routing: apply capacity factor

We multiply the apriori probability with a factor to take capacity into
account:

P *= 1 - 1 / [1 + exp(-(amount - cutoff)/smearing)]

The factor is a function value between 1 (small amount) and 0 (high
amount). The zero limit may not be reached exactly depending on the
smearing and cutoff combination. The function is a logistic function
mirrored about the y-axis. The cutoff determines the amount at which a
significant reduction in probability takes place and the smearing
parameter defines how smooth the transition from 1 to 0 is. Both, the
cutoff and smearing parameters are defined in terms of fixed fractions
of the capacity.

routing/missioncontrol_test.go

@@ -113,9 +113,12 @@ func (ctx *mcTestContext) expectP(amt lnwire.MilliSatoshi, expected float64) {
 	ctx.t.Helper()
 
 	p := ctx.mc.GetProbability(mcTestNode1, mcTestNode2, amt, testCapacity)
-	if p != expected {
-		ctx.t.Fatalf("expected probability %v but got %v", expected, p)
-	}
+
+	// We relax the accuracy for the probability check because of the
+	// capacity cutoff factor.
+	require.InDelta(
+		ctx.t, expected, p, 0.001, "probability does not match",
+	)
 }
 
 // reportFailure reports a failure by using a test route.