function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)
% Multi-taper cross-spectral matrix - another routine, allows for multiple trials and channels
% Does not do confidence intervals. Also this routine always averages over trials - continuous process
%
% Usage:
%
% [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)
% Input:
% Note units have to be consistent. See chronux.m for more information.
% data (in form samples x channels x trials)
% win (duration of non-overlapping window)
% params: structure with fields tapers, pad, Fs, fpass
% - optional
% tapers : precalculated tapers from dpss or in the one of the following
% forms:
% (1) A numeric vector [TW K] where TW is the
% time-bandwidth product and K is the number of
% tapers to be used (less than or equal to
% 2TW-1).
% (2) A numeric vector [W T p] where W is the
% bandwidth, T is the duration of the data and p
% is an integer such that 2TW-p tapers are used. In
% this form there is no default i.e. to specify
% the bandwidth, you have to specify T and p as
% well. Note that the units of W and T have to be
% consistent: if W is in Hz, T must be in seconds
% and vice versa. Note that these units must also
% be consistent with the units of params.Fs: W can
% be in Hz if and only if params.Fs is in Hz.
% The default is to use form 1 with TW=3 and K=5
%
% pad (padding factor for the FFT) - optional. Defaults to 0.
% e.g. For N = 500, if PAD = 0, we pad the FFT
% to 512 points; if PAD = 2, we pad the FFT
% to 2048 points, etc.
% Fs (sampling frequency) - optional. Default 1.
% fpass (frequency band to be used in the calculation in the form
% [fmin fmax])- optional.
% Default all frequencies between 0 and Fs/2
% Output:
% Sc (cross spectral matrix frequency x channels x channels)
% Cmat Coherence matrix frequency x channels x channels
% Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
% Cvec leading Eigenvector (frequency x channels)
% Cent A different measure of total coherence: GM/AM of SV^2s
% f (frequencies)
d=ndims(data);
if d<2, error('Need multidimensional array'); end
if d==2, [N,C]=size(data); end;
if d==3, [N,C,Ntr]=size(data); end;
if nargin < 3; params=[]; end;
[tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
clear err trialave params
nwin=round(win*Fs); nfft=max(2^(nextpow2(nwin)+pad),nwin);
[f,findx]=getfgrid(Fs,nfft,fpass);
tapers=dpsschk(tapers,nwin,Fs); % check tapers
Sc=zeros(length(findx),C,C);
Nwins=floor(N/nwin);
if d==3, % If there are multiple trials
for iwin=1:Nwins,
for i=1:Ntr,
data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:,i));
J1=mtfftc(detrend(data1),tapers,nfft,Fs);
J1=J1(findx,:,:);
for k=1:C,
for l=1:C,
spec=squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2));
Sc(:,k,l)=Sc(:,k,l)+spec;
end
end
end
end
Sc=Sc/(Nwins*Ntr);
end
if d==2, % only one trial
for iwin=1:Nwins,
data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:));
J1=mtfftc(data1,tapers,nfft,Fs);
J1=J1(findx,:,:);
for k=1:C,
for l=1:C,
Sc(:,k,l)=Sc(:,k,l)+squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2));
end
end
end
Sc=Sc/Nwins;
end
Cmat=Sc;
Sdiag=zeros(length(findx),C);
for k=1:C,
Sdiag(:,k)=squeeze(Sc(:,k,k));
end
for k=1:C,
for l=1:C,
Cmat(:,k,l)=Sc(:,k,l)./sqrt(abs(Sdiag(:,k).*Sdiag(:,l)));
end
end
Ctot=zeros(length(findx),1); Cent=Ctot;
Cvec=zeros(length(findx),C);
for i=1:length(findx),
[u s]=svd(squeeze(Sc(i,:,:)));s=diag(s);
Ctot(i)=s(1).^2/sum(s.^2); Cent(i)=exp(mean(log(s.^2)))/mean(s.^2);
Cvec(i,:)=transpose(u(:,1));
end