cosine_similarity

std.linalg.cosine_similarity · Level L1

Cosine of the angle between two non-zero vectors. Calls dot and norm.

x·y / (‖x‖·‖y‖)

Signature

cosine_similarity(x: f64[n], y: f64[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.

xf64[n]yf64[n]normnxnormnydotxyMultiplydenDivideccf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference x @ y / (np.linalg.norm(x) * np.linalg.norm(y)) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 35% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
53%
bit-equal to the NumPy formula in float64
95%
largest error, in units in the last place
3.07

Identity

Calls
dotnorm
Called by
—
sha256:064f169f0f5179cf458716e0bf2c6921c49e40cb001a3c2f68457a7e14f4a76e

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.cosine_similarity · Ω:cosine_similarity
Pins
sha256:666f0e98aff80f32aef4a966d57805297dd53bb7ecfa085949c9d2bf819a6b3bthis graph and the 3 it reaches through calls
Evidence
sha256:78a996bd7736386f1950fed8a8ed874b56646c81bf1e523691e2b2dca13fcb45the 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.