Continuing drama
I think today I had a decisive breakthrough in battle with my continuation problem. There's still some mopping-up to do, and an interesting discrepancy, but in principle, things may finally be working. Three ideas led to today's victory:
Oh yes. Imagine you have a black box sitting in front of you, with a knob and a gauge. Continuation, in simple terms, involves twiddling the knob, and writing down how the value shown on the gauge moves. Sometimes this is linear (a 10% move of the knob gives a 10% change in value), but for "fun" black boxes, that's not the cases.
- If Y is a function of X (and is monotone, and continuous), then X is a function of Y too. Sometimes, it's easier to hunt for X given Y than for Y given X.
- If you're looking for a small parameter (or one close to 1), try looking for its logarithm instead. Moving from 0.001 to 0.0001 can be problematic, while moving from 3 to 4 is straight-forward.
- Nothing beats having the answer already in hand. It's worth investing time in finding a good initial condition.
- Bonus software engineering lesson: Structure your code right. A clear interface between sections makes it easier to try these things out, and more likely that you'll be home on time for dinner.
Oh yes. Imagine you have a black box sitting in front of you, with a knob and a gauge. Continuation, in simple terms, involves twiddling the knob, and writing down how the value shown on the gauge moves. Sometimes this is linear (a 10% move of the knob gives a 10% change in value), but for "fun" black boxes, that's not the cases.