crude hack to allow Carlos and my home directories. Feel free to add more.
[CommonLispStat.git] / optimize.lisp
blobb9fab442ef846b6ea8931a525fcc6d1a31597091
1 ;;; -*- mode: lisp -*-
2 ;;; Copyright (c) 2005--2007, by A.J. Rossini <blindglobe@gmail.com>
3 ;;; See COPYRIGHT file for any additional restrictions (BSD license).
4 ;;; Since 1991, ANSI was finally finished. Edited for ANSI Common Lisp.
6 (in-package :cl-user)
8 (defpackage :lisp-stat-optimize
9 (:use :common-lisp
10 :lisp-stat-ffi-int
11 :lisp-stat-object-system
12 :lisp-stat-types
13 :lisp-stat-compound-data
14 :lisp-stat-math
15 :lisp-stat-float
16 :lisp-stat-basics
17 :lisp-stat-matrix
18 :lisp-stat-linalg-data
19 :lisp-stat-linalg)
20 (:shadowing-import-from :lisp-stat-object-system
21 slot-value call-method call-next-method)
22 (:shadowing-import-from :lisp-stat-math
23 expt + - * / ** mod rem abs 1+ 1- log exp sqrt sin cos tan
24 asin acos atan sinh cosh tanh asinh acosh atanh float random
25 truncate floor ceiling round minusp zerop plusp evenp oddp
26 < <= = /= >= > complex conjugate realpart imagpart phase
27 min max logand logior logxor lognot ffloor fceiling
28 ftruncate fround signum cis)
29 (:export
30 ;; derivatives
31 numgrad numhess
33 ;; optimization
34 newtonmax nelmeadmax))
36 ;; matrix is in statistics, but should that be a predecessor?
38 ;;; FIXME:AJR: There is a need to figure out the proper symbols to
39 ;;; export. more importantly should there be any specialty package
40 ;;; that are exported for maximization?
42 (in-package :lisp-stat-optimize)
44 (defvar *maximize-callback-function* nil
45 "Used in generic optimization to determine function name -- symbol or string?")
47 (defvar *maximize-callback-arg* nil
48 "args to function to maximize")
51 ;;;
52 ;;; CFFI support using library for optimization work.
53 ;;;
55 ;; There is a problem with this particular approach, in terms of
56 ;; circular dependencies. We can not have this out-of-object call
57 ;; into optimize, at least not from here.
58 (cffi:defcallback ccl-maximize-callback :void ((n :int)
59 (px :pointer)
60 (pfval :pointer)
61 (pgrad :pointer)
62 (phess :pointer)
63 (pderivs :pointer))
64 (lisp-stat-optimize::maximize-callback n px pfval pgrad phess pderivs))
66 (cffi:defcfun ("register_maximize_callback" register-maximize-callback)
67 :void (x :pointer))
68 (register-maximize-callback (cffi:callback ccl-maximize-callback))
70 (cffi:defcfun ("ccl_numgrad_front" ccl-numgrad-front)
71 :int (x :int) (y :pointer) (z :pointer) (u :double) (v :pointer))
72 (defun numgrad-front (x y z u v)
73 (ccl-numgrad-front x y z (float u 1d0) v))
75 (cffi:defcfun ("ccl_numhess_front" ccl-numhess-front)
76 :int (x :int) (y :pointer) (z :pointer) (u :pointer) (v :pointer) (w :double) (a :pointer))
77 (defun numhess-front (x y z u v w a)
78 (ccl-numhess-front x y z u v (float w 1d0) a))
80 (cffi:defcfun ("ccl_minfo_maximize" ccl-minfo-maximize)
81 :int (x :pointer) (y :pointer) (z :pointer) (u :pointer) (v :pointer) (w :int))
82 (defun base-minfo-maximize (x y z u v w)
83 (ccl-minfo-maximize x y z u v w))
87 ;;;;
88 ;;;; minfo basics (internal??)
89 ;;;;
91 (defun init-minfo-ipar-values (n ipars &key
92 (TRUE 1)
93 (FALSE 0)
94 (k 0)
95 (m 0)
96 (itnlimit -1)
97 (backtrack TRUE)
98 (verbose 0)
99 (vals_suppl FALSE)
100 (exptilt TRUE)
101 (count 0)
102 (termcode 0))
103 "Initialize ipars (iteration parameters) by destructive modification."
