Get the first column of a matrix represented by a vector of vectors

Question

Suppose I'm representing a matrix foo of values using std::vector:

int rows = 5;
int cols = 10;    
auto foo = vector<vector<double>>(rows, vector<double>(cols));

Is there a cleverly simple way for me to get a vector<int> of size rows that contains the first "column" of foo:

{foo[0][0], foo[0][1], foo[0][2], foo[0][3], foo[0][4] }

Put another way, can I "transpose" foo so that the following three things are true:

foo_transpose.size() == cols
foo_transpose[0].size() == rows
foo_transpose[0] == {foo[0][0], foo[0][1], foo[0][2], foo[0][3], foo[0][4] }

Clarifying Note

There are a few good suggestions for alternative ways to represent a "matrix". When I use the term "matrix" I simply mean that each of the second level vector's will be the same size. I don't mean to suggest that I will be using this data structure for linear algebra type operation. I actually DO need a vector of vectors, or a data structure from which you can "pull out" 1D vectors, because I have functions that operate on vectors like:

double sum(vector<double> const & v);

That I call by:

sum(foo[0]);

It's just in a special case I came up to a situation that need to do:

sum({foo[0][0], foo[0][1], foo[0][2], foo[0][3], foo[0][4] };

For Loop Solution

There is an obvious for loop solution, but I was looking for something more robust and efficient.

Solution

As I mentioned in the comments, it's not practical to represent matrices using vector-of-vector for a few reasons:

1. It is fiddly to set up;
2. It is difficult to change;
3. Cache locality is bad.

Here is a very simple class I have created that will hold a 2D matrix in a single vector. This is pretty much how software like MATLAB does it... albeit a huge simplification.

template <class T>
class SimpleMatrix
{
public:
    SimpleMatrix( int rows, int cols, const T& initVal = T() );

    // Size and structure
    int NumRows() const                       { return m_rows; }
    int NumColumns() const                    { return m_cols; }
    int NumElements() const                   { return m_data.size(); }

    // Direct vector access and indexing
    operator const vector<T>& () const        { return m_data; }
    int Index( int row, int col ) const       { return row * m_cols + col; }

    // Get a single value
          T & Value( int row, int col )       { return m_data[Index(row,col)]; }
    const T & Value( int row, int col ) const { return m_data[Index(row,col)]; }
          T & operator[]( size_t idx )        { return m_data[idx]; }
    const T & operator[]( size_t idx ) const  { return m_data[idx]; }

    // Simple row or column slices
    vector<T> Row( int row, int colBegin = 0, int colEnd = -1 ) const;
    vector<T> Column( int row, int colBegin = 0, int colEnd = -1 ) const;

private:
    vector<T> StridedSlice( int start, int length, int stride ) const;

    int m_rows;
    int m_cols;

    vector<T> m_data;
};

This class is basically sugar-coating around a single function -- StridedSlice. The implementation of that is:

template <class T>
vector<T> SimpleMatrix<T>::StridedSlice( int start, int length, int stride ) const
{
    vector<T> result;
    result.reserve( length );
    const T *pos = &m_data[start];
    for( int i = 0; i < length; i++ ) {
        result.push_back(*pos);
        pos += stride;
    }
    return result;
}

And the rest is pretty straight-forward:

template <class T>
SimpleMatrix<T>::SimpleMatrix( int rows, int cols, const T& initVal )
    : m_data( rows * cols, initVal )
    , m_rows( rows )
    , m_cols( cols )
{    
}

template <class T>
vector<T> SimpleMatrix<T>::Row( int row, int colBegin, int colEnd ) const
{
    if( colEnd < 0 ) colEnd = m_cols-1;
    if( colBegin <= colEnd )
        return StridedSlice( Index(row,colBegin), colEnd-colBegin+1, 1 );
    else
        return StridedSlice( Index(row,colBegin), colBegin-colEnd+1, -1 );
}

template <class T>
vector<T> SimpleMatrix<T>::Column( int col, int rowBegin, int rowEnd ) const
{
    if( rowEnd < 0 ) rowEnd = m_rows-1;
    if( rowBegin <= rowEnd )
        return StridedSlice( Index(rowBegin,col), rowEnd-rowBegin+1, m_cols );
    else
        return StridedSlice( Index(rowBegin,col), rowBegin-rowEnd+1, -m_cols );
}

Note that the Row and Column functions are set up in such a way that you can easily request an entire row or column, but are a little more powerful because you can slice a range by passing one or two more parameters. And yes, you can return the row/column in reverse by making your start value larger than your end value.

There is no bounds-checking built into these functions, but you can easily add that.

You could also add something to return an area slice as another SimpleMatrix<T>.

Have fun.