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snpm_cp.m
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snpm_cp.m
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function snpm_cp(CWD)
% Nonparametric Perm/Rando statistical analysis with General linear model
% FORMAT snpm_cp(CWD)
%
% CWD - Directory containing SnPMcfg.mat configuration file
%_______________________________________________________________________
%
% snpm_cp is the engine of the SnPM toolbox and implements the general
% linear model for a set of design matrices, each design matrix
% constituting one permutation. First the "correct" permutation
% is calculated in its entirety, then all subsequent permutations are
% calculated, possibly on a plane-by-plane basis.
%
% The output of snpm_cp parallels spm_spm: for the correct permutation
% image files containing parameter estimates, statistic values, and F
% values are saved (this is in distinction from SnPM2 and previous
% versions, where this information was saved in .mat files); the permutation
% distribution of the statistic interest and (optionally) suprathreshold
% stats are also saved. All results are written to the directory
% that CfgFile resides in. IMPORTANT: Existing results are overwritten
% without prompting.
%
% Unlike spm_spm, voxels are not discarded on the basis of the F statistic.
% All gray matter voxels (as defined by the gray matter threshold) are
% retained for analysis; note that this will increase the size of all .mat
% files.
%
%
%-----------------------------------------------------------------------
%
% Output File Descriptions:
%
% XYZ.mat contains a 3 x N matrix of the x,y and z location of the
% voxels in SPMF in mm (usually referring the the standard anatomical
% space (Talairach and Tournoux 1988)} (0,0,0) corresponds to the
% centre of the voxel specified by ORIGIN in the *.hdr of the original
% and related data.
%
% BETA.mat contains a p x S matrix of the p parameter estimates at
% each of the S voxels for the correct permutation. These parameters
% include all effects specified by the design matrix.
%
% SnPMt.mat contains a 1 x S matrix of the statistic of interest (either
% t or pseudo-t if variance smoothing is used) supplied for all S voxels at
% locations XYZ.
%
% SnPMucp.mat contains a 1 x S matrix of the nonparametric P values of
% the statistic of interest supplied for all S voxels at locations XYZ.
%
% SnPM.mat contains a collection of strings and matrices that pertain
% to the analysis. In contrast to spm_spm's SPM.mat, most of the essential
% matrices are in the any of the matrices stored here in the CfgFile
% and hence are not duplicated here. Included are the number of voxels
% analyzed (S) and the image and voxel dimensions [V]. See below
% for complete listing.
%
% snpm_cp writes out the following image files (for each image, there are
% two files: .img and .hdr files)
%
% beta_**** (from 0001 to p): p images of p parameter estimates at each
% voxel for the correct permutation. These p parameters include all
% effects specified by the design matrix.
%
% ResMS: One image of residual mean square errors at each voxel.
%
% (SnPM, like SPM, only implements single tailed tests. In the following
% files, '+' or '-' correspond to 'positive' or 'negative' effects (as in
% snpm_pp.m). Here, '+' images are the images for large values,
% indicating evidence against the null hypothesis in favour of a positive
% alternative (activation, or positive slope in a covariate analysis))
%
% snpmT+ & snpmT-: Images of the statistic of interest (either t or
% pseduo-t if variance smoothing is used), positive or negative.
% The numbers (i.e. not NaN) saved in snpmT+ images are also saved in the
% SnPMt.mat file.
%
% lP+ & lP-: Images of -log10(uncorrected non-parametric P-values,
% positive or negative).
%
% lP_FWE+ & lP_FWE-: Images of -log10(FWE-corrected non-parametric
% P-values, positive or negative). Here, FWE-corrected non-parametric
% P-values are the proportion of the permutation distribution for the
% maximal statistic which exceeds the statistic image at the voxel.
%
% lP_FDR+ & lP_FDR-: Images of -log10(FDR-corrected non-parametric
% P-values, positive or negative).
%
% The following is an example of matlab codes for reading in an image file.
% P='.../.../beta_0001.img';
% V=spm_vol(P);
% Y=spm_read_vols(V);
% Y(~isfinite(Y))=[]; %delete NaN values from vector Y.
%
%
%-----------------------------------------------------------------------
%
% As an "engine", snpm_cp does not produce any graphics; if the SPM windows
% are open, a progress thermometer bar will be displayed.
%
% If out-of-memory problems are encountered, the first line of defense is to
% run snpm_cp in a virgin matlab session with out first starting SPM.
%
%
% Variables saved in SnPM.mat
%=======================================================================
%
% S Volume analyzed (in voxels)
% V Volume handles (see spm_vol)
% df Residual degrees of freedom of raw t-statistic
% MaxT nPerm x 2 matrix of [max;min] t-statistics per perm
% ST_Ut Threshold above which suprathreshold info was collected.