104 (setf (aref ipars 0) n)
105 (setf (aref ipars 1) m)
106 (setf (aref ipars 2) k)
107 (setf (aref ipars 3) itnlimit)
108 (setf (aref ipars 4) backtrack)
109 (setf (aref ipars 5) verbose)
110 (setf (aref ipars 6) vals_suppl)
111 (setf (aref ipars 7) exptilt)
112 (setf (aref ipars 8) count)
113 (setf (aref ipars 9) termcode))
115 (defun init-minfo-dpar-values (h dpars &key
116 (typf 1.0)
117 (gradtol -1.0)
118 (steptol -1.0)
119 (maxstep -1.0)
120 (dflt 0.0)
121 (tilt 0.0)
122 (newtilt 0.0)
123 (hessadd 0.0))
124 "Initialize dpars (derivative parameters) by destructive modification."
125 (setf (aref dpars 0) typf)
126 (setf (aref dpars 1) h)
127 (setf (aref dpars 2) gradtol)
128 (setf (aref dpars 3) steptol)
129 (setf (aref dpars 4) maxstep)
130 (setf (aref dpars 5) dflt)
131 (setf (aref dpars 6) tilt)
132 (setf (aref dpars 7) newtilt)
133 (setf (aref dpars 8) hessadd))
135 (defun init-minfo-internals (n h internals)
136 (let ((ipars (aref internals 8))
137 (dpars (aref internals 9)))
138 (init-minfo-ipar-values n ipars)
139 (init-minfo-dpar-values h dpars)))
141 (defun new-minfo-internals (f x &key scale ((:derivstep h) -1.0))
142 (check-sequence x)
143 (check-real x)
144 (check-one-real h)
145 (let ((n (length x)))
146 (when scale
147 (check-sequence scale)
148 (check-real scale)
149 (if (/= n (length scale)) (error "scale and x not the same length")))
150 (let ((internals (make-array 12)))
151 (setf (aref internals 0) f)
152 (setf (aref internals 3) (if (consp x) (copy-list x) (coerce x 'list)))
153 (setf (aref internals 4)
154 (if scale (copy-seq scale) (make-array n :initial-element 1.0)))
155 (setf (aref internals 5) (make-list (+ 1 n (* n n))))
156 (setf (aref internals 8) (make-array 10))
157 (setf (aref internals 9) (make-array 9))
158 (init-minfo-internals n h internals)
159 internals)))
161 (defun minfo-maximize (internals &optional verbose)
162 "This function does what?"
163 (let* ((f (aref internals 0))
164 (x (aref internals 3))
165 (fvals (aref internals 5))
166 (n (length x))
167 (v (if verbose (if (integerp verbose) verbose 1) -1)))
168 (setf (aref internals 3) (copy-list x))
169 (setf (aref internals 5) (copy-list fvals))
170 (let ((*maximize-callback-function* f)
171 (*maximize-callback-arg* (make-list n)))
172 (let* ((x (aref internals 3))
173 (scale (aref internals 4))
174 (fvals (aref internals 5))
175 (ip (aref internals 8))
176 (dp (aref internals 9))
177 (px (la-data-to-vector x +mode-re+))
178 (pscale (la-data-to-vector scale +mode-re+))
179 (pfvals (la-vector (length fvals) +mode-re+))
180 (pip (la-data-to-vector ip +mode-in+))
181 (pdp (la-data-to-vector dp +mode-re+)))
182 (unwind-protect
183 (progn
184 (base-minfo-maximize px pfvals pscale pip pdp v)) ;; access to C
185 (la-vector-to-data px n +mode-re+ x)
186 (la-vector-to-data pfvals (+ 1 n (* n n)) +mode-re+ fvals)
187 (la-vector-to-data pip (length ip) +mode-in+ ip)
188 (la-vector-to-data pdp (length dp) +mode-re+ dp))
189 (get-buf)))))
193 ;;;;
194 ;;;; Mode Info Prototype
195 ;;;;
197 (defproto minfo-proto '(internals))
199 #+xlisp (send minfo-proto :add-method :isnew #'|minfo-isnew|)
200 #+xlisp (send minfo-proto :add-method :maximize #'|minfo-maximize|)
201 #+xlisp (send minfo-proto :add-method :loglaplace #'|minfo-loglap|)
