eig2
std.linalg.eig2 · Level L2The eigenvalues of a real 2×2 matrix, symmetric or not: the roots of λ² − tr(M)·λ + det(M) = 0, through quadratic_roots. A complex pair is λ ± i·imag, and imag = 0 for real eigenvalues.
λ² − tr(M)λ + det(M) = 0
Signature
eig2(M: f64[2, 2]) → 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.
- Agrees with the reference
roots of λ² − tr·λ + det, in quadratic_roots' orderto 80 digits (100-digit arithmetic), on all 40 test cases. - All 120 float64 results inside the running error bound; the closest uses 31% 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 24% of it.
Accuracy in detail
- correctly rounded (the float64 nearest the exact value)
- 86%
- bit-equal to the NumPy formula in float64
- 82%
- largest error, in units in the last place
- 5.64
Identity
sha256:5544ccff3e54595455732846b1ffd5fa20770e891d28921cb38010998bcd7997The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.linalg.eig2 · Ω:eig2
- Pins
sha256:29ab9a79ea1a0aeeeb83d4b3e16d537cf8792c574802822f418af756febadf2fthis graph and the 1 it reaches through calls- Evidence
sha256:87e6da9d5851ecdba08e546d268e3aeba1ea6a8bd4771ce8a6b72166b09d1284the 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.