[](https://travis-ci.com/titsuki/raku-Algorithm-LBFGS)
NAME
====
Algorithm::LBFGS - A Raku bindings for libLBFGS
SYNOPSIS
========
use Algorithm::LBFGS;
use Algorithm::LBFGS::Parameter;
my Algorithm::LBFGS $lbfgs .= new;
my &evaluate = sub ($instance, $x, $g, $n, $step --> Num) {
my Num $fx = ($x[0] - 2.0) ** 2 + ($x[1] - 5.0) ** 2;
$g[0] = 2.0 * $x[0] - 4.0;
$g[1] = 2.0 * $x[1] - 10.0;
return $fx;
};
my Algorithm::LBFGS::Parameter $parameter .= new;
my Num @x0 = [0e0, 0e0];
my @x = $lbfgs.minimize(:@x0, :&evaluate, :$parameter);
@x.say; # [2e0, 5e0]
DESCRIPTION
===========
Algorithm::LBFGS is a Raku bindings for libLBFGS. libLBFGS is a C port of the implementation of Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method written by Jorge Nocedal.
The L-BFGS method solves the unconstrainted minimization problem,
minimize F(x), x = (x1, x2, ..., xN),
only if the objective function F(x) and its gradient G(x) are computable.
CONSTRUCTOR
-----------
my $lbfgs = Algorithm::LBFGS.new;
my Algorithm::LBFGS $lbfgs .= new; # with type restrictions
METHODS
-------
### minimize(:@x0!, :&evaluate!, :&progress, Algorithm::LBFGS::Parameter :$parameter!) returns Array
my @x = $lbfgs.minimize(:@x0!, :&evaluate, :&progress, :$parameter); # use &progress callback
my @x = $lbfgs.minimize(:@x0!, :&evaluate, :$parameter);
Runs the optimization and returns the resulting variables.
`:@x0` is the initial value of the variables.
`:&evaluate` is the callback function. This requires the definition of the objective function F(x) and its gradient G(x).
`:&progress` is the callback function. This gets called on every iteration and can output the internal state of the current iteration.
`:$parameter` is the instance of the `Algorithm::LBFGS::Parameter` class.
#### :&evaluate
The one of the simplest `&evaluate` callback function would be like the following:
my &evaluate = sub ($instance, $x, $g, $n, $step --> Num) {
my Num $fx = ($x[0] - 2.0) ** 2 + ($x[1] - 5.0) ** 2; # F(x) = (x0 - 2.0)^2 + (x1 - 5.0)^2
# G(x) = [∂F(x)/∂x0, ∂F(x)/∂x1]
$g[0] = 2.0 * $x[0] - 4.0; # ∂F(x)/∂x0 = 2.0 * x0 - 4.0
$g[1] = 2.0 * $x[1] - 10.0; # ∂F(x)/∂x1 = 2.0 * x1 - 10.0
return $fx;
};
* `$instance` is the user data. (NOTE: NYI in this binder. You must set it as a first argument, but you can't use it in the callback.)
* `$x` is the current values of variables.
* `$g` is the current gradient values of variables.
* `$n` is the number of variables.
* `$step` is the line-search step used for this iteration.
`&evaluate` requires all of these five arguments in this order.
After writing the definition of the objective function F(x) and its gradient G(x), it requires returning the value of the F(x).
#### :&progress
The one of the simplest `&progress` callback function would be like the following:
my &progress = sub ($instance, $x, $g, $fx, $xnorm, $gnorm, $step, $n, $k, $ls --> Int) {
"Iteration $k".say;
"fx = $fx, x[0] = $x[0], x[1] = $x[1]".say;
return 0;
}
* `$instance` is the user data. (NOTE: NYI in this binder. You must set it as a first argument, but you can't use it in the callback.)
* `$x` is the current values of variables.
* `$g` is the current gradient values of variables.
* `$fx` is the current value of the objective function.
* `$xnorm` is the Euclidean norm of the variables.
* `$gnorm` is the Euclidean norm of the gradients.
* `$step` is the line-search step used for this iteration.
* `$n` is the number of variables.
* `$k` is the iteration count.
* `$ls` the number of evaluations called for this iteration.
`&progress` requires all of these ten arguments in this order.
#### Algorithm::LBFGS::Parameter :$parameter
Below is the examples of creating a <Algorithm::LBFGS::Parameter> instance:
my Algorithm::LBFGS::Parameter $parameter .= new; # sets default parameter
my Algorithm::LBFGS::Parameter $parameter .= new(max_iterations => 100); # sets max_iterations => 100
##### OPTIONS
* Int `m` is the number of corrections to approximate the inverse hessian matrix.
* Num `epsilon` is epsilon for convergence test.
* Int `past` is the distance for delta-based convergence test.
* Num `delta` is delta for convergence test.
* Int `max_iterations` is the maximum number of iterations.
* Int `linesearch` is the line search algorithm. This requires one of `LBFGS_LINESEARCH_DEFAULT`, `LBFGS_LINESEARCH_MORETHUENTE`, `LBFGS_LINESEARCH_BACKTRACKING_ARMIJO`, `LBFGS_LINESEARCH_BACKTRACKING`, `LBFGS_LINESEARCH_BACKTRACKING_WOLFE` and `LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE`. The default value is `LBFGS_LINESEARCH_MORETHUENTE`.
* Int `max_linesearch` is the maximum number of trials for the line search.
* Num `min_step` is the minimum step of the line search routine.
* Num `max_step` is the maximum step of the line search.
* Num `ftol` is a parameter to control the accuracy of the line search routine.
* Num `wolfe` is a coefficient for the Wolfe condition.
* Num `gtol` is a parameter to control the accuracy of the line search routine.
* Num `xtol` is the machine precision for floating-point values.
* Num `orthantwise_c` is a coeefficient for the L1 norm of variables.
* Int `orthantwise_start` is the start index for computing L1 norm of the variables.
* Int `orthantwise_end` is the end index for computing L1 norm of the variables.
STATUS CODES
------------
TBD
AUTHOR
======
titsuki <titsuki@cpan.org>
COPYRIGHT AND LICENSE
=====================
Copyright 2016 titsuki
Copyright 1990 Jorge Nocedal
Copyright 2007-2010 Naoki Okazaki
libLBFGS by Naoki Okazaki is licensed under the MIT License.
This library is free software; you can redistribute it and/or modify it under the terms of the MIT License.
SEE ALSO
========
* libLBFGS [http://www.chokkan.org/software/liblbfgs/index.html](http://www.chokkan.org/software/liblbfgs/index.html)