202 #-xlisp
203 (defmeth minfo-proto :isnew (&rest args)
204 (setf (slot-value 'internals) (apply #'new-minfo-internals args)))
205 #-xlisp
206 (defmeth minfo-proto :maximize (&rest args)
207 (apply #'minfo-maximize (slot-value 'internals) args))
209 (defmeth minfo-proto :x () (aref (slot-value 'internals) 3))
210 (defmeth minfo-proto :scale () (aref (slot-value 'internals) 4))
211 (defmeth minfo-proto :derivstep () (aref (aref (slot-value 'internals) 9) 1))
212 (defmeth minfo-proto :tilt () (aref (aref (slot-value 'internals) 9) 6))
214 (defmeth minfo-proto :f (&optional (val nil set))
215 (when set
216 (send self :set-no-vals-supplied)
217 (setf (aref (slot-value 'internals) 0) val))
218 (aref (slot-value 'internals) 0))
220 (defmeth minfo-proto :set-no-vals-supplied ()
221 (setf (aref (aref (slot-value 'internals) 8) 6) 0))
223 (defmeth minfo-proto :exptilt (&optional (val nil set))
224 (if set
225 (let ((old (send self :exptilt)))
226 (setf (aref (aref (slot-value 'internals) 8) 7) (if val 1 0))
227 (if (and (not (or (and old val) (and (not old) (not val))))
228 (/= (send self :tilt) 0.0))
229 (send self :set-no-vals-supplied))))
230 (= 1 (aref (aref (slot-value 'internals) 8) 7)))
232 (defmeth minfo-proto :newtilt (&optional (val nil set))
233 (when set
234 (setf (aref (aref (slot-value 'internals) 9) 7) (float val))
235 (if (/= (send self :tilt) 0.0) (send self :set-no-vals-supplied)))
236 (aref (aref (slot-value 'internals) 9) 7))
238 (defmeth minfo-proto :gfuns (&optional (val nil set))
239 (when set
240 (if (or (not (consp val))
241 (not (every #'functionp val)))
242 (error "not all functions"))
243 (setf (aref (slot-value 'internals) 1) val)
244 (setf (aref (aref (slot-value 'internals) 8) 1) (length val))
245 (setf (aref (slot-value 'internals) 10) (repeat 1.0 (length val)))
246 (if (/= (send self :tilt) 0.0) (send self :set-no-vals-supplied)))
247 (aref (slot-value 'internals) 1))
249 (defmeth minfo-proto :cfuns (&optional (val nil set))
250 (when set
251 (if (or (not (consp val))
252 (not (every #'functionp val)))
253 (error "not all functions"))
254 (setf (aref (slot-value 'internals) 2) val)
255 (setf (aref (aref (slot-value 'internals) 8) 2) (length val))
256 (setf (aref (slot-value 'internals) 7) (repeat 0.0 (length val)))
257 (setf (aref (slot-value 'internals) 11) (repeat 0.0 (length val)))
258 (send self :set-no-vals-supplied))
259 (aref (slot-value 'internals) 2))
261 (defmeth minfo-proto :ctarget (&optional (val nil set))
262 (when set
263 (if (/= (length val) (length (send self :ctarget)))
264 (error "bad target length"))
265 (setf (aref (slot-value 'internals) 7) val))
266 (aref (slot-value 'internals) 7))
268 (defmeth minfo-proto :fvals ()
269 (let* ((fv (aref (slot-value 'internals) 5))
270 (n (length (send self :x)))
271 (val (select fv 0))
272 (grad (select fv (iseq 1 n)))
273 (hess (matrix (list n n) (select fv (iseq (+ 1 n) (+ n (* n n)))))))
274 (list val grad hess)))
276 (defmeth minfo-proto :copy ()
277 (let ((obj (make-object minfo-proto))
278 (internals (copy-seq (slot-value 'internals))))
279 (dotimes (i (length internals))
280 (let ((x (aref internals i)))
281 (if (sequencep x)
282 (setf (aref internals i) (copy-seq x)))))
283 (send obj :add-slot 'internals internals)
