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updated eigen value documentation

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Signed-off-by: Krishna Vedala <7001608+kvedala@users.noreply.github.com>
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Krishna Vedala
2020-06-08 20:18:44 -04:00
parent 37b7389de7
commit 28410ec389
1 changed files with 18 additions and 3 deletions
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21
numerical_methods/qr_eigen_values.cpp
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@@ -74,9 +74,24 @@ void mat_mul(const std::valarray<std::valarray<double>> &A,
}
namespace qr_algorithm {
/** Compute eigen values
* \param[in,out] A matric to compute eigen values for \note This matrix gets
* modified
/** Compute eigen values using iterative shifted QR decomposition algorithm as
* follows:
* 1. Use last diagonal element of A as eigen value approximation \f$c\f$
* 2. Shift diagonals of matrix \f$A' = A + cI\f$
* 3. Decompose matrix \f$A'=QR\f$
* 4. Compute next approximation \f$A'_1 = RQ \f$
* 5. Shift diagonals back \f$A_1 = A'_1 - cI\f$
* 6. Termination condition check: last element below diagonal is almost 0
* 1. If not 0, go back to step 1 with the new approximation \f$A_1\f$
* 2. If 0, continue to step 7
* 7. Save last known \f$c\f$ as the eigen value.
* 8. Are all eigen values found?
* 1. If not, remove last row and column of \f$A_1\f$ and go back to step 1.
* 2. If yes, stop.
*
* \note The matrix \f$A\f$ gets modified
*
* \param[in,out] A matrix to compute eigen values for
* \param[in] print_intermediates (optional) whether to print intermediate A, Q
* and R matrices (default = `false`)
*/