Home > chronux > spectral_analysis > helper > coherr.m

coherr

PURPOSE

Function to compute lower and upper confidence intervals on the coherency

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
Jackknife uses the following transform of the coherence
z=sqrt(2*dim-2)atanh(C). Asymptotically (and for Gaussian data) var(z)=1.```

CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• cohmathelper Helper function called by coherency matrix computations.

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
0003 % given the tapered fourier transforms, errchk, trialave.
0004 %
0005 % Usage: [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,numsp1,numsp2)
0006 % Inputs:
0007 % C     - coherence
0008 % J1,J2 - tapered fourier transforms
0009 % err - [errtype p] (errtype=1 - asymptotic estimates; errchk=2 - Jackknife estimates;
0010 %                   p - p value for error estimates)
0011 % trialave - 0: no averaging over trials/channels
0012 %            1 : perform trial averaging
0013 % numsp1    - number of spikes for data1. supply only if finite size corrections are required
0014 % numsp2    - number of spikes for data2. supply only if finite size corrections are required
0015 %
0016 % Outputs:
0017 %          confC - confidence level for C - only for err(1)>=1
0018 %          phistd - theoretical or jackknife standard deviation for phi for err(1)=1 and err(1)=2
0019 %                   respectively. returns zero if coherence is 1
0020 %          Cerr  - Jacknife error bars for C  - only for err(1)=2
0021 % Jackknife uses the following transform of the coherence
0022 % z=sqrt(2*dim-2)atanh(C). Asymptotically (and for Gaussian data) var(z)=1.
0023
0024 if nargin < 5; error('Need at least 5 input arguments'); end;
0025 if err(1)==0; error('Need err=[1 p] or [2 p] for error bar calculation'); end;
0026 if nargout==4  && err(1)==1; error('Cerr contains Jackknife errors: only computed when err(1) is 2'); end;
0027 [nf,K,Ch]=size(J1);
0028 errchk=err(1);
0029 p=err(2);
0030 pp=1-p/2;
0031 %
0032 % Find the number of degrees of freedom
0033 %
0034 if trialave;
0035    dim=K*Ch;
0036    dof=2*dim;
0037    dof1=dof;
0038    dof2=dof;
0039    Ch=1;
0040    if nargin>=6 && ~isempty(numsp1)
0041       totspikes1=sum(numsp1);
0042       dof1=fix(2*totspikes1*dof/(2*totspikes1+dof));
0043    end
0044    if nargin==7 && ~isempty(numsp2);
0045       totspikes2=sum(numsp2);
0046       dof2=fix(2*totspikes2*dof/(2*totspikes2+dof));
0047    end;
0048    dof=min(dof1,dof2);
0049    J1=reshape(J1,nf,dim);
0050    J2=reshape(J2,nf,dim);
0051 else
0052    dim=K;
0053    dof=2*dim;
0054    dof1=dof;
0055    dof2=dof;
0056    for ch=1:Ch;
0057       if nargin>=6 && ~isempty(numsp1);
0058          totspikes1=numsp1(ch);
0059         dof1=fix(2*totspikes1*dof/(2*totspikes1+dof));
0060       end;
0061       if nargin==7 && ~isempty(numsp2);
0062          totspikes2=numsp2(ch);
0063         dof2=fix(2*totspikes2*dof/(2*totspikes2+dof));
0064       end;
0065       dof(ch)=min(dof1,dof2);
0066    end;
0067 end;
0068 %
0069 % variance of the phase
0070 %
0071 %
0072 % Old code is the next few lines - new code is in the if statement below
0073 % beginning line 87
0074 %
0075 % if isempty(find((C-1).^2 < 10^-16));
0076 %    phierr = sqrt((2./dof(ones(nf,1),:)).*(1./(C.^2) - 1));
0077 % else
0078 %    phierr = zeros(nf,Ch);
0079 % end
0080
0081 %
0082 % theoretical, asymptotic confidence level
0083 %
0084 if dof <= 2
0085    confC = 1;
0086 else
0087    df = 1./((dof/2)-1);
0088    confC = sqrt(1 - p.^df);
0089 end;
0090 %
0091 % Phase standard deviation (theoretical and jackknife) and jackknife
0092 % confidence intervals for C
0093 %
0094 if errchk==1;
0095    totnum=nf*Ch;
0096    phistd=zeros(totnum,1);
0097    CC=reshape(C,[totnum,1]);
0098    indx=find(abs(CC-1)>=1.e-16);
0099    dof=repmat(dof,[nf,1]);
0100    dof=reshape(dof,[totnum 1]);
0101    phistd(indx)= sqrt((2./dof(indx).*(1./(C(indx).^2) - 1)));
0102    phistd=reshape(phistd,[nf Ch]);
0103 elseif errchk==2;
0104     tcrit=tinv(pp,dof-1);
0105     for k=1:dim; % dim is the number of 'independent' estimates
0106         indxk=setdiff(1:dim,k);
0107         J1k=J1(:,indxk,:);
0108         J2k=J2(:,indxk,:);
0109         eJ1k=squeeze(sum(J1k.*conj(J1k),2));
0110         eJ2k=squeeze(sum(J2k.*conj(J2k),2));
0111         eJ12k=squeeze(sum(conj(J1k).*J2k,2));
0112         Cxyk=eJ12k./sqrt(eJ1k.*eJ2k);
0113         absCxyk=abs(Cxyk);
0114         atanhCxyk(k,:,:)=sqrt(2*dim-2)*atanh(absCxyk); % 1-drop estimate of z
0115         phasefactorxyk(k,:,:)=Cxyk./absCxyk;
0116 %         indxk=setdiff(1:dim,k);
0117 %         J1jk=J1(:,indxk,:);
0118 %         J2jk=J2(:,indxk,:);
0119 %         eJ1jk=squeeze(sum(J1jk.*conj(J1jk),2));
0120 %         eJ2jk=squeeze(sum(J2jk.*conj(J2jk),2));
0121 %         eJ12jk=squeeze(sum(conj(J1jk).*J2jk,2));
0122 %         atanhCxyjk(k,:,:)=sqrt(2*dim-2)*atanh(abs(eJ12jk)./sqrt(eJ1jk.*eJ2jk));
0123     end;
0124     atanhC=sqrt(2*dim-2)*atanh(C); % z
0125     sigma12=sqrt(dim-1)*squeeze(std(atanhCxyk,1,1)); % Jackknife estimate std(z)=sqrt(dim-1)*std of 1-drop estimates
0126 %     sigma12=sqrt(dim-1)*squeeze(std(atanhCxyjk,1,1));
0127     if Ch==1; sigma12=sigma12'; end;
0128     Cu=atanhC+tcrit(ones(nf,1),:).*sigma12;
0129     Cl=atanhC-tcrit(ones(nf,1),:).*sigma12;
0130     %Cerr(1,:,:) = tanh(Cl/sqrt(2*dim-2));
0131     Cerr(1,:,:) = max(tanh(Cl/sqrt(2*dim-2)),0); % This ensures that the lower confidence band remains positive
0132     Cerr(2,:,:) = tanh(Cu/sqrt(2*dim-2));
0133     %phistd=(2*dim-2)*(1-abs(squeeze(mean(phasefactorxyk))));
0134     phistd = sqrt( (2*dim-2)*(1-abs(squeeze(mean(phasefactorxyk)))) );
0135     if trialave; phistd=phistd'; end;
0136 end
0137 % ncrit=norminv(pp);
0138 % phierr=zeros([2 size(phistd)]);
0139 % phierr(1,:,:)=phi-ncrit*phistd; phierr(2,:,:)=phi+ncrit*phistd;```

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