% Voxel locations, t and perm are saved in SnPM_ST.mat for
% t's greater than ST_Ut. ST_Ut=Inf if not saving STCdata
%
% s_SnPM_save List of variables saved in SnPM.mat file
% CfgFile SnPM config sile used (full pathname)
% s_SnPMcfg_save List of variables saved in SnPMcfg.mat file
%
% Data structure of SnPM_ST.mat: suprathreshold stats (if collected)
%-----------------------------------------------------------------------
% 5xn matrix, each column containing:
% [x, y, z, abs(T), perm]'
% perm is negative if T was negative
%
%_______________________________________________________________________
% Copyright (C) 2013-2014 The University of Warwick
% Id: snpm_cp.m SnPM13.01 2014/01/31
% Thomas Nichols, Andrew Holmes
%-----------------------------functions-called------------------------
% spm_append_96
% spm_conv
% spm_figure
% spm_select
% spm_hread
% spm_invTcdf
% spm_matrix
% spm_progress_bar
% spm_smooth
% spm_str_manip
%-----------------------------functions-called------------------------
% Programmers / Hackers help / Code notes...
%=======================================================================
% snpm_cp is modeled after SPM95's spm_spm, which is different from the
% current spm_spm (which is similar to SPM99). While the current
% (SPM99-SPM5) spm_spm reads data in 'planks' (a partial or whole slice),
% snpm_cp reads either a plane at a time or reads the entire dataset into
% memory ('Volumetric mode', bVolm=1).
%
% If bVolm is true, this function will load the entire dataset (all
% planes, all subjects) into memory. If bVolm is false the dataset
% will be loaded a plane at a time (all subjects), but smoothing the
% variance in the z-direction is not permitted. A version that
% does not load the whole volume but allows volumetric smoothing
% is under development.
%
% For designs with large number of permutations AND bVolm true, a possible
% approach would be have a stopping feature where the user had decided
% "enough" permutations had run. Not sure if this is useful.
%-Variable "decoder"
%-----------------------------------------------------------------------
% bWin - Do we have windows?
% bVarSm - Variance Smoothing?
% bVolm - Work on whole volume at once?
% q - number of observations
% p - number of predictors
% r - Model degrees of freedom
% df - Residual degrees of freedom
% nPerm - number of permutations
% WorkDim - Number of voxels read in (either a plane's worth or the whole lot)
% MaxT - Permutation Distribution of intensity maximum
% nP - WorkDim vector of nonparametric P-values
%
%-Supratreshold Threshold
%
% STalpha - if parametric T, critical val for STalpha ised
% STprop - if pseudo T, 100*(1-STprop)%ile of correct perm's values used
%-Setup
%=======================================================================
global defaults
if isempty(defaults), spm_defaults; end
fprintf('\nSnPM: snpm_cp\n'),fprintf('%c','='*ones(1,72)),fprintf('\n')
disp('Initialising...');
bWin = ~isempty(spm_figure('FindWin','Interactive'));
s_SnPM_save = 's_SnPM_save CfgFile s_SnPMcfg_save S V df1 df MaxT ST_Ut STAT';
%-Check arguments & parameters from CfgFile
%-----------------------------------------------------------------------
if nargin == 0
tmp = spm_select(1,'SnPMcfg.mat','Select SnPMcfg.mat CfgFile...');
drawnow
CWD = spm_str_manip(tmp,'hd');
end
if strcmp(CWD, '.')
CWD=pwd;
end
if ~strcmp(pwd,CWD)
cd(CWD)
CWD=pwd;
fprintf('Changing directory to %s\n',CWD);
end
CfgFile = fullfile(CWD,'SnPMcfg.mat');
%-Load config file & catch all problem cases now
%-----------------------------------------------------------------------
load(CfgFile);
if isempty([H C])
error('SnPM:NoModel', 'No model specified; [H C] empty');
end
if ~isempty(H) && ~isempty(C)
error('SnPM:HierarchicalAndCov', 'Cannot have both heirachical and covariate effects');
end
if size(CONT,2) ~= size([H C B G],2)
error('SnPM:InvalidContrast','Contrast problem; wrong number of columns');
end
if size(CONT,1) > 1
warning('SnPM:FContrast', ...
