# coherencypt

## PURPOSE

Multi-taper coherency - point process times

## SYNOPSIS

function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(data1,data2,params,fscorr,t)

## DESCRIPTION

     Multi-taper coherency - point process times

     Usage:

     [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(data1,data2,params,fscorr,t)
     Input:
           data1  (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- required
           data2  (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- required
           params: structure with fields tapers, pad, Fs, fpass, err, trialave
           - 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
               err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
                                       [0 p] or 0 - no error bars) - optional. Default 0.
               trialave (average over trials when 1, don't average when 0) - optional. Default 0
           fscorr   (finite size corrections, 0 (don't use finite size corrections)
                    or 1 (use finite size corrections) - optional
                    (available only for spikes). Defaults 0.
           t        (time grid over which the tapers are to be calculated:
                          this argument is useful when calling the spectrum
                          calculation routine from a moving window spectrogram
                          calculation routine). If left empty, the spike times
                          are used to define the grid.
     Output:
           C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           S12 (cross spectrum -  frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           f (frequencies)
           zerosp (1 for trials where no spikes were found, 0 otherwise)
           confC (confidence level for C at 1-p %) - only for err(1)>=1
           phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
                    Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
                    bands for phi - only for err(1)>=1
           Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)

## CROSS-REFERENCE INFORMATION

This function calls:

- check_consistency Helper routine to check consistency of data dimensions
- coherr Function to compute lower and upper confidence intervals on the coherency
- dpsschk Helper function to calculate tapers and, if precalculated tapers are supplied,
- getfgrid Helper function that gets the frequency grid associated with a given fft based computation
- getparams Helper function to convert structure params to variables used by the
- minmaxsptimes Find the minimum and maximum of the spike times in each channel
- mtfftpt Multi-taper fourier transform for point process given as times

This function is called by:

- coherencysegpt Multi-taper coherency computed by segmenting two univariate point processes into chunks
- cohgrampt Multi-taper time-frequency coherence - two point processes given as times
- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(data1,data2,params,fscorr,t)
    0002 % Multi-taper coherency - point process times
    0003 %
    0004 % Usage:
    0005 %
    0006 % [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypt(data1,data2,params,fscorr,t)
    0007 % Input:
    0008 %       data1  (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- required
    0009 %       data2  (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- required
    0010 %       params: structure with fields tapers, pad, Fs, fpass, err, trialave
    0011 %       - optional
    0012 %           tapers : precalculated tapers from dpss or in the one of the following
    0013 %                    forms:
    0014 %                    (1) A numeric vector [TW K] where TW is the
    0015 %                        time-bandwidth product and K is the number of
    0016 %                        tapers to be used (less than or equal to
    0017 %                        2TW-1).
    0018 %                    (2) A numeric vector [W T p] where W is the
    0019 %                        bandwidth, T is the duration of the data and p
    0020 %                        is an integer such that 2TW-p tapers are used. In
    0021 %                        this form there is no default i.e. to specify
    0022 %                        the bandwidth, you have to specify T and p as
    0023 %                        well. Note that the units of W and T have to be
    0024 %                        consistent: if W is in Hz, T must be in seconds
    0025 %                        and vice versa. Note that these units must also
    0026 %                        be consistent with the units of params.Fs: W can
    0027 %                        be in Hz if and only if params.Fs is in Hz.
    0028 %                        The default is to use form 1 with TW=3 and K=5
    0029 %
    0030 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0031 %                    -1 corresponds to no padding, 0 corresponds to padding
    0032 %                    to the next highest power of 2 etc.
    0033 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0034 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0035 %                       Defaults to 0.
    0036 %           Fs   (sampling frequency) - optional. Default 1.
    0037 %           fpass    (frequency band to be used in the calculation in the form
    0038 %                                   [fmin fmax])- optional.
    0039 %                                   Default all frequencies between 0 and Fs/2
    0040 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0041 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0042 %           trialave (average over trials when 1, don't average when 0) - optional. Default 0
    0043 %       fscorr   (finite size corrections, 0 (don't use finite size corrections)
    0044 %                or 1 (use finite size corrections) - optional
    0045 %                (available only for spikes). Defaults 0.
    0046 %       t        (time grid over which the tapers are to be calculated:
    0047 %                      this argument is useful when calling the spectrum
    0048 %                      calculation routine from a moving window spectrogram
    0049 %                      calculation routine). If left empty, the spike times
    0050 %                      are used to define the grid.
    0051 % Output:
    0052 %       C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0053 %       phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0054 %       S12 (cross spectrum -  frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0055 %       S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0056 %       S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0057 %       f (frequencies)
    0058 %       zerosp (1 for trials where no spikes were found, 0 otherwise)
    0059 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
    0060 %       phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
    0061 %                Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
    0062 %                bands for phi - only for err(1)>=1
    0063 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
    0064 if nargin < 2; error('Need data1 and data2'); end;
    0065 if nargin < 3; params=[]; end;
    0066 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0067 clear params
    0068 if nargin < 4 || isempty(fscorr); fscorr=0; end;
    0069 if nargin < 5 || isempty(t);
    0070    [mintime1,maxtime1]=minmaxsptimes(data1);
    0071    [mintime2,maxtime2]=minmaxsptimes(data2);
    0072    mintime=min(mintime1,mintime2);
    0073    maxtime=max(maxtime1,maxtime2);
    0074    dt=1/Fs;
    0075    t=mintime:dt:maxtime+dt; % time grid for prolates
    0076 end;
    0077
    0078 if nargout > 9 && err(1)~=2;
    0079     error('Cerr computed only for Jackknife. Correct inputs or outputs and run again');
    0080 end;
    0081 if nargout > 7 && err(1)==0;
    0082     error('Errors computed only if err(1) is not equal to zero');
    0083 end;
    0084
    0085 [N,Ch]=check_consistency(data1,data2);
    0086
    0087 N=length(t); % number of points in grid for dpss
    0088 nfft=max(2^(nextpow2(N)+pad),N); % number of points in fft of prolates
    0089 [f,findx]=getfgrid(Fs,nfft,fpass);
    0090 tapers=dpsschk(tapers,N,Fs); % check tapers
    0091 [J1,Msp1,Nsp1]=mtfftpt(data1,tapers,nfft,t,f,findx);
    0092 [J2,Msp2,Nsp2]=mtfftpt(data2,tapers,nfft,t,f,findx);
    0093 zerosp=zeros(1,Ch); % initialize the zerosp variable
    0094 zerosp(Nsp1==0 | Nsp2==0)=1; % set the zerosp variable
    0095 S12=squeeze(mean(conj(J1).*J2,2));
    0096 S1=squeeze(mean(conj(J1).*J1,2));
    0097 S2=squeeze(mean(conj(J2).*J2,2));
    0098 if trialave; S12=squeeze(mean(S12,2)); S1=squeeze(mean(S1,2)); S2=squeeze(mean(S2,2)); end;
    0099 C12=S12./sqrt(S1.*S2);
    0100 C=abs(C12);
    0101 phi=angle(C12);
    0102 if nargout==10;
    0103     if fscorr==1;
    0104        [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,Nsp1,Nsp2);
    0105     else
    0106        [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave);
    0107     end;
    0108 elseif nargout==9;
    0109     if fscorr==1;
    0110         [confC,phistd]=coherr(C,J1,J2,err,trialave,Nsp1,Nsp2);
    0111     else
    0112         [confC,phistd]=coherr(C,J1,J2,err,trialave);
    0113     end;
    0114 end;
    0115 clear Msp1 Msp2