//=====================================================================
/// <summary>
/// Metodo de Gauss-Jordan
/// </summary>
/// <param name="matrix"></param>
internal static void EscalonadaReducidaPorFilas(Matrix matrix)
{
//1. Obtein the matrix EscalonadaPorFilas
List <ElementalOperation.Data> inData;
EscalonadaPorFilas(matrix, out inData);
//2. With elemental operation III, make null the index up the pivote starting by the end
for (int i = matrix.Rows - 1; i > 0; i--)
{
int pivoteIndex = Utilities.GetFirtsIndexNoNull(matrix, i);
for (int k = i - 1; k > -1; k--)
{
if (matrix[k, pivoteIndex] != 0)
{
ElementalOperation.Operation(matrix, ElementalOperation.Data.DataOperationIII(k, -matrix[k, pivoteIndex] / matrix[i, pivoteIndex], 0));
}
}
}
//3. With elemental operation II, make 1 the pivote
for (int i = 0; i > matrix.Rows; i++)
{
int pivoteIndex = Utilities.GetFirtsIndexNoNull(matrix, i);
ElementalOperation.Operation(matrix, ElementalOperation.Data.DataOperationII(i, 1 / matrix[1, pivoteIndex]));
}
}
//=====================================================================
/// <summary>
/// Metodo de Gauss para la obtención de la matriz escalonada por filas
/// </summary>
/// <param name="matrix"></param>
internal static void EscalonadaPorFilas(Matrix matrix, out List <ElementalOperation.Data> elementalOperantions)
{
elementalOperantions = new List <ElementalOperation.Data>();
//1.With elemental operation I, order the row to obtain the first row with the index no null lower. The first input no null is called PIVOTE
for (int i = 1; i < matrix.Rows; i++)
{
if (Utilities.GetFirtsIndexNoNull(matrix, i) < Utilities.GetFirtsIndexNoNull(matrix, i - 1))
{
ElementalOperation.Data data = ElementalOperation.Data.DataOperationI(i, i - 1);
ElementalOperation.Operation(matrix, data);
elementalOperantions.Add(data);
i = Math.Max(0, i - 2);
}
}
//2. With elemental operation III, make null the index down the pivote
int pivoteIndex = Utilities.GetFirtsIndexNoNull(matrix, 0);
if (!(pivoteIndex < matrix.Cols))
{
return;
}
for (int i = 1; i < matrix.Rows; i++)
{
if (matrix[i, pivoteIndex] != 0)
{
ElementalOperation.Data data = ElementalOperation.Data.DataOperationIII(i, -matrix[i, pivoteIndex] / matrix[0, pivoteIndex], 0);
ElementalOperation.Operation(matrix, data);
elementalOperantions.Add(data);
}
}
List <ElementalOperation.Data> inData;
//3. Delete the first line and make the steps 1 and 3
if (matrix.Rows > 1)
{
EscalonadaPorFilas(matrix[1, 0, matrix.Rows - 1, matrix.Cols], out inData);
foreach (ElementalOperation.Data d in inData)
{
elementalOperantions.Add(d);
}
}
}