///<inheritdoc cref="SingularValueDecomposition.Decompose(
///DoubleMatrix, out DoubleMatrix, out DoubleMatrix)"/>
public static DoubleMatrix Decompose(
ComplexMatrix matrix,
out ComplexMatrix leftSingularVectors,
out ComplexMatrix conjugateTransposedRightSingularVectors)
{
#region Input validation
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
#endregion
int m = matrix.NumberOfRows;
int n = matrix.NumberOfColumns;
int min_m_n = m < n ? m : n;
Complex[] a = matrix.AsColumnMajorDenseArray();
double[] s = new double[min_m_n];
Complex[] u = new Complex[m * m];
Complex[] vt = new Complex[n * n];
int lapackInfo;
double[] superb = new double[min_m_n - 1];
lapackInfo = SafeNativeMethods.LAPACK.ZGESVD(
matrix_layout: SafeNativeMethods.LAPACK.ORDER.ColMajor,
jobu: 'A',
jobvt: 'A',
m,
n,
a,
lda: m,
s,
u,
ldu: m,
vt,
ldvt: n,
superb);
if (lapackInfo > 0)
{
throw new InvalidOperationException(
ImplementationServices.GetResourceString(
"STR_EXCEPT_ALG_DOES_NOT_CONVERGE"));
}
DoubleMatrix values = DoubleMatrix.Dense(m, n);
for (int i = 0; i < min_m_n; i++)
{
values[i, i] = s[i];
}
leftSingularVectors =
ComplexMatrix.Dense(m, m, u, copyData: false);
conjugateTransposedRightSingularVectors =
ComplexMatrix.Dense(n, n, vt, copyData: false);
return(values);
}
/// <summary>
/// Computes eigenvalues and eigenvectors of the
/// specified Hermitian complex matrix.
/// </summary>
/// <param name="matrix">
/// The matrix containing the lower or upper triangular part of the matrix
/// whose spectral decomposition must be computed.
/// </param>
/// <param name="lowerTriangularPart">
/// <c>true</c> if <paramref name="matrix"/> contains the lower
/// triangular part of the matrix to be decomposed;
/// <c>false</c> if <paramref name="matrix"/> contains
/// its upper triangular part.
/// </param>
/// <param name="eigenvectors">
/// A matrix whose columns represent the eigenvectors
/// of the decomposed matrix.
/// </param>
/// <returns>
/// A diagonal matrix containing the eigenvalues
/// of the decomposed matrix, in ascending order.
/// </returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="matrix"/> is <b>null</b>.
/// </exception>
/// <exception cref="ArgumentException">
/// <paramref name="matrix"/> is not square.
/// </exception>
public static DoubleMatrix Decompose(
ComplexMatrix matrix,
bool lowerTriangularPart,
out ComplexMatrix eigenvectors)
{
#region Input validation
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
if (!matrix.IsSquare)
{
throw new ArgumentException(
message: ImplementationServices.GetResourceString(
"STR_EXCEPT_PAR_MUST_BE_SQUARE"),
paramName: nameof(matrix));
}
#endregion
int m = matrix.NumberOfRows;
double[] valuesArray = new double[m];
Complex[] vectorsArray = matrix.AsColumnMajorDenseArray();
int info = SafeNativeMethods.LAPACK.ZHEEV(
matrix_layout: SafeNativeMethods.LAPACK.ORDER.ColMajor,
jobz: 'V',
uplo: lowerTriangularPart ? 'L' : 'U',
n: m,
a: vectorsArray,
lda: m,
w: valuesArray);
if (info > 0)
{
throw new InvalidOperationException(
message: ImplementationServices.GetResourceString(
"STR_EXCEPT_ALG_DOES_NOT_CONVERGE"));
}
DoubleMatrix eigenvalues = DoubleMatrix.Sparse(m, m, m);
for (int i = 0; i < m; i++)
{
eigenvalues[i, i] = valuesArray[i];
}
eigenvectors =
ComplexMatrix.Dense(m, m, vectorsArray, copyData: false);
Debug.Assert(eigenvalues != null);
Debug.Assert(eigenvectors != null);
return(eigenvalues);
}
///<inheritdoc cref="SingularValueDecomposition
///.GetSingularValues(DoubleMatrix)"/>
public static DoubleMatrix GetSingularValues(
ComplexMatrix matrix)
{
#region Input validation
if (matrix is null)
{
throw new ArgumentNullException(nameof(matrix));
}
#endregion
int m = matrix.NumberOfRows;
int n = matrix.NumberOfColumns;
int min_m_n = m < n ? m : n;
Complex[] a = matrix.AsColumnMajorDenseArray();
double[] s = new double[min_m_n];
Complex[] u = null;
Complex[] vt = null;
int lapackInfo;
double[] superb = new double[min_m_n - 1];
lapackInfo = SafeNativeMethods.LAPACK.ZGESVD(
matrix_layout: SafeNativeMethods.LAPACK.ORDER.ColMajor,
jobu: 'N',
jobvt: 'N',
m,
n,
a,
lda: m,
s: s,
u,
ldu: m,
vt,
ldvt: n,
superb);
if (lapackInfo > 0)
{
throw new InvalidOperationException(
ImplementationServices.GetResourceString(
"STR_EXCEPT_ALG_DOES_NOT_CONVERGE"));
}
DoubleMatrix values =
DoubleMatrix.Dense(min_m_n, 1, s, copyData: false);
return(values);
}