convex_quadratic_on_interval

std.optim.convex_quadratic_on_interval · Level L1

Minimizing f(x) = A·x² + B·x + C over a closed interval [lo, hi]: whether f is convex there (A ≥ 0, which makes the problem a convex optimization problem, the interval being convex), as 1 or 0; a minimizer, the vertex −B/(2A) clipped to the interval when A > 0, otherwise the better endpoint (the first, lo, on a tie); and the minimum value. Comparing two feasible points, or one Jensen instance, decides nothing in general; the global answer here comes from the closed form.

argmin_{[lo,hi]} Ax² + Bx + C

Signature

convex_quadratic_on_interval(A: f64[], B: f64[], C: f64[], lo: f64[], hi: f64[]) → f64[], f64[], f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the vertex or the endpoints, in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 120 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:403434335acaa07b721a15d117c5a08f1e6b19ed0fa930230e04c6a5f7a59a3a

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.optim.convex_quadratic_on_interval · Ω:convex_quadratic_on_interval
Pins: sha256:a5c61c1ad711d139a44b82b8d8bb6be5e0feec24d0b93dc43cea9896202e3299this graph alone
Evidence: sha256:5d33d2b6ea2d389dc191d378fa5e735cad919ccd40bf72741b2341a771470102the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.