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EigenTridiagonalPosDefQ

Compute eigenvalues and eigenvectors of a symmetric positive definite tridiagonal matrix using the QR algorithm (lapack function PTEQR). This method can be used to compute the eigenvectors of both the input tridiagonal matrix and the original positive definite symmetric matrix. This is achieved using the orthogonal matrix Q obtained during the reduction to tridiagonal form.

Computing for type matrix<double>

bool  matrix::EigenTridiagonalPosDefQ(
   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::EigenTridiagonalPosDefQ(
   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::EigenTridiagonalPosDefQ(
   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::EigenTridiagonalPosDefQ(
   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 positive definite tridiagonal matrix.

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