cond2

std.linalg.cond2 · Level L4

The condition number of A in the 2-norm, largest over smallest singular value: how much A can amplify a relative error.

κ₂(A) = σ₁/σₙ

Signature

cond2(A: f64[n+k, n]) → 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.

Af64[n+k, n]SVDValuessReduceMaxhiReduceMinloDividecondcondf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.cond(A) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 9% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
25%
bit-equal to the NumPy formula in float64
48%
largest error, in units in the last place
7.49

Identity

Calls
—
Called by
—
sha256:5a0323ad4df40af9aeda7892a28d27b79f69a9946a6d239583b4f4ea254fcbe7

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

Control handle

Symbol
Ω:std.linalg.cond2 · Ω:cond2
Pins
sha256:03b531db5c50af667c4b80f1db6d612d4d4a26cb0d0550410846bebe2fd41bc5this graph alone
Evidence
sha256:3c40bf267abe321ea517e6e704ee5f5b1d5ebf4186572cdf1292a7e6d537aa4athe 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.