#include <anderson_stable_mixer.hpp>
Inherits sirius::mixer::Mixer< FUNCS... >.
Public Member Functions | |
| Anderson_stable (std::size_t max_history, double beta) | |
| void | mix_impl () override |
 Public Member Functions inherited from sirius::mixer::Mixer< FUNCS... > | |
| Mixer (std::size_t max_history) | |
| Construct a mixer. Functions have to initialized individually. More... | |
| void | initialize_function (const FunctionProperties< typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type > &function_prop, const typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type &init_value, ARGS &&... args) |
| void | set_input (const typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type &input) |
| Set input for next mixing step. More... | |
| void | get_output (typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type &output) |
| Access last generated output. Mixing must have been performed at least once. More... | |
| double | mix (double rms_min__) |
| Mix input and stored history. Returns the root mean square error computed by inner products of residuals. More... | |
Private Attributes | |
| double | beta_ |
| sddk::mdarray< double, 2 > | R_ |
| std::size_t | history_size_ |
Additional Inherited Members | |
| Static Public Attributes inherited from sirius::mixer::Mixer< FUNCS... > | |
| static constexpr std::size_t | number_of_functions |
| Protected Member Functions inherited from sirius::mixer::Mixer< FUNCS... > | |
| virtual void | mix_impl ()=0 |
| void | update_residual () |
| void | update_rms () |
| std::size_t | idx_hist (std::size_t step) const |
| double | inner_product (const std::tuple< std::unique_ptr< FUNCS >... > &x, const std::tuple< std::unique_ptr< FUNCS >... > &y) |
| void | scale (double alpha, std::tuple< std::unique_ptr< FUNCS >... > &x) |
| void | copy (const std::tuple< std::unique_ptr< FUNCS >... > &x, std::tuple< std::unique_ptr< FUNCS >... > &y) |
| void | axpy (double alpha, const std::tuple< std::unique_ptr< FUNCS >... > &x, std::tuple< std::unique_ptr< FUNCS >... > &y) |
| void | rotate (double c, double s, std::tuple< std::unique_ptr< FUNCS >... > &x, std::tuple< std::unique_ptr< FUNCS >... > &y) |
| Protected Attributes inherited from sirius::mixer::Mixer< FUNCS... > | |
| std::size_t | step_ |
| std::size_t | max_history_ |
| std::vector< double > | rmse_history_ |
| std::tuple< FunctionProperties< FUNCS >... > | functions_ |
| std::tuple< std::unique_ptr< FUNCS >... > | input_ |
| std::vector< std::tuple< std::unique_ptr< FUNCS >... > > | output_history_ |
| std::vector< std::tuple< std::unique_ptr< FUNCS >... > > | residual_history_ |
Detailed Description
class sirius::mixer::Anderson_stable< FUNCS >
Anderson mixer.
Quasi-Newton limited-memory method which updates \( x_{n+1} = x_n - G_nf_n \) where \( G_n \) is an approximate inverse Jacobian. Anderson is derived by taking the low-rank update to the inverse Jacobian
\[ G_{n+1} = (G_n + \Delta X_n - G_n \Delta F_n)(\Delta F_n^T \Delta F_n)^{-1}\Delta F_n^T \]
such that the secant equations \( G_{n+1} \Delta F_n = \Delta X_n \) are satisfied for previous iterations. Then \( G_n \) is taken \( -\beta I \). This implementation uses Gram-Schmidt to orthogonalize \( \Delta F_n \) to solve the least-squares problem. If stability is not an issue, use Anderson instead.
Reference paper: Fang, Haw‐ren, and Yousef Saad. "Two classes of multisecant methods for nonlinear acceleration." Numerical Linear Algebra with Applications 16.3 (2009): 197-221.
Definition at line 65 of file anderson_stable_mixer.hpp.
Constructor & Destructor Documentation
◆ Anderson_stable()
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inline |
Definition at line 73 of file anderson_stable_mixer.hpp.
Member Function Documentation
◆ mix_impl()
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inlineoverridevirtual |
Implements sirius::mixer::Mixer< FUNCS... >.
Definition at line 82 of file anderson_stable_mixer.hpp.
Member Data Documentation
◆ beta_
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private |
Definition at line 68 of file anderson_stable_mixer.hpp.
◆ R_
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private |
Definition at line 69 of file anderson_stable_mixer.hpp.
◆ history_size_
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private |
Definition at line 70 of file anderson_stable_mixer.hpp.
The documentation for this class was generated from the following file:
