Conjugate gradients on the three-dimensional model problem with every iterate cut to rank 3

At its defaults it draws conjugate gradients on the three-dimensional model problem with every iterate cut to rank 3. The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 3.85·10⁻⁴. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 3. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

truncated-cg is one function in lib/figures/ttrain.js — the train — one rank per cut of the index list, and the iterate that must be cut back. 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.

The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 3.85·10⁻⁴. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 3. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 1.61·10⁻¹⁴. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 7. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 3.85·10⁻⁴. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 3. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 0.119. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 1. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 0.0112. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 2. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

The falling curves are relative residuals: the lower one is the same method with no budget, which reaches 1.61·10⁻¹⁴ in 40 steps, and the upper one is the budgeted run, which stops at 6.32·10⁻⁶. The two step curves near the top are ranks, on their own scale: the un-truncated step asks for 5 at every step from the third onwards and the budget allows 4. The truncation is therefore not an occasional tidy-up — it is happening at every step, and the distance between the two residual curves is what it costs. The solution of this problem is itself a train of rank five, so a budget of five or more removes nothing and the two curves coincide.

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.

4 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 truncatedCg, 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 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.