% useful numeric functions
%  sum 
%  mean 
%  max
%  min
%  std 
%  var
%  median 
%  prctile
%  sort
%  sortrows

a = randn(5,3);  % 5 x 3 matrix of random zero-mean unit-variance normals

sum(a)    % sum along first dimension (row)
sum(a,2)  % sum along second dimension (column)

mean(a)   % mean along rows
mean(a,2) % mean along columns

min(a)      % min along rows
min(a,[],2) % min along columns -- why blank second argument?
            % becaues min with two arguments returns the minimum
            % between first and second argument

% let's capture outputs of min

mina = min(a,[],2)            % the minimum values across columns

[mina,mina_loc] = min(a,[],2) % the index of each column at which the min
                              % occurs is also captured in a second
                              % argument
            
% max, like min, also has up to to output arguments (not shown below)

max(a)      % max along rows
max(a,[],2) % max along columns (two-argument case similar to min)


std(a)      % standard deviation of values along rows
var(a)      % variance is just square of standard deviation
            % follows same function input/output conventions

var(a,[],2) % variance deviation of values along columns            
            % why blank second arugment?
            % second arugment used to tell matlab what kind of estimate
            % to make for the standard deviation. the default case is
            % to divide by n-1 in order to get an unbiased estimate 
            % (default is best)
            
median(a)   % median along rows
median(a,2) % median along columns

prctile(a,10)    % 10th percentile along rows
prctile(a,10,2)  % 10th percentile along columns
prctile(a(:),10) % 10th percentile of all values in a
                 % note m(:) for any matrix m will always produce
                 % a row vector with the same number of elements as m
                 % (it linearizes m)
                 
sort(a)           % this produces a matrix, where each column has the same
                  % values as each column in a, but in which the values
                  % in those columns are sorted into increasing order
                  % (we are sorting ALONG first dimension - row)

sort(a,'descend') % same as before only descending

sort(a,2)        % this outputs a matrix in which each row has the same values
                 % as a , except they are in increasing order
                 % (we are sorting ALONG second dimension - column)
                 
sort(a,2,'descend') % sort along columns, descending

% as with min and max, we can capture a second "index" arugment
% here, asortedi will contain the column indexes sorted in descending order
% for each row
[asorted,asortedi] = sort(a,2,'descend')
                                   


sortrows(a)     % this is a matrix in which entire rows are preserved in order,
                % but in which the rows have been re-shuffled, so that the
                % first element is increasing down the matrix

sortrows(a,-1)     % same as above, except descending
sortrows(a,[-1 2]) % break ties with first element according to increasing 
                   % second (column) element

[arows,arowsi] = sortrows(a,2)  % just increasing along second (column) element
                                % arowsi contains the row indices of each
                                % row, in order of increasing second column
                                % value