'F contrast! F statistic images are being created.');
STAT = 'F';
if (CONT(1,:) == -CONT(2,:))
CONT = CONT(1,:);
end
else
STAT = 'T';
end
if rank(CONT)<size(CONT,1)
[u, s] = spm_svd(CONT'); % Kill zero-rank components
CONT = full(u*sqrt(s))';
end
if ~bVolm && bVarSm && vFWHM(3)
error('SnPM:ZSmoothVolume', 'Cannot z-smooth variance in non-volumetric mode');
end
if exist('bVarAlph')~=1
bVarAlph=0;
end
if bVarAlph && ~(~bVarSm && bVolm)
error('SnPM:AlphaVolumePseudo', 'No pseudo t or nonvolumetric w/ variable alpha');
end
if ~bVolm && pU_ST_Ut>=0
error('SnPM:STCSNotVolume', 'Must work volumetrically to computer STCS on-the-fly');
end
% Re-map files to avoid Endian headaches; note if NaN's available
NaNrep=0;
for i = 1:length(V)
curr_pinfo = V(i).pinfo;% Added to keep scaling
V(i) = spm_vol([V(i).fname ',' num2str(V(i).n)]);
original_pinfo = V(i).pinfo;
V(i).pinfo = curr_pinfo;
NaNrep = NaNrep | spm_type(V(i).dt(1),'nanrep');
end
%-Delete files from previous analyses, if they exist
%-----------------------------------------------------------------------
files = { '^ResMS\..{3}$','^beta_.{4}\..{3}', '^lP_.{4}\..{3}',...
'^lP.{1}\..{3}','^snpm.{2}\..{3}','^snpm.{1}\..{3}'};
for i=1:length(files)
j = spm_select('List',pwd,files{i});
for k=1:size(j,1)
spm_unlink(deblank(j(k,:)));
end
end
spm_unlink SnPM.mat SnPM_ST.mat SnPMt.mat SnPMucp.mat XYZ.mat SnPM_pp.mat ...
SnPM_pp_Neg.mat STCS.mat
%-Parameters & Initialisation
%=======================================================================
%-Suprathreshold parameters
%-----------------------------------------------------------------------
STalpha = snpm_get_defaults('STalpha');
STprop = snpm_get_defaults('STprop');
s_SnPM_save = [s_SnPM_save ' STalpha STprop']; % Save for PP
%-Work out degrees of freedom
%-----------------------------------------------------------------------
q = size([H C B G],1); %-# observations
p = size([H C B G],2); %-# predictors
r = rank([H C B G]); %-Model degrees of freedom
df = q - r; %-Residual degrees of freedom
nPerm = size(PiCond,1); %-# permutations
%-Get ORIGIN, etc
%-----------------------------------------------------------------------
DIM = [V(1).dim(1) V(1).dim(2) V(1).dim(3)];
M=V(1).mat(1:3, 1:3);
VOX=sqrt(diag(M'*M))';
MAT = V(1).mat;
IMAT = inv(MAT);
ORIGIN = IMAT(1:3,4);
%-Var-alpha stuff
%-----------------------------------------------------------------------
bMask = 0;
if bVarAlph
Vwt = spm_vol(Pwt);
MinwP = repmat(Inf,nPerm,2);
s_SnPM_save = [s_SnPM_save ' MinwP Pwt Vwt'];
bMask = 1;
elseif exist('Pwt')==1
Vwt = spm_vol(Pwt);
s_SnPM_save = [s_SnPM_save ' Pwt Vwt'];
bMask = 1;
elseif ~isempty(MASK)
Vwt = spm_vol(MASK);
s_SnPM_save = [s_SnPM_save ' Vwt'];
bMask = 1;
end
%-Useful quantities - handy for later
%-----------------------------------------------------------------------
xdim = DIM(1); %-X dimension
ydim = DIM(2); %-Y dimension
zdim = DIM(3); %-Z dimension
PlDim = xdim*ydim; %-Plane size in voxels
VolDim = xdim*ydim*zdim; %-Volume size in voxels
if bVolm
WorkDim = VolDim; %-Working dimension (if volumetric)
else
WorkDim = PlDim; %-Working dimension (if plane by plane)
end
%-Location vectors --> In units of mm <--
%-----------------------------------------------------------------------
[y,x] = meshgrid([1:ydim],[1:xdim]');
x = x(:)';
y = y(:)';
z = (1:zdim);
xyPl = [x;y]; % All x & y's in one plane
%-Initialize variables
%-----------------------------------------------------------------------
TH = TH*ones(1,WorkDim); %-Global activities
S = 0; %-Volume analyzed
MaxT = repmat(-Inf,nPerm,2); %-Max t
nP = zeros(1,WorkDim); %-Nonparam P's
XYZ_total=[]; %-the variable for keeping all XYZ
%-If working plane by plane, preallocate Q & XYZ for speed/mem. efficiency
if ~bVolm
Q = zeros(1,PlDim);
XYZ = zeros(3,PlDim);
end
SmTime = 0; %-Smoothing time
perm = 0;
% Initialize structure template
%----------------------------------------
Vt=V(1);
%
%-Initialize image structures.
