It could even be quite interesting to compare E@H to other supercomputers working in the same field of astronomy at AEI/MPG ie. the other assets available to researchers there. Here is a short precis of the contenders. It's clearly horses for courses I think. Note that E@H is a rather plastic proposition as its compute elements are always altering, generally in the direction of upgrading, so it has evolved over time.
BTW the E@H workunits are not solving linear systems of equations in the traditional sense, but still use linear algebraic methods (a fine distinction perhaps) to effect a linear transformation (in our case from the time domain to frequency domain). The relationship b/w the Fourier matrices F2n and Fn is a gorgeous one provided you're happy with complex numbers, as matrices with all real entries can have complex eigenvalues! Now these matrices can be broken down into parts with lots of zero entries: Fourier perhaps didn't credit this but Gauss certainly did. Cooley & Tukey around 1965 triggered a revolution which gave us the FFT we use today. Anyhow the upshot is that FFTs are revved up DFTs and so one is comparing the (order of) the speed of N2 vs N*log(N), the latter winning hands down when N = 222.
Cheers, Mike.
(edit) Try doing 244 operations rather than 222*log(222). You see log(222) ~ 6.6 ~ 8 = 23 and so N2/[N*logN] = N/logN = 222/23 = 222-3 = 219 or around 500,000 times slower than the FFT, more or less. And you may have thought that some E@H workunits were slow to finish! Many problems in physics would be insoluble if not for this aspect.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
It could even be quite
)
It could even be quite interesting to compare E@H to other supercomputers working in the same field of astronomy at AEI/MPG ie. the other assets available to researchers there. Here is a short precis of the contenders. It's clearly horses for courses I think. Note that E@H is a rather plastic proposition as its compute elements are always altering, generally in the direction of upgrading, so it has evolved over time.
BTW the E@H workunits are not solving linear systems of equations in the traditional sense, but still use linear algebraic methods (a fine distinction perhaps) to effect a linear transformation (in our case from the time domain to frequency domain). The relationship b/w the Fourier matrices F2n and Fn is a gorgeous one provided you're happy with complex numbers, as matrices with all real entries can have complex eigenvalues! Now these matrices can be broken down into parts with lots of zero entries: Fourier perhaps didn't credit this but Gauss certainly did. Cooley & Tukey around 1965 triggered a revolution which gave us the FFT we use today. Anyhow the upshot is that FFTs are revved up DFTs and so one is comparing the (order of) the speed of N2 vs N*log(N), the latter winning hands down when N = 222.
Cheers, Mike.
(edit) Try doing 244 operations rather than 222*log(222). You see log(222) ~ 6.6 ~ 8 = 23 and so N2/[N*logN] = N/logN = 222/23 = 222-3 = 219 or around 500,000 times slower than the FFT, more or less. And you may have thought that some E@H workunits were slow to finish! Many problems in physics would be insoluble if not for this aspect.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal