CrossSpecMatpb

 Multi-taper cross-spectral matrix - another routine, this one allows for multiple trials and channels 
 Does not do confidence intervals. 
 Also this routine always averages over trials - binned point process

 Usage:

 [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpb(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 (can take values -1,0,1,2...). 
                    -1 corresponds to no padding, 0 corresponds to padding
                    to the next highest power of 2 etc.
                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
                       to 512 points, if pad=1, we pad to 1024 points etc.
                       Defaults to 0.
           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)

0001 function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpb(data,win,params)
0002 %
0003 %
0004 % Multi-taper cross-spectral matrix - another routine, this one allows for multiple trials and channels
0005 % Does not do confidence intervals.
0006 % Also this routine always averages over trials - binned point process
0007 %
0008 % Usage:
0009 %
0010 % [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatpb(data,win,params)
0011 % Input:
0012 % Note units have to be consistent. See chronux.m for more information.
0013 %       data (in form samples x channels x trials)
0014 %       win  (duration of non-overlapping window)
0015 %       params: structure with fields tapers, pad, Fs, fpass
0016 %       - optional
0017 %           tapers : precalculated tapers from dpss or in the one of the following
0018 %                    forms:
0019 %                    (1) A numeric vector [TW K] where TW is the
0020 %                        time-bandwidth product and K is the number of
0021 %                        tapers to be used (less than or equal to
0022 %                        2TW-1).
0023 %                    (2) A numeric vector [W T p] where W is the
0024 %                        bandwidth, T is the duration of the data and p
0025 %                        is an integer such that 2TW-p tapers are used. In
0026 %                        this form there is no default i.e. to specify
0027 %                        the bandwidth, you have to specify T and p as
0028 %                        well. Note that the units of W and T have to be
0029 %                        consistent: if W is in Hz, T must be in seconds
0030 %                        and vice versa. Note that these units must also
0031 %                        be consistent with the units of params.Fs: W can
0032 %                        be in Hz if and only if params.Fs is in Hz.
0033 %                        The default is to use form 1 with TW=3 and K=5
0034 %
0035 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
0036 %                    -1 corresponds to no padding, 0 corresponds to padding
0037 %                    to the next highest power of 2 etc.
0038 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
0039 %                       to 512 points, if pad=1, we pad to 1024 points etc.
0040 %                       Defaults to 0.
0041 %           Fs   (sampling frequency) - optional. Default 1.
0042 %           fpass    (frequency band to be used in the calculation in the form
0043 %                                   [fmin fmax])- optional.
0044 %                                   Default all frequencies between 0 and Fs/2
0045 % Output:
0046 %       Sc (cross spectral matrix frequency x channels x channels)
0047 %       Cmat Coherence matrix frequency x channels x channels
0048 %       Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
0049 %       Cvec leading Eigenvector (frequency x channels)
0050 %       Cent A different measure of total coherence: GM/AM of SV^2s
0051 %       f (frequencies)
0052 d=ndims(data);
0053 if d<2, error('Need multidimensional array'); end
0054 if d==2, [N,C]=size(data); end;
0055 if d==3, [N,C,Ntr]=size(data); end; 
0056 if nargin < 3; params=[]; end;
0057 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
0058 clear err trialave params
0059 nwin=round(win*Fs); nfft=max(2^(nextpow2(nwin)+pad),nwin); 
0060 [f,findx]=getfgrid(Fs,nfft,fpass); 
0061 tapers=dpsschk(tapers,nwin,Fs); % check tapers
0062 Sc=zeros(length(findx),C,C);
0063 Nwins=floor(N/nwin);
0064 
0065 if d==3, % If there are multiple trials
0066 for iwin=1:Nwins,
0067     for i=1:Ntr, 
0068         data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:,i));
0069         J1=mtfftpb(data1,tapers,nfft);
0070         J1=J1(findx,:,:);
0071         for k=1:C,
0072             for l=1:C,
0073                 spec=squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2)); 
0074                 Sc(:,k,l)=Sc(:,k,l)+spec;
0075             end
0076         end
0077     end
0078 end
0079 Sc=Sc/(Nwins*Ntr);
0080 end
0081 
0082 if d==2, % only one trial
0083 for iwin=1:Nwins,
0084         data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:));
0085         J1=mtfftpb(data1,tapers,nfft);
0086         J1=J1(findx,:,:);
0087         for k=1:C,
0088             for l=1:C,
0089             Sc(:,k,l)=Sc(:,k,l)+squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2));
0090             end
0091         end
0092 end
0093 Sc=Sc/Nwins;
0094 end
0095 
0096 Cmat=Sc;
0097 Sdiag=zeros(length(findx),C);
0098 for k=1:C,
0099     Sdiag(:,k)=squeeze(Sc(:,k,k));
0100 end
0101 
0102 for k=1:C,
0103     for l=1:C,
0104         Cmat(:,k,l)=Sc(:,k,l)./sqrt(abs(Sdiag(:,k).*Sdiag(:,l)));
0105     end
0106 end
0107 
0108 Ctot=zeros(length(findx),1); Cent=Ctot;
0109 Cvec=zeros(length(findx),C);
0110 for i=1:length(findx),
0111     [u s]=svd(squeeze(Sc(i,:,:)));s=diag(s);
0112 %     Ctot(i)=s(1)/sum(s); Cent(i)=exp(mean(log(s.^2)))/mean(s.^2);
0113     Ctot(i)=s(1)/sum(s); Cent(i)=exp(mean(log(s)))/mean(s);             
0114     Cvec(i,:)=transpose(u(:,1));
0115 end
0116