gauss-jordan method

[rey9]

can anyone teach me how to make a simple c++ program that solves a linear eqations using gauss-jordan method?
any help will be highly appreciated :) thank you

[Stewbond]

Here's something that I wrote a little while ago. The problem is that it will not work if there is no inverse of the matrix.

Matrix& Matrix::rowEchelonForm()
{    
    if (m_cols <= m_rows)
        throw MatrixException(wrongSizeCalc, __FUNCTION__, __LINE__, __FILE__);

    // Step 1, remove the lower terms
    for (int col = 0; col < m_rows; ++col)
    {
        // It's a zero, Swap with another row
        if ( at(col,col)==0 )
        {
            for (int row = col+1; row < m_rows; ++row)
                if ( at(row,col) ) 
                    rowSwap(row,col);
            if( ! at(col,col) )
                throw MatrixException(unsolvable, __FUNCTION__, __LINE__, __FILE__);
        }
    
        // Set the first element to 1
        rowGain(col, ((T)1) / at(col,col) );

        // Set the rest of the rows to 0
        for (int row = col+1; row < m_rows; ++row)
            rowGainAndAdd(T(-1) * at(row,col) , col, row);
    }

    // Step 2, remove the upper terms
    for (int col = 1; col < m_rows; ++col)
        for (int row = 0; row < col; ++row)
            rowGainAndAdd( T(-1) * at(row,col) , col, row);

    return *this;
}

void Matrix::rowGain(int row, T gain)
{
    if (row >= m_rows)
        throw MatrixException(invSet, __FUNCTION__, __LINE__, __FILE__);
        
    for (int i = 0; i < m_cols; ++i)
        m_data[row*m_cols + i] *= gain;
}

void Matrix::rowSwap(int row1, int row2)
{
    if (row1 >= m_rows || row2 >= m_rows)
        throw MatrixException(invSet, __FUNCTION__, __LINE__, __FILE__);
        
    T* row = new T[m_cols];
    
    for (int i = 0; i < m_cols; ++i)
    {
        row[i] = at(row1, i);
        set(row1, i,  at(row2, i) );
        set(row2, i,  row[i]);
    }
    
    delete[] row;    
}

void Matrix::rowGainAndAdd(T gain, int SourceRow, int DestinationRow)
{
    if (SourceRow >= m_rows || DestinationRow >= m_rows)
        throw MatrixException(invSet, __FUNCTION__, __LINE__, __FILE__);    
    
    for (int i = 0; i < m_cols; ++i)
        m_data[DestinationRow*m_cols + i] += gain * m_data[SourceRow*m_cols + i];
}

[rey9]

thank you very much Stewbond :D this will really help me alot. thank you :)

[ne555]

Some comments:

In `(the diagonal) It's a zero, Swap with another row' you may want to break the loop after the first swap.

for (int col = 0; col < m_rows; ++col) looks obfuscated. You could change `col' by `current_row'

`Step 2, remove the upper terms' has the same code as `Step 1, remove the lower terms'. You could simply put a continue so it does not operate on the current row.

You do not want that dynamic allocation in `rowSwap'

Your class is not for matrices, maybe LES would be a better name.