algorithm for index numbers of triangular matrix coefficients

Question

I think this must be simple but I can\'t get it right...

I have an MxM triangular matrix, the coefficients of which are stored in a vector, row by row. For example:

Answer 1

There may be a clever one liner for these, but (minus any error checking):

unsigned int row_index( unsigned int i, unsigned int M ){
    unsigned int row = 0;
    unsigned int delta = M - 1;
    for( unsigned int x = delta; x < i; x += delta-- ){
        row++;
    }
    return row;
}

unsigned int column_index( unsigned int i, unsigned int M ){
    unsigned int row = 0;
    unsigned int delta = M - 1;
    unsigned int x;
    for( x = delta; x < i; x += delta-- ){
        row++;
    }
    return M + i - x - 1;
}