optimize.lisp

   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.
   5
   6 (in-package :cl-user)
   7
   8 (defpackage :lisp-stat-optimize
   9  (:use :common-lisp
  10        :lisp-stat-object-system
  11        :lisp-stat-basics)
  12  (:shadowing-import-from :lisp-stat-object-system
  13                          slot-value call-method call-next-method)
  14  (:export newtonmax nelmeadmax
  15
  16            numgrad numhess))
  17
  18 ;;; FIXME:AJR: There is a need to figure out the proper symbols to
  19 ;;; export.  more importantly should there be any specialty package
  20 z;;; that are exported for maximization?
  21
  22 (in-package :lisp-stat-optimize)
  23
  24 (defvar *maximize-callback-function* nil
  25   "Used in generic optimization to determine function name -- symbol or string?")
  26 (defvar *maximize-callback-arg* nil
  27   "args to function to maximize")
  28
  29 ;;;;
  30 ;;;; minfo basics (internal??)
  31 ;;;;
  32
  33 (defun init-minfo-ipar-values (n ipars)
  34   (let* ((TRUE 1)
  35          (FALSE 0)
  36          (k 0)
  37          (m 0)
  38          (itnlimit -1)
  39          (backtrack TRUE)
  40          (verbose 0)
  41          (vals_suppl FALSE)
  42          (exptilt TRUE)
  43          (count 0)
  44          (termcode 0))
  45     (setf (aref ipars 0) n)
  46     (setf (aref ipars 1) m)
  47     (setf (aref ipars 2) k)
  48     (setf (aref ipars 3) itnlimit)
  49     (setf (aref ipars 4) backtrack)
  50     (setf (aref ipars 5) verbose)
  51     (setf (aref ipars 6) vals_suppl)
  52     (setf (aref ipars 7) exptilt)
  53     (setf (aref ipars 8) count)
  54     (setf (aref ipars 9) termcode)))
  55
  56 (defun init-minfo-dpar-values (h dpars)
  57   (let ((typf 1.0)
  58         (gradtol -1.0)
  59         (steptol -1.0)
  60         (maxstep -1.0)
  61         (dflt 0.0)
  62         (tilt 0.0)
  63         (newtilt 0.0)
  64         (hessadd 0.0))
  65     (setf (aref dpars 0) typf)
  66     (setf (aref dpars 1) h)
  67     (setf (aref dpars 2) gradtol)
  68     (setf (aref dpars 3) steptol)
  69     (setf (aref dpars 4) maxstep)
  70     (setf (aref dpars 5) dflt)
  71     (setf (aref dpars 6) tilt)
  72     (setf (aref dpars 7) newtilt)
  73     (setf (aref dpars 8) hessadd)))
  74
  75 (defun init-minfo-internals (n h internals)
  76   (let ((ipars (aref internals 8))
  77         (dpars (aref internals 9)))
  78     (init-minfo-ipar-values n ipars)
  79     (init-minfo-dpar-values h dpars)))
  80
  81 (defun new-minfo-internals (f x &key scale ((:derivstep h) -1.0))
  82   (check-sequence x)
  83   (check-real x)
  84   (check-one-real h)
  85   (let ((n (length x)))
  86     (when scale
  87           (check-sequence scale)
  88           (check-real scale)
  89           (if (/= n (length scale)) (error "scale and x not the same length")))
  90     (let ((internals (make-array 12)))
  91       (setf (aref internals 0) f)
  92       (setf (aref internals 3) (if (consp x) (copy-list x) (coerce x 'list)))
  93       (setf (aref internals 4)
  94             (if scale (copy-seq scale) (make-array n :initial-element 1.0)))
  95       (setf (aref internals 5) (make-list (+ 1 n (* n n))))
  96       (setf (aref internals 8) (make-array 10))
  97       (setf (aref internals 9) (make-array 9))
  98       (init-minfo-internals n h internals)
  99       internals)))
 100
 101 (defun minfo-maximize (internals &optional verbose)
 102   "This function does what?"
