Historical note: the FFT algorithm was originally discovered by Carl Friedrich Gauss in 1866 (though not published), not by Cooley & Tukey in 1965 as is often stated. Cooley & Tukey rediscovered it independently, unaware of Gauss's work.
Gauss, Carl Friedrich <https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss> (1866). "Theoria interpolationis methodo nova tractata" [Theory regarding a new method of interpolation]. *Nachlass* <https://babel.hathitrust.org/cgi/pt?id=uc1.c2857678;view=1up;seq=279> (Unpublished manuscript). Werke (in Latin and German). *3*. Göttingen, Germany: Königlichen Gesellschaft der Wissenschaften zu Göttingen. pp. 265–303. Cooley, James W. <https://en.wikipedia.org/wiki/James_Cooley>; Tukey, John W. <https://en.wikipedia.org/wiki/John_Tukey> (1965). "An algorithm for the machine calculation of complex Fourier series" <http://www.ams.org/mcom/1965-19-090/S0025-5718-1965-0178586-1/>. *Mathematics of Computation <https://en.wikipedia.org/wiki/Mathematics_of_Computation>*. *19* (90): 297–301. Cooley, James W. <https://en.wikipedia.org/wiki/James_W._Cooley> (1987). *The Re-Discovery of the Fast Fourier Transform Algorithm* <https://carma.newcastle.edu.au/jon/Preprints/Talks/CARMA-CE/FFT.pdf> (PDF). *Mikrochimica Acta*. *III*. Vienna, Austria. pp. 33–45. Cheers -- Ian On 19 April 2018 at 14:18, Ian Tickle <[email protected]> wrote: > > Correction: maps are produced by Refmac & FFT. Original references are: > > Read, R.J.: Acta Cryst. A42 (1986) 140-149 for map coefficients, and type > 'FFT' in Wikipedia for FFT algorithm & references. > > Cheers > > -- Ian > > > On 19 April 2018 at 13:57, Ian Tickle <[email protected]> wrote: > >> >> Hi, first maps are produced by Refmac, not Coot, and second it shouldn't >> be called sigma because it's not an uncertainty, it's a root-mean-square >> deviation from the mean. The equation for the RMSD can be found in any >> basic text on statistics, e.g. just type 'RMSD' in Wikipedia. >> >> Cheers >> >> -- Ian >> >> >> On 19 April 2018 at 13:20, Mohamed Ibrahim <[email protected]> >> wrote: >> >>> Dear COOT users, >>> >>> Do you know how to extract the equations that COOT uses for generating >>> the maps and calculating the sigma values? >>> >>> Best regards, >>> Mohamed >>> >>> -- >>> >>> -- >>> *----------------------------------* >>> *Mohamed Ibrahim * >>> >>> *Humboldt University * >>> *Berlin, Germany * >>> >>> *Tel: +49 30 209347931 * >>> >> >> >
