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spm_DesMtx.m
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function [X,Pnames,Index,idx,jdx,kdx]=spm_DesMtx(varargin)
% Design matrix construction from factor level and covariate vectors
% FORMAT [X,Pnames] = spm_DesMtx(<FCLevels-Constraint-FCnames> list)
% FORMAT [X,Pnames,Index,idx,jdx,kdx] = spm_DesMtx(FCLevels,Constraint,FCnames)
%
% <FCLevels-Constraints-FCnames>
% - set of arguments specifying a portion of design matrix (see below)
% - FCnames parameter, or Constraint and FCnames parameters, are optional
% - a list of multiple <FCLevels-Constraint-FCnames> triples can be
% specified, where FCnames or Constraint-FCnames may be omitted
% within any triple. The program then works recursively.
%
% X - design matrix
% Pnames - paramater names as (constructed from FCnames) - a cellstr
% Index - integer index of factor levels
% - only returned when computing a single design matrix partition
%
% idx,jdx,kdx - reference vectors mapping I & Index (described below)
% - only returned when computing a single design matrix partition
% for unconstrained factor effects ('-' or '~')
%
% ----------------
%
% FORMAT [nX,nPnames] = spm_DesMtx('sca',X1,Pnames1,X2,Pnames2,...)
% Produces a scaled design matrix nX with max(abs(nX(:))<=1, suitable
% for imaging with: image((nX+1)*32)
% X1,X2,... - Design matrix partitions
% Pnames1, Pnames2,... - Corresponding parameter name string mtx/cellstr (opt)
% nX - Scaled design matrix
% nPnames - Concatenated parameter names for columns of nX
%
%__________________________________________________________________________
%
% Returns design matrix corresponding to given vectors containing
% levels of a factor; two way interactions; covariates (n vectors);
% ready-made sections of design matrix; and factor by covariate
% interactions.
%
% The specification for the design matrix is passed in sets of arguments,
% each set corresponding to a particular Factor/Covariate/&c., specifying
% a section of the design matrix. The set of arguments consists of the
% FCLevels matrix (Factor/Covariate levels), an optional constraint string,
% and an optional (string) name matrix containing the names of the
% Factor/Covariate/&c.
%
% MAIN EFFECTS: For a main effect, or single factor, the FCLevels
% matrix is an integer vector whose values represent the levels of the
% factor. The integer factor levels need not be positive, nor in
% order. In the '~' constraint types (below), a factor level of zero
% is ignored (treated as no effect), and no corresponding column of
% design matrix is created. Effects for the factor levels are entered
% into the design matrix *in increasing order* of the factor levels.
% Check Pnames to find out which columns correspond to which levels of
% the factor.
%
% TWO WAY INTERACTIONS: For a two way interaction effect between two
% factors, the FCLevels matrix is an nx2 integer matrix whose columns
% indicate the levels of the two factors. An effect is included for
% each unique combination of the levels of the two factors. Again,
% factor levels must be integer, though not necessarily positive.
% Zero levels are ignored in the '~' constraint types described below.
%
% CONSTRAINTS: Each FactorLevels vector/matrix may be followed by an
% (optional) ConstraintString.
%
% ConstraintStrings for main effects are:
% '-' - No Constraint
% '~' - Ignore zero level of factor
% (I.e. cornerPoint constraint on zero level,
% (same as '.0', except zero level is always ignored,
% (even if factor only has zero level, in which case
% (an empty DesMtx results and a warning is given
% '+0' - sum-to-zero constraint
% '+0m' - Implicit sum-to-zero constraint
% '.' - CornerPoint constraint
% '.0' - CornerPoint constraint applied to zero factor level
% (warns if there is no zero factor level)
% Constraints for two way interaction effects are
% '-' - No Constraints
% '~' - Ignore zero level of any factor
% (I.e. cornerPoint constraint on zero level,
% (same as '.ij0', except zero levels are always ignored
% '+i0','+j0','+ij0' - sum-to-zero constraints
% '.i', '.j', '.ij' - CornerPoint constraints
% '.i0','.j0','.ij0' - CornerPoint constraints applied to zero factor level
% (warns if there is no zero factor level)
% '+i0m', '+j0m' - Implicit sum-to-zero constraints
%
% With the exception of the "ignore zero" '~' constraint, constraints
% are only applied if there are sufficient factor levels. CornerPoint
% and explicit sum-to-zero Constraints are applied to the last level of
% the factor.
