sicmutils.numerical.unimin.bracket — sicmutils 0.14.0

ascending-by clj/s

(ascending-by f a b)

Returns the points ordered as f(a) < f(b)

bracket-max clj/s

(bracket-max f)

(bracket-max f opts)

Identical to bracket-min, except brackets a maximum of the supplied fn.

bracket-max-scmutils clj/s

(bracket-max-scmutils f)

(bracket-max-scmutils f opts)

Identical to bracket-min-scmutils, except brackets a maximum of the supplied fn.

bracket-min clj/s

(bracket-min f)

(bracket-min f
             {:keys [xa xb maxiter maxfun]
              :or {xa 0.0 xb 1.0 maxiter 1000 maxfun 1000}
              :as opts})

Generates an interval [lo, hi] that is guaranteed to contain a minimum of the function f, along with a candidate point [mid, (f mid)] that the user can use to start a minimum search.

Returns a dictionary of the form:

{:lo lower end of the bracket :mid candidate point :hi upper end of the bracket :fncalls # of fn evaluations so far :iterations total iterations}

:lo, :mid and :hi are each pairs of the form [x, (f x)].

The implementation works by growing the bounds using either:

• a step outside the bounds that places one bound at the golden-ratio cut point between the new bounds, or
• a parabola with a minimum interpolated outside the current bounds, bounded b a max.

This implementation was ported from scipy.optimize.optimize.bracket: https://github.com/scipy/scipy/blob/v1.5.2/scipy/optimize/optimize.py#L2450

bracket-min supports the following optional keyword arguments:

:xa the initial guess for the lower end of the bracket. Defaults to 0.0.

:xb the initial guess for the upper end of the bracket. Defaults to 1.0. (If these points aren't supplied in sorted order they'll be switched.)

:grow-limit The maximum factor that the parabolic interpolation can jump the function. Defaults to 110.0.

:maxiter Maximum number of iterations allowed for the minimizer. Defaults to 1000.

:maxfun Maximum number of times the function can be evaluated before exiting. Defaults to 1000.

bracket-min-scmutils clj/s

(bracket-min-scmutils f)

(bracket-min-scmutils f
                      {:keys [start step maxiter]
                       :or {start 0 step 10 maxiter 1000}})

Given a function f, a starting point and a step size, try to bracket a local extremum for f.

Return a list (retcode a b c fa fb fc iter-count) where a < b < c, and fa, fb, fc are the function values at these points. In the case of a minimum, fb <= (min fa fc); the opposite inequality holds in the case of a maximum.

iter-count is the number of function evaluations required. retcode is 'okay if the search succeeded, or 'maxcount if it was abandoned.

bracket-step-fn clj/s

(bracket-step-fn f {:keys [grow-limit] :or {grow-limit 110.0}})

Returns a function that performs steps of bracket extension.

:grow-limit is the maximum factor that the parabolic interpolation can jump the function.

parabolic-pieces clj/s

(parabolic-pieces [xa fa] [xb fb] [xc fc])

Accepts three pairs of [x, (f x)], fits a quadratic function to all three points and returns the step from xb (the coordinate of the second argument) to the minimum of the fitted quadratic.

Returns the numerator and denominator p and q of the required step. If q is 0, then the supplied points were colinear.

q is guaranteed to be >= 0, while p might be negative.

See these notes for the derivation of this method: http://fourier.eng.hmc.edu/e176/lectures/NM/node25.html

parabolic-step clj/s

(parabolic-step a [xb :as b] c)

Fits a parabola through all three points, and returns the coordinate of the minimum of the parabola.

If the supplied points are colinear, returns a point that takes a large jump in the direction of the downward slope of the line.