The cost of a drifting sequence of nonlinear solves, against how often the Jacobian is refactorised

At its defaults it draws the cost of a drifting sequence of nonlinear solves, against how often the jacobian is refactorised. Twenty members, each warm-started from the last, each solved by a chord iteration on a factorisation that may be several members old. Refactorising at every member costs 16.42 MFlop; refactorising every 5 costs 9.27. Past a period of 20 the chord iteration stops converging altogether, which is drawn as an open circle on the ceiling rather than omitted. The filled square is the rule that refactorises when the observed contraction ratio exceeds 0.2: 4 factorisations, 9.22 MFlop, and it was never told the drift rate.

refresh-crossover is one function in lib/figures/reuse.js — reuse — what a kept factorisation or preconditioner is worth, and for how long. 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.

Twenty members, each warm-started from the last, each solved by a chord iteration on a factorisation that may be several members old. Refactorising at every member costs 16.42 MFlop; refactorising every 5 costs 9.27. Past a period of 20 the chord iteration stops converging altogether, which is drawn as an open circle on the ceiling rather than omitted. The filled square is the rule that refactorises when the observed contraction ratio exceeds 0.2: 4 factorisations, 9.22 MFlop, and it was never told the drift rate.

Twenty members, each warm-started from the last, each solved by a chord iteration on a factorisation that may be several members old. Refactorising at every member costs 16.42 MFlop; refactorising every 5 costs 9.27. Past a period of 20 the chord iteration stops converging altogether, which is drawn as an open circle on the ceiling rather than omitted. The filled square is the rule that refactorises when the observed contraction ratio exceeds 0.2: 4 factorisations, 9.22 MFlop, and it was never told the drift rate.

Twenty members, each warm-started from the last, each solved by a chord iteration on a factorisation that may be several members old. Refactorising at every member costs 14.11 MFlop; refactorising every 20 costs 4.85. Past a period of the range drawn the chord iteration stops converging altogether, which is drawn as an open circle on the ceiling rather than omitted. The filled square is the rule that refactorises when the observed contraction ratio exceeds 0.2: 1 factorisations, 4.85 MFlop, and it was never told the drift rate.

Twenty members, each warm-started from the last, each solved by a chord iteration on a factorisation that may be several members old. Refactorising at every member costs 15.26 MFlop; refactorising every 10 costs 6.71. Past a period of the range drawn the chord iteration stops converging altogether, which is drawn as an open circle on the ceiling rather than omitted. The filled square is the rule that refactorises when the observed contraction ratio exceeds 0.2: 2 factorisations, 7.46 MFlop, and it was never told the drift rate.

Twenty members, each warm-started from the last, each solved by a chord iteration on a factorisation that may be several members old. Refactorising at every member costs 19.01 MFlop; refactorising every 3 costs 14.50. Past a period of 6 the chord iteration stops converging altogether, which is drawn as an open circle on the ceiling rather than omitted. The filled square is the rule that refactorises when the observed contraction ratio exceeds 0.2: 8 factorisations, 12.33 MFlop, and it was never told the drift rate.

Every figure above checked its own claims on the way to being drawn, and a claim that failed would have stopped the picture rather than shipped a wrong one. Those checks 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 5 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 217 of 397 generators — 199 print a residual and 18 are exempt with a published reason; 180 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.