one-trade

At its defaults it draws three tolerances from three fields: work not done, against backward error accepted. A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.051, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

one-trade is one function in lib/figures/tolerance.js — tolerances — the zeros nobody meets and everybody writes. 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.

A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.051, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.051, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.188, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.057, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.040, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

A deflation criterion writes a zero into a subdiagonal entry of a Hessenberg matrix; a drop tolerance discards an entry of an incomplete Cholesky factor; a truncation discards a singular value. The three are described in different vocabularies, live in different fields and share no arithmetic. Plotted as the fraction of the work not done against the relative backward error the choice introduces, they are three samples of one curve: fitted slopes of 0.039, 0.054, 0.225 of the work a decade of error. Nothing is rescaled to make that happen. The low-rank curve goes below zero at the tight end, which is the part nobody plots: a rank-k factored form of an n×n symmetric matrix costs more to store than the matrix once k passes n/2.

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.

9 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 oneTrade, 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.