%
% The implicit sum-to-zero constraints "mean correct" appropriate rows
% of the relevant design matrix block. For a main effect, constraint
% '+0m' "mean corrects" the main effect block across columns,
% corresponding to factor effects B_i, where B_i = B'_i - mean(B'_i) :
% The B'_i are the fitted parameters, effectively *relative* factor
% parameters, relative to their mean. This leads to a rank deficient
% design matrix block. If Matlab's pinv, which implements a
% Moore-Penrose pseudoinverse, is used to solve the least squares
% problem, then the solution with smallest L2 norm is found, which has
% mean(B'_i)=0 provided the remainder of the design is unique (design
% matrix blocks of full rank). In this case therefore the B_i are
% identically the B'_i - the mean correction imposes the constraint.
%
%
% COVARIATES: The FCLevels matrix here is an nxc matrix whose columns
% contain the covariate values. An effect is included for each covariate.
% Covariates are identified by ConstraintString 'C'.
%
%
% PRE-SPECIFIED DESIGN BLOCKS: ConstraintString 'X' identifies a
% ready-made bit of design matrix - the effect is the same as 'C'.
%
%
% FACTOR BY COVARIATE INTERACTIONS: are identified by ConstraintString
% 'FxC'. The last column is understood to contain the covariate. Other
% columns are taken to contain integer FactorLevels vectors. The
% (unconstrained) interaction of the factors is interacted with the
% covariate. Zero factor levels are ignored if ConstraintString '~FxC'
% is used.
%
%
% NAMES: Each Factor/Covariate can be 'named', by passing a name
% string. Pass a string matrix, or cell array (vector) of strings,
% with rows (cells) naming the factors/covariates in the respective
% columns of the FCLevels matrix. These names default to <Fac>, <Cov>,
% <Fac1>, <Fac2> &c., and are used in the construction of the Pnames
% parameter names.
% E.g. for an interaction, spm_DesMtx([F1,F2],'+ij0',['subj';'cond'])
% giving parameter names such as subj*cond_{1,2} etc...
%
% Pnames returns a string matrix whose successive rows describe the
% effects parameterised in the corresponding columns of the design
% matrix. `Fac1*Fac2_{2,3}' would refer to the parameter for the
% interaction of the two factors Fac1 & Fac2, at the 2nd level of the
% former and the 3rd level of the latter. Other forms are
% - Simple main effect (level 1) : <Fac>_{1}
% - Three way interaction (level 1,2,3) : <Fac1>*<Fac2>*<Fac3>_{1,2,3}
% - Two way factor interaction by covariate interaction :
% : <Cov>@<Fac1>*<Fac2>_{1,1}
% - Column 3 of prespecified DesMtx block (if unnamed)
% : <X> [1]
% The special characters `_*()[]{}' are recognised by the scaling
% function (spm_DesMtx('sca',...), and should therefore be avoided
% when naming effects and covariates.
%
%
% INDEX: An Integer Index matrix is returned if only a single block of
% design matrix is being computed (single set of parameters). It
% indexes the actual order of the effect levels in the design matrix block.
% (Factor levels are introduced in order, regardless of order of
% appearence in the factor index matrices, so that the parameters
% vector has a sensible order.) This is used to aid recursion.
%
% Similarly idx,jdx & kdx are indexes returned for a single block of
% design matrix consisting of unconstrained factor effects ('-' or '~').
