/usr/share/libctl/base/simplex.scm is in libctl5 3.2.2-4build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | ; libctl: flexible Guile-based control files for scientific software
; Copyright (C) 1998-2014 Massachusetts Institute of Technology and Steven G. Johnson
;
; This library is free software; you can redistribute it and/or
; modify it under the terms of the GNU Lesser General Public
; License as published by the Free Software Foundation; either
; version 2 of the License, or (at your option) any later version.
;
; This library is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
; Lesser General Public License for more details.
;
; You should have received a copy of the GNU Lesser General Public
; License along with this library; if not, write to the
; Free Software Foundation, Inc., 59 Temple Place - Suite 330,
; Boston, MA 02111-1307, USA.
;
; Steven G. Johnson can be contacted at stevenj@alum.mit.edu.
; ****************************************************************
; The Nelder-Mead simplex algorithm for multidimensional minimization.
; See the simplex-minimize function, below.
(define (ax+by a x b y)
(define (cdr-null x) (if (null? x) '() (cdr x)))
(if (and (null? x) (null? y))
'()
(let ((ax (if (null? x) 0 (* a (car x))))
(by (if (null? y) 0 (* b (car y)))))
(cons (+ ax by) (ax+by a (cdr-null x) b (cdr-null y))))))
(define (simplex-point x val) (cons x val))
(define simplex-point-x car)
(define simplex-point-val cdr)
(define (simplex-high s)
(car (sort s (lambda (s1 s2) (> (simplex-point-val s1)
(simplex-point-val s2))))))
(define (simplex-high2 s)
(cadr (sort s (lambda (s1 s2) (> (simplex-point-val s1)
(simplex-point-val s2))))))
(define (simplex-low s)
(car (sort s (lambda (s1 s2) (< (simplex-point-val s1)
(simplex-point-val s2))))))
(define (simplex-replace s s-old s-new)
(if (null? s)
'()
(if (eq? (car s) s-old)
(cons s-new (cdr s))
(cons (car s) (simplex-replace (cdr s) s-old s-new)))))
(define (simplex-sum-x s)
(if (null? s)
'()
(ax+by 1 (simplex-point-x (car s)) 1 (simplex-sum-x (cdr s)))))
(define (simplex-centroid-x s)
(let ((sum (ax+by 1 (simplex-sum-x s)
-1 (simplex-point-x (simplex-high s)))))
(ax+by (/ (- (length s) 1)) sum 0.0 '())))
(define (simplex-shrink s-min f s)
(if (null? s)
'()
(if (eq? s-min (car s))
(cons (car s) (simplex-shrink s-min f (cdr s)))
(let ((x (ax+by 0.5 (simplex-point-x s-min)
0.5 (simplex-point-x (car s)))))
(cons (simplex-point x (apply f x))
(simplex-shrink s-min f (cdr s)))))))
(define simplex-reflect-ratio 1.0)
(define simplex-expand-ratio 2.0)
(define simplex-contract-ratio 0.5)
(define (simplex-contract f s)
(let ((s-h (simplex-high s))
(s-l (simplex-low s))
(x0 (simplex-centroid-x s)))
(let ((xc (ax+by (- 1 simplex-contract-ratio) x0
simplex-contract-ratio (simplex-point-x s-h))))
(let ((vc (apply f xc)))
(if (< vc (simplex-point-val s-h))
(simplex-replace s s-h (simplex-point xc vc))
(simplex-shrink s-l f s))))))
(define (simplex-iter f s)
(let ((s-h (simplex-high s))
(s-h2 (simplex-high2 s))
(s-l (simplex-low s))
(x0 (simplex-centroid-x s)))
(let ((xr (ax+by (+ 1 simplex-reflect-ratio) x0
(- simplex-reflect-ratio) (simplex-point-x s-h))))
(let ((vr (apply f xr)))
(if (and (<= vr (simplex-point-val s-h2))
(>= vr (simplex-point-val s-l)))
(simplex-replace s s-h (simplex-point xr vr))
(if (< vr (simplex-point-val s-l))
(let ((xe (ax+by (- 1 simplex-expand-ratio) x0
simplex-expand-ratio xr)))
(let ((ve (apply f xe)))
(if (>= ve vr)
(simplex-replace s s-h (simplex-point xr vr))
(simplex-replace s s-h (simplex-point xe ve)))))
(if (and (< vr (simplex-point-val s-h))
(> vr (simplex-point-val s-h2)))
(simplex-contract f (simplex-replace
s s-h (simplex-point xr vr)))
(simplex-contract f s))))))))
(define (simplex-iterate f s tol)
(let ((s-h (simplex-high s))
(s-l (simplex-low s)))
(if (<= (magnitude (- (simplex-point-val s-h) (simplex-point-val s-l)))
(* 0.5 tol (+ tol (magnitude (simplex-point-val s-h))
(magnitude (simplex-point-val s-l)))))
s-l
(begin
(print "extremization: best so far is " s-l "\n")
(simplex-iterate f (simplex-iter f s) tol)))))
(define (simplex-shift-x x i)
(let ((xv (list->vector x)))
(let ((xv-i (vector-ref xv i)))
(if (< (magnitude xv-i) 1e-6)
(vector-set! xv i 0.1)
(vector-set! xv i (* 0.9 xv-i)))
(vector->list xv))))
(define (simplex-shift-list x)
(define (ssl-aux i)
(if (< i 0)
'()
(cons (simplex-shift-x x i) (ssl-aux (- i 1)))))
(cons x (ssl-aux (- (length x) 1))))
; Use the Simplex method to minimize the function (f . x), where
; the initial guess is x0 and the fractional tolerance on the value
; of the solution is tol.
(define (simplex-minimize f x0 tol)
(let ((s0 (map (lambda (x) (simplex-point x (apply f x)))
(simplex-shift-list x0))))
(simplex-iterate f s0 tol)))
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