outer

std.linalg.outer · Level L0

Outer product: every product xᵢ·yⱼ, by broadcasting. Exact up to one rounding per entry.

(x ⊗ y)ᵢⱼ = xᵢ·yⱼ

Signature

outer(x: f64[m], y: f64[n]) → f64[m, n]

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.

xf64[m]yf64[n]ReshapexcReshapeyrMultiplyOOf64[m, n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.outer(x, y) in exact rational arithmetic, on all 40 test cases.
  • All 560 float64 results inside the running error bound; the closest uses 91% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
100%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.50

Identity

Calls
—
Called by
—
sha256:6c4c5b135f409814541b330ebfb605527159f3f381a96d38875bf9d3427be0b7

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.outer · Ω:outer
Pins
sha256:7632a33f83f007825a44c8dbabb1b1f48f3f1ddf5543cde264a62127f67e3775this graph alone
Evidence
sha256:3c05920a9ea45b750862aa2fe13e00896ae3b8ab7aa4ab2456bfa6bfdde93cf3the 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.