fourier_info with small numbers

Hi NCL,

I just discovered that fourier_info has some sensitivity to the magnitude of the input data. The issue is that the "variance explained" becomes exactly zero if the input data is sufficiently small. The amplitude and phase don't seem affected, so I think this might just be a bug (maybe going from correlation coefficient to percent variance explained?). The switch to zero happens for the same value of the input to fourier_info regardless of it being single or double precision. Here is a minimal script that shows the drop off to zero when the amplitude of the input reaches 10^-4 (this works on at least two systems of different architecture, using NCL 6.2.0 or 6.1.2):

; test fourier_info precision sensitivity
pi = 4.*atan(1.)
F = 1. ; FREQUENCY
P = pi/4. ; PHASE
x = fspan( 0., 2.*pi, 50)
E0 = 4 ; exponent parameter starting value
do i = 0,10
  A = 10. * 10.^(E0-i) ; AMPLITUDE ... increment down by iteration
  s = A*sin( F*x + P) ; pure sine wave
  fi = fourier_info( s, 0, 1.)
  print("[INPUT AMPLITUDE: "+sprintf("%4.2e",A)+"] A: " + sprintf( "%4.2e",fi(0,0))+", P: "+ fi(1,0) + " VARIANCE EXPLAINED: " + fi(2,0) )
end do

Here's my output:
(0) [INPUT AMPLITUDE: 1.00e+05] A: 9.99e+04, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e+04] A: 9.99e+03, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e+03] A: 9.99e+02, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e+02] A: 9.99e+01, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e+01] A: 9.99e+00, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e+00] A: 9.99e-01, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e-01] A: 9.99e-02, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e-02] A: 9.99e-03, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e-03] A: 9.99e-04, P: 5.6694 VARIANCE EXPLAINED: 99.9134
(0) [INPUT AMPLITUDE: 1.00e-04] A: 9.99e-05, P: 5.6694 VARIANCE EXPLAINED: 0
(0) [INPUT AMPLITUDE: 1.00e-05] A: 9.99e-06, P: 5.6694 VARIANCE EXPLAINED: 0

If this isn't a bug, I'd be interested to hear an explanation for this behavior.

thanks,

.brian

_______________
Brian Medeiros
Project Scientist
NCAR/NESL/CGD/AMP
brianpm@ucar.edu
http://www.cgd.ucar.edu/~brianpm

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Received on Wed Jul 31 15:17:00 2013