284 obj))
286 (defmeth minfo-proto :derivscale ()
287 (let* ((step (^ machine-epsilon (/ 1 6)))
288 (hess (numhess (send self :f) (send self :x) (send self :scale) step))
289 (scale (pmax (abs (send self :x)) (sqrt (abs (/ (diagonal hess)))))))
290 (setf hess (numhess (send self :f) (send self :x) scale step))
291 (setf scale (pmax (abs (send self :x)) (sqrt (abs (/ (diagonal hess))))))
292 (setf (aref (slot-value 'internals) 4) scale)
293 (setf (aref (aref (slot-value 'internals) 9) 1) step)))
295 (defmeth minfo-proto :verbose (&optional (val nil set))
296 (when set
297 (setf (aref (aref (slot-value 'internals) 8) 5)
298 (cond ((integerp val) val)
299 ((null val) 0)
300 (t 1))))
301 (aref (aref (slot-value 'internals) 8) 5))
303 (defmeth minfo-proto :backtrack (&optional (val nil set))
304 (if set (setf (aref (aref (slot-value 'internals) 8) 4) (if val 1 0)))
305 (aref (aref (slot-value 'internals) 8) 4))
307 (defmeth minfo-proto :maxiter (&optional (val nil set))
308 (if set (setf (aref (aref (slot-value 'internals) 8) 3)
309 (if (integerp val) val -1)))
310 (aref (aref (slot-value 'internals) 8) 3))
312 (defmeth minfo-proto :tiltscale (&optional (val nil set))
313 (when set
314 (if (/= (length val) (length (send self :gfuns)))
315 (error "wrong size tilt scale sequence"))
316 (setf (aref (slot-value 'internals) 10) val))
317 (aref (slot-value 'internals) 10))
319 ;;;;
320 ;;;;
321 ;;;; Newton's Method with Backtracking
322 ;;;;
323 ;;;;
325 (defun newtonmax (f start &key
326 scale
327 (derivstep -1.0)
328 (count-limit -1)
329 (verbose 1)
330 return-derivs)
331 "Args:(f start &key scale derivstep (verbose 1) return-derivs)
332 Maximizes F starting from START using Newton's method with backtracking.
333 If RETURN-DERIVS is NIL returns location of maximum; otherwise returns
334 list of location, unction value, gradient and hessian at maximum.
335 SCALE should be a list of the typical magnitudes of the parameters.
336 DERIVSTEP is used in numerical derivatives and VERBOSE controls printing
337 of iteration information. COUNT-LIMIT limits the number of iterations"
338 (let ((verbose (if verbose (if (integerp verbose) verbose 1) 0))
339 (minfo (send minfo-proto :new f start
340 :scale scale :derivstep derivstep)))
341 (send minfo :maxiter count-limit)
342 (send minfo :derivscale)
343 (send minfo :maximize verbose)
344 (if return-derivs
345 (cons (send minfo :x) (- (send minfo :fvals)))
346 (send minfo :x))))
348 ;;;;
349 ;;;;
350 ;;;; Nelder-Mead Simplex Method
351 ;;;;
352 ;;;;
354 (defun nelmeadmax (f start &key
355 (size 1)
356 (epsilon (sqrt machine-epsilon))
357 (count-limit 500)
358 (verbose t)
359 (alpha 1.0)
360 (beta 0.5)
361 (gamma 2.0)
362 (delta 0.5))
363 "Args: (f start &key (size 1) (epsilon (sqrt machine-epsilon))
364 (count-limit 500) (verbose t) alpha beta gamma delta)
365 Maximizes F using the Nelder-Mead simplex method. START can be a
366 starting simplex - a list of N+1 points, with N=dimension of problem,
367 or a single point. If start is a single point you should give the
368 size of the initial simplex as SIZE, a sequence of length N. Default is
369 all 1's. EPSILON is the convergence tolerance. ALPHA-DELTA can be used to
370 control the behavior of simplex algorithm."