%
for ii=1:p
fname= sprintf('beta_%04d.img',ii);
descrip=sprintf('beta_%04d hats',ii);
Vbeta(ii)=snpm_clone_vol(Vt,fname,descrip);
end
Vbeta = spm_create_vol(Vbeta);
VResMS=snpm_clone_vol(Vt,'ResMS.img','Residual sum-of-squares');
VResMS=spm_create_vol(VResMS);
if bVarSm==0
str = sprintf('%c_{%d} statistic',STAT,df);
else
if STAT=='T'
str = sprintf('SmVar T_{%d} statistic, %fx%fx%f VarSm',df,vFWHM);
elseif STAT=='F'
str = sprintf('SmVar F_{%d,%d} statistic, %fx%fx%f VarSm',...
[rank(CONT) df],vFWHM);
end
end
if STAT=='T'
VT_pos=snpm_clone_vol(Vt,'snpmT+.img',[str,' (+ve)']);
VT_pos=spm_create_vol(VT_pos);
VT_neg=snpm_clone_vol(Vt,'snpmT-.img',[str,' (-ve)']);
VT_neg=spm_create_vol(VT_neg);
elseif STAT=='F'
VF=snpm_clone_vol(Vt,'snpmF.img',str);
VF=spm_create_vol(VF);
end
VlP_pos=snpm_clone_vol(Vt, 'lP+.img', '-log10(uncor. non-para. P, +ve)');
VlP_pos=spm_create_vol(VlP_pos);
VlP_FWE_pos=snpm_clone_vol(Vt, 'lP_FWE+.img','-log10(FWE-corr. P, +ve)');
VlP_FWE_pos=spm_create_vol(VlP_FWE_pos);
VlP_FDR_pos=snpm_clone_vol(Vt, 'lP_FDR+.img','-log10(FDR-corr. P, +ve)');
VlP_FDR_pos=spm_create_vol(VlP_FDR_pos);
if STAT=='T'
VlP_neg=snpm_clone_vol(Vt, 'lP-.img', '-log10(uncor. non-para. P, -ve)');
VlP_neg=spm_create_vol(VlP_neg);
VlP_FWE_neg=snpm_clone_vol(Vt, 'lP_FWE-.img','-log10(FWE-corr. P, -ve)');
VlP_FWE_neg=spm_create_vol(VlP_FWE_neg);
VlP_FDR_neg=snpm_clone_vol(Vt, 'lP_FDR-.img','-log10(FDR-corr. P, -ve)');
VlP_FDR_neg=spm_create_vol(VlP_FDR_neg);
end
if bVarAlph
VlwP=snpm_clone_vol(Vt, 'lwP.img','-log10(weighted p-value)');
VlwP=spm_create_vol(VlwP);
end
%
%-Initialize image data.
%
lP_pos_image=repmat(NaN,1,VolDim);
lP_FWE_pos_image=repmat(NaN,1, VolDim);
lP_FDR_pos_image=repmat(NaN,1, VolDim);
if STAT=='T'
lP_neg_image=repmat(NaN,1,VolDim);
lP_FWE_neg_image=repmat(NaN,1, VolDim);
lP_FDR_neg_image=repmat(NaN,1, VolDim);
end
%=======================================================================
% - C O R R E C T P E R M U T A T I O N
%=======================================================================
% Work out correct permuation completely. Separating the first
% permutation simplifies the permutation loop (fewer conditionals) and
% allows determination of pseudo-t threshold when saving supratheshold
% statistics.
disp('Working on correct permutation...');
SnPMt=[]; %Initialzie SnPMt,which will store the t's from correct permutation.
for i = 1:zdim
%-Initialize the image data for this slice/volume
%---------------------------------------------------------------------
BETA_image=repmat(NaN,p,WorkDim);
ResSS_image=repmat(NaN,1,WorkDim);
if STAT=='T'
T_pos_image=repmat(NaN,1,WorkDim);
T_neg_image=repmat(NaN,1,WorkDim);
elseif STAT=='F'
F_image=repmat(NaN,1,WorkDim);
end
if bVarAlph
lwP_image=repmat(NaN, 1, WorkDim);
end
%-Form data matrix for this slice/volume
%---------------------------------------------------------------------
X = zeros(q,WorkDim);
if bMask
Wt = zeros(1,WorkDim);
else
Wt = 1;
end
if bVolm
for j = 1:q
for k = 1:zdim
tmp = spm_slice_vol(V(j),spm_matrix([0 0 k]), ...
