## [4ad237]: inst / lsreal.m  Maximize  Restore  History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79``` ```## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{transform} =} lsreal (@var{time}, @var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctaves}) ## ## Return the real least-squares transform of the time series ## defined, based on the maximal frequency @var{maxfreq}, the ## number of coefficients @var{numcoeff}, and the number of ## octaves @var{numoctaves}. Each complex-valued result is the ## pair (c_o, s_o) defining the coefficients which best fit the ## function y = c_o * cos(ot) + s_o * sin(ot) to the (@var{time}, @var{mag}) data. ## ## @seealso{lscomplex} ## @end deftypefn function transform = lsreal (t, x, omegamax, ncoeff, noctave) ## FIXME : THIS IS VECTOR-ONLY. I'd need to add another bit of code to ## make it array-safe, and that's not knowing right now what else ## will be necessary. k = n = length (t); transform = zeros (1, (noctave * ncoeff)); od = 2 ^ (- 1 / ncoeff); o = omegamax; n1 = 1 / n; ncoeffp = ncoeff * noctave; for iter = 1:ncoeffp ## This method is an application of Eq. 8 on ## page 6 of the text, as well as Eq. 7 ot = o .* t; zeta = n1 * sum ((cos (ot) - i * sin (ot)) .* x); ot *= 2; iota = n1 * sum (cos (ot) - i * sin (ot)); transform(iter) = (2 * (conj (zeta) - (conj (iota) * zeta)) / (1 - (real (iota) ^ 2) - (imag (iota) ^ 2))); o *= od; endfor endfunction %!test %! maxfreq = 4 / ( 2 * pi ); %! t = linspace(0,8); %! x = ( 2 .* sin ( maxfreq .* t ) + %! 3 .* sin ( (3/4) * maxfreq .* t ) - %! 0.5 .* sin ( (1/4) * maxfreq .* t ) - %! 0.2 .* cos ( maxfreq .* t ) + %! cos ( (1/4) * maxfreq .* t ) ); %! # In the assert here, I've got an error bound large enough to catch %! # individual system errors which would present no real issue. %! assert (lsreal (t,x,maxfreq,2,2), %! [(-1.68275915310663 + 4.70126183846743i), ... %! (1.93821553170889 + 4.95660209883437i), ... %! (4.38145452686697 + 2.14403733658600i), ... %! (5.27425332281147 - 0.73933440226597i)], %! 5e-10) ```