371 (let ((s (send simplex-proto :new f start size)))
372 (do ((best (send s :best-point) (send s :best-point))
373 (count 0 (+ count 1))
374 next)
375 ((or (< (send s :relative-range) epsilon) (>= count count-limit))
376 (if (and verbose (>= count count-limit))
377 (format t "Iteration limit exceeded.~%"))
378 (send s :point-location (send s :best-point)))
379 (setf next (send s :extrapolate-from-worst (- alpha)))
380 (if (send s :is-worse best next)
381 (setf next (send s :extrapolate-from-worst gamma))
382 (when (send s :is-worse next (send s :second-worst-point))
383 (setf next (send s :extrapolate-from-worst beta))
384 (if (send s :is-worse next (send s :worst-point))
385 (send s :shrink-to-best delta))))
386 (if verbose
387 (format t "Value = ~10g~%"
388 (send s :point-value (send s :best-point)))))))
392 ;;; Simplex Prototype
395 (defproto simplex-proto '(f simplex))
398 ;;; Simplex Points
401 (defmeth simplex-proto :make-point (x)
402 (let ((f (send self :f)))
403 (if f
404 (let ((val (funcall f x)))
405 (cons (if (consp val) (car val) val) x))
406 (cons nil x))))
408 (defmeth simplex-proto :point-value (x) (car x))
410 (defmeth simplex-proto :point-location (x) (cdr x))
412 (defmeth simplex-proto :is-worse (x y)
413 (< (send self :point-value x) (send self :point-value y)))
416 ;;; Making New Simplices
419 (defmeth simplex-proto :isnew (f start &optional size)
420 (send self :simplex start size)
421 (send self :f f))
424 ;;; Slot Accessors and Mutators
427 (defmeth simplex-proto :simplex (&optional new size)
428 (if new
429 (let ((simplex
430 (if (and (consp new) (sequencep (car new)))
431 (if (/= (length new) (+ 1 (length (car new))))
432 (error "bad simplex data")
433 (copy-list new))
434 (let* ((n (length new))
435 (size (if size size (repeat 1 n)))
436 ; (pts (- (* 2 (uniform-rand (repeat n (+ n 1)))) 1)))
437 (diag (* 2 size (- (random (repeat 2 n)) .5)))
438 (pts (cons (repeat 0 n)
439 (mapcar #'(lambda (x) (coerce x 'list))
440 (column-list (diagonal diag))))))
441 (mapcar #'(lambda (x) (reduce #'+ (list (* size x) new))) pts)))))
442 (setf (slot-value 'simplex)
443 (mapcar #'(lambda (x) (send self :make-point x)) simplex))
444 (send self :sort-simplex)))
445 (slot-value 'simplex))
447 (defmeth simplex-proto :f (&optional f)
448 (when f
449 (setf (slot-value 'f) f)
450 (let ((simplex
451 (mapcar #'(lambda (x) (send self :point-location x))
452 (send self :simplex))))
453 (send self :simplex simplex)))
454 (slot-value 'f))
456 (defmeth simplex-proto :sort-simplex ()
457 (if (send self :f)
458 (setf (slot-value 'simplex)
459 (sort (slot-value 'simplex)
460 #'(lambda (x y) (send self :is-worse x y))))))
463 ;;; Other Methods Using List Representation of SImplex
466 (defmeth simplex-proto :best-point () (car (last (send self :simplex))))
467 (defmeth simplex-proto :worst-point () (first (send self :simplex)))
468 (defmeth simplex-proto :second-worst-point () (second (send self :simplex)))
469 (defmeth simplex-proto :replace-point (new old)
470 (let* ((simplex (send self :simplex))
471 (n (position old simplex)))
472 (when n
473 (setf (nth n simplex) new)
474 (send self :sort-simplex))))
475 (defmeth simplex-proto :mean-opposite-face (x)
476 (let ((face (mapcar #'(lambda (x) (send self :point-location x))
477 (remove x (send self :simplex)))))
478 (/ (reduce #'+ face) (length face))))
481 ;;; Iteration Step Methods
484 (defmeth simplex-proto :extrapolate-from-worst (fac)
485 (let* ((worst (send self :worst-point))
486 (wloc (send self :point-location worst))
487 (delta (- (send self :mean-opposite-face worst) wloc))
488 (new (send self :make-point (+ wloc (* (- 1 fac) delta)))))
489 (if (send self :is-worse worst new) (send self :replace-point new worst))
