Three filters at their own optima, on one problem
At its defaults it draws three filters at their own optima, on one problem. Filter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.
filter-comparison is one function in lib/figures/compose.js —
four knobs — one floor under them, and a fifth that is not a knob at all. 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.
At its defaults
Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.
Filter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.
noise: 0.01
The arguments are the ones Four knobs and one floor passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
Filter factors against the singular-value index. Truncation at K = 21 is a step from one to zero; Tikhonov at λ = 0.0215 is a smooth descent; the 20-step conjugate gradient filter rises above one and changes direction 5 times. The three reach errors within a few per cent of each other while differing by up to 0.99 in individual factors.
What it checked while drawing
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 2 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.
a noise level small enough to be noise
a size the SVD is affordable at
and the CGLS filter is not monotone
the filters differ substantially at their own optima
Against the rule
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 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.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.