vandermonde
std.linalg.vandermonde · Level L2The Vandermonde matrix with decreasing powers, Vᵢⱼ = xᵢ^(p−1−j), p the length of k (only its length is read): V·c evaluates the polynomial c, highest degree first, at every x. NumPy's np.vander(x, p). Each power is the previous one times x, by a reverse Scan of vandermonde_step.
Signature
vandermonde(x: f64[m], k: f64[p]) → f64[m, p]
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
np.vander(x, p)in exact rational arithmetic, on all 40 test cases. - All 558 float64 results inside the running error bound; the closest uses 83% of it.
- Interpreter and NumPy backend return bit-identical results.
- At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 97% of it.
- correctly rounded (the float64 nearest the exact value)
- 84%
- bit-equal to the NumPy formula in float64
- 100%
- largest error, in units in the last place
- 1.96
Identity
sha256:ae3207d3a668ed16a35c04ab59d42f6a7b199a2b5d46c1459ffa292387899beaThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.linalg.vandermonde · Ω:vandermonde
- Pins
sha256:4a084ef7b50be6efc7efc9df9c90d0231334f080672dcddfbf6c38bc565c9e83this graph and the 1 it reaches through calls- Evidence
sha256:fc8c44ca94ed5ea2c5310fe0dddf498701f40ddf3836f30a1080936dbcb4f25fthe 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.