# EigenSolver

Compute eigenvalues and eigenvectors of a regular square matrix using the classical algorithm (LAPACK function [GEEV](https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-fortran/2025-2/geev.html)).

Computing for type matrix<double>

```
bool  matrix::EigenSolver(
   ENUM_EIG_VECTORS      jobv,                    // compute left and right eigenvectors
   vectorc&              eigen_values,            // vector of computed eigenvalues
   matrix&               left_eigenvectors,       // matrix of computed left vectors
   matrix&               right_eigenvectors       // matrix of computed right vectors
   );

```

Computing for type matrix<float>

```
bool  matrixf::EigenSolver(
   ENUM_EIG_VECTORS      jobv,                    // compute left and right eigenvectors
   vectorcf&             eigen_values,            // vector of computed eigenvalues
   matrixf&              left_eigenvectors,       // matrix of computed left vectors
   matrixf&              right_eigenvectors       // matrix of computed right vectors
   );

```

Computing for type matrix<complex>

```
bool  matrixc::EigenSolver(
   ENUM_EIG_VECTORS      jobv,                    // compute left and right vectors
   vectorc&              eigen_values,            // vector of computed eigenvalues
   matrixc&              left_eigenvectors,       // matrix of computed left vectors
   matrixc&              right_eigenvectors       // matrix of computed right vectors  
   );

```

Computing for type matrix<complexf>

```
bool  matrixcf::EigenSolver(
   ENUM_EIG_VECTORS      jobv,                    // compute left and right vectors
   vectorcf&             eigen_values,            // vector of computed eigenvalues
   matrixcf&             left_eigenvectors,       // matrix of computed left vectors
   matrixcf&             right_eigenvectors       // matrix of computed right vectors  
   );

```

Parameters

jobv

[in]  [ENUM_EIG_VECTORS](/en/docs/matrix/openblas/eigen_values/general_matrices/eigensolver#enum_eig_vectors) enumeration value which determines the method for computing left and right eigenvectors.

EV

[out] Vector of eigenvalues.

left_eigenvectors

[out] Matrix of left eigenvectors.

right_eigenvectors

[out] Matrix of right eigenvectors.

Return Value

Return true if successful, otherwise false in case of an [error](/en/docs/constants/errorswarnings/errorcodes).

Note

Computation depends on the value of the jobv parameter.

If EIGVECTORS_N is set, the left and right vectors are not computed. Only eigenvalues are computed.

With EIGVECTORS_L, only left eigenvectors are computed, right eigenvectors are not computed.

When EIGVECTORS_R is set, only the right eigenvectors are computed, the left vectors are not computed.

With EIGVECTORS_LR, the left and right eigenvectors are computed, Eigenvalues are always computed.

Real (non-complex) matrices can have a complex solution. Therefore, the vector of eigenvalues must be complex. In case of a complex solution, the error code is set to 4019 (ERR_MATH_OVERFLOW). Otherwise, only the real parts of the complex values of the eigenvalue vector should be used.

ENUM_EIG_VECTORS

An enumeration that specifies whether to calculate eigenvectors.

| ID | Description |
| --- | --- |
| EIGVECTORS_N | Only eigenvalues are calculated, without vectors. |
| EIGVECTORS_L | Only left eigenvectors are computed. |
| EIGVECTORS_R | Only right eigenvectors are computed. |
| EIGVECTORS_LR | Left and right eigenvectors are computed, eigenvalues are always computed. |