# perl-Math-Brent

Math::Brent Perl module

This is an implementation of Brents method for One-Dimensional minimisation of a function without using derivatives. This algorithm cleverly uses both the Golden Section Search and parabolic interpolation. The main function *Brent*, given a function reference *\&func* and a bracketing triplet of abcissas *\$ax*, *\$bx*, *\$cx* (such that *\$bx* is between *\$ax* and *\$cx* and *func(\$bx)* is less than both *func(\$ax)* and *func(\$cx)*), isolates the minimum to a fractional precision of about *\$tol* using Brents method. A maximum number of iterations *\$itmax* may be specified for this search - it defaults to 100. Returned is an array consisting of the abcissa of the minum and the function value there. The function *BracketMinimum*, given a function *\&func* and distinct initial points *\$ax* and *\$bx* searches in the downhill direction (defined by the function as evaluated at the initial points) and returns an array of the three points *\$ax*, *\$bx*, *\$cx* which bracket the minimum of the function and the function values at those points. The function *Minimise1D* provides a simple interface to the above two routines. Given a function *\&func*, an initial guess for its minimum, and its scaling (*\$guess*,*\$scale*) this routine isolates the minimum to a fractional precision of about *\$tol* using Brents method. A maximum number of iterations *\$itmax* may be specified for this search - it defaults to 100. It returns an array consisting of the abcissa of the minum and the function value there.

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