function [x, xm, xs] = standardize(x, scale)%STANDARDIZE   Centers and normalizes data.%%    [XC, XM, XS] = STANDARDIZE(X) centers and normalizes the data in X to%    XC by subtracting the mean XM of each column and dividing each%    column by its standard deviation XS. If X contains missing%    values, indicated by NaNs, the mean and standard deviation of X%    are computed from the available data.%%    [XC, XM, XS] = STANDARDIZE(X, SCALE) centers and normalizes the data%    in X to zero mean and standard deviation SCALE. The column means%    are returned as XM and the scale factors as XS = std(X) ./ SCALE.%%    Constant columns of X are not scaled.  %%    See also CENTER, NANMEAN, MEAN, NANSTD, STD.  error(nargchk(1,2,nargin))          % check number of input arguments     if nargin < 2     scale = 1;  end    if ndims(x) > 2,  error('X must be vector or 2-D array.'); end    % if x is a vector, make sure it is a row vector  if length(x)==prod(size(x))             x = x(:);                           end   [m,n]  = size(x);  % get mean and standard deviation of x  if any(any(isnan(x)))               % there are missing values in x    xm   = nanmean(x);    xs   = nanstd(x) ./ scale;  else                                % no missing values    xm   = mean(x);    xs   = std(x) ./ scale;  end  % test for constant columns  const  = (abs(xs) < eps);  nconst = ~const;  if sum(const) ~= 0    warning('Constant or nearly constant columns not rescaled.');    xm   = xm .* nconst + 0*const;    xs   = xs .* nconst + 1*const;  end     % remove mean and divide by standard deviation  x      = (x - repmat(xm, m, 1) ) ./ repmat(xs, m, 1);