% These indexes map I and Index (in a similar fashion to the `unique`
% function) as follows:
% - idx & jdx are such that I = Index(:,jdx)' and Index = I(idx,:)'
% where vector I is given as a column vector
% - If the "ignore zeros" constraint '~' is used, then kdx indexes the
% non-zero (combinations) of factor levels, such that
% I(kdx,:) = Index(:,jdx)' and Index == I(kdx(idx),:)'
%
% ----------------
%
% The design matrix scaling feature is designed to return a scaled
% version of a design matrix, with values in [-1,1], suitable for
% visualisation. Special care is taken to apply the same normalisation
% to blocks of design matrix reflecting a single effect, to preserve
% appropriate relationships between columns. Identification of effects
% corresponding to columns of design matrix portions is via the parameter
% names matrices. The design matrix may be passed in any number of
% parts, provided the corresponding parameter names are given. It is
% assumed that the block representing an effect is contained within a
% single partition. Partitions supplied without corresponding parameter
% names are scaled on a column by column basis, the parameters labelled as
% <UnSpec> in the returned nPnames matrix.
%
% Effects are identified using the special characters `_*()[]{}' used in
% parameter naming as follows: (here ? is a wildcard)
% - ?(?) - general block (column normalised)
% - ?[?] - specific block (block normalised)
% - ?_{?} - main effect or interaction of main effects
% - ?@?_{?} - factor by covariate interaction
% Blocks are identified by looking for runs of parameters of the same type
% with the same names: E.g. a block of main effects for factor 'Fac1'
% would have names like Fac1_{?}.
%
% Scaling is as follows:
% * fMRI blocks are scaled around zero to lie in [-1,1]
% * No scaling is carried out if max(abs(tX(:))) is in [.4,1]
% This protects dummy variables from normalisation, even if
% using implicit sum-to-zero constraints.
% * If the block has a single value, it's replaced by 1's
% * FxC blocks are normalised so the covariate values cover [-1,1]
% but leaving zeros as zero.
% * Otherwise, block is scaled to cover [-1,1].
%
%__________________________________________________________________________
% Copyright (C) 1994-2011 Wellcome Trust Centre for Neuroimaging
% Andrew Holmes
% $Id: spm_DesMtx.m 5219 2013-01-29 17:07:07Z spm $
%-Parse arguments for recursive construction of design matrices
%==========================================================================
if ~nargin, error('Insufficient arguments'); end
if ischar(varargin{1})
%-Non-recursive action string usage
Constraint=varargin{1};
elseif nargin>=2 && ~(ischar(varargin{2}) || iscell(varargin{2}))
[X1,Pnames1] = spm_DesMtx(varargin{1});
[X2,Pnames2] = spm_DesMtx(varargin{2:end});
X = [X1,X2]; Pnames = [Pnames1;Pnames2];
return
elseif nargin>=3 && ~(ischar(varargin{3}) || iscell(varargin{3}))
[X1,Pnames1] = spm_DesMtx(varargin{1:2});
[X2,Pnames2] = spm_DesMtx(varargin{3:end});
X = [X1,X2]; Pnames = [Pnames1;Pnames2];
return
elseif nargin>=4
[X1,Pnames1] = spm_DesMtx(varargin{1:3});
[X2,Pnames2] = spm_DesMtx(varargin{4:end});
X = [X1,X2]; Pnames = [Pnames1;Pnames2];
return
else
%-If I is a vector, make it a column vector
I = varargin{1}; if size(I,1)==1, I=I'; end
%-Sort out constraint and Factor/Covariate name parameters
if nargin<2, Constraint = '-'; else Constraint = varargin{2}; end
if isempty(I), Constraint = 'mt'; end
if nargin<3, FCnames = {}; else FCnames = varargin{3}; end
if char(FCnames), FCnames = cellstr(FCnames); end
end
switch lower(Constraint), case 'mt' %-Empty I case
%==========================================================================