[xdim ydim],0);
X(j,(k-1)*PlDim+1:k*PlDim) = tmp(:)';
end
end
else
for j = 1:q
tmp = spm_slice_vol(V(j),spm_matrix([0 0 i]), ...
[xdim ydim],0);
X(j,:) = tmp(:)';
end
end
if bMask
if bVolm
for k = 1:zdim
j = Vwt.mat\MAT*[xyPl;repmat(k,1,PlDim);ones(1,PlDim)];
tmp = spm_get_data(Vwt,j,false);
tmp(~isfinite(tmp) | tmp<0) = 0;
Wt(1,(k-1)*PlDim+1:k*PlDim) = tmp(:)';
end
else
j = Vwt.mat\MAT*[xyPl;repmat(i,1,PlDim);ones(1,PlDim)];
tmp = spm_get_data(Vwt,j,false);
tmp(~isfinite(tmp) | tmp<0) = 0;
Wt = tmp(:)';
end
end
%-Eliminate background voxels (based on threshold TH), and
% eliminate voxels where there are no differences across scans.
%---------------------------------------------------------------------
if ImMASK && NaNrep==0
Q = find(all(X>TH) & any(diff(X)) & Wt & all(X~=0));
else
Q = find(all(X>TH) & any(diff(X)) & Wt);
end
if length(Q)
X = X(:,Q);
S = S + length(Q); %-Volume
if bVolm
XYZ = [ x(rem(Q-1,PlDim)+1); ...
y(rem(Q-1,PlDim)+1); ...
z(ceil(Q/PlDim)) ]; %-Locations
else
XYZ = [ x(rem(Q-1,PlDim)+1); ...
y(rem(Q-1,PlDim)+1); ...
z(i)*ones(1,length(Q))]; %-Locations
end
% Convert Voxels to mm's
XYZ = MAT*[XYZ;ones(1,length(Q))]; XYZ(4,:) = [];
if (bMask)
Wt = Wt(1,Q);
end
perm = 1;
%-Estimate parameters and sum of squares due to error.
% Use pseudo inverse rather than BETA=inv(D'*D)*D'*X for
% D = DesMtx, to allow for non-unique designs. See matlab help.
%-----------------------------------------------------------------
BETA = pinv([H C B G])*X;
ResSS = sum((X - [H C B G]*BETA).^2);
%-Variance smoothing.
% Blurred mask is used to truncate kernal to brain; if not
% used variance at edges would be underestimated due to
% convolution with zero activity out side the brain.
%-----------------------------------------------------------------
if bVarSm
if bVolm
SmResSS = zeros(xdim, ydim, zdim);
SmMask = zeros(xdim, ydim, zdim);
TmpVol = zeros(xdim, ydim, zdim);
TmpVol(Q) = ones(size(Q));
% FWHM in voxels (and not in mm) as TmpVol is not a struct
spm_smooth(TmpVol,SmMask,vFWHM./VOX);
TmpVol(Q) = ResSS;
% FWHM in voxels (and not in mm) as TmpVol is not a struct
spm_smooth(TmpVol,SmResSS,vFWHM./VOX);
ResSS = SmResSS(Q)./SmMask(Q);
else
TmpPl = zeros(xdim,ydim);
TmpPl(Q) = ones(size(Q));
SmMask = spm_conv(TmpPl, vFWHM(1)/VOX(1),vFWHM(2)/VOX(2));
TmpPl(Q) = ResSS;
SmResSS = spm_conv(TmpPl, vFWHM(1)/VOX(1),vFWHM(2)/VOX(2));
ResSS = SmResSS(Q)./SmMask(Q);
end
end
%-Compute t-statistics for specified compounds of parameters
%-----------------------------------------------------------
T = zeros(1,size(BETA,2));
Co = CONT;
if STAT=='T'
% t, as usual
T(1,:) = Co*BETA./sqrt((ResSS*(Co*pinv([H C B G]'*[H C B G])*Co'))/df);
else
% F!
pX = pinv([H C B G]);
T(1,:) = (sum(((Co*BETA)'*inv(Co*pinv([H C B G]'*[H C B G])*Co'))' .* ...
(Co*BETA),1)/rank(Co)) ./ (ResSS/df);
end
%-Save Max T statistic
%-----------------------------------------------------------
MaxT(perm,:) = max([ max(T(1,:)), -min(T(1,:)); ...
MaxT(perm,1), MaxT(perm,2) ]);
%-Save min weighted p-value
%-----------------------------------------------------------
if bVarAlph
MinwP(perm,:) = min([ min(Wt.*(1-spm_Tcdf(T(1,:),df))), ...
min(Wt.*(1-spm_Tcdf(-T(1,:),df))); ...