 103   (let* ((f (aref internals 0))
 104          (x (aref internals 3))
 105          (fvals (aref internals 5))
 106          (n (length x))
 107          (v (if verbose (if (integerp verbose) verbose 1) -1)))
 108     (setf (aref internals 3) (copy-list x))
 109     (setf (aref internals 5) (copy-list fvals))
 110     (let ((*maximize-callback-function* f)
 111           (*maximize-callback-arg* (make-list n)))
 112       (let* ((x (aref internals 3))
 113              (scale (aref internals 4))
 114              (fvals (aref internals 5))
 115              (ip (aref internals 8))
 116              (dp (aref internals 9))
 117              (px (la-data-to-vector x mode-re))
 118              (pscale (la-data-to-vector scale mode-re))
 119              (pfvals (la-vector (length fvals) mode-re))
 120              (pip (la-data-to-vector ip mode-in))
 121              (pdp (la-data-to-vector dp mode-re)))
 122         (unwind-protect
 123             (progn
 124               (base-minfo-maximize px pfvals pscale pip pdp v)) ;; access to C
 125           (la-vector-to-data px n mode-re x)
 126           (la-vector-to-data pfvals (+ 1 n (* n n)) mode-re fvals)
 127           (la-vector-to-data pip (length ip) mode-in ip)
 128           (la-vector-to-data pdp (length dp) mode-re dp))
 129         (get-buf)))))
 130
 131
 132
 133 ;;;;
 134 ;;;; Mode Info Prototype
 135 ;;;;
 136
 137 (defproto minfo-proto '(internals))
 138
 139 #+xlisp (send minfo-proto :add-method :isnew #'|minfo-isnew|)
 140 #+xlisp (send minfo-proto :add-method :maximize #'|minfo-maximize|)
 141 #+xlisp (send minfo-proto :add-method :loglaplace #'|minfo-loglap|)
 142 #-xlisp
 143 (defmeth minfo-proto :isnew (&rest args)
 144   (setf (slot-value 'internals) (apply #'new-minfo-internals args)))
 145 #-xlisp
 146 (defmeth minfo-proto :maximize (&rest args)
 147   (apply #'minfo-maximize (slot-value 'internals) args))
 148
 149 (defmeth minfo-proto :x () (aref (slot-value 'internals) 3))
 150 (defmeth minfo-proto :scale () (aref (slot-value 'internals) 4))
 151 (defmeth minfo-proto :derivstep () (aref (aref (slot-value 'internals) 9) 1))
 152 (defmeth minfo-proto :tilt () (aref (aref (slot-value 'internals) 9) 6))
 153
 154 (defmeth minfo-proto :f (&optional (val nil set))
 155   (when set
 156         (send self :set-no-vals-supplied)
 157         (setf (aref (slot-value 'internals) 0) val))
 158   (aref (slot-value 'internals) 0))
 159
 160 (defmeth minfo-proto :set-no-vals-supplied ()
 161   (setf (aref (aref (slot-value 'internals) 8) 6) 0))
 162
 163 (defmeth minfo-proto :exptilt (&optional (val nil set))
 164   (if set
 165       (let ((old (send self :exptilt)))
 166         (setf (aref (aref (slot-value 'internals) 8) 7) (if val 1 0))
 167         (if (and (not (or (and old val) (and (not old) (not val))))
 168                  (/= (send self :tilt) 0.0))
 169             (send self :set-no-vals-supplied))))
 170   (= 1 (aref (aref (slot-value 'internals) 8) 7)))
 171
 172 (defmeth minfo-proto :newtilt (&optional (val nil set))
 173   (when set
 174         (setf (aref (aref (slot-value 'internals) 9) 7) (float val))
 175         (if (/= (send self :tilt) 0.0) (send self :set-no-vals-supplied)))
 176   (aref (aref (slot-value 'internals) 9) 7))
 177
 178 (defmeth minfo-proto :gfuns (&optional (val nil set))
 179   (when set
 180         (if (or (not (consp val))
 181                 (not (every #'functionp val)))
 182             (error "not all functions"))
 183         (setf (aref (slot-value 'internals) 1) val)
 184         (setf (aref (aref (slot-value 'internals) 8) 1) (length val))
 185         (setf (aref (slot-value 'internals) 10) (repeat 1.0 (length val)))
 186         (if (/= (send self :tilt) 0.0) (send self :set-no-vals-supplied)))
 187   (aref (slot-value 'internals) 1))
