Home > chronux_1_50 > helper > coherr.m

coherr

PURPOSE ^

Function to compute lower and upper confidence intervals on the coherency given the tapered fourier transforms,

SYNOPSIS ^

function [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)

DESCRIPTION ^

 Function to compute lower and upper confidence intervals on the coherency given the tapered fourier transforms, 
 errchk, trialave.
 Usage: [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)
 Inputs:
 C     - coherence
 J1,J2 - tapered fourier transforms 
 err - [errtype p] (errtype=1 - asymptotic estimates; errchk=2 - Jackknife estimates; 
                   p - p value for error estimates)
 trialave - 0: no averaging over trials/channels
            1 : perform trial averaging
 numsp1    - number of spikes for data1. supply only if finite size corrections are required
 numsp2    - number of spikes for data2. supply only if finite size corrections are required

 Outputs: 
          confC - confidence level for C - only for err(1)>=1
          phistd - theoretical or jackknife standard deviation for phi for err(1)=1 and err(1)=2 respectively
                   returns zero if coherence is 1
          Cerr  - Jacknife error bars for C  - only for err(1)=2

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)
0002 % Function to compute lower and upper confidence intervals on the coherency given the tapered fourier transforms,
0003 % errchk, trialave.
0004 % Usage: [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)
0005 % Inputs:
0006 % C     - coherence
0007 % J1,J2 - tapered fourier transforms
0008 % err - [errtype p] (errtype=1 - asymptotic estimates; errchk=2 - Jackknife estimates;
0009 %                   p - p value for error estimates)
0010 % trialave - 0: no averaging over trials/channels
0011 %            1 : perform trial averaging
0012 % numsp1    - number of spikes for data1. supply only if finite size corrections are required
0013 % numsp2    - number of spikes for data2. supply only if finite size corrections are required
0014 %
0015 % Outputs:
0016 %          confC - confidence level for C - only for err(1)>=1
0017 %          phistd - theoretical or jackknife standard deviation for phi for err(1)=1 and err(1)=2 respectively
0018 %                   returns zero if coherence is 1
0019 %          Cerr  - Jacknife error bars for C  - only for err(1)=2
0020 
0021 if nargin < 5; error('Need at least 5 input arguments'); end;
0022 if err(1)==0; error('Need err=[1 p] or [2 p] for error bar calculation'); end;
0023 if nargout==4  && err(1)==1; error('Cerr contains Jackknife errors: only computed when err(1) is 2'); end;
0024 [nf,K,Ch]=size(J1);
0025 errchk=err(1);
0026 p=err(2);
0027 pp=1-p/2;
0028 %
0029 % Find the number of degrees of freedom
0030 %
0031 if trialave;
0032    dim=K*Ch;
0033    dof=2*dim;
0034    dof1=dof;
0035    dof2=dof;
0036    Ch=1;
0037    if nargin>=6 && ~isempty(numsp1) 
0038       totspikes1=sum(numsp1);
0039       dof1=fix(2*totspikes1*dof/(2*totspikes1+dof));
0040    end
0041    if nargin==7 && ~isempty(numsp2); 
0042       totspikes2=sum(numsp2);
0043       dof2=fix(2*totspikes2*dof/(2*totspikes2+dof));