MinwP(perm,1), MinwP(perm,2) ]);
end
%-Save weighted p-value (later converted into corr'd wt'd p-val)
%-----------------------------------------------------------
if bVarAlph
wP = [Wt.*(1-spm_Tcdf( T(1,:),df)); ...
Wt.*(1-spm_Tcdf(-T(1,:),df))];
end
%-Adjustment (remove effects of no interest) & save
%-----------------------------------------------------------
XA = X - [zeros(size([H C])) B G]*BETA;
%
%- New! Write out data images.
%- Input image data.
BETA_image(:,Q)=BETA;
ResSS_image(:,Q)=ResSS;
if STAT=='T'
T_pos_image(:,Q)=T;
T_neg_image(:,Q)=-T;
elseif STAT=='F'
F_image(:,Q)=T;
end
if bVarAlph
lwP_image(:,Q)=-log10(wP);
end
if bVolm
SnPMt=T; % save T's
else
SnPMt=[SnPMt,T]; % save T's.
end
XYZ_total=[XYZ_total, XYZ];
%if bVarAlph,
% spm_append_96('SnPMwP',wP); % wt'd p-val of Stat du jour
%end
end %(if length(Q))
%-The image of the volume or the slice should be written out no matter length(Q)=1
%or 0.
if bVolm
for ii=1:p
BETA_vol=reshape(BETA_image(ii,:),DIM(1),DIM(2),DIM(3));
spm_write_vol(Vbeta(ii),BETA_vol);
end
ResSS_vol=reshape(ResSS_image,DIM(1),DIM(2),DIM(3));
spm_write_vol(VResMS, ResSS_vol);
if STAT=='T'
T_pos_vol=reshape(T_pos_image,DIM(1),DIM(2),DIM(3));
spm_write_vol(VT_pos,T_pos_vol);
T_neg_vol=reshape(T_neg_image,DIM(1),DIM(2),DIM(3));
spm_write_vol(VT_neg,T_neg_vol);
elseif STAT=='F'
F_vol=reshape(F_image,DIM(1),DIM(2),DIM(3));
spm_write_vol(VF,F_vol);
end
if bVarAlph
lwP_vol=reshape(lwP_image, DIM(1), DIM(2), DIM(3));
spm_write_vol(VlwP, lwP_vol);
end
else
for ii=1:p
BETA_plate=reshape(BETA_image(ii,:), DIM(1), DIM(2));
spm_write_plane(Vbeta(ii),BETA_plate,i);
end
ResSS_plate=reshape(ResSS_image, DIM(1), DIM(2));
spm_write_plane(VResMS,ResSS_plate,i);
if STAT=='T'
T_pos_plate=reshape(T_pos_image, DIM(1), DIM(2));
spm_write_plane(VT_pos,T_pos_plate,i);
T_neg_plate=reshape(T_neg_image, DIM(1), DIM(2));
spm_write_plane(VT_neg,T_neg_plate,i);
elseif STAT=='F'
F_plate=reshape(F_image, DIM(1), DIM(2));
spm_write_plane(VF,F_plate,i);
end
if bVarAlph
lwP_plate=reshape(lwP_image, DIM(1), DIM(2));
spm_write_plane(VlwP, lwP_plate,i);
end
end
%-Whole volume complete in one pass if volumetric
if bVolm
break
end
end
% Make an error if actually 'no voxels in brain'.
if perm==0, error('SnPM:NoVoxelsInBrain', 'No voxels in brain'); end
save SnPMt.mat SnPMt
%save XYZ in a XYZ.mat file.
%===============
XYZ=XYZ_total;
save XYZ.mat XYZ
%-Set SupraThreshold t-threshold
%=======================================================================
if bST
if pU_ST_Ut==-1 % No threshold has been set yet.
if bVarSm
load SnPMt
SnPMt = sort(SnPMt')';
ST_Ut = SnPMt(round((1-STprop)*length(SnPMt)));
% clear SnPMt
else
ST_Ut = spm_invTcdf(1 - STalpha, df);
end
else % A threshold has been set.
if bVarSm
if (pU_ST_Ut < 1)
ST_Ut = spm_invNcdf(1-pU_ST_Ut);
warning('snpm_cp:pseudoTFormingThresholdP',...
['Pseudo-T cluster-forming threshold defined by '...
'P-value using Gaussian approximation P=' num2str(pU_ST_Ut)...
' -> Z=' num2str(ST_Ut) '; actual Pseudo-T threshold '...
