## Nitpicker! [Two-Stage / GS Designs]

Hi again,

» (...) I don’t get the point of initializing a large vector of values and later picking out the suitable one.

The secant method is terrible if the initial guess is wrong. Terrible as in, converges to plus/minus infinity and will give errors, so it isn't a matter of many iterations.

What the code above does: The n'th CV is probably going to be not so far from the (n-1)'th CV, and therefore it is a good guess. Therefore, if we only guess one CV reasonably (the 6th) then we get the corresponding 6'th critical CV, and from that point and onwards we can use the previously generated critical CV as the guess, i.e. when we want the 7'th value we use the 6th value as a guess, and so on. That's how these lines seem to work very fast.

You can also play around with regula falsi or whatever the heck Wikipedia calls it:

It is a little faster than bisection and does not require a good guess apart from the above. It is stable for power here since the power does not misbehave within any CV-interval of interest; there are no minima or maxima or things that can screw it badly up

» (...) I don’t get the point of initializing a large vector of values and later picking out the suitable one.

The secant method is terrible if the initial guess is wrong. Terrible as in, converges to plus/minus infinity and will give errors, so it isn't a matter of many iterations.

What the code above does: The n'th CV is probably going to be not so far from the (n-1)'th CV, and therefore it is a good guess. Therefore, if we only guess one CV reasonably (the 6th) then we get the corresponding 6'th critical CV, and from that point and onwards we can use the previously generated critical CV as the guess, i.e. when we want the 7'th value we use the 6th value as a guess, and so on. That's how these lines seem to work very fast.

You can also play around with regula falsi or whatever the heck Wikipedia calls it:

```
FindCritCV.rf=function(Pwr.T, GMR, Nps, Is.St2=1, toler=0.000001)
```

{

CV1=0.0123

CV2=8.7654

Iter=0

while (abs(CV1-CV2)>toler)

{

p1=Power.calc(Nps, GMR, CV1, Is.St2)-Pwr.T

p2=Power.calc(Nps, GMR, CV2, Is.St2)-Pwr.T

Iter=Iter+1

CV3=CV2-p2*((CV2-CV1)/(p2-p1))

##cat("Noi=", Noi, "\n")

tmp=Power.calc(Nps, GMR, CV3, Is.St2) -Pwr.T

if (tmp<0) CV2=CV3

else CV1=CV3

cat("CV1=", CV1, "CV2=", CV2, "dCV=", abs(CV2-CV1), "\n")

}

##cat("Iterations RF:", Iter,"\n")

return(0.5*(CV2+CV1) )

}

It is a little faster than bisection and does not require a good guess apart from the above. It is stable for power here since the power does not misbehave within any CV-interval of interest; there are no minima or maxima or things that can screw it badly up

—

I could be wrong, but...

Best regards,

ElMaestro

I could be wrong, but...

Best regards,

ElMaestro

### Complete thread:

- Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 15:04
- Initial sample size guess for the Potvin methods Helmut 2017-08-19 16:06
- Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 16:14
- Initial sample size guess for the Potvin methods Helmut 2017-08-19 17:12
- Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 17:17
- Confuse-a-Cat Helmut 2017-08-19 17:33
- Confuse-a-Cat ElMaestro 2017-08-19 17:56

- Confuse-a-Cat Helmut 2017-08-19 17:33

- Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 17:17
- loop ↔ vectorized ↔ direct Helmut 2017-08-20 14:40
- loop ↔ vectorized ↔ direct ElMaestro 2017-08-20 15:22
- loop ↔ vectorized ↔ direct Helmut 2017-08-20 16:23
- loop ↔ vectorized ↔ direct ElMaestro 2017-08-20 17:22

- loop ↔ vectorized ↔ direct Helmut 2017-08-20 16:23

- loop ↔ vectorized ↔ direct ElMaestro 2017-08-20 15:22

- Initial sample size guess for the Potvin methods Helmut 2017-08-19 17:12

- Initial sample size guess for the Potvin methods ElMaestro 2017-08-19 16:14
- The n ext crackpot iteration ElMaestro 2017-08-19 20:04
- The n ext crackpot iteration Helmut 2017-08-20 02:20

- The ultimate crackpot iteration! ElMaestro 2017-08-20 14:35
- The ultimate crackpot iteration! Helmut 2017-08-20 15:11
- The ultimate crackpot iteration! ElMaestro 2017-08-20 15:28
- The ultimate crackpot iteration! Helmut 2017-08-20 16:06
- The ultimate crackpot iteration! ElMaestro 2017-08-20 16:15
- The ultimate crackpot iteration! Helmut 2017-08-20 18:58
- The ultimate crackpot iteration! ElMaestro 2017-08-20 19:32
- Suggested code ElMaestro 2017-08-21 18:13
- Nitpicker! Helmut 2017-08-22 13:33
- Nitpicker! ElMaestro 2017-08-22 17:27
- Nitpicker! Helmut 2017-08-22 17:49
- Nitpicker!ElMaestro 2017-08-22 17:59
- Nitpicker! Helmut 2017-08-22 19:15
- Benchmark code ElMaestro 2017-08-22 22:29
- Benchmark code Helmut 2017-08-23 01:48

- Benchmark code ElMaestro 2017-08-22 22:29

- Nitpicker! Helmut 2017-08-22 19:15

- Nitpicker!ElMaestro 2017-08-22 17:59

- Nitpicker! Helmut 2017-08-22 17:49

- Nitpicker! ElMaestro 2017-08-22 17:27

- Nitpicker! Helmut 2017-08-22 13:33

- Suggested code ElMaestro 2017-08-21 18:13

- The ultimate crackpot iteration! ElMaestro 2017-08-20 19:32

- The ultimate crackpot iteration! Helmut 2017-08-20 18:58

- The ultimate crackpot iteration! ElMaestro 2017-08-20 16:15

- The ultimate crackpot iteration! Helmut 2017-08-20 16:06

- The ultimate crackpot iteration! ElMaestro 2017-08-20 15:28

- The ultimate crackpot iteration! Helmut 2017-08-20 15:11

- Initial sample size guess for the Potvin methods Helmut 2017-08-19 16:06