func TestNoiseMultiplierConvention(t *testing.T) · hand computed closed form epsilon(alpha)

Read the equation

This relation defines hand computed closed form epsilon(alpha) in the source section “func TestNoiseMultiplierConvention(t *testing.T) · hand computed closed form epsilon(alpha)”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read hand computed closed form epsilon(alpha) as the quantity being defined or updated by this relation.

2. Uses logarithmic scaling; its base and the positivity of its argument matter.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

	}
	if !almostEqual(a.noiseMultiplier(), 2, 1e-12) {
		t.Fatalf("noise multiplier = %v, want 2", a.noiseMultiplier())
	}
}

// TestRDPToEpsilonConversionClosedForm pins the RDP to (epsilon, delta) conversion at one order against the
// hand computed closed form epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1).
func TestRDPToEpsilonConversionClosedForm(t *testing.T) {
	// rdp=0.25 at alpha=2, delta=1e-5: 0.25 + ln(1e5) / 1 = 0.25 + 11.512925465 = 11.762925465.
	got := epsilonAtOrder(0.25, 2, 1e-5)
	want := 0.25 + math.Log(1/1e-5)/(2-1)
	if !almostEqual(got, want, 1e-12) {
		t.Fatalf("epsilonAtOrder(0.25, 2, 1e-5) = %v, want %v", got, want)
	}
	// A second independent point: rdp=5 at alpha=10, delta=1e-6: 5 + ln(1e6)/9.
	got2 := epsilonAtOrder(5, 10, 1e-6)
	want2 := 5 + math.Log(1/1e-6)/(10-1)

hand computed closed form epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1).

Related builds