'unknown but may be higher than ' num2str(ST_Ut) '.']);
else
ST_Ut=pU_ST_Ut;
end
else
if (pU_ST_Ut>1)
ST_Ut=pU_ST_Ut;
else
if STAT == 'T'
ST_Ut = spm_invTcdf(1-pU_ST_Ut, df);
else
ST_Ut = spm_invFcdf(1-pU_ST_Ut, df1, df);
end
end
end
end
StartPerm = 1; % redo 1st perm for ST stats
else
ST_Ut = Inf;
StartPerm = 2;
end
%-Save correctly labeled T's
if bVolm && (StartPerm==2)
T0 = T;
nPtmp = ones(size(T));
if bhPerms
nPtmp = nPtmp + (T0<=0);
end
else
StartPerm = 1;
nPtmp=[];
end
%=======================================================================
% - C O M P U T E F O R P E R M U T A T I O N S
%=======================================================================
%-Cycle over planes (or just once for volumetric mode)
%-If working plane by plane, preallocate Q & XYZ for speed/mem. efficiency
if ~bVolm
Q = zeros(1,PlDim);
XYZ = zeros(3,PlDim);
end
%-Setup progress bar
if bWin && ~bVolm
spm_progress_bar('Init',zdim,'Looping over (perms within) planes...','Plane')
elseif bWin
spm_progress_bar('Init',nPerm,'Volumetric mode...','Permutation')
spm_progress_bar('Set',StartPerm-1)
end
tic %-Start the clock: Timing code is commented with "clock" symbol: (>)
%-Loop over planes (breaks out after first loop if bVolm)
%-----------------------------------------------------------------------
nP = [];
for i = 1:zdim
PlStart=toc;SmTime=0; %-Timestamp (>)
if bVolm
disp('Working on the whole volume');
else
fprintf('\tPlane %3d: ',i);
end
%-Form data matrix for this slice (done in correctPerm code above if bVolm)
%---------------------------------------------------------------------
if ~bVolm
X = zeros(q,PlDim);
for j = 1:q
tmp = spm_slice_vol(V(j),spm_matrix([0 0 i]),[xdim ydim],0);
X(j,:) = tmp(:)';
end
if bMask
j = Vwt.mat\MAT*[xyPl;repmat(i,1,PlDim);ones(1,PlDim)];
tmp = spm_get_data(Vwt,j,false);
tmp(~isfinite(tmp) | tmp<0) = 0;
Wt = tmp(:)';
end
%-Eliminate background voxels (based on global threshold TH),
% and eliminate voxels where there are no differences across scans.
%-----------------------------------------------------------------
Q = find(all(X > TH) & any(diff(X)) & Wt);
end % (if ~bVolm)
if length(Q)
if ~bVolm
X = X(:,Q);
end %-Already done if bVolm
if bST && ~bVolm %-XYZ already done if bVolm
XYZ = [ x(rem(Q-1,PlDim)+1); ...
y(rem(Q-1,PlDim)+1); ...
z(i)*ones(1,length(Q))];%-Locations
XYZ = MAT*[XYZ;ones(1,length(Q))];
XYZ(4,:) = [];
end
if bVarSm && ~bVolm %-Smoothing & plane-by-plane
SmStart = toc; %-Timestamp (>)
TmpPl = zeros(xdim,ydim);
TmpPl(Q) = ones(size(Q));
SmMask = spm_conv(TmpPl, vFWHM(1)/VOX(1),vFWHM(2)/VOX(2));
SmTime = SmTime + toc-SmStart; %-Timestamp (>)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialize structure STCS
if bST && pU_ST_Ut>=0
STCS = snpm_STcalc('init',nPerm);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-Loop over permutations
%-----------------------------------------------------------------
for perm = StartPerm:nPerm
PmStart = toc; %-Timestamp (>)
if bVolm
SmTime=0; %-Timestamp (>)
else
clear T BETA ResSS; %-Clean up
end
%-Rebuild H C for current permuation
%-----------------------------------------------------------
HC = eval(sHCform);
%-Estimate parameters and sum of squares due to error
%-Use pseudo inverse rather than BETA=inv(D'*D)*D'*X
% for D = DesMtx, to allow for non-unique designs.
% See matlab help.
