Safe Haskell	None

Numeric.LBFGSB

Description

Minimize functions using the Fortran L-BFGS-B library for limited-memory Broyden–Fletcher–Goldfarb–Shanno bound-constrained minimization. More information on assumptions and function parameters can be found at the L-BFGS-B homepage http://users.eecs.northwestern.edu/~nocedal/lbfgsb.html and in its source code.

A bound-constrained domain is one that is a finite product of the reals, closed intervals, and half-infinite intervals. We describe the factors by (Maybe Double, Maybe Double), with (Just a, Just b) describing the closed interval [a,b], and so forth.

Synopsis

Documentation

minimize

Arguments

:: Int	`m`: The maximum number of variable metric corrections used to define the limited memory matrix. Suggestion: `5`.
-> Double	`factr`: Iteration stops when the relative change in function value is smaller than `factreps`, where `eps` is a measure of machine precision generated by the Fortran code. `1e12` is low accuracy, `1e7` is moderate, and `1e1` is extremely high. Must be `>=1`. Suggestion:* `1e7`.
-> Double	`pgtol`: Iteration stops when the largest component of the projected gradient is smaller than `pgtol`. Must be `>=0`. Suggestion: `1e-5`.
-> Maybe Int	`Just steps` means the minimization is aborted if it has not converged after `steps>0` iterations. `Nothing` signifies no limit.
-> [(Maybe Double, Maybe Double)]	Constraints, as described in the beginning of this module. If there are fewer bounds than components in `x0`, the remaining dimensions are assumed to be unbounded. `[]` thus gives unbounded minimization. Moreover, if there are more bounds than components in `x0`, only as many as needed are used. `repeat (Just 0, Just 1)` thus specifies the unit cube of any dimension as constraint.
-> Vector Double	`x0`: Starting point. The point must be within the bounds.
-> (Vector Double -> Double)	`f`: Function to minimize. Must take `Vector`s of precisely the same length as `x0`, or else behavior is undefined (the program may crash)!
-> (Vector Double -> Vector Double)	`g`: Gradient of `f`. Must take and return `Vector`s of precisely the same length as `x0`, or else behavior is undefined (the program may crash)! Numeric.LBFGSB.Convenience provides a simple approximation of the gradient if you do not have the real one.
-> Result

Minimization using L-BFGS-B. If you only require the solution point, and not the full Result, see minimize'. Take care to satisfy the requirements on the arguments. Failure to do so may result in a runtime error, or, when noted, undefined behavior/crash.

minimize' :: Int -> Double -> Double -> Maybe Int -> [(Maybe Double, Maybe Double)] -> Vector Double -> (Vector Double -> Double) -> (Vector Double -> Vector Double) -> Maybe (Vector Double)

If L-BFGS-B converges within the specified number of steps, the solution point is returned as Just solution. Otherwise Nothing is returned. The arguments are the same as for minimize.