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       1           1 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : /// \file
       5             : /// Defines function find_generalized_eigenvalues.
       6             : 
       7             : #pragma once
       8             : 
       9             : /// \cond
      10             : class DataVector;
      11             : class Matrix;
      12             : namespace gsl {
      13             : template <typename T>
      14             : class not_null;
      15             : }  // namespace gsl
      16             : /// \endcond
      17             : 
      18             : /*!
      19             :  * \ingroup NumericalAlgorithmsGroup
      20             :  * \brief Solve the generalized eigenvalue problem for two matrices.
      21             :  *
      22             :  * This function uses the lapack routine dggev
      23             :  * (http://www.netlib.org/lapack/explore-3.1.1-html/dggev.f.html)
      24             :  * to solve the
      25             :  * generalized eigenvalue problem \f$A v_a =\lambda_a B v_a \f$
      26             :  * for the generalized eigenvalues \f$\lambda_a\f$ and corresponding
      27             :  * eigenvectors \f$v_a\f$.
      28             :  * `matrix_a` and `matrix_b` are each a `Matrix`; they correspond to square
      29             :  * matrices \f$A\f$ and \f$B\f$ that are the same dimension \f$N\f$.
      30             :  * `eigenvalues_real_part` is a `DataVector` of size \f$N\f$ that
      31             :  * will store the real parts of the eigenvalues,
      32             :  * `eigenvalues_imaginary_part` is a `DataVector` of size \f$N\f$
      33             :  * that will store the imaginary parts of the eigenvalues.
      34             :  * Complex eigenvalues always form complex conjugate pairs, and
      35             :  * the \f$j\f$ and \f$j+1\f$ eigenvalues will have the forms
      36             :  * \f$a+ib\f$ and \f$a-ib\f$, respectively. The eigenvectors
      37             :  * are returned as the columns of a square `Matrix` of dimension \f$N\f$
      38             :  * called `eigenvectors`. If eigenvalue \f$j\f$ is real, then column \f$j\f$ of
      39             :  * `eigenvectors` is
      40             :  * the corresponding eigenvector. If eigenvalue \f$j\f$ and \f$j+1\f$ are
      41             :  * complex-conjugate pairs, then the eigenvector for
      42             :  * eigenvalue \f$j\f$ is (column j) + \f$i\f$ (column j+1), and the
      43             :  * eigenvector for eigenvalue \f$j+1\f$ is (column j) - \f$i\f$ (column j+1).
      44             :  *
      45             :  */
      46           1 : void find_generalized_eigenvalues(
      47             :     gsl::not_null<DataVector*> eigenvalues_real_part,
      48             :     gsl::not_null<DataVector*> eigenvalues_imaginary_part,
      49             :     gsl::not_null<Matrix*> eigenvectors, Matrix matrix_a, Matrix matrix_b);