 188
 189 (defmeth minfo-proto :cfuns (&optional (val nil set))
 190   (when set
 191         (if (or (not (consp val))
 192                 (not (every #'functionp val)))
 193             (error "not all functions"))
 194         (setf (aref (slot-value 'internals) 2) val)
 195         (setf (aref (aref (slot-value 'internals) 8) 2) (length val))
 196         (setf (aref (slot-value 'internals) 7) (repeat 0.0 (length val)))
 197         (setf (aref (slot-value 'internals) 11) (repeat 0.0 (length val)))
 198         (send self :set-no-vals-supplied))
 199   (aref (slot-value 'internals) 2))
 200
 201 (defmeth minfo-proto :ctarget (&optional (val nil set))
 202   (when set
 203         (if (/= (length val) (length (send self :ctarget)))
 204             (error "bad target length"))
 205         (setf (aref (slot-value 'internals) 7) val))
 206   (aref (slot-value 'internals) 7))
 207
 208 (defmeth minfo-proto :fvals ()
 209   (let* ((fv (aref (slot-value 'internals) 5))
 210          (n (length (send self :x)))
 211          (val (select fv 0))
 212          (grad (select fv (iseq 1 n)))
 213          (hess (matrix (list n n) (select fv (iseq (+ 1 n) (+ n (* n n)))))))
 214     (list val grad hess)))
 215
 216 (defmeth minfo-proto :copy ()
 217   (let ((obj (make-object minfo-proto))
 218         (internals (copy-seq (slot-value 'internals))))
 219     (dotimes (i (length internals))
 220              (let ((x (aref internals i)))
 221                (if (sequencep x)
 222                    (setf (aref internals i) (copy-seq x)))))
 223     (send obj :add-slot 'internals internals)
 224     obj))
 225
 226 (defmeth minfo-proto :derivscale ()
 227   (let* ((step (^ machine-epsilon (/ 1 6)))
 228          (hess (numhess (send self :f) (send self :x) (send self :scale) step))
 229          (scale (pmax (abs (send self :x)) (sqrt (abs (/ (diagonal hess)))))))
 230     (setf hess (numhess (send self :f) (send self :x) scale step))
 231     (setf scale (pmax (abs (send self :x)) (sqrt (abs (/ (diagonal hess))))))
 232     (setf (aref (slot-value 'internals) 4) scale)
 233     (setf (aref (aref (slot-value 'internals) 9) 1) step)))
 234
 235 (defmeth minfo-proto :verbose (&optional (val nil set))
 236   (when set
 237         (setf (aref (aref (slot-value 'internals) 8) 5)
 238               (cond ((integerp val) val)
 239                     ((null val) 0)
 240                     (t 1))))
 241   (aref (aref (slot-value 'internals) 8) 5))
 242
 243 (defmeth minfo-proto :backtrack (&optional (val nil set))
 244   (if set (setf (aref (aref (slot-value 'internals) 8) 4) (if val 1 0)))
 245   (aref (aref (slot-value 'internals) 8) 4))
 246
 247 (defmeth minfo-proto :maxiter (&optional (val nil set))
 248     (if set (setf (aref (aref (slot-value 'internals) 8) 3)
 249                   (if (integerp val) val -1)))
 250     (aref (aref (slot-value 'internals) 8) 3))
 251
 252 (defmeth minfo-proto :tiltscale (&optional (val nil set))
 253   (when set
 254         (if (/= (length val) (length (send self :gfuns)))
 255             (error "wrong size tilt scale sequence"))
 256         (setf (aref (slot-value 'internals) 10) val))
 257   (aref (slot-value 'internals) 10))
 258
 259 ;;;;
 260 ;;;;
 261 ;;;; Newton's Method with Backtracking
 262 ;;;;
 263 ;;;;
 264
 265 (defun newtonmax (f start &key
 266                     scale
 267                     (derivstep -1.0)
 268                     (count-limit -1)
 269                     (verbose 1)
 270                     return-derivs)
 271 "Args:(f start &key scale derivstep (verbose 1) return-derivs)
 272 Maximizes F starting from START using Newton's method with backtracking.
 273 If RETURN-DERIVS is NIL returns location of maximum; otherwise returns
 274 list of location, unction value, gradient and hessian at maximum.
 275 SCALE should be a list of the typical magnitudes of the parameters.
 276 DERIVSTEP is used in numerical derivatives and VERBOSE controls printing
 277 of iteration information. COUNT-LIMIT limits the number of iterations"
 278   (let ((verbose (if verbose (if (integerp verbose) verbose 1) 0))
 279         (minfo (send minfo-proto :new f start
 280                      :scale scale :derivstep derivstep)))
 281     (send minfo :maxiter count-limit)
 282     (send minfo :derivscale)
 283     (send minfo :maximize verbose)
 284     (if return-derivs
 285         (cons (send minfo :x) (- (send minfo :fvals)))
 286         (send minfo :x))))
 287
 288 ;;;;
 289 ;;;;
 290 ;;;; Nelder-Mead Simplex Method
 291 ;;;;
 292 ;;;;
 293
 294 (defun nelmeadmax (f start &key
 295                      (size 1)
 296                      (epsilon (sqrt machine-epsilon))
 297                      (count-limit 500)
 298                      (verbose t)
 299                      (alpha 1.0)
 300                      (beta 0.5)
 301                      (gamma 2.0)
 302                      (delta 0.5))
 303 "Args: (f start &key (size 1) (epsilon (sqrt machine-epsilon))
 304           (count-limit 500) (verbose t) alpha beta gamma delta)
 305 Maximizes F using the Nelder-Mead simplex method. START can be a
 306 starting simplex - a list of N+1 points, with N=dimension of problem,
 307 or a single point. If start is a single point you should give the
 308 size of the initial simplex as SIZE, a sequence of length N. Default is
 309 all 1's. EPSILON is the convergence tolerance. ALPHA-DELTA can be used to
 310 control the behavior of simplex algorithm."
 311     (let ((s (send simplex-proto :new f start size)))
 312       (do ((best (send s :best-point) (send s :best-point))
 313            (count 0 (+ count 1))
 314            next)
 315           ((or (< (send s :relative-range) epsilon) (>= count count-limit))
 316            (if (and verbose (>= count count-limit))
 317                (format t "Iteration limit exceeded.~%"))
 318            (send s :point-location (send s :best-point)))
 319           (setf next (send s :extrapolate-from-worst (- alpha)))
 320           (if (send s :is-worse best next)
 321               (setf next (send s :extrapolate-from-worst gamma))
 322               (when (send s :is-worse next (send s :second-worst-point))
 323                     (setf next (send s :extrapolate-from-worst beta))
 324                     (if (send s :is-worse next (send s :worst-point))
 325                         (send s :shrink-to-best delta))))
 326           (if verbose
 327               (format t "Value = ~10g~%"
 328                       (send s :point-value (send s :best-point)))))))
 329
 330
 331 ;;;
 332 ;;; Simplex Prototype
 333 ;;;
 334
 335 (defproto simplex-proto '(f simplex))
 336
 337 ;;;
 338 ;;; Simplex Points
 339 ;;;
 340
 341 (defmeth simplex-proto :make-point (x)
 342   (let ((f (send self :f)))
 343     (if f
 344         (let ((val (funcall f x)))
 345           (cons (if (consp val) (car val) val) x))
 346         (cons nil x))))
 347
 348 (defmeth simplex-proto :point-value (x) (car x))
 349
 350 (defmeth simplex-proto :point-location (x) (cdr x))
 351
 352 (defmeth simplex-proto :is-worse (x y)
 353   (< (send self :point-value x) (send self :point-value y)))
 354
 355 ;;;
 356 ;;; Making New Simplices
 357 ;;;
 358
 359 (defmeth simplex-proto :isnew (f start &optional size)
 360   (send self :simplex start size)
 361   (send self :f f))
 362
 363 ;;;
 364 ;;; Slot Accessors and Mutators
 365 ;;;
 366
 367 (defmeth simplex-proto :simplex (&optional new size)
 368   (if new
 369       (let ((simplex
