The 12×12 grid Laplacian and its Cholesky factor, ordered by natural
At its defaults it draws the 12×12 grid laplacian and its cholesky factor, ordered by natural. Two square sparsity plots side by side. The left shows the nonzeros of the matrix; the right shows the nonzeros of its Cholesky factor, with the entries created by elimination marked in a second colour.
fill-pattern is one function in lib/figures/sparse.js —
sparsity — fill counted two ways, and the ordering that decides the memory. 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.
Two square sparsity plots side by side. The left shows the nonzeros of the matrix; the right shows the nonzeros of its Cholesky factor, with the entries created by elimination marked in a second colour.
ordering: 0
The arguments are the ones The factor is not sparse passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
Two square sparsity plots side by side. The left shows the nonzeros of the matrix; the right shows the nonzeros of its Cholesky factor, with the entries created by elimination marked in a second colour.
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.
and the factorisation is exact to rounding
matmul shapes agree
the factor is denser than the matrix
the fill counted symbolically and numerically agree
Against the rule
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.
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.