X = [];
Pnames = {};
Index = [];
case {'c','x'} %-Covariate effect, or ready-made design matrix
%==========================================================================
%-I contains a covariate (C), or is to be inserted "as is" (X)
X = I;
%-Construct parameter name index
%--------------------------------------------------------------------------
if isempty(FCnames)
if strcmp(Constraint,'C'), FCnames={'<Cov>'}; else FCnames={'<X>'}; end
end
if length(FCnames)==1 && size(X,2)>1
Pnames = cell(size(X,2),1);
for i=1:size(X,2)
Pnames{i} = sprintf('%s [%d]',FCnames{1},i);
end
elseif length(FCnames)~=size(X,2)
error('FCnames doesn''t match covariate/X matrix')
else
Pnames = FCnames;
end
case {'-(1)','~(1)'} %-Simple main effect ('~' ignores zero levels)
%==========================================================================
%-Sort out arguments
%--------------------------------------------------------------------------
if size(I,2)>1, error('Simple main effect requires vector index'), end
if any(I~=floor(I)), error('Non-integer indicator vector'), end
if isempty(FCnames), FCnames = {'<Fac>'};
elseif length(FCnames)>1, error('Too many FCnames'), end
nXrows = size(I,1);
% Sort out unique factor levels - ignore zero level in '~(1)' usage
%--------------------------------------------------------------------------
if Constraint(1)~='~'
[Index,idx,jdx] = unique(I');
kdx = [1:nXrows];
else
[Index,idx,jdx] = unique(I(I~=0)');
kdx = find(I~=0)';
if isempty(Index)
X=[]; Pnames={}; Index=[];
warning(['factor has only zero level - ',...
'returning empty DesMtx partition'])
return
end
end
%-Set up unconstrained X matrix & construct parameter name index
%--------------------------------------------------------------------------
nXcols = length(Index);
%-Columns in ascending order of corresponding factor level
X = zeros(nXrows,nXcols);
Pnames = cell(nXcols,1);
for ii=1:nXcols %-ii indexes i in Index
X(:,ii) = I==Index(ii);
%-Can't use: for i=Index, X(:,i) = I==i; end
% in case Index has holes &/or doesn't start at 1!
Pnames{ii} = sprintf('%s_{%d}',FCnames{1},Index(ii));
end
%-Don't append effect level if only one level
if nXcols==1, Pnames=FCnames; end
case {'-','~'} %-Main effect / interaction ('~' ignores zero levels)
%==========================================================================
if size(I,2)==1
%-Main effect - process directly
[X,Pnames,Index,idx,jdx,kdx] = spm_DesMtx(I,[Constraint,'(1)'],FCnames);
return
end
if any((I(:))~=floor(I(:))), error('Non-integer indicator vector'), end
% Sort out unique factor level combinations & build design matrix
%--------------------------------------------------------------------------
%-Make "raw" index to unique effects
nI = I - ones(size(I,1),1)*min(I);
tmp = max(I)-min(I)+1;
tmp = [fliplr(cumprod(tmp(end:-1:2))),1];
rIndex = sum(nI.*(ones(size(I,1),1)*tmp),2)+1;
%-Ignore combinations where any factor has level zero in '~' usage
if Constraint(1)=='~'
rIndex(any(I==0,2))=0;
if all(rIndex==0)
X=[]; Pnames={}; Index=[];
warning(['no non-zero factor level combinations - ',...
'returning empty DesMtx partition'])
return
end
end
%-Build design matrix based on unique factor combinations
[X,Pnames,sIndex,idx,jdx,kdx]=spm_DesMtx(rIndex,[Constraint,'(1)']);
%-Sort out Index matrix
Index = I(kdx(idx),:)';
%-Construct parameter name index
%--------------------------------------------------------------------------
if isempty(FCnames)
tmp = ['<Fac1>',sprintf('*<Fac%d>',2:size(I,2))];
elseif length(FCnames)==size(I,2)
tmp = [FCnames{1},sprintf('*%s',FCnames{2:end})];
else
error('#FCnames mismatches #Factors in interaction')
end
Pnames = cell(size(Index,2),1);
for c = 1:size(Index,2)
Pnames{c} = ...
