[![Build Status](https://travis-ci.org/titsuki/p6-Algorithm-LBFGS.svg?branch=master)](https://travis-ci.org/titsuki/p6-Algorithm-LBFGS) NAME ==== Algorithm::LBFGS - A Perl6 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 Perl6 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 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 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)