MQL5 RiferimentoMetodi Matriciali e VettorialiOpenBLASEigen ValuesTridiagonal MatricesEigenTridiagonalDCQ

EigenTridiagonalDCQ

Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (lapack function STEDC). Unlike EigenTridiagonalDC, this method can be used to compute the eigenvectors of the original symmetric matrix. A symmetric matrix can be reduced to tridiagonal form using the ReduceSymmetricToTridiagonal method. The orthogonal matrix Q obtained from this transformation is then used to compute the eigenvectors of the original symmetric matrix.

Computing for type matrix<double>

bool  matrix::EigenTridiagonalDCQ(
   ENUM_EIGTRIDIAG_Z     compv,              // compute eigenvectors or not
   matrix&               Q,                  // orthogonal matrix used in the reduction to tridiagonal form
   vector&               eigen_values,       // vector of computed eigenvalues
   matrix&               eigen_vectors       // matrix of computed eigenvectors
   );

Computing for type matrix<float>

bool  matrixf::EigenTridiagonalDCQ(
   ENUM_EIGTRIDIAG_Z     compv,              // compute eigenvectors or not
   matrixf&              Q,                  // orthogonal matrix used in the reduction to tridiagonal form
   vectorf&              eigen_values,       // vector of computed eigenvalues
   matrixf&              eigen_vectors       // matrix of computed eigenvectors
   );

Computing for type matrix<complex>

bool  matrixc::EigenTridiagonalDCQ(
   ENUM_EIGTRIDIAG_Z     compv,              // compute eigenvectors or not
   matrixc&              Q,                  // orthogonal matrix used in the reduction to tridiagonal form
   vector&               eigen_values,       // vector of computed eigenvalues
   matrixc&              eigen_vectors       // matrix of computed eigenvectors
   );

Computing for type matrix<complexf>

bool  matrixcf::EigenTridiagonalDCQ(
   ENUM_EIGTRIDIAG_Z     compv,              // compute eigenvectors or not
   matrixcf&             Q,                  // orthogonal matrix used in the reduction to tridiagonal form
   vectorf&              eigen_values,       // vector of computed eigenvalues
   matrixcf&             eigen_vectors       // matrix of computed eigenvectors
   );

Parameters

compv

[in] ENUM_EIGTRIDIAG_Z enumeration value which determines the method for computing eigenvectors.

[in] Orthogonal matrix Q produced by method ReflectTridiagonalToQ.

eigen_values

[out] Vector of eigenvalues.

eigen_vectors

[out] Matrix of eigenvectors.

Return Value

Return true if successful, otherwise false in case of an error.

Note

Computation depends on the value of the compv parameter.

When compv = EIGCOMPZ_N, compute eigenvalues only, eigenvectors are not calculated.

If EIGCOMPZ_V is set, eigenvalues are computed and eigenvectors of original symmetric matrix are calculated also.

If EIGCOMPZ_I is set, eigenvalues are computed and eigenvectors of tridiagonal matrix are calculated also.

The input must be a symmetric matrix in the tridiagonal form.

ENUM_EIGTRIDIAG_Z

An enumeration that specifies whether to calculate eigenvectors.

ID	Description
EIGCOMPZ_N	'N': Compute eigenvalues only
EIGCOMPZ_V	'V': Compute eigenvectors of original symmetric matrix also
EIGCOMPZ_I	'I': Compute eigenvectors of tridiagonal matrix also

EigenTridiagonalQL

EigenTridiagonalQRQ