# cohmatrixpb

## PURPOSE

Multi-taper coherency matrix - binned point process

## SYNOPSIS

function [C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpb(data,params,fscorr)

## DESCRIPTION

     Multi-taper coherency matrix - binned point process

     Usage:

     [C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpb(data,params,fscorr)
     Input:
           data (in form samples x channels) -- required
           params: structure with fields tapers, pad, Fs, fpass, err
           - 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.
           fscorr   (finite size corrections, 0 (don't use finite size corrections) or
                    1 (use finite size corrections) - optional
                    (available only for spikes). Defaults 0.
     Output:
           C (magnitude of coherency frequency x channels x channels)
           phi (phase of coherency frequency x channels x channels)
           S12 (cross-spectral matrix frequency x channels x channels)
           f (frequencies)
           zerosp (1 for channels where no spikes were found, zero otherwise)
           confC (confidence level for C at 1-p %) - only for err(1)>=1
           phistd - jackknife/theoretical 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:

- cohmathelper Helper function called by coherency matrix computations.
- 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
- mtfftpb Multi-taper fourier transform - binned point process data

This function is called by:

- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpb(data,params,fscorr)
    0002 % Multi-taper coherency matrix - binned point process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [C,phi,S12,f,zerosp,confC,phistd,Cerr]=cohmatrixpb(data,params,fscorr)
    0007 % Input:
    0008 %       data (in form samples x channels) -- required
    0009 %       params: structure with fields tapers, pad, Fs, fpass, err
    0010 %       - optional
    0011 %           tapers : precalculated tapers from dpss or in the one of the following
    0012 %                    forms:
    0013 %                    (1) A numeric vector [TW K] where TW is the
    0014 %                        time-bandwidth product and K is the number of
    0015 %                        tapers to be used (less than or equal to
    0016 %                        2TW-1).
    0017 %                    (2) A numeric vector [W T p] where W is the
    0018 %                        bandwidth, T is the duration of the data and p
    0019 %                        is an integer such that 2TW-p tapers are used. In
    0020 %                        this form there is no default i.e. to specify
    0021 %                        the bandwidth, you have to specify T and p as
    0022 %                        well. Note that the units of W and T have to be
    0023 %                        consistent: if W is in Hz, T must be in seconds
    0024 %                        and vice versa. Note that these units must also
    0025 %                        be consistent with the units of params.Fs: W can
    0026 %                        be in Hz if and only if params.Fs is in Hz.
    0027 %                        The default is to use form 1 with TW=3 and K=5
    0028 %
    0029 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0030 %                    -1 corresponds to no padding, 0 corresponds to padding
    0031 %                    to the next highest power of 2 etc.
    0032 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0033 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0034 %                       Defaults to 0.
    0035 %           Fs   (sampling frequency) - optional. Default 1.
    0036 %           fpass    (frequency band to be used in the calculation in the form
    0037 %                                   [fmin fmax])- optional.
    0038 %                                   Default all frequencies between 0 and Fs/2
    0039 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0040 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0041 %       fscorr   (finite size corrections, 0 (don't use finite size corrections) or
    0042 %                1 (use finite size corrections) - optional
    0043 %                (available only for spikes). Defaults 0.
    0044 % Output:
    0045 %       C (magnitude of coherency frequency x channels x channels)
    0046 %       phi (phase of coherency frequency x channels x channels)
    0047 %       S12 (cross-spectral matrix frequency x channels x channels)
    0048 %       f (frequencies)
    0049 %       zerosp (1 for channels where no spikes were found, zero otherwise)
    0050 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
    0051 %       phistd - jackknife/theoretical standard deviation for phi - Note that
    0052 %                phi + 2 phistd and phi -2 phistd will give 95% confidence bands for phi
    0053 %                - only for err(1)>=1
    0054 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
    0055
    0056 [N,Ch]=size(data);
    0057 if Ch==1; error('Need at least two channels of data'); end;
    0058 if nargin < 2; params=[]; end;
    0059 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0060 clear trialave params
    0061 if nargin < 3 || isempty(fscorr); fscorr=0; end;
    0062
    0063 nfft=max(2^(nextpow2(N)+pad),N);
    0064 [f,findx]=getfgrid(Fs,nfft,fpass);
    0065 tapers=dpsschk(tapers,N,Fs); % check tapers
    0066 [J,Msp,Nsp]=mtfftpb(data,tapers,nfft);
    0067 C1=size(J,3);
    0068 zerosp=zeros(1,C1); % initialize the zerosp variable
    0069 zerosp(Nsp==0)=0; % set the zerosp variable
    0070 J=J(findx,:,:);
    0071 if err(1)==0;
    0072      [C,phi,S12]=cohmathelper(J,err);
    0073 elseif err(1)==1;
    0074      if fscorr==0;
    0075        [C,phi,S12,confC,phistd]=cohmathelper(J,err);
    0076     else
    0077        [C,phi,S12,confC,phistd]=cohmathelper(J,err,Nsp);
    0078     end;
    0079 elseif err(1)==2;
    0080      if fscorr==0;
    0081        [C,phi,S12,confC,phistd,Cerr]=cohmathelper(J,err);
    0082     else
    0083        [C,phi,S12,confC,phistd,Cerr]=cohmathelper(J,err,Nsp);
    0084     end;
    0085 end
    0086 clear Msp