cohmathelper

 Helper function called by coherency matrix computations.

 Usage: [C,phi,S12,confC,phierr,Cerr]=cohmathelper(J,err,Nsp)
 Inputs:
 J   : Fourier transforms of data
 err : [0 p] or 0 for no errors; [1 p] for theoretical confidence level, 
       [2 p] for Jackknife (p - p value)
 Nsp : pass the number of spikes in each channel if finite size corrections are desired

 Outputs:

 C   : coherence
 phi : phase of coherency
 S12 : cross spectral matrix
 confC : confidence level for coherency - only for err(1)>=1
       phierr - standard deviation for phi (note that the routine gives phierr as phierr(1,...) 
                and phierr(2,...) in order to incorporate Jackknife (eventually). 
                Currently phierr(1,...)=phierr(2,...). Note that phi + 2 phierr(1,...) and phi -2 
                phierr(2,...) will give 95% confidence bands for phi - only for err(1)>=1
 Cerr  : error bars for coherency (only for Jackknife estimates)-only for err(1)=2

0001 function  [C,phi,S12,confC,phierr,Cerr]=cohmathelper(J,err,Nsp)
0002 % Helper function called by coherency matrix computations.
0003 %
0004 % Usage: [C,phi,S12,confC,phierr,Cerr]=cohmathelper(J,err,Nsp)
0005 % Inputs:
0006 % J   : Fourier transforms of data
0007 % err : [0 p] or 0 for no errors; [1 p] for theoretical confidence level,
0008 %       [2 p] for Jackknife (p - p value)
0009 % Nsp : pass the number of spikes in each channel if finite size corrections are desired
0010 %
0011 % Outputs:
0012 %
0013 % C   : coherence
0014 % phi : phase of coherency
0015 % S12 : cross spectral matrix
0016 % confC : confidence level for coherency - only for err(1)>=1
0017 %       phierr - standard deviation for phi (note that the routine gives phierr as phierr(1,...)
0018 %                and phierr(2,...) in order to incorporate Jackknife (eventually).
0019 %                Currently phierr(1,...)=phierr(2,...). Note that phi + 2 phierr(1,...) and phi -2
0020 %                phierr(2,...) will give 95% confidence bands for phi - only for err(1)>=1
0021 % Cerr  : error bars for coherency (only for Jackknife estimates)-only for err(1)=2
0022 %
0023 
0024 errtype=err(1);
0025 trialave=0;
0026 [nf,K,Ch]=size(J);
0027 clear K
0028 confC=zeros(Ch,Ch);
0029 C=zeros(nf,Ch,Ch);
0030 S12=zeros(nf,Ch,Ch);
0031 phi=zeros(nf,Ch,Ch);
0032 phierr=zeros(2,nf,Ch,Ch);
0033 if errtype==2; Cerr=zeros(2,nf,Ch,Ch);end;
0034 
0035 for ch1=1:Ch;
0036      J1=squeeze(J(:,:,ch1));
0037      C(1:nf,ch1,ch1)=1;
0038      phi(1:nf,ch1,ch1)=0;
0039 %      if errtype==2;
0040 %           phierr(1:nf,ch1,ch1)=0;
0041 %           Cerr(1:2,1:nf,ch1,ch1)=0;
0042 %      elseif errtype==1
0043 %            phierr(1:2,1:nf,ch1,ch1)=0;
0044 %      end;
0045      s1=squeeze(mean(conj(J1).*J1,2));
0046      for ch2=1:ch1-1;
0047           J2=squeeze(J(:,:,ch2));
0048           s12=squeeze(mean(conj(J1).*J2,2));
0049           s2=squeeze(mean(conj(J2).*J2,2));
0050           C12=s12./sqrt(s1.*s2);
0051           C(:,ch1,ch2)=abs(C12);
0052           C(:,ch2,ch1)=C(:,ch1,ch2);
0053           phi(:,ch1,ch2)=angle(C12);
0054           phi(:,ch2,ch1)=phi(:,ch1,ch2);
0055           S12(:,ch1,ch2)=s12;
0056           S12(:,ch2,ch1)=S12(:,ch1,ch2);
0057           if errtype==2 
0058              if nargin<3;
0059                  [conf,phie,Ce]=coherr(abs(C12),J1,J2,err,trialave);
0060              else
0061                  [conf,phie,Ce]=coherr(abs(C12),J1,J2,err,trialave,Nsp(ch1),Nsp(ch2));
0062              end
0063              confC(ch1,ch2)=conf; 
0064              phierr(1,:,ch1,ch2)=phie;phierr(2,:,ch1,ch2)=phie;
0065              Cerr(1,:,ch1,ch2)=Ce(1,:);
0066              Cerr(2,:,ch1,ch2)=Ce(2,:);
0067              confC(ch2,ch1)=conf; 
0068              phierr(1,:,ch2,ch1)=phie;phierr(2,:,ch2,ch1)=phie;
0069              Cerr(:,:,ch2,ch1)=Ce;
0070           elseif errtype==1
0071              if nargin<3;
0072                  [conf,phie]=coherr(abs(C12),J1,J2,err,trialave);
0073              else
0074                  [conf,phie]=coherr(abs(C12),J1,J2,err,trialave,Nsp(ch1),Nsp(ch2));
0075              end
0076              confC(ch1,ch2)=conf; 
0077              phierr(1,:,ch1,ch2)=phie;phierr(2,:,ch1,ch2)=phie;
0078              confC(ch2,ch1)=conf; 
0079              phierr(1,:,ch2,ch1)=phie;phierr(2,:,ch2,ch1)=phie;
0080           end;
0081      end;
0082 end;