speed up the calculation for a larger set of parameters
The time taken for non-linear least squares scales as the square of the number of residuals and as the square of the number of fitted parameters. Back in the days of mainframe computers that occupied an entire room and had 1/10000th of the processing power of my current smart phone, I ran some least squares optimizations that took two days to converge. So the length of time it takes to solve a "large" problem hasn't changed, just the definition of "large" has 
Richard Jackson wrote:
speed up the calculation for a larger set of parameters
The time taken for non-linear least squares scales as the square of the number of residuals and as the square of the number of fitted parameters.
As I understand it Chih-Yu Jen will have 25 to be fitted parameters und a residual vector of approx. 1500 elements (or 3000 if real and imaginary parts are stacked as per your suggestion). Every try with a set of different parameters TT will have to call a function make_Theory(TT) which returns a vector of 1500 complex numbers. The method to gain those values is rather complex and would involve creating and multiplying 25 2x2 matrices for every single value of that vector. Some methods how are in this post http://communities.ptc.com/message/211040#211040 and the following (which is more compact, maybe a bit faster and has two errors (m-->M, n-->TT)).
So I think that speeding up make_Theory(TT) would help in speeding up the overall calculation.
Back in the days of mainframe computers that occupied an entire room and had 1/10000th of the processing power of my current smart phone, I ran some least squares optimizations that took two days to converge.
You are showing your age 
But two days would be fine, in a prior post in this thread, when Chih-Yu Jen sent some information about calc time with fewer parameters and smaller residual vector, I made an estimation that the calculation with the real values would take up three weeks or 5 and ahalf days with a minor improvement of mine. Not sure if that would have been true - think he didn't bother trying. Guess he will let us know how speedy we got in the meantime.
Hi Werner:
I would like to thank you and Richard of helping me the coding.
Now I am trying to find constraints for a better approach.
I haven't tried the stack idea and still use the equation containing absolute value.
For 13 TTs 100 elements, each run takes 10-20mins.
Double the element will double the time.
However, double TTs take much long time.
In the next few days I will try 25 TTs 100 elements and then 25 TTs 1500 elements to check the calculation time.
I will let you know how many day(s)
it will take.
In the future I believe I still have questions to ask.
In here I want to thank again your great help.
Square, not square root. If 13/100 takes 10 to 20 minutes, I expect 13/200 to take 40 to 80 minutes. 25/1500 I expect to take 14 to 28 hours. That's less than two days though
Richard Jackson wrote:
Square, not square root.
Oh yes, my fault. Was too quick in reading your second post about calc time.
If 13/100 takes 10 to 20 minutes, I expect 13/200 to take 40 to 80 minutes. 25/1500 I expect to take 14 to 28 hours. That's less than two days though
Hmm, something wrong with the following calculations? And those are the minimum values based on 13/100 -> 10 minutes.
Or, as an estimation: doubling the number (either TT or N) means calc time times four. 25 is approx 13 doubled and 1500 is approx 100 doubled four times. So in total we have numbers doubled five time. So we have to calculate 10 minutes times 4^5 which results in somewhat more than 7 days (that would be 26/1600).
and as of the other post - yes, I know that I'm showing my age. Not in the wheelchair, too, but maybe close 😉
Hmm, something wrong with my calculations here?
My mistake. I calculated the factor, but forgot to multiply by the 10 minutes. I did it on a calculator, so I guess it's a good example of why one should use Mathcad, not a pocket calculator! With the correct calculation I get 5.8 days. Ouch! Time to buy either a much faster computer, or a UPS!
Not in the wheelchair, too, but maybe close 😉
If the time comes, keep on rollin'. As long as the mind works, life has many rewards. Anyone that disagrees can go argue the point with Stephen Hawking 
Ouch! Time to buy either a much faster computer, or a UPS!
The latter would be handy in any case. A better algorithm, our in our case here, a better way to calculate vector Theory could be worth more than a machine four times as fast.
If the time comes, keep on rollin'. As long as the mind works, life has many rewards. Anyone that disagrees can go argue the point with Stephen Hawking
good point!
You are showing your age
I think I will make the observation that computing power has advanced extremely rapidly. The PC was only invented just over 30 years ago, and at that time, and for many years afterwards, had such limited processing power that serious computing was still in the domain of mainframes. I'm not in a wheelchair quite yet
I'm not in a wheelchair quite yet
Glad to hear that!
Students priority was rather low at university and I remember using punched cards and having to wait for the next day to get the printed output - unimaginable nowadays to wait a day for "Hello world!". And then the first time being privileged and allowed to use a terminal - what incredible comfort. Seems like things have changed a bit in the meantime.
Punched cards? You are showing your age . I started out with paper tapes, a huge advance over those primitive cards! I always had terminal access though (but it was a teleprinter to begin with, not a fancy CRT terminal), and only used the tapes for data transfer. I had to walk halfway across the university campus to drop them off at central computing, and I could access the data the next day. Now I can access data on the other side of the world in seconds, using a phone! Things have changed more than a bit, and in such a short time that even as a technophile it blows my mind!
