GaussMatrixF.cs

using System;

public class GaussMatrixF
{
    public class Row
    {
        public float[] cols;
        public Row(int aCols)
        {
            cols = new float[aCols];
        }
        public void Multiply(float aVal)
        {
            for (int i = 0; i < cols.Length; i++)
                cols[i] *= aVal;
        }
        public void Add(Row aRow, float aVal)
        {
            for (int i = 0; i < cols.Length; i++)
                cols[i] = cols[i] + aRow.cols[i] * aVal;
        }
        public override string ToString()
        {
            var sb = new System.Text.StringBuilder();
            sb.Append(cols[0]);
            for (int i = 1; i < cols.Length; i++)
                sb.Append(",\t").Append(cols[i]);
            return sb.ToString();
        }
    }

    public Row[] rows;

    public GaussMatrixF(int aCols, int aRows)
    {
        rows = new Row[aRows];
        for (int i = 0; i < aRows; i++)
            rows[i] = new Row(aCols);
    }

    public bool CreateUpperTriangle(out float det)
    {
        det = 1;
        for(int i = 0; i < rows.Length; i++)
        {
            var index = FindPivot(i);
            if (index == -1)
            {
                det = 0;
                return false;
            }
            if (index != i)
            {
                Swap(i, index);
                det = -det;
            }
            var r = rows[i];
            if (r.cols[i] != 1)
            {
                det *= r.cols[i];
                r.Multiply(1 / r.cols[i]);
                r.cols[i] = 1;
            }
            for (int n = i + 1; n < rows.Length; n++)
            {
                if (rows[n].cols[i] != 0)
                {
                    rows[n].Add(r, -rows[n].cols[i]);
                    rows[n].cols[i] = 0;
                }
            }
        }
        return true;
    }

    public bool Solve()
    {
        float det;
        if (!CreateUpperTriangle(out det))
            return false;
        for (int i = 1; i < rows.Length; i++)
        {
            var r = rows[i];
            for (int n = 0; n < i; n++)
            {
                if (rows[n].cols[i] != 0)
                {
                    rows[n].Add(r, -rows[n].cols[i]);
                    rows[n].cols[i] = 0;
                }
            }
        }
        return true;
    }


    void Swap(int a, int b)
    {
        var tmp = rows[a];
        rows[a] = rows[b];
        rows[b] = tmp;
    }

    private int FindPivot(int aCol)
    {
        int index = -1;
        float val = 0;
        for(int i = aCol; i < rows.Length; i++)
        {
            var v = rows[i].cols[aCol];
            if (v < 0)
                v = -v;
            if (v > 1)
                v = 1 / v;

            if (v > val )
            {
                val = v;
                index = i;
            }
        }
        return index;
    }
    public override string ToString()
    {
        var sb = new System.Text.StringBuilder();
        sb.Append(rows[0]);
        for (int i = 1; i < rows.Length; i++)
            sb.AppendLine().Append(rows[i]);
        return sb.ToString();
    }

}