%-----------------------------------------------------------
BETA = pinv([HC B G])*X;
ResSS = sum((X - [HC B G]*BETA).^2);
if bVarSm
SmStart=toc; %-Timestamp (>)
if bVolm
TmpVol(Q) = ResSS;
% FWHM in voxels (and not in mm) as TmpVol is not a struct
spm_smooth(TmpVol,SmResSS,vFWHM./VOX);
ResSS = SmResSS(Q)./SmMask(Q);
else
TmpPl(Q) = ResSS;
SmResSS = spm_conv(TmpPl,vFWHM(1)/VOX(1),vFWHM(2)/VOX(2));
ResSS = SmResSS(Q)./SmMask(Q);
end
SmTime = SmTime + toc-SmStart; %-Timestamp (>)
end
%-Compute t-statistics for specified contrast of parameters
%-----------------------------------------------------------
T = zeros(1,size(BETA,2));
Co = CONT;
if STAT=='T'
% t, as usual
T(1,:) = Co*BETA./sqrt((ResSS*(Co*pinv([HC B G]'*[HC B G])*Co'))/df);
else
% F!
pX = pinv([HC B G]);
T(1,:) = (sum(((Co*BETA)'*inv(Co*pinv([HC B G]'*[HC B G])*Co'))' .* ...
(Co*BETA),1)/size(Co,1)) ./ (ResSS/df);
end
%-Save Max T statistic
%-----------------------------------------------------------
MaxT(perm,:) = max([ max(T(1,:)), -min(T(1,:)); ...
MaxT(perm,1), MaxT(perm,2) ]);
%-Update nonparametric P-value
%-----------------------------------------------------------
if (perm==1)
T0 = T;
nPtmp = ones(size(T));
if bhPerms
nPtmp = nPtmp + (T0<=0);
end
else
if bhPerms
nPtmp = nPtmp + (T>=T0) + (-T>=T0); % NB: Worry if T0=T=0
% if STAT=='T', then T,
% T0 >=0, so (-T>=T0)
% will be empty.
else
nPtmp = nPtmp + (T>=T0);
end
end
%-Save min weighted p-value
%-----------------------------------------------------------
if bVarAlph
MinwP(perm,:) = min([ min(Wt.*(1-spm_Tcdf( T(1,:),df))), ...
min(Wt.*(1-spm_Tcdf(-T(1,:),df))); ...
MinwP(perm,1), MinwP(perm,2) ]);
end
%-Save T,XYZ,perm for suprathreshold analysis
%-----------------------------------------------------------
if bST
if pU_ST_Ut==-1 % No threshold set - save mountain tops
clear d1 d2
d1 = find(T(1,:) > ST_Ut);
d2 = find(T(1,:) < -ST_Ut);
spm_append_96('SnPM_ST',[ ...
XYZ(:,d1), XYZ(:,d2); ...
T(1,d1), -T(1,d2); ...
perm*ones(1,length(d1)), -perm*ones(1,length(d2)) ...
],'Consider using ''set cluster-forming threshold now (fast)'' option');
else % pU_ST_Ut>=0 - threshold set
clear d1 d2 SnPM_ST_Pos SnPM_ST_Neg
d1 = find(T(1,:) > ST_Ut);
d2 = find(T(1,:) < -ST_Ut);
SnPM_ST_Pos=[ ...
XYZ(:,d1); ...
T(1,d1)];
SnPM_ST_Neg=[ ...
XYZ(:,d2); ...
-T(1,d2)];
if STAT== 'F'
loop = 1;
else
loop = 1:2;
end
for isPos = loop %1 for positive; 2 for negative
if isPos==1
SnPM_ST = SnPM_ST_Pos;
else
SnPM_ST = SnPM_ST_Neg;
end
% consider Permuation NO. perm
if ~isempty(SnPM_ST)
Locs_mm=SnPM_ST(1:3,:);
Locs_mm (4,:) = 1;
Locs_vox = IMAT * Locs_mm;
% Sometimes Locs_vox are not exactly integers and this raises an
% error later in the code. Here check that the values are
% integers with respect to a level of absolute tolerance (~10^-14)
% and enforce Locs_vox to be integers.
diffWithRounded = max(abs(Locs_vox(:)-round(Locs_vox(:))));
tolerance = 10^-10;
if diffWithRounded > tolerance
Locs_vox_alter = MAT\Locs_mm;
diffWithRounded_alter = max(abs(Locs_vox_alter(:)-round(Locs_vox(:))));
error('SnPM:NonIntegerLocs', ['''Locs_vox'' must be integers (difference is ' num2str(diffWithRounded) ...
' or ' num2str(diffWithRounded_alter) ')']);
else
Locs_vox = round(Locs_vox);
end
STCS = snpm_STcalc('update',STCS, SnPM_ST(4,:),...
Locs_vox(1:3,:),isPos,perm,pU_ST_Ut,df);
%save perm 1 stats for use later -[X;Y;Z;T;perm;STCno]
if (perm==1)
tmp = spm_clusters(Locs_vox(1:3,:));
STCstats=[SnPM_ST;perm*ones(1,size(SnPM_ST,2));tmp];
if isPos==1
save SnPM_pp.mat STCstats
else