0044    end;
0045    dof=min(dof1,dof2);
0046    J1=reshape(J1,nf,dim);
0047    J2=reshape(J2,nf,dim);
0048 else
0049    dim=K;
0050    dof=2*dim;
0051    dof1=dof;
0052    dof2=dof;
0053    for ch=1:Ch;
0054       if nargin>=6 && ~isempty(numsp1);
0055          totspikes1=numsp1(ch); 
0056         dof1=fix(2*totspikes1*dof/(2*totspikes1+dof));
0057       end;
0058       if nargin==7 && ~isempty(numsp2);
0059          totspikes2=numsp2(ch);
0060         dof2=fix(2*totspikes2*dof/(2*totspikes2+dof));
0061       end;
0062       dof(ch)=min(dof1,dof2);
0063    end;
0064 end;
0065 %
0066 % variance of the phase
0067 %
0068 %
0069 % Old code is the next few lines - new code is in the if statement below
0070 % beginning line 87
0071 %
0072 % if isempty(find((C-1).^2 < 10^-16));
0073 %    phierr = sqrt((2./dof(ones(nf,1),:)).*(1./(C.^2) - 1));
0074 % else
0075 %    phierr = zeros(nf,Ch);
0076 % end
0077 
0078 %
0079 % theoretical, asymptotic confidence level
0080 %
0081 if dof <= 2
0082    confC = 1;
0083 else     
0084    df = 1./((dof/2)-1);
0085    confC = sqrt(1 - p.^df);
0086 end;
0087 %
0088 % Phase standard deviation (theoretical and jackknife) and jackknife
0089 % confidence intervals for C
0090 %
0091 if errchk==1;
0092    totnum=nf*Ch;
0093    phistd=zeros(totnum,1); 
0094    CC=reshape(C,[totnum,1]); 
0095    indx=find(abs(CC-1)>=1.e-16);
0096    dof=repmat(dof,[nf,1]);
0097    dof=reshape(dof,[totnum 1]); 
0098    phistd(indx)= sqrt((2./dof(indx).*(1./(C(indx).^2) - 1))); 
0099    phistd=reshape(phistd,[nf Ch]);
0100 elseif errchk==2;
0101     tcrit=tinv(pp,dof-1);
0102     for k=1:dim;
0103         indxk=setdiff(1:dim,k);
0104         J1k=J1(:,indxk,:);
0105         J2k=J2(:,indxk,:);
0106         eJ1k=squeeze(sum(J1k.*conj(J1k),2));
0107         eJ2k=squeeze(sum(J2k.*conj(J2k),2));
0108         eJ12k=squeeze(sum(conj(J1k).*J2k,2)); 
0109         Cxyk=eJ12k./sqrt(eJ1k.*eJ2k);
0110         absCxyk=abs(Cxyk);
0111         atanhCxyk(k,:,:)=sqrt(2*dim-2)*atanh(absCxyk);
0112         phasefactorxyk(k,:,:)=Cxyk./absCxyk;
0113 %         indxk=setdiff(1:dim,k);
0114 %         J1jk=J1(:,indxk,:);
0115 %         J2jk=J2(:,indxk,:);
0116 %         eJ1jk=squeeze(sum(J1jk.*conj(J1jk),2));
0117 %         eJ2jk=squeeze(sum(J2jk.*conj(J2jk),2));
0118 %         eJ12jk=squeeze(sum(conj(J1jk).*J2jk,2));
0119 %         atanhCxyjk(k,:,:)=sqrt(2*dim-2)*atanh(abs(eJ12jk)./sqrt(eJ1jk.*eJ2jk));
0120     end; 
0121     atanhC=sqrt(2*dim-2)*atanh(C);
0122     sigma12=sqrt(dim-1)*squeeze(std(atanhCxyk,1,1));
0123 %     sigma12=sqrt(dim-1)*squeeze(std(atanhCxyjk,1,1));
0124     if Ch==1; sigma12=sigma12'; end;
0125     Cu=atanhC+tcrit(ones(nf,1),:).*sigma12;
0126     Cl=atanhC-tcrit(ones(nf,1),:).*sigma12;
0127     Cerr(1,:,:) = tanh(Cl/sqrt(2*dim-2));
0128     Cerr(2,:,:) = tanh(Cu/sqrt(2*dim-2));
0129     phistd=(2*dim-2)*(1-abs(squeeze(mean(phasefactorxyk))));
0130     if trialave; phistd=phistd'; end;
0131 end
0132 % ncrit=norminv(pp);
0133 % phierr=zeros([2 size(phistd)]);
0134 % phierr(1,:,:)=phi-ncrit*phistd; phierr(2,:,:)=phi+ncrit*phistd;

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