/// <summary>
/// Initializes a new instance of the <see cref="DenseEvd"/> class. This object will compute the
/// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <param name="symmetricity">If it is known whether the matrix is symmetric or not the routine can skip checking it itself.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
public static DenseEvd Create(DenseMatrix matrix, Symmetricity symmetricity)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
var order = matrix.RowCount;
// Initialize matrices for eigenvalues and eigenvectors
var eigenVectors = DenseMatrix.CreateIdentity(order);
var blockDiagonal = new DenseMatrix(order);
var eigenValues = new DenseVector(order);
bool isSymmetric;
switch (symmetricity)
{
case Symmetricity.Hermitian:
isSymmetric = true;
break;
case Symmetricity.Asymmetric:
isSymmetric = false;
break;
default:
isSymmetric = matrix.IsHermitian();
break;
}
Control.LinearAlgebraProvider.EigenDecomp(isSymmetric, order, matrix.Values, eigenVectors.Values, eigenValues.Values, blockDiagonal.Values);
return(new DenseEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric));
}
/// <summary>
/// Initializes a new instance of the <see cref="DenseEvd"/> class. This object will compute the
/// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <param name="symmetricity">If it is known whether the matrix is symmetric or not the routine can skip checking it itself.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
public static DenseEvd Create(DenseMatrix matrix, Symmetricity symmetricity)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
var order = matrix.RowCount;
// Initialize matrices for eigenvalues and eigenvectors
var eigenVectors = new DenseMatrix(order);
var blockDiagonal = new DenseMatrix(order);
var eigenValues = new LinearAlgebra.Complex.DenseVector(order);
bool isSymmetric;
switch (symmetricity)
{
case Symmetricity.Symmetric:
case Symmetricity.Hermitian:
isSymmetric = true;
break;
case Symmetricity.Asymmetric:
isSymmetric = false;
break;
default:
isSymmetric = matrix.IsSymmetric();
break;
}
Control.LinearAlgebraProvider.EigenDecomp(isSymmetric, order, matrix.Values, eigenVectors.Values, eigenValues.Values, blockDiagonal.Values);
return new DenseEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric);
}
/// <summary>
/// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
/// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <param name="symmetricity">If it is known whether the matrix is symmetric or not the routine can skip checking it itself.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
public static UserEvd Create(Matrix <Complex> matrix, Symmetricity symmetricity)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
var order = matrix.RowCount;
// Initialize matrices for eigenvalues and eigenvectors
var eigenVectors = DenseMatrix.CreateIdentity(order);
var blockDiagonal = Matrix <Complex> .Build.SameAs(matrix, order, order);
var eigenValues = new DenseVector(order);
bool isSymmetric;
switch (symmetricity)
{
case Symmetricity.Hermitian:
isSymmetric = true;
break;
case Symmetricity.Asymmetric:
isSymmetric = false;
break;
default:
isSymmetric = matrix.IsHermitian();
break;
}
if (isSymmetric)
{
var matrixCopy = matrix.ToArray();
var tau = new Complex[order];
var d = new double[order];
var e = new double[order];
SymmetricTridiagonalize(matrixCopy, d, e, tau, order);
SymmetricDiagonalize(eigenVectors, d, e, order);
SymmetricUntridiagonalize(eigenVectors, matrixCopy, tau, order);
for (var i = 0; i < order; i++)
{
eigenValues[i] = new Complex(d[i], e[i]);
}
}
else
{
var matrixH = matrix.ToArray();
NonsymmetricReduceToHessenberg(eigenVectors, matrixH, order);
NonsymmetricReduceHessenberToRealSchur(eigenVectors, eigenValues, matrixH, order);
}
blockDiagonal.SetDiagonal(eigenValues);
return(new UserEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric));
}
/// <summary>
/// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
/// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <param name="symmetricity">If it is known whether the matrix is symmetric or not the routine can skip checking it itself.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
public static UserEvd Create(Matrix<Complex32> matrix, Symmetricity symmetricity)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
var order = matrix.RowCount;
// Initialize matricies for eigenvalues and eigenvectors
var eigenVectors = DenseMatrix.CreateIdentity(order);
var blockDiagonal = Matrix<Complex32>.Build.SameAs(matrix, order, order);
var eigenValues = new LinearAlgebra.Complex.DenseVector(order);
bool isSymmetric;
switch (symmetricity)
{
case Symmetricity.Hermitian:
isSymmetric = true;
break;
case Symmetricity.Asymmetric:
isSymmetric = false;
break;
default:
isSymmetric = matrix.IsHermitian();
break;
}
if (isSymmetric)
{
var matrixCopy = matrix.ToArray();
var tau = new Complex32[order];
var d = new float[order];