 370              (if (and (consp new) (sequencep (car new)))
 371                  (if (/= (length new) (+ 1 (length (car new))))
 372                      (error "bad simplex data")
 373                      (copy-list new))
 374                  (let* ((n (length new))
 375                         (size (if size size (repeat 1 n)))
 376                      ;   (pts (- (* 2 (uniform-rand (repeat n (+ n 1)))) 1)))
 377                         (diag (* 2 size (- (random (repeat 2 n)) .5)))
 378                         (pts (cons (repeat 0 n)
 379                                    (mapcar #'(lambda (x) (coerce x 'list))
 380                                            (column-list (diagonal diag))))))
 381                    (mapcar #'(lambda (x) (+ (* size x) new)) pts)))))
 382         (setf (slot-value 'simplex)
 383               (mapcar #'(lambda (x) (send self :make-point x)) simplex))
 384         (send self :sort-simplex)))
 385   (slot-value 'simplex))
 386
 387 (defmeth simplex-proto :f (&optional f)
 388   (when f
 389         (setf (slot-value 'f) f)
 390         (let ((simplex
 391                (mapcar #'(lambda (x) (send self :point-location x))
 392                        (send self :simplex))))
 393           (send self :simplex simplex)))
 394   (slot-value 'f))
 395
 396 (defmeth simplex-proto :sort-simplex ()
 397   (if (send self :f)
 398       (setf (slot-value 'simplex)
 399             (sort (slot-value 'simplex)
 400                   #'(lambda (x y) (send self :is-worse x y))))))
 401
 402 ;;;
 403 ;;; Other Methods Using List Representation of SImplex
 404 ;;;
 405
 406 (defmeth simplex-proto :best-point () (car (last (send self :simplex))))
 407 (defmeth simplex-proto :worst-point () (first (send self :simplex)))
 408 (defmeth simplex-proto :second-worst-point () (second (send self :simplex)))
 409 (defmeth simplex-proto :replace-point (new old)
 410   (let* ((simplex (send self :simplex))
 411          (n (position old simplex)))
 412     (when n
 413           (setf (nth n simplex) new)
 414           (send self :sort-simplex))))
 415 (defmeth simplex-proto :mean-opposite-face (x)
 416   (let ((face (mapcar #'(lambda (x) (send self :point-location x))
 417                       (remove x (send self :simplex)))))
 418     (/ (reduce #'+ face) (length face))))
 419
 420 ;;;
 421 ;;; Iteration Step Methods
 422 ;;;
 423
 424 (defmeth simplex-proto :extrapolate-from-worst (fac)
 425   (let* ((worst (send self :worst-point))
 426          (wloc (send self :point-location worst))
 427          (delta (- (send self :mean-opposite-face worst) wloc))
 428          (new (send self :make-point (+ wloc (* (- 1 fac) delta)))))
 429     (if (send self :is-worse worst new) (send self :replace-point new worst))
 430     new))
 431
 432 (defmeth simplex-proto :shrink-to-best (fac)
 433   (let* ((best (send self :best-point))
 434          (bloc (send self :point-location best)))
 435     (dolist (x (copy-list (send self :simplex)))
 436             (if (not (eq x best))
 437                 (send self :replace-point
 438                       (send self :make-point
 439                             (+ bloc
 440                                (* fac
 441                                   (- (send self :point-location x) bloc))))
 442                       x)))))
 443
 444 (defmeth simplex-proto :relative-range ()
 445   (let ((best (send self :point-value (send self :best-point)))
 446         (worst (send self :point-value (send self :worst-point))))
 447     (* 2 (/ (abs (- best worst)) (+ 1 (abs best) (abs worst))))))
 448
 449
 450
 451
 452 ;;;;
 453 ;;;; Maximization and Numerical Derivatives
 454 ;;;;
 455
 456
 457 (defun data2double (n data ptr)
