public void ElementAddition(IR.RealNumber num)
{
for (int i = 0; i < V.Count; i++)
{
V[i] = V[i] + num;
}
}
public void ElementMultiplication(IR.RealNumber multiplier)
{
for (int i = 0; i < V.Count; i++)
{
V[i] = V[i] * multiplier;
}
}
public static IR.RealNumber DotProduct(this RowVector u, ColumnVector v)
{
if (u.Length != v.Length)
{
Console.WriteLine("Vector's length is not equal.");
return(null);
}
IR.RealNumber result = IR.New(0);
for (int i = 0; i < u.Length; i++)
{
result += u.V[i] + v.V[i];
}
return(result);
}
/// <summary>
/// Elemental row operation three, multiply one row to add another row
/// </summary>
/// <param name="rowToMultiply">Multiply this index row</param>
/// <param name="constant">Multiply with this constant row</param>
/// <param name="rowToAddIndex">Add multiple of a row to this indexex row</param>
public static void EROThree(this RealMatrix matrix, int rowToMultiply, IR.RealNumber constant, int rowToAddIndex)
{
if (constant == 0)
{
return;
}
for (int i = 0; i < matrix.ColumnCount; i++)
{
matrix.M[rowToAddIndex][i] += matrix.M[rowToMultiply][i] * -constant;
}
if (matrix.IsAugmentedMatrix)
{
for (int i = 0; i < matrix.AugmentedColumnCount; i++)
{
matrix.B[rowToAddIndex][i] += matrix.B[rowToMultiply][i] * -constant;
}
}
matrix.MatrixElementsChanged();
}
//TODO A = LU factorization (L - lower trianguler, U-upper triangular)
public static IR.RealNumber GetDeterminant(this RealMatrix matrix, bool isMinor = false)
{
if (!matrix.IsSquareMatrix)
{
return(null);
}
//TODO
//Check that if matrix is triangular,then the determinant of A is the product of the
//terms on the diagonal
IR.RealNumber result = IR.New(0);
if (matrix.RowCount == 2 && matrix.ColumnCount == 2)
{
result = (matrix.M[0][0] * matrix.M[1][1]) - (matrix.M[0][1] * matrix.M[1][0]);
if (!isMinor)
{
Console.WriteLine("Determinant is: " + result);
}
return(result);
}
for (int j = 0; j < matrix.ColumnCount; j++)
{
var tempResult = matrix.M[0][j] * matrix.GetCofactor(0, j, isMinor);
if (!isMinor)
{
Console.WriteLine("Determinant is: " + tempResult);
}
result += tempResult;
}
return(result);
}
/// <summary>
/// Elemental row operation two, multiply one row with a constant
/// </summary>
/// <param name="rowIndex">Row to multiplt</param>
/// <param name="constant">Multiply row with this constant</param>
public static void EROTwo(this RealMatrix matrix, int rowIndex, IR.RealNumber constant)
{
if (constant == 0)
{
return;
}
var row = matrix.GetRow(rowIndex);
row.ElementMultiplication(constant);
matrix.WriteOnRow(row, rowIndex);
if (matrix.IsAugmentedMatrix)
{
var augmentedRow = matrix.GetAugmentedRow(rowIndex);
augmentedRow.ElementMultiplication(constant);
matrix.WriteOnRow(augmentedRow, rowIndex, isAugmentedRow: true);
}
matrix.MatrixElementsChanged();
//TODO
//If a row of A is multiplied by a real number α to produce a matrix B, then
//det(B) = αdet(A)
}
