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MQL5 リファレンス行列とベクトルのメソッドOpenBLASEigen ValuesTridiagonal MatricesEigenTridiagonalQRQ 

EigenTridiagonalQRQ

Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (lapack function STEQR). Unlike EigenTridiagonalQR, 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::EigenTridiagonalQRQ(
  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::EigenTridiagonalQRQ(
  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::EigenTridiagonalQRQ(
  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::EigenTridiagonalQRQ(
  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.

Q

[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