99 lines
4.0 KiB
Markdown
99 lines
4.0 KiB
Markdown
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# EigenSolver
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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)).
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Computing for type matrix<double>
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```
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bool matrix::EigenSolver(
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ENUM_EIG_VECTORS jobv, // compute left and right eigenvectors
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vectorc& eigen_values, // vector of computed eigenvalues
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matrix& left_eigenvectors, // matrix of computed left vectors
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matrix& right_eigenvectors // matrix of computed right vectors
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);
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```
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Computing for type matrix<float>
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```
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bool matrixf::EigenSolver(
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ENUM_EIG_VECTORS jobv, // compute left and right eigenvectors
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vectorcf& eigen_values, // vector of computed eigenvalues
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matrixf& left_eigenvectors, // matrix of computed left vectors
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matrixf& right_eigenvectors // matrix of computed right vectors
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);
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```
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Computing for type matrix<complex>
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```
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bool matrixc::EigenSolver(
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ENUM_EIG_VECTORS jobv, // compute left and right vectors
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vectorc& eigen_values, // vector of computed eigenvalues
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matrixc& left_eigenvectors, // matrix of computed left vectors
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matrixc& right_eigenvectors // matrix of computed right vectors
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);
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```
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Computing for type matrix<complexf>
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```
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bool matrixcf::EigenSolver(
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ENUM_EIG_VECTORS jobv, // compute left and right vectors
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vectorcf& eigen_values, // vector of computed eigenvalues
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matrixcf& left_eigenvectors, // matrix of computed left vectors
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matrixcf& right_eigenvectors // matrix of computed right vectors
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);
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```
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Parameters
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jobv
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[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.
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EV
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[out] Vector of eigenvalues.
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left_eigenvectors
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[out] Matrix of left eigenvectors.
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right_eigenvectors
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[out] Matrix of right eigenvectors.
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Return Value
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Return true if successful, otherwise false in case of an [error](/en/docs/constants/errorswarnings/errorcodes).
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Note
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Computation depends on the value of the jobv parameter.
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If EIGVECTORS_N is set, the left and right vectors are not computed. Only eigenvalues are computed.
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With EIGVECTORS_L, only left eigenvectors are computed, right eigenvectors are not computed.
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When EIGVECTORS_R is set, only the right eigenvectors are computed, the left vectors are not computed.
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With EIGVECTORS_LR, the left and right eigenvectors are computed, Eigenvalues are always computed.
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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.
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ENUM_EIG_VECTORS
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An enumeration that specifies whether to calculate eigenvectors.
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| ID | Description |
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| --- | --- |
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| EIGVECTORS_N | Only eigenvalues are calculated, without vectors. |
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| EIGVECTORS_L | Only left eigenvectors are computed. |
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| EIGVECTORS_R | Only right eigenvectors are computed. |
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| EIGVECTORS_LR | Left and right eigenvectors are computed, eigenvalues are always computed. |
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