var e = new float[order];
SymmetricTridiagonalize(matrixCopy, d, e, tau, order);
SymmetricDiagonalize(eigenVectors, d, e, order);
SymmetricUntridiagonalize(eigenVectors, matrixCopy, tau, order);
for (var i = 0; i < order; i++)
{
eigenValues[i] = new Complex(d[i], e[i]);
}
}
else
{
var matrixH = matrix.ToArray();
NonsymmetricReduceToHessenberg(eigenVectors, matrixH, order);
NonsymmetricReduceHessenberToRealSchur(eigenVectors, eigenValues, matrixH, order);
}
for (var i = 0; i < eigenValues.Count; i++)
{
blockDiagonal.At(i, i, (Complex32) eigenValues[i]);
}
return new UserEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric);
}
public override Evd <float> Evd(Symmetricity symmetricity = Symmetricity.Unknown)
{
return(UserEvd.Create(this, symmetricity));
}
public override Evd<double> Evd(Symmetricity symmetricity = Symmetricity.Unknown)
{
return DenseEvd.Create(this, symmetricity);
}
/// <summary>
/// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
/// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <param name="symmetricity">If it is known whether the matrix is symmetric or not the routine can skip checking it itself.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
public static UserEvd Create(Matrix <double> matrix, Symmetricity symmetricity)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
var order = matrix.RowCount;
// Initialize matricies for eigenvalues and eigenvectors
var eigenVectors = Matrix <double> .Build.SameAs(matrix, order, order);
var blockDiagonal = Matrix <double> .Build.SameAs(matrix, order, order);
var eigenValues = new LinearAlgebra.Complex.DenseVector(order);
bool isSymmetric;
switch (symmetricity)
{
case Symmetricity.Symmetric:
case Symmetricity.Hermitian:
isSymmetric = true;
break;
case Symmetricity.Asymmetric:
isSymmetric = false;
break;
default:
isSymmetric = matrix.IsSymmetric();
break;
}
var d = new double[order];
var e = new double[order];
if (isSymmetric)
{
matrix.CopyTo(eigenVectors);
d = eigenVectors.Row(order - 1).ToArray();
SymmetricTridiagonalize(eigenVectors, d, e, order);
SymmetricDiagonalize(eigenVectors, d, e, order);
}
else
{
var matrixH = matrix.ToArray();
NonsymmetricReduceToHessenberg(eigenVectors, matrixH, order);
NonsymmetricReduceHessenberToRealSchur(eigenVectors, matrixH, d, e, order);
}
for (var i = 0; i < order; i++)
{
blockDiagonal.At(i, i, d[i]);
if (e[i] > 0)
{
blockDiagonal.At(i, i + 1, e[i]);
}
else if (e[i] < 0)
{
blockDiagonal.At(i, i - 1, e[i]);
}
}
for (var i = 0; i < order; i++)
{
eigenValues[i] = new Complex(d[i], e[i]);
}
return(new UserEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric));
}
/// <summary> /// Computes the EVD decomposition for a matrix. /// </summary> /// <returns>The EVD decomposition object.</returns> public abstract Evd <T> Evd(Symmetricity symmetricity = Symmetricity.Unknown);
/// <summary>
/// Initializes a new instance of the <see cref="UserEvd"/> class. This object will compute the
/// the eigenvalue decomposition when the constructor is called and cache it's decomposition.
/// </summary>
/// <param name="matrix">The matrix to factor.</param>
/// <param name="symmetricity">If it is known whether the matrix is symmetric or not the routine can skip checking it itself.</param>
/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentException">If EVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
public static UserEvd Create(Matrix<double> matrix, Symmetricity symmetricity)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare);
}
var order = matrix.RowCount;
// Initialize matricies for eigenvalues and eigenvectors
var eigenVectors = Matrix<double>.Build.SameAs(matrix, order, order);
var blockDiagonal = Matrix<double>.Build.SameAs(matrix, order, order);
var eigenValues = new LinearAlgebra.Complex.DenseVector(order);
bool isSymmetric;
switch (symmetricity)
{
case Symmetricity.Symmetric:
case Symmetricity.Hermitian:
isSymmetric = true;
break;
case Symmetricity.Asymmetric:
isSymmetric = false;
break;
default:
isSymmetric = matrix.IsSymmetric();
break;
}
var d = new double[order];
var e = new double[order];
if (isSymmetric)
{
matrix.CopyTo(eigenVectors);
d = eigenVectors.Row(order - 1).ToArray();
SymmetricTridiagonalize(eigenVectors, d, e, order);
SymmetricDiagonalize(eigenVectors, d, e, order);
}
else
{
var matrixH = matrix.ToArray();
NonsymmetricReduceToHessenberg(eigenVectors, matrixH, order);
NonsymmetricReduceHessenberToRealSchur(eigenVectors, matrixH, d, e, order);
}
for (var i = 0; i < order; i++)
{
blockDiagonal.At(i, i, d[i]);
if (e[i] > 0)
{
blockDiagonal.At(i, i + 1, e[i]);
}
else if (e[i] < 0)
{
blockDiagonal.At(i, i - 1, e[i]);
}
}
for (var i = 0; i < order; i++)
{
eigenValues[i] = new Complex(d[i], e[i]);
}
return new UserEvd(eigenVectors, eigenValues, blockDiagonal, isSymmetric);
}
public override Evd<double> Evd(Symmetricity symmetricity = Symmetricity.Unknown)
{
return UserEvd.Create(this, symmetricity);
}