490 new))
492 (defmeth simplex-proto :shrink-to-best (fac)
493 (let* ((best (send self :best-point))
494 (bloc (send self :point-location best)))
495 (dolist (x (copy-list (send self :simplex)))
496 (if (not (eq x best))
497 (send self :replace-point
498 (send self :make-point
499 (+ bloc
500 (* fac
501 (- (send self :point-location x) bloc))))
502 x)))))
504 (defmeth simplex-proto :relative-range ()
505 (let ((best (send self :point-value (send self :best-point)))
506 (worst (send self :point-value (send self :worst-point))))
507 (* 2 (/ (abs (- best worst)) (+ 1 (abs best) (abs worst))))))
512 ;;;;
513 ;;;; Maximization and Numerical Derivatives
514 ;;;;
517 (defun data2double (n data ptr)
518 (declare (fixnum n))
519 (let* ((seq (compound-data-seq data))
520 (elem (make-next-element seq)))
521 (if (/= (length seq) n) (error "bad data size"))
522 (dotimes (i n)
523 (declare (fixnum i))
524 (la-put-double ptr i (get-next-element elem i)))))
526 (defun maximize-callback (n px pfval pgrad phess pderivs)
527 (la-vector-to-data px n +mode-re+ *maximize-callback-arg*)
528 (let* ((val (funcall *maximize-callback-function* *maximize-callback-arg*))
529 (derivs (if (consp val) (- (length val) 1) 0)))
530 (la-put-integer pderivs 0 derivs)
531 (la-put-double pfval 0 (if (consp val) (first val) val))
532 (if (<= 1 derivs) (data2double n (second val) pgrad))
533 (if (<= 2 derivs) (data2double (* n n) (third val) phess))))
535 (defun numgrad (f x &optional scale (h -1.0))
536 "Args: (f x &optional scale derivstep)
537 Computes the numerical gradient of F at X."
538 (check-sequence x)
539 (check-real x)
540 (when scale
541 (check-sequence scale)
542 (check-real scale))
543 (check-one-real h)
544 (let* ((n (length x))
545 (result (make-list n)))
546 (if (and scale (/= n (length scale)))
547 (error "scale not the same length as x"))
548 (let ((*maximize-callback-function* f)
549 (*maximize-callback-arg* (make-list n)))
550 (let ((px (la-data-to-vector x +mode-re+))
551 (pgrad (la-vector n +mode-re+))
552 (pscale (la-data-to-vector
553 (if scale scale (make-list n :initial-element 1.0))
554 +mode-re+)))
555 (unwind-protect
556 (progn
557 (numgrad-front n px pgrad h pscale)
558 (la-vector-to-data pgrad n +mode-re+ result))
559 (la-free-vector px)
560 (la-free-vector pgrad)
561 (la-free-vector pscale))))
562 result))
564 (defun numhess (f x &optional scale (h -1.0) all)
565 "Args: (f x &optional scale derivstep)
566 Computes the numerical Hessian matrix of F at X."
567 (check-sequence x)
568 (check-real x)
569 (when scale
570 (check-sequence scale)
571 (check-real scale))
572 (check-one-real h)
573 (let* ((n (length x))
574 (result (if all
575 (list nil (make-list n) (make-array (list n n)))
576 (make-array (list n n)))))
577 (if (and scale (/= n (length scale)))
578 (error "scale not the same length as x"))
579 (let ((*maximize-callback-function* f)
580 (*maximize-callback-arg* (make-list n)))
581 (let ((hess-data (compound-data-seq (if all (third result) result)))
582 (px (la-data-to-vector x +mode-re+))
583 (pf (la-vector 1 +mode-re+))
584 (pgrad (la-vector n +mode-re+))
585 (phess (la-vector (* n n) +mode-re+))
586 (pscale (la-data-to-vector
587 (if scale scale (make-list n :initial-element 1.0))
588 +mode-re+)))
589 (unwind-protect
590 (progn
591 (numhess-front n px pf pgrad phess h pscale)
592 (when all
593 (setf (first result) (la-get-double pf 0))
594 (la-vector-to-data pgrad n +mode-re+ (second result)))
595 (la-vector-to-data phess (* n n) +mode-re+ hess-data))
596 (la-free-vector pf)
597 (la-free-vector px)
598 (la-free-vector pgrad)
599 (la-free-vector phess)
600 (la-free-vector pscale))))
601 result))