%======================================================================

%                    V E C _ C O H E R E N C E . M 

%                    doc: Wed Aug  8 09:01:59 2012

%                    dlm: Wed Aug  8 10:19:53 2012

%                    (c) 2012 A.M. Thurnherr

%                    uE-Info: 58 27 NIL 0 0 72 10 2 4 NIL ofnI

%======================================================================

% calculate coherence between two 2-D vector time-series or profiles

%	- time or space is coded in 1st vector dimension

%	- code based on [ladcp_cohere.m] by X. Liang

%	- XL had hard-coded nsegs=4

function coh = vec_coherence(v1,v2,nsegs,conf)

valid = find(isfinite(v1(:,2)));

v1 = v1(find(isfinite(v1(:,2))),:);

v2 = v2(find(isfinite(v2(:,2))),:);

rez1 = median(diff(v1(:,1)));

rez2 = median(diff(v2(:,1)));

if (rez1 ~= rez2)

	error('incompatible vector resolutions');

end

first = max(min(v1(:,1)),min(v2(:,1)));

last  = min(max(v1(:,1)),max(v2(:,1)));

cv1 = v1(find(v1(:,1)>=first&v1(:,1)<=last),2) + sqrt(-1)*v1(find(v1(:,1)>=first&v1(:,1)<=last),3);

cv2 = v2(find(v2(:,1)>=first&v2(:,1)<=last),2) + sqrt(-1)*v2(find(v2(:,1)>=first&v2(:,1)<=last),3);

if (length(cv1) ~= length(cv2))

	error('incompatible vectors');

end

NFFT = floor(length(cv1)/nsegs) ;						% segment data

freq = -1/(2*rez1):1/((NFFT-1)*rez1):1/(2*rez1);		% spectral frequencies

coh.conf = conf;

coh.clim = sqrt(1-(1-conf)^(1/(nsegs-1)));				% Confidence limit (Data analysis methods in physical oceanography, p488)

s1 = fftshift(fft(cv1,NFFT));							% power spectra

s2 = fftshift(fft(cv2,NFFT));

s12 = conj(s1).*s2;  %Inner-cross spectrum				% cross spectra

s21 = fliplr(s1).*s2; %outer-cross spectrum

s11 = abs(s1).^2;

s22 = abs(s2).^2;

for i = 1:NFFT/nsegs									% frequency-average spectra

	as12(i) = mean(s12((i-1)*nsegs+1:i*nsegs));

	as21(i) = mean(s21((i-1)*nsegs+1:i*nsegs));

	as11(i) = mean(s11((i-1)*nsegs+1:i*nsegs));

	as22(i) = mean(s22((i-1)*nsegs+1:i*nsegs));

	coh.freq(i) = mean(freq((i-1)*nsegs+1:i*nsegs));

end

coh.period = 1 ./ coh.freq;

coh.mag   = sqrt(abs(as12).^2./(as11.*as22));

coh.phase = atan2(-imag(as12),real(as12))*(180/pi);

figure

subplot(211)

plot(coh.freq,coh.mag)

hold on

line([coh.freq(1) coh.freq(end)],[coh.clim coh.clim],'color','r')

xlim([coh.freq(1) coh.freq(end)])

xlabel('Frequency/Wavenumber [cycles/unit]')

ylabel('Inner Rotary Coherence')

grid on

text(coh.freq(fix(0.8*length(coh.freq))), coh.clim+0.05, sprintf('%d%%',100*coh.conf));

subplot(212)

plot(coh.freq,coh.phase)

xlim([coh.freq(1) coh.freq(end)])

ylim([-180 180])

xlabel('Frequency/Wavenumber [cycles/unit]')

ylabel('Phase angle [deg]')

grid on