2 Downloaded from http://www.netlib.org/opt/subplex.tgz
4 README file for SUBPLEX
7 subplex - subspace-searching simplex method for unconstrained
11 Subplex is a subspace-searching simplex method for the
12 unconstrained optimization of general multivariate functions.
13 Like the Nelder-Mead simplex method it generalizes, the subplex
14 method is well suited for optimizing noisy objective functions.
15 The number of function evaluations required for convergence
16 typically increases only linearly with the problem size, so for
17 most applications the subplex method is much more efficient than
21 To build subplex on UNIX systems, edit the Makefile as necessary
26 This will create a linkable library named subplex.a and a
27 demonstration executable named demo.
30 To run subplex on a simple objective function type:
34 To run subplex on other problems, edit a copy of the sample driver
39 Oak Ridge National Laboratory
40 Mathematical Sciences Section
41 P.O. Box 2008, Bldg. 6012
42 Oak Ridge, TN 37831-6367
46 Email: na.rowan@na-net.ornl.gov
49 T. Rowan, "Functional Stability Analysis of Numerical Algorithms",
50 Ph.D. thesis, Department of Computer Sciences, University of Texas
54 Please send comments, suggestions, or bug reports to
55 na.rowan@na-net.ornl.gov.
65 typedef double doublereal;
72 typedef subplex_func D_fp;
74 #define MAX2(a,b) ((a) > (b) ? (a) : (b))
75 #define MIN2(a,b) ((a) < (b) ? (a) : (b))
77 /****************************************************************************/
78 /****************************************************************************/
80 /* dasum.f -- translated by f2c (version 19991025).
81 You must link the resulting object file with the libraries:
82 -lf2c -lm (in that order)
85 static doublereal dasum_(integer *n, doublereal *dx, integer *incx)
87 /* System generated locals */
89 doublereal ret_val, d__1, d__2, d__3, d__4, d__5, d__6;
97 /* takes the sum of the absolute values. */
98 /* uses unrolled loops for increment equal to one. */
99 /* jack dongarra, linpack, 3/11/78. */
100 /* modified to correct problem with negative increment, 8/21/90. */
103 /* Parameter adjustments */
116 /* code for increment not equal to 1 */
120 ix = (-(*n) + 1) * *incx + 1;
123 for (i__ = 1; i__ <= i__1; ++i__) {
124 dtemp += (d__1 = dx[ix], fabs(d__1));
131 /* code for increment equal to 1 */
142 for (i__ = 1; i__ <= i__1; ++i__) {
143 dtemp += (d__1 = dx[i__], fabs(d__1));
152 for (i__ = mp1; i__ <= i__1; i__ += 6) {
153 dtemp = dtemp + (d__1 = dx[i__], fabs(d__1)) + (d__2 = dx[i__ + 1],
154 fabs(d__2)) + (d__3 = dx[i__ + 2], fabs(d__3)) + (d__4 = dx[i__
155 + 3], fabs(d__4)) + (d__5 = dx[i__ + 4], fabs(d__5)) + (d__6 =
156 dx[i__ + 5], fabs(d__6));
164 /* daxpy.f -- translated by f2c (version 19991025).
165 You must link the resulting object file with the libraries:
166 -lf2c -lm (in that order)
169 static int daxpy_(integer *n, doublereal *da, doublereal *dx,
170 integer *incx, doublereal *dy, integer *incy)
172 /* System generated locals */
175 /* Local variables */
176 integer i__, m, ix, iy, mp1;
179 /* constant times a vector plus a vector. */
180 /* uses unrolled loops for increments equal to one. */
181 /* jack dongarra, linpack, 3/11/78. */
184 /* Parameter adjustments */
195 if (*incx == 1 && *incy == 1) {
199 /* code for unequal increments or equal increments */
205 ix = (-(*n) + 1) * *incx + 1;
208 iy = (-(*n) + 1) * *incy + 1;
211 for (i__ = 1; i__ <= i__1; ++i__) {
212 dy[iy] += *da * dx[ix];
219 /* code for both increments equal to 1 */
230 for (i__ = 1; i__ <= i__1; ++i__) {
231 dy[i__] += *da * dx[i__];
240 for (i__ = mp1; i__ <= i__1; i__ += 4) {
241 dy[i__] += *da * dx[i__];
242 dy[i__ + 1] += *da * dx[i__ + 1];
243 dy[i__ + 2] += *da * dx[i__ + 2];
244 dy[i__ + 3] += *da * dx[i__ + 3];
250 /* dcopy.f -- translated by f2c (version 19991025).
251 You must link the resulting object file with the libraries:
252 -lf2c -lm (in that order)
255 static int dcopy_(integer *n, const doublereal *dx, integer *incx,
256 doublereal *dy, integer *incy)
258 /* System generated locals */
261 /* Local variables */
262 integer i__, m, ix, iy, mp1;
265 /* copies a vector, x, to a vector, y. */
266 /* uses unrolled loops for increments equal to one. */
267 /* jack dongarra, linpack, 3/11/78. */
270 /* Parameter adjustments */
278 if (*incx == 1 && *incy == 1) {
282 /* code for unequal increments or equal increments */
288 ix = (-(*n) + 1) * *incx + 1;
291 iy = (-(*n) + 1) * *incy + 1;
294 for (i__ = