share/minpack/lisp/dogleg.lisp

   1 ;;; Compiled by f2cl version:
   2 ;;; ("f2cl1.l,v 1.215 2009/04/07 22:05:21 rtoy Exp $"
   3 ;;;  "f2cl2.l,v 1.37 2008/02/22 22:19:33 rtoy Exp $"
   4 ;;;  "f2cl3.l,v 1.6 2008/02/22 22:19:33 rtoy Exp $"
   5 ;;;  "f2cl4.l,v 1.7 2008/02/22 22:19:34 rtoy Exp $"
   6 ;;;  "f2cl5.l,v 1.200 2009/01/19 02:38:17 rtoy Exp $"
   7 ;;;  "f2cl6.l,v 1.48 2008/08/24 00:56:27 rtoy Exp $"
   8 ;;;  "macros.l,v 1.112 2009/01/08 12:57:19 rtoy Exp $")
   9
  10 ;;; Using Lisp CMU Common Lisp 19f (19F)
  11 ;;;
  12 ;;; Options: ((:prune-labels nil) (:auto-save t) (:relaxed-array-decls nil)
  13 ;;;           (:coerce-assigns :as-needed) (:array-type ':array)
  14 ;;;           (:array-slicing t) (:declare-common nil)
  15 ;;;           (:float-format double-float))
  16
  17 (in-package :minpack)
  18
  19
  20 (let ((one 1.0) (zero 0.0))
  21   (declare (type (double-float) one zero))
  22   (defun dogleg (n r lr diag qtb delta x wa1 wa2)
  23     (declare (type (double-float) delta)
  24              (type (array double-float (*)) wa2 wa1 x qtb diag r)
  25              (type (f2cl-lib:integer4) lr n))
  26     (f2cl-lib:with-multi-array-data
  27         ((r double-float r-%data% r-%offset%)
  28          (diag double-float diag-%data% diag-%offset%)
  29          (qtb double-float qtb-%data% qtb-%offset%)
  30          (x double-float x-%data% x-%offset%)
  31          (wa1 double-float wa1-%data% wa1-%offset%)
  32          (wa2 double-float wa2-%data% wa2-%offset%))
  33       (prog ((alpha 0.0) (bnorm 0.0) (epsmch 0.0) (gnorm 0.0) (qnorm 0.0)
  34              (sgnorm 0.0) (sum 0.0) (temp 0.0) (i 0) (j 0) (jj 0) (jp1 0) (k 0)
  35              (l 0))
  36         (declare (type (f2cl-lib:integer4) l k jp1 jj j i)
  37                  (type (double-float) temp sum sgnorm qnorm gnorm epsmch bnorm
  38                                       alpha))
  39         '"     **********"
  40         '""
  41         '"     subroutine dogleg"
  42         '""
  43         '"     given an m by n matrix a, an n by n nonsingular diagonal"
  44         '"     matrix d, an m-vector b, and a positive number delta, the"
  45         '"     problem is to determine the convex combination x of the"
  46         '"     gauss-newton and scaled gradient directions that minimizes"
  47         '"     (a*x - b) in the least squares sense, subject to the"
  48         '"     restriction that the euclidean norm of d*x be at most delta."
  49         '""
  50         '"     this subroutine completes the solution of the problem"
  51         '"     if it is provided with the necessary information from the"
  52         '"     qr factorization of a. that is, if a = q*r, where q has"
  53         '"     orthogonal columns and r is an upper triangular matrix,"
  54         '"     then dogleg expects the full upper triangle of r and"
  55         '"     the first n components of (q transpose)*b."
  56         '""
  57         '"     the subroutine statement is"
  58         '""
  59         '"       subroutine dogleg(n,r,lr,diag,qtb,delta,x,wa1,wa2)"
  60         '""
  61         '"     where"
  62         '""
  63         '"       n is a positive integer input variable set to the order of r."
  64         '""
  65         '"       r is an input array of length lr which must contain the upper"
  66         '"         triangular matrix r stored by rows."
  67         '""
  68         '"       lr is a positive integer input variable not less than"
  69         '"         (n*(n+1))/2."
  70         '""
  71         '"       diag is an input array of length n which must contain the"
  72         '"         diagonal elements of the matrix d."
  73         '""
  74         '"       qtb is an input array of length n which must contain the first"
  75         '"         n elements of the vector (q transpose)*b."
  76         '""
  77         '"       delta is a positive input variable which specifies an upper"
  78         '"         bound on the euclidean norm of d*x."
  79         '""
  80         '"       x is an output array of length n which contains the desired"
  81         '"         convex combination of the gauss-newton direction and the"
  82         '"         scaled gradient direction."
  83         '""
  84         '"       wa1 and wa2 are work arrays of length n."
  85         '""
  86         '"     subprograms called"
  87         '""
  88         '"       minpack-supplied ... dpmpar,enorm"
  89         '""
  90         '"       fortran-supplied ... dabs,dmax1,dmin1,dsqrt"
  91         '""
  92         '"     argonne national laboratory. minpack project. march 1980."
  93         '"     burton s. garbow, kenneth e. hillstrom, jorge j. more"
  94         '""
  95         '"     **********"
  96         '""
  97         '"     epsmch is the machine precision."
  98         '""
  99         (setf epsmch (dpmpar 1))
 100         '""
 101         '"     first, calculate the gauss-newton direction."
 102         '""
 103         (setf jj (+ (the f2cl-lib:integer4 (truncate (* n (+ n 1)) 2)) 1))
 104         (f2cl-lib:fdo (k 1 (f2cl-lib:int-add k 1))
 105                       ((> k n) nil)
 106           (tagbody
 107             (setf j (f2cl-lib:int-add (f2cl-lib:int-sub n k) 1))
 108             (setf jp1 (f2cl-lib:int-add j 1))
 109             (setf jj (f2cl-lib:int-sub jj k))
 110             (setf l (f2cl-lib:int-add jj 1))
 111             (setf sum zero)
 112             (if (< n jp1) (go label20))
 113             (f2cl-lib:fdo (i jp1 (f2cl-lib:int-add i 1))
 114                           ((> i n) nil)
 115               (tagbody
 116                 (setf sum
 117                         (+ sum
 118                            (* (f2cl-lib:fref r-%data% (l) ((1 lr)) r-%offset%)
 119                               (f2cl-lib:fref x-%data%
 120                                              (i)
 121                                              ((1 n))
 122                                              x-%offset%))))
 123                 (setf l (f2cl-lib:int-add l 1))
 124                label10))
 125            label20
 126             (setf temp (f2cl-lib:fref r-%data% (jj) ((1 lr)) r-%offset%))
 127             (if (/= temp zero) (go label40))
 128             (setf l j)
 129             (f2cl-lib:fdo (i 1 (f2cl-lib:int-add i 1))
 130                           ((> i j) nil)
 131               (tagbody
 132                 (setf temp
 133                         (f2cl-lib:dmax1 temp
 134                                         (f2cl-lib:dabs
 135                                          (f2cl-lib:fref r-%data%
 136                                                         (l)
 137                                                         ((1 lr))
 138                                                         r-%offset%))))
 139                 (setf l (f2cl-lib:int-sub (f2cl-lib:int-add l n) i))
 140                label30))
 141             (setf temp (* epsmch temp))
 142             (if (= temp zero) (setf temp epsmch))
 143            label40
 144             (setf (f2cl-lib:fref x-%data% (j) ((1 n)) x-%offset%)
 145                     (/
 146                      (- (f2cl-lib:fref qtb-%data% (j) ((1 n)) qtb-%offset%)
 147                         sum)
 148                      temp))
 149            label50))
 150         '""
 151         '"     test whether the gauss-newton direction is acceptable."
 152         '""
 153         (f2cl-lib:fdo (j 1 (f2cl-lib:int-add j 1))
 154                       ((> j n) nil)
 155           (tagbody
 156             (setf (f2cl-lib:fref wa1-%data% (j) ((1 n)) wa1-%offset%) zero)
 157             (setf (f2cl-lib:fref wa2-%data% (j) ((1 n)) wa2-%offset%)
 158                     (* (f2cl-lib:fref diag-%data% (j) ((1 n)) diag-%offset%)
 159                        (f2cl-lib:fref x-%data% (j) ((1 n)) x-%offset%)))
 160            label60))
 161         (setf qnorm (enorm n wa2))
 162         (if (<= qnorm delta) (go label140))
 163         '""
 164         '"     the gauss-newton direction is not acceptable."
 165         '"     next, calculate the scaled gradient direction."
 166         '""
 167         (setf l 1)
 168         (f2cl-lib:fdo (j 1 (f2cl-lib:int-add j 1))
 169                       ((> j n) nil)
 170           (tagbody
 171             (setf temp (f2cl-lib:fref qtb-%data% (j) ((1 n)) qtb-%offset%))
 172             (f2cl-lib:fdo (i j (f2cl-lib:int-add i 1))
 173                           ((> i n) nil)
 174               (tagbody
 175                 (setf (f2cl-lib:fref wa1-%data% (i) ((1 n)) wa1-%offset%)
 176                         (+ (f2cl-lib:fref wa1-%data% (i) ((1 n)) wa1-%offset%)
 177                            (* (f2cl-lib:fref r-%data% (l) ((1 lr)) r-%offset%)
 178                               temp)))
 179                 (setf l (f2cl-lib:int-add l 1))
 180                label70))
 181             (setf (f2cl-lib:fref wa1-%data% (j) ((1 n)) wa1-%offset%)
 182                     (/ (f2cl-lib:fref wa1-%data% (j) ((1 n)) wa1-%offset%)
 183                        (f2cl-lib:fref diag-%data% (j) ((1 n)) diag-%offset%)))
 184            label80))
 185         '""
 186         '"     calculate the norm of the scaled gradient and test for"
 187         '"     the special case in which the scaled gradient is zero."
 188         '""
 189         (setf gnorm (enorm n wa1))
 190         (setf sgnorm zero)
 191         (setf alpha (/ delta qnorm))
 192         (if (= gnorm zero) (go label120))
 193         '""
 194         '"     calculate the point along the scaled gradient"
 195         '"     at which the quadratic is minimized."
 196         '""
 197         (f2cl-lib:fdo (j 1 (f2cl-lib:int-add j 1))
 198                       ((> j n) nil)
 199           (tagbody
 200             (setf (f2cl-lib:fref wa1-%data% (j) ((1 n)) wa1-%offset%)
 201                     (/
 202                      (/ (f2cl-lib:fref wa1-%data% (j) ((1 n)) wa1-%offset%)
 203                         gnorm)
 204                      (f2cl-lib:fref diag-%data% (j) ((1 n)) diag-%offset%)))
 205            label90))
 206         (setf l 1)
 207         (f2cl-lib:fdo (j 1 (f2cl-lib:int-add j 1))
 208                       ((> j n) nil)
 209           (tagbody
 210             (setf sum zero)
 211             (f2cl-lib:fdo (i j (f2cl-lib:int-add i 1))
 212                           ((> i n) nil)
 213               (tagbody
 214                 (setf sum
 215                         (+ sum
 216                            (* (f2cl-lib:fref r-%data% (l) ((1 lr)) r-%offset%)
 217                               (f2cl-lib:fref wa1-%data%
 218                                              (i)
 219                                              ((1 n))
 220                                              wa1-%offset%))))
 221                 (setf l (f2cl-lib:int-add l 1))
 222                label100))
 223             (setf (f2cl-lib:fref wa2-%data% (j) ((1 n)) wa2-%offset%) sum)
 224            label110))
 225         (setf temp (enorm n wa2))
 226         (setf sgnorm (/ (/ gnorm temp) temp))
 227         '""
 228         '"     test whether the scaled gradient direction is acceptable."
 229         '""
 230         (setf alpha zero)
 231         (if (>= sgnorm delta) (go label120))
 232         '""
 233         '"     the scaled gradient direction is not acceptable."
 234         '"     finally, calculate the point along the dogleg"
 235         '"     at which the quadratic is minimized."
 236         '""
 237         (setf bnorm (enorm n qtb))
 238         (setf temp (* (/ bnorm gnorm) (/ bnorm qnorm) (/ sgnorm delta)))
 239         (setf temp
 240                 (+ (- temp (* (/ delta qnorm) (expt (/ sgnorm delta) 2)))
 241                    (f2cl-lib:dsqrt
 242                     (+ (expt (- temp (/ delta qnorm)) 2)
 243                        (* (- one (expt (/ delta qnorm) 2))
 244                           (- one (expt (/ sgnorm delta) 2)))))))
 245         (setf alpha
 246                 (/ (* (/ delta qnorm) (- one (expt (/ sgnorm delta) 2))) temp))
 247        label120
 248         '""
 249         '"     form appropriate convex combination of the gauss-newton"
 250         '"     direction and the scaled gradient direction."
 251         '""
 252         (setf temp (* (- one alpha) (f2cl-lib:dmin1 sgnorm delta)))
 253         (f2cl-lib:fdo (j 1 (f2cl-lib:int-add j 1))
 254                       ((> j n) nil)
 255           (tagbody
 256             (setf (f2cl-lib:fref x-%data% (j) ((1 n)) x-%offset%)
 257                     (+
 258                      (* temp
 259                         (f2cl-lib:fref wa1-%data% (j) ((1 n)) wa1-%offset%))
 260                      (* alpha
 261                         (f2cl-lib:fref x-%data% (j) ((1 n)) x-%offset%))))
 262            label130))
 263        label140
 264         (go end_label)
 265         '""
 266         '"     last card of subroutine dogleg."
 267         '""
 268        end_label
 269         (return (values nil nil nil nil nil nil nil nil nil))))))
 270
 271 (in-package #:cl-user)
 272 #+#.(cl:if (cl:find-package '#:f2cl) '(and) '(or))
 273 (eval-when (:load-toplevel :compile-toplevel :execute)
 274   (setf (gethash 'fortran-to-lisp::dogleg
 275                  fortran-to-lisp::*f2cl-function-info*)
 276           (fortran-to-lisp::make-f2cl-finfo
 277            :arg-types '((fortran-to-lisp::integer4) (array double-float (*))
 278                         (fortran-to-lisp::integer4) (array double-float (*))
 279                         (array double-float (*)) (double-float)
 280                         (array double-float (*)) (array double-float (*))
 281                         (array double-float (*)))
 282            :return-values '(nil nil nil nil nil nil nil nil nil)
 283            :calls '(fortran-to-lisp::enorm fortran-to-lisp::dpmpar))))
 284