/// <summary>
/// Computes all eigenvalues and eigenvectors of a of a real symmetric matrix A.
/// </summary>
/// <param name="A">The real symmetric matrix A.</param>
/// <param name="EigenVects">The eigenvectors.</param>
/// <returns>The eigenvalues.</returns>
public Matrix GetEigenvalues(SymmetricMatrix A, out Matrix EigenVects)
{
if (this._dsyev == null) this._dsyev = new DSYEV();
this.CheckDimensions(A);
EigenVects = new Matrix(A.RowCount, A.ColumnCount, A.Data);
double[] EigenVectsData = EigenVects.Data;
Matrix EigenVals = new Matrix(A.RowCount, 1);
double[] EigenValsData = EigenVals.Data;
int Info = 0;
double[] Work = new double[1];
int LWork = -1;
//Calculamos LWORK ideal
_dsyev.Run("V", "U", A.RowCount, ref EigenVectsData, 0, A.RowCount, ref EigenValsData, 0, ref Work, 0, LWork, ref Info);
LWork = Convert.ToInt32(Work[0]);
if (LWork > 0)
{
Work = new double[LWork];
_dsyev.Run("V", "U", A.RowCount, ref EigenVectsData, 0, A.RowCount, ref EigenValsData, 0, ref Work, 0, LWork, ref Info);
}
else
{
//Error
}
#region Error
/// = 0: successful exit
/// .LT. 0: if INFO = -i, the i-th argument had an illegal value
/// .GT. 0: if INFO = i, the algorithm failed to converge; i
/// off-diagonal elements of an intermediate tridiagonal
/// form did not converge to zero.
if (Info < 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new ArgumentException("the " + infoSTg + " -th argument had an illegal value");
}
else if (Info > 0)
{
string infoSTg = Math.Abs(Info).ToString();
throw new Exception("The algorithm failed to converge.");
}
#endregion
return EigenVals;
}
public SymmetricMatrix Clone()
{
SymmetricMatrix NewMatrix = new SymmetricMatrix(this._RowCount, this._Data);
return NewMatrix;
}
/// <summary>
/// Matrix subtraction.
/// </summary>
/// <param name="A"> The left side matrix of the subtraction operator.</param>
/// <param name="B">The right side matrix of the subtraction operator.</param>
/// <returns>A matrix that represents the result of the matrix subtraction.</returns>
public static SymmetricMatrix operator -(SymmetricMatrix A, SymmetricMatrix B)
{
if (B.RowCount != A.RowCount || B.ColumnCount != A.ColumnCount)
{
throw new System.ArgumentException("Matrix dimensions are not valid.");
}
SymmetricMatrix C = new SymmetricMatrix(A.RowCount);
double[] AData = A.Data;
double[] BData = B.Data;
double[] CData = C.Data;
for (int i = 0; i < AData.Length; i++)
{
CData[i] = AData[i] - BData[i];
}
return C;
}
/// <summary>
/// Generate a matrix with random elements
/// </summary>
/// <param name="size">Size</param>
/// <param name="Seed">
/// A number used to calculate a starting value for the pseudo-random number
/// sequence. If a negative number is specified, the absolute value of the number
/// is used.
/// </param>
/// <returns>An m-by-n matrix with uniformly distributed
/// random elements in <c>[0, 1)</c> interval.</returns>
public static SymmetricMatrix Random(int size, int Seed)
{
System.Random random = new System.Random(Seed);
SymmetricMatrix X = new SymmetricMatrix(size);
double[] XData = X.Data;
for (int j = 0; j < X.ColumnCount; j++)
{
for (int i = 0; i < X.RowCount; i++)
{
X[i, j] = random.NextDouble();
}
}
return X;
}
/// <summary>
/// Scalar-Matrix multiplication.
/// </summary>
/// <param name="s"> The left side scalar of the multiplication operator.</param>
/// <param name="A">The right side matrix of the multiplication operator.</param>
/// <returns>A matrix that represents the result of the multiplication.</returns>
public static SymmetricMatrix operator *(double s, SymmetricMatrix A)
{
SymmetricMatrix C = new SymmetricMatrix(A.RowCount);
double[] AData = A.Data;
double[] CData = C.Data;
Matrix.MultiplicationSM(s, AData, CData);
return C;
}