Implementation of classical Jacobi diagonalization #3328
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eggrobin
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Feb 13, 2022
numerics/matrix_computations.hpp
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| // <matrix> rotation; | ||
| // <vector> eigenvalues; | ||
| // }; | ||
| // Note that in the |rotation| field the eigenvectors appear in column. They |
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Let’s not use the word field, it sounds like we are talking about a field.
Note that in |rotation| the […]
numerics/matrix_computations.hpp
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| template<typename V, typename U> | ||
| struct ᵗRDRDecompositionGenerator; | ||
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| // Declares: | ||
| // using Result = <vector>; |
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| // See [GV13] section 8.5.2, algorithm 8.5.1. | ||
| template<typename Scalar, typename Matrix> | ||
| JacobiRotation SymmetricShurDecomposition2(Matrix const& A, |
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Schur.
Also, 2By2 rather than 2, otherwise it sounds like it is the second algorithm for that decomposition, like PlotMethod2.
| DCHECK_LE(0, p); | ||
| DCHECK_LT(p, q); | ||
| DCHECK_LT(q, A.rows()); | ||
| static Scalar const zero{}; |
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constexpr Scalar zero{}, let’s not have locking to initialize a local static zero.
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| // A becomes ᵗJ A. | ||
| template<typename Matrix> | ||
| void Premultiplication(JacobiRotation const& J, Matrix& A) { |
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| // A becomes A J. | ||
| template<typename Matrix> | ||
| void Postmultiplication(Matrix& A, JacobiRotation const& J) { |
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PostMultiply, or just operator*=.
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On top of #3327.
Related to #2966.