence coefficients agree to 6.9·10⁻¹⁴ and are drawn as one curve. It rises above one — 1.070 at its largest — and changes direction several times. Tikhonov's filter at the matching cutoff is monotone and never exceeds one.

cg-filter-shape is one function in lib/figures/krylovreg.js — iterative regularisation — a step count as the parameter, and the filter it applies. 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.

Filter factors against the singular-value index. The factors measured off the iterate and the polynomial predicted from the recurrence coefficients agree to 6.9·10⁻¹⁴ and are drawn as one curve. It rises above one — 1.070 at its largest — and changes direction several times. Tikhonov's filter at the matching cutoff is monotone and never exceeds one.

Filter factors against the singular-value index. The factors measured off the iterate and the polynomial predicted from the recurrence coefficients agree to 1.2·10⁻¹¹ and are drawn as one curve. It rises above one — 1.203 at its largest — and changes direction several times. Tikhonov's filter at the matching cutoff is monotone and never exceeds one.

Filter factors against the singular-value index. The factors measured off the iterate and the polynomial predicted from the recurrence coefficients agree to 6.9·10⁻¹⁴ and are drawn as one curve. It rises above one — 1.070 at its largest — and changes direction several times. Tikhonov's filter at the matching cutoff is monotone and never exceeds one.

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.

6 distinct claims across 3 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 cgls, 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 66 of 131 generators — 51 print a residual and 15 are exempt with a published reason; 65 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.