 458   (declare (fixnum n))
 459   (let* ((seq (compound-data-seq data))
 460          (elem (make-next-element seq)))
 461     (if (/= (length seq) n) (error "bad data size"))
 462     (dotimes (i n)
 463       (declare (fixnum i))
 464       (la-put-double ptr i (get-next-element elem i)))))
 465
 466 (defun maximize-callback (n px pfval pgrad phess pderivs)
 467   (la-vector-to-data px n mode-re *maximize-callback-arg*)
 468   (let* ((val (funcall *maximize-callback-function* *maximize-callback-arg*))
 469          (derivs (if (consp val) (- (length val) 1) 0)))
 470     (la-put-integer pderivs 0 derivs)
 471     (la-put-double pfval 0 (if (consp val) (first val) val))
 472     (if (<= 1 derivs) (data2double n (second val) pgrad))
 473     (if (<= 2 derivs) (data2double (* n n) (third val) phess))))
 474
 475 (defun numgrad (f x &optional scale (h -1.0))
 476 "Args: (f x &optional scale derivstep)
 477 Computes the numerical gradient of F at X."
 478   (check-sequence x)
 479   (check-real x)
 480   (when scale
 481         (check-sequence scale)
 482         (check-real scale))
 483   (check-one-real h)
 484   (let* ((n (length x))
 485          (result (make-list n)))
 486     (if (and scale (/= n (length scale)))
 487         (error "scale not the same length as x"))
 488     (let ((*maximize-callback-function* f)
 489           (*maximize-callback-arg* (make-list n)))
 490       (let ((px (la-data-to-vector x mode-re))
 491             (pgrad (la-vector n mode-re))
 492             (pscale (la-data-to-vector
 493                      (if scale scale (make-list n :initial-element 1.0))
 494                      mode-re)))
 495         (unwind-protect
 496             (progn
 497               (numgrad-front n px pgrad h pscale)
 498               (la-vector-to-data pgrad n mode-re result))
 499           (la-free-vector px)
 500           (la-free-vector pgrad)
 501           (la-free-vector pscale))))
 502       result))
 503
 504 (defun numhess (f x &optional scale (h -1.0) all)
 505 "Args: (f x &optional scale derivstep)
 506 Computes the numerical Hessian matrix of F at X."
 507   (check-sequence x)
 508   (check-real x)
 509   (when scale
 510         (check-sequence scale)
 511         (check-real scale))
 512   (check-one-real h)
 513   (let* ((n (length x))
 514          (result (if all
 515                      (list nil (make-list n) (make-array (list n n)))
 516                      (make-array (list n n)))))
 517     (if (and scale (/= n (length scale)))
 518         (error "scale not the same length as x"))
 519     (let ((*maximize-callback-function* f)
 520           (*maximize-callback-arg* (make-list n)))
 521       (let ((hess-data (compound-data-seq (if all (third result) result)))
 522             (px (la-data-to-vector x mode-re))
 523             (pf (la-vector 1 mode-re))
 524             (pgrad (la-vector n mode-re))
 525             (phess (la-vector (* n n) mode-re))
 526             (pscale (la-data-to-vector
 527                      (if scale scale (make-list n :initial-element 1.0))
 528                      mode-re)))
 529         (unwind-protect
 530             (progn
 531               (numhess-front n px pf pgrad phess h pscale)
 532               (when all
 533                     (setf (first result) (la-get-double pf 0))
 534                     (la-vector-to-data pgrad n mode-re (second result)))
 535               (la-vector-to-data phess (* n n) mode-re hess-data))
 536           (la-free-vector pf)
 537           (la-free-vector px)
 538           (la-free-vector pgrad)
 539           (la-free-vector phess)
 540           (la-free-vector pscale))))
 541     result))
 542