computing column sums of matrix vector<vector<double> > with iterators?

Question

In a previous post column vector with row means -- with std::accumulate? I asked if it was possible, using STL functionality, to compute row means of a matrix

vector< vector<double> > data ( rows, vector<double> ( columns ) );

The top answer by @benjaminlindley is not only just what I was looking for, it is a thing of beauty. Forever hopeful I thought it would be as easy to compute column means, so an STL equivalent of

vector<double> colmeans( data[0].size() );
    for ( int i=0; i<data.size(); i++ )
        for ( int j=0; j<data[i].size(); j++ )            
            colmeans[j] += data[i][j]/data.size();

where the mean is not computed inside each vector<double>, but across the same index in all the vectors:

colmeans[0]       == ( data[0][0] + data[1][0] + ... data[rows][0] ) / rows
colmeans[1]       == ( data[0][1] + data[1][1] + ... data[rows][1] ) / rows
colmeans[2]       == ( data[0][2] + data[1][2] + ... data[rows][2] ) / rows
...
colmeans[columns] == ( data[0]   [columns] + 
                       data[1]   [columns] + 
                       ... 
                       data[rows][columns] ) / rows

It turns out to be quite different -- accumulate does not want to work on vectors of vectors. Is it somehow possible using accumulate with the [] operator? I cannot even come up with an intermediate form (to get rid of eather the for i or for j loop) which does not seem right.

Something with accumulate and the [] operator? Or bind?

Answer 1

Here's something I came up with, using for_each and transform:

std::vector<std::vector<double>> data { {1,2,3}, {1,2,3}, {1,2,3} };

std::vector<double> colsums( data[0].size() ); // initialize the size
                                                // to number of columns

std::for_each(data.begin(), data.end(),

    [&](const std::vector<double>& row)
    {
        // Use transform overload that takes two input ranges.
        // Note that colsums is the second input range as well as the output range.
        // We take each element of the row and add it to the corresponding
        // element of colsums vector:
        std::transform(row.begin(), row.end(), colsums.begin(), colsums.begin(),
                       [](double d1, double d2) { return d1 + d2; });
    });

std::cout << "Column means: ";
std::transform(
    colsums.begin(), colsums.end(),
    std::ostream_iterator<double>(std::cout, " "),
    [&data](double d) { return d / data.size(); });

LWS Demo