Class min_brent_gsl (o2scl)

O2scl : Class List

template<class func_t = funct>
class min_brent_gsl : public o2scl::min_bkt_base<funct>

One-dimensional minimization using Brent’s method (GSL)

The minimization in the function min_bkt() is complete when the bracketed interval is smaller than \( \mathrm{tol} = \mathrm{tol\_abs} + \mathrm{tol\_rel} \cdot \mathrm{min} \), where \( \mathrm{min} = \mathrm{min}(|\mathrm{lower}|,|\mathrm{upper}|) \).

Note that this algorithm requires that the initial guess already brackets the minimum, i.e. \( x_1 < x_2 < x_3 \), \( f(x_1) > f(x_2) \) and \( f(x_3) > f(x_2) \). This is different from min_cern, where the initial value of the first parameter to min_cern::min_bkt() is ignored.

The set functions throw an error if the initial bracket is not correctly specified. The function iterate() never calls the error handler. The function min_bkt() calls the error handler if the tolerances are negative or if the number of iterations is insufficient to give the specified tolerance.

Setting min_base::err_nonconv to false will force min_bkt() not to call the error handler when the number of iterations is insufficient.

Note that if there are more than 1 local minima in the specified interval, there is no guarantee that this method will find the global minimum.

See also root_brent_gsl for a similar algorithm applied as a solver rather than a minimizer.

Note

There was a bug in this minimizer which was fixed for GSL-1.11 which has also been fixed here.

Temporary storage

double d

double e

double v

double w

double f_v

double f_w

double x_minimum

Location of minimum.

double x_lower

Lower bound.

double x_upper

Upper bound.

double f_minimum

Minimum value.

double f_lower

Value at lower bound.

double f_upper

Value at upper bound.

inline int compute_f_values(func_t &func, double xminimum, double *fminimum, double xlower, double *flower, double xupper, double *fupper)

Compute the function values at the various points.

inline min_brent_gsl()

inline virtual ~min_brent_gsl()

inline int set(func_t &func, double xmin, double lower, double upper)

Set the function and the initial bracketing interval.

inline int set_with_values(func_t &func, double xmin, double fmin, double lower, double fl, double upper, double fu)

Set the function, the initial bracketing interval, and the corresponding function values.

inline int iterate()

Perform an iteration.

Idea for Future:

It looks like x_left and x_right can be removed. Also, it would be great to replace the one-letter variable names with something more meaningful.

inline virtual int min_bkt(double &x2, double x1, double x3, double &fmin, func_t &func)

Calculate the minimum fmin of func with x2 bracketed between x1 and x3.

Note that this algorithm requires that the initial guess already brackets the minimum, i.e. \( x_1 < x_2 < x_3 \), \( f(x_1) > f(x_2) \) and \( f(x_3) > f(x_2) \). This is different from min_cern, where the initial value of the first parameter to min_cern::min_bkt() is ignored.

inline virtual const char *type()

Return string denoting type (“min_brent_gsl”)

Protected Attributes

func_t *uf

The function.