私立・プログラミングキャンプ成果物(最急降下法による３次元制約つき最適化ソルバ)

solver.scm

#!/usr/bin/env gosh
(use srfi-27)
(use gauche.uvector)
(use gauche.collection)

(define v f64vector)
(define <v> <f64vector>)
(define v-ref f64vector-ref)
(define v-map (pa$ map-to <v>))


(define (projection a b c d x)
  (let* ((det (- (+ (* a (v-ref x 0)) (* b (v-ref x 1)) (* c (v-ref x 2))) d))
         (dif (/ det (+ (expt a 2) (expt b 2) (expt c 2)))))
    (if (<= det 0)
      x
      (v-map - x (v-map (pa$ * dif) (v a b c))))))

(define (p0 x)
  (v (max 0 (v-ref x 0))
     (max 0 (v-ref x 1))
     (max 0 (v-ref x 2))))

(define p1 (pa$ projection 3 5 2 500))

(define p2 (pa$ projection 2 7 4 400))

(define project (compose p0 p1 p2))

(define (gradient x)
  (v 4 5 3))

(define (evaluate x)
  (+ (* 4 (v-ref x 0)) (* 5 (v-ref x 1)) (* 3 (v-ref x 2))))


(let lp ((n 0) (x (v 0 0 0)))
  (format #t "~D ~D ~D ~D ~D~%" n (evaluate x) (v-ref x 0) (v-ref x 1) (v-ref x 2))
  (when (< n 100000)
    (lp (+ n 1) (project (v-map + x (v-map (cut / <> (expt n 0.45)) (gradient x)))))))