grading-sweep

At its defaults it draws the worst relative error over the whole spectrum, against how many decades the matrix is graded over, n = 8. Each point is one bidiagonal matrix and the worst relative error any of its singular values suffers, measured against a Sturm bisection in exact rationals. The route through BᵀB is as good as anything at 2.1 decades — 3.63·10⁻¹⁴ — and by 11 decades it is at 14.5, which is not an error in the answer, it is the answer. One-sided Jacobi and the zero-shift bidiagonal sweep are flat at about the unit roundoff across the whole range, which is the claim this site's own SVD has been making in a source comment since it was written and had never measured.

grading-sweep is one function in lib/figures/relacc.js — relative accuracy — small compared to what, against an exact rational answer. 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.

Each point is one bidiagonal matrix and the worst relative error any of its singular values suffers, measured against a Sturm bisection in exact rationals. The route through BᵀB is as good as anything at 2.1 decades — 3.63·10⁻¹⁴ — and by 11 decades it is at 14.5, which is not an error in the answer, it is the answer. One-sided Jacobi and the zero-shift bidiagonal sweep are flat at about the unit roundoff across the whole range, which is the claim this site's own SVD has been making in a source comment since it was written and had never measured.

Each point is one bidiagonal matrix and the worst relative error any of its singular values suffers, measured against a Sturm bisection in exact rationals. The route through BᵀB is as good as anything at 2.1 decades — 3.63·10⁻¹⁴ — and by 11 decades it is at 14.5, which is not an error in the answer, it is the answer. One-sided Jacobi and the zero-shift bidiagonal sweep are flat at about the unit roundoff across the whole range, which is the claim this site's own SVD has been making in a source comment since it was written and had never measured.

Each point is one bidiagonal matrix and the worst relative error any of its singular values suffers, measured against a Sturm bisection in exact rationals. The route through BᵀB is as good as anything at 1.5 decades — 6.79·10⁻¹⁵ — and by 11 decades it is at 55.4, which is not an error in the answer, it is the answer. One-sided Jacobi and the zero-shift bidiagonal sweep are flat at about the unit roundoff across the whole range, which is the claim this site's own SVD has been making in a source comment since it was written and had never measured.

Each point is one bidiagonal matrix and the worst relative error any of its singular values suffers, measured against a Sturm bisection in exact rationals. The route through BᵀB is as good as anything at 3.3 decades — 9.14·10⁻¹³ — and by 10 decades it is at 2.02, which is not an error in the answer, it is the answer. One-sided Jacobi and the zero-shift bidiagonal sweep are flat at about the unit roundoff across the whole range, which is the claim this site's own SVD has been making in a source comment since it was written and had never measured.

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.

40 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.

It draws a decomposition and prints its residual. It calls gradingSweep, 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 113 of 219 generators — 98 print a residual and 15 are exempt with a published reason; 106 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.