[sprintf('%s_{%d',tmp,Index(1,c)),sprintf(',%d',Index(2:end,c)),'}'];
end
case {'fxc','-fxc','~fxc'} %-Factor dependent covariate effect
% ('~' ignores zero factor levels)
%==========================================================================
%-Check
%--------------------------------------------------------------------------
if size(I,2)==1, error('FxC requires multi-column I'), end
F = I(:,1:end-1);
C = I(:,end);
if ~all(all(F==floor(F),1),2)
error('non-integer indicies in F partition of FxC'), end
if isempty(FCnames)
Fnames = '';
Cnames = '<Cov>';
elseif length(FCnames)==size(I,2)
Fnames = FCnames(1:end-1);
Cnames = FCnames{end};
else
error('#FCnames mismatches #Factors+#Cov in FxC')
end
%-Set up design matrix X & names matrix - ignore zero levels if '~FxC' use
%--------------------------------------------------------------------------
if Constraint(1)~='~', [X,Pnames,Index] = spm_DesMtx(F,'-',Fnames);
else [X,Pnames,Index] = spm_DesMtx(F,'~',Fnames); end
X = X.*(C*ones(1,size(X,2)));
Pnames = cellstr([repmat([Cnames,'@'],size(Index,2),1),char(Pnames)]);
case {'.','.0','+0','+0m'} %-Constrained simple main effect
%==========================================================================
if size(I,2)~=1, error('Simple main effect requires vector index'), end
[X,Pnames,Index] = spm_DesMtx(I,'-(1)',FCnames);
%-Impose constraint if more than one effect
%--------------------------------------------------------------------------
%-Apply uniqueness constraints ('.' & '+0') to last effect, which is
% in last column, since column i corresponds to level Index(i)
%-'.0' corner point constraint is applied to zero factor level only
nXcols = size(X,2);
zCol = find(Index==0);
if nXcols==1 && ~strcmp(Constraint,'.0')
error('only one level: can''t constrain')
elseif strcmp(Constraint,'.')
X(:,nXcols)=[]; Pnames(nXcols)=[]; Index(nXcols)=[];
elseif strcmp(Constraint,'.0')
zCol = find(Index==0);
if isempty(zCol), warning('no zero level to constrain')
elseif nXcols==1, error('only one level: can''t constrain'), end
X(:,zCol)=[]; Pnames(zCol)=[]; Index(zCol)=[];
elseif strcmp(Constraint,'+0')
X(find(X(:,nXcols)),:)=-1;
X(:,nXcols)=[]; Pnames(nXcols)=[]; Index(nXcols)=[];
elseif strcmp(Constraint,'+0m')
X = X - 1/nXcols;
end
case {'.i','.i0','.j','.j0','.ij','.ij0','+i0','+j0','+ij0','+i0m','+j0m'}
%-Two way interaction effects
%==========================================================================
if size(I,2)~=2, error('Two way interaction requires Nx2 index'), end
[X,Pnames,Index] = spm_DesMtx(I,'-',FCnames);
%-Implicit sum to zero
%--------------------------------------------------------------------------
if any(strcmp(Constraint,{'+i0m','+j0m'}))
SumIToZero = strcmp(Constraint,'+i0m');
SumJToZero = strcmp(Constraint,'+j0m');
if SumIToZero %-impose implicit SumIToZero constraints
Js = sort(Index(2,:)); Js = Js([1,1+find(diff(Js))]);
for j = Js
rows = find(I(:,2)==j);
cols = find(Index(2,:)==j);
if length(cols)==1
error('Only one level: Can''t constrain')
end
X(rows,cols) = X(rows,cols) - 1/length(cols);
end
end
if SumJToZero %-impose implicit SumJToZero constraints
Is = sort(Index(1,:)); Is = Is([1,1+find(diff(Is))]);
for i = Is
rows = find(I(:,1)==i);
cols = find(Index(1,:)==i);
if length(cols)==1
error('Only one level: Can''t constrain')
end
X(rows,cols) = X(rows,cols) - 1/length(cols);
end
end
%-Explicit sum to zero
%--------------------------------------------------------------------------
elseif any(strcmp(Constraint,{'+i0','+j0','+ij0'}))
SumIToZero = any(strcmp(Constraint,{'+i0','+ij0'}));
SumJToZero = any(strcmp(Constraint,{'+j0','+ij0'}));
if SumIToZero %-impose explicit SumIToZero constraints
i = max(Index(1,:));
if i==min(Index(1,:))
error('Only one i level: Can''t constrain'), end
cols = find(Index(1,:)==i); %-columns to delete
for c=cols
j=Index(2,c);
t_cols=find(Index(2,:)==j);
t_rows=find(X(:,c));
%-This ij equals -sum(ij) over other i
% (j fixed for this col c).
