emmy.numerical.unimin.golden — org.mentat/emmy 0.32.0

best-of clj/s

(best-of & pairs)

Default selection function for the best possible point. This function chooses the point out of (a, l, r, b) with the minimum function value.

convergence-fn clj/s

(convergence-fn {:keys [converged? fn-tolerance arg-tolerance]})

Returns a fn that returns true if any of the following are true:

• the max interior value is within fn-tolerance of the smallest bound,
• convergence? (if supplied) returns true
• the bounds are within arg-tolerance absolute distance,

false otherwise.

extend-pt clj/s

(extend-pt x away-from)

generate a new point by extending x away from away-from. The invariant is that x sits between the new point and away-from at the golden ratio point.

golden-cut clj/s

(golden-cut from to)

Returns the point between from and to that cuts the region between the two into two sections in golden-ratioed proportion to each other.

For example, depending on the ordering of from and to, x would be either:

from------x1---to
to---x2------from

Such that from->x1 / from->to == to->x2 / from->x1.

golden-section-max clj/s

(golden-section-max f xa xb)

(golden-section-max f xa xb opts)

For convenience, we also provide the sister-procedure for finding the maximum of a unimodal function using the golden section method.

Negate the function, minimize, negate the result.

golden-section-min clj/s

(golden-section-min f xa xb)

(golden-section-min f
                    xa
                    xb
                    {:keys [choose callback]
                     :or {choose best-of callback (constantly nil)}
                     :as opts})

Golden Section search attempts to locate the minimum of the supplied function f by evaluating points located at golden-ratioed intervals between the two starting endpoints a and b. This method is slow, steady and reliable.

Supports the following optional keyword arguments:

:converged? is an optional predicate accepting five arguments:

• [a fa]
• [l fl]
• [r fr]
• [b fb]
• current-iteration

If the supplied fn returns true, it will signal convergence and the optimizer will return. Returning false will continue.

:choose is called at the final step of optimization with all 4 points and their fn values (see the first four arguments to :converged?), and returns the final choice.

:callback receives all 5 arguments on every iteration.

: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.

:fn-tolerance check that the minimal value of any of the checked points is within the maximum of f(a) or f(b).

:arg-tolerance check that a and b are within this supplied absolute distance.

inv-phi clj/s

$1 \over \phi$. Multiply by this to scale some distance down to the larger-sized golden ratio piece.

inv-phi2 clj/s

$1 \over \phi^2$. Scales down twice, compared to inv-phi.

phi clj/s

$\phi$, the golden ratio.

stop-fn clj/s

(stop-fn {:keys [maxiter maxfun fn-counter]})

Returns a fn that returns true if any of the following are true::

• the supplied fn-counter atom contains a value > maxfun
• the loop has exceeded maxiter iterations

false otherwise.