BALL::LineSearch Class Reference
[Energy
Minimizer]
Basic
line search class. More...
#include <lineSearch.h>
Public Member Functions |
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Constructors and Destructors
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| LineSearch () | |
| Default constructor. |
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| LineSearch (EnergyMinimizer &minimizer) | |
| Detailed constructor. |
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| LineSearch (const LineSearch &line_search) | |
| Copy constructor. |
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| virtual | ~LineSearch () |
| Destructor. |
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Assignments
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| const LineSearch & | operator= (const LineSearch &LineSearch) |
| Assignment operator. |
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Accessors
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| void | setAlpha (double alpha) |
| Set the parameter alpha (convergence
criterion for the line search). |
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| void | setBeta (double beta) |
| Set the parameter beta (convergence
criterion for the line search). |
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| double | getAlpha () const |
| Get the parameter alpha (convergence
criterion for the line search). |
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| double | getBeta () const |
| Get the parameter beta (convergence
criterion for the line search). |
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| Size | getMaxSteps () const |
| Get the parameter
max_steps. |
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| void | setMaxSteps (Size steps) |
| Set the parameter
max_steps. |
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| void | setLowerBound (double lbound) |
| Set the lower bound on energy
values. |
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| double | getLowerBound () const |
| Get the lower bound on energy
values. |
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| void | setXTol (double xtol) |
| Set the nonnegative relative
tolerance for an acceptable step length. |
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| double | getXTol () const |
| Get the nonnegative relative
tolerance for an acceptable step length. |
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| void | setBracketedFlag (bool bracktd) |
Set the flag
is_bracketed_. |
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| bool | isBracketed () const |
| Return whether a minimizer has
already been bracketed. |
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| void | setMinimizer (EnergyMinimizer &minimizer) |
| Set the minimizer class which
provides the search direction and the force field among
other things. |
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| virtual void | takeStep (double &st_a, double &f_a, double &g_a, double &st_b, double &f_b, double &g_b, double &stp, double f, double g, double minstp, double maxstp) |
| Computes a safeguarded step for a
search procedure by case differentiation dependend on
whether a minimum could already be bracketed or not.
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Minimization
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| virtual bool | minimize (double &stp, bool keep_gradient=false) |
| Perform a line search. |
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Protected Attributes |
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| double | alpha_ |
| double | beta_ |
| Size | max_steps_ |
| double | lower_energy_bound_ |
| double | stptol_ |
| bool | is_bracketed_ |
| EnergyMinimizer * | minimizer_ |
Detailed Description
Basic line search class.This method minimizes the energy of a system along a given direction using a two stage algorithm. It is based on cubic and quadratic interpolation methods of Jorge J. More and David J. Thuente. See
[1] J. More and D. Thuente, "Line search algorithms with guaranteed sufficient decrease," ACM Transactions on Mathematical Software 20 (1994), no. 3, pp. 286-307.
Member Function Documentation
| double BALL::LineSearch::getAlpha | ( | ) | const |
Get the parameter alpha (convergence criterion for the line search).
- See also:
- minimize
| double BALL::LineSearch::getBeta | ( | ) | const |
Get the parameter beta (convergence criterion for the line search).
- See also:
- minimize
| bool BALL::LineSearch::isBracketed | ( | ) | const |
Return whether a minimizer has already been bracketed.
Warning: this returns only the flag
is_bracketed_. If this flag has not been set
by the algorithm but changed by
setBracketedFlag this might not be
trustworthy!
| virtual bool BALL::LineSearch::minimize | ( | double & | stp, | |
| bool | keep_gradient =
false |
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| ) | [virtual] |
Perform a line search.
Find the minimum position for all atoms along the direction provided by the minimization algorithm. A two stage algorithm is used proposed by Jorge J. More and David J. Thuente. If necessary (the convergence criterion is not fulfilled) a minimizer along the given direction is bracketed in the first stage. In the second stage this function looks for a minimizer whithin the bracketed interval. The routine exits
(1) if the strong Wolfe conditions are satisfied (convergence criterion for the line search), that are
![\[E_{k+1} \leq E_k + \alpha\cdot stp\cdot<g_k, d_k>\]](form_54.png)
and
![\[|<g_{k+1}, d_k>| \leq \beta\cdot |<g_k, d_k>|\]](form_55.png)
where 
and 
are the initial and the
current gradient and 
is the search direction, 
is the
current and 
the initial energy (stp = 0), 
and
are two parameters (usually 0.9 and 0.0001).
(2) if the relative tolerance for an acceptable step is reached (length of the bracketing interval).
(3) if there has been some numerical problems. In this case the best step length which could be found is returned.
- Parameters:
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stp Unused on entry since the line search always starts with stp = 1.0. On exit the step length corresponding to a successful step or just the best this function was able to find. keep_gradient If true, we will not calculate the gradient for stp = 1 but assume that this has already been performed instead.
| void BALL::LineSearch::setAlpha | ( | double | alpha | ) |
Set the parameter alpha (convergence criterion for the line search).
- See also:
- minimize
| void BALL::LineSearch::setBeta | ( | double | beta | ) |
Set the parameter beta (convergence criterion for the line search).
- See also:
- minimize
| void BALL::LineSearch::setBracketedFlag | ( | bool | bracktd | ) |
Set the flag is_bracketed_.
The algorithm will act as if a minimizer has already been bracketed (true) or not (false). Warning: this can be useful if a user exactly knows what they are doing. Usually, this flag should not be touched! The algorithm sets this flag automatically if a minimizer could be bracketed.
| void BALL::LineSearch::setLowerBound | ( | double | lbound | ) |
Set the lower bound on energy values.
An estimation for the maximum step length is computed based on this value.
| virtual void BALL::LineSearch::takeStep | ( | double & | st_a, | |
| double & | f_a, | |||
| double & | g_a, | |||
| double & | st_b, | |||
| double & | f_b, | |||
| double & | g_b, | |||
| double & | stp, | |||
| double | f, | |||
| double | g, | |||
| double | minstp, | |||
| double | maxstp | |||
| ) | [virtual] |
Computes a safeguarded step for a search procedure by case differentiation dependend on whether a minimum could already be bracketed or not.
All computations are done by safeguarded quadratic and cubic interpolation. The interval that contains a step that satisfies a sufficient decrease and the curvature condition is updated. This function is based on the proposed step computation of Jorge J. More and David J. Thuente. Don't worry if interval bounds are changed after this routine exits.
- Parameters:
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st_a Best step obtained so far and an endpoint of the interval that contains the minimizer. f_a Energy value at st_a.g_a Directional derivative at st_a.st_b Second endpoint of the interval that contains the minimizer. f_b Energy value at st_b.g_b Directional derivative at st_b.stp Current step. If is_bracketed_is set totruethenstpmust be betweenst_aandst_b.f Energy value at stp.g Directional derivative at stp.minstp Lower bound for the step. maxstp Upper bound for the step.