%-So subtract weight of this ij factor from
% weights for all other ij factors for this j
% to impose the constraint.
X(t_rows,t_cols) = X(t_rows,t_cols)...
-X(t_rows,c)*ones(1,length(t_cols));
%-( Next line would do it, but only first time round, when all )
% ( weights are 1, and only one weight per row for this j. )
% X(t_rows,t_cols)=-1*ones(length(t_rows),length(t_cols));
end
%-delete columns
X(:,cols)=[]; Pnames(cols)=[]; Index(:,cols)=[];
end
if SumJToZero %-impose explicit SumJToZero constraints
j = max(Index(2,:));
if j==min(Index(2,:))
error('Only one j level: Can''t constrain'), end
cols=find(Index(2,:)==j);
for c=cols
i=Index(1,c);
t_cols=find(Index(1,:)==i);
t_rows=find(X(:,c));
X(t_rows,t_cols) = X(t_rows,t_cols)...
-X(t_rows,c)*ones(1,length(t_cols));
end
%-delete columns
X(:,cols)=[]; Pnames(cols)=[]; Index(:,cols)=[];
end
%-Corner point constraints
%--------------------------------------------------------------------------
elseif any(strcmp(Constraint,{'.i','.i0','.j','.j0','.ij','.ij0'}))
CornerPointI = any(strcmp(Constraint,{'.i','.i0','.ij','.ij0'}));
CornerPointJ = any(strcmp(Constraint,{'.j','.j0','.ij','.ij0'}));
if CornerPointI %-impose CornerPointI constraints
if Constraint(end)~='0', i = max(Index(1,:));
else i = 0; end
cols=find(Index(1,:)==i); %-columns to delete
if isempty(cols)
warning('no zero i level to constrain')
elseif all(Index(1,:)==i)
error('only one i level: can''t constrain')
end
%-delete columns
X(:,cols)=[]; Pnames(cols)=[]; Index(:,cols)=[];
end
if CornerPointJ %-impose CornerPointJ constraints
if Constraint(end)~='0', j = max(Index(2,:));
else j = 0; end
cols=find(Index(2,:)==j);
if isempty(cols)
warning('no zero j level to constrain')
elseif all(Index(2,:)==j)
error('only one j level: can''t constrain')
end
X(:,cols)=[]; Pnames(cols)=[]; Index(:,cols)=[];
end
end
case {'sca'} %-Scale DesMtx for visualisation
%==========================================================================
nX = []; nPnames = {}; Carg = 2;
%-Loop through the arguments accumulating scaled design matrix nX
%--------------------------------------------------------------------------
while Carg <= nargin
rX = varargin{Carg}; Carg=Carg+1;
if Carg<=nargin && ~isempty(varargin{Carg}) && ...
(ischar(varargin{Carg}) || iscellstr(varargin{Carg}))
rPnames = char(varargin{Carg}); Carg=Carg+1;
else %-No names to work out blocks from - normalise by column
rPnames = repmat('<UnSpec>',size(rX,2),1);
end
%-Pad out rPnames with 20 spaces to permit looking past line ends
rPnames = [rPnames,repmat(' ',size(rPnames,1),20)];
while ~isempty(rX)
if size(rX,2)>1 && max([1,find(rPnames(1,:)=='(')]) < ...
max([0,find(rPnames(1,:)==')')])
%-Non-specific block: find the rest & column normalise round zero
%======================================================================
c1 = max(find(rPnames(1,:)=='('));
d = any(diff(abs(rPnames(:,1:c1))),2)...
| ~any(rPnames(2:end,c1+1:end)==')',2);
t = min(find([d;1]));
%-Normalise columns of block around zero
%------------------------------------------------------------------
tmp = size(nX,2);
nX = [nX, zeros(size(rX,1),t)];
for i=1:t
if ~any(rX(:,i))
nX(:,tmp+i) = 0;
else
nX(:,tmp+i) = rX(:,i)/max(abs(rX(:,i)));
end
end
nPnames = [nPnames; cellstr(rPnames(1:t,:))];
rX(:,1:t) = []; rPnames(1:t,:)=[];
elseif size(rX,2)>1 && max([1,find(rPnames(1,:)=='[')]) < ...
max([0,find(rPnames(1,:)==']')])
%-Block: find the rest & normalise together
%======================================================================
c1 = max(find(rPnames(1,:)=='['));
d = any(diff(abs(rPnames(:,1:c1))),2)...
| ~any(rPnames(2:end,c1+1:end)==']',2);
t = min(find([d;1]));
%-Normalise block
%------------------------------------------------------------------
nX = [nX,sf_tXsca(rX(:,1:t))];
nPnames = [nPnames; cellstr(rPnames(1:t,:))];
rX(:,1:t) = []; rPnames(1:t,:)=[];
elseif size(rX,2)>1 && max([1,strfind(rPnames(1,:),'_{')]) < ...
max([0,find(rPnames(1,:)=='}')])
%-Factor, interaction of factors, or FxC: find the rest...
%======================================================================
c1 = max(strfind(rPnames(1,:),'_{'));
d = any(diff(abs(rPnames(:,1:c1+1))),2)...
| ~any(rPnames(2:end,c1+2:end)=='}',2);
t = min(find([d;1]));
%-Normalise block
%------------------------------------------------------------------
tX = rX(:,1:t);
if any(rPnames(1,1:c1)=='@') %-FxC interaction
C = tX(tX~=0);
tX(tX~=0) = 2*(C-min(C))/max(C-min(C))-1;
nX = [nX,tX];
else %-Straight interaction
nX = [nX,sf_tXsca(tX)];
end
nPnames = [nPnames; cellstr(rPnames(1:t,:))];
rX(:,1:t) = []; rPnames(1:t,:)=[];
else %-Dunno! Just column normalise
%======================================================================
nX = [nX,sf_tXsca(rX(:,1))];
nPnames = [nPnames; cellstr(rPnames(1,:))];
rX(:,1) = []; rPnames(1,:)=[];
end
end
end
X = nX;
Pnames = nPnames;
otherwise %-Mis-specified arguments - ERROR
%==========================================================================
if ischar(varargin{1})
error('unrecognised action string')
else
error('unrecognised constraint type')
end
end
%==========================================================================
% function nX = sf_tXsca(tX)
%==========================================================================
function nX = sf_tXsca(tX)
if nargin==0, nX=[]; return, end
if abs(max(abs(tX(:)))-0.7)<(.3+1e-10)
nX = tX;
elseif all(tX(:)==tX(1))
nX = ones(size(tX));
elseif max(abs(tX(:)))<1e-10
nX = zeros(size(tX));
else
nX = 2*(tX-min(tX(:)))/max(tX(:)-min(tX(:)))-1;
end
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