estimator-walk

At its defaults it draws every column's 1-norm on a 12×12 matrix built to stop hager's walk one column short. 12 bars, one per column, each the sum of the absolute values in that column — the quantity the estimator maximises, whose largest is the matrix's 1-norm. The walk visits 1 of them and returns 12.00; column 2 has 1-norm 114.00 and is never visited, because its entries alternate in sign and cancel against every sign vector the walk stands on.

estimator-walk is one function in lib/figures/condest.js — condition estimation — the number a library prints, and the matrix it flatters. 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.

12 bars, one per column, each the sum of the absolute values in that column — the quantity the estimator maximises, whose largest is the matrix's 1-norm. The walk visits 1 of them and returns 12.00; column 2 has 1-norm 114.00 and is never visited, because its entries alternate in sign and cancel against every sign vector the walk stands on.

12 bars, one per column, each the sum of the absolute values in that column — the quantity the estimator maximises, whose largest is the matrix's 1-norm. The walk visits 1 of them and returns 12.00; column 2 has 1-norm 114.00 and is never visited, because its entries alternate in sign and cancel against every sign vector the walk stands on.

6 bars, one per column, each the sum of the absolute values in that column — the quantity the estimator maximises, whose largest is the matrix's 1-norm. The walk visits 1 of them and returns 6.00; column 2 has 1-norm 26.22 and is never visited, because its entries alternate in sign and cancel against every sign vector the walk stands on.

24 bars, one per column, each the sum of the absolute values in that column — the quantity the estimator maximises, whose largest is the matrix's 1-norm. The walk visits 1 of them and returns 24.00; column 2 has 1-norm 474.24 and is never visited, because its entries alternate in sign and cancel against every sign vector the walk stands on.

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.

8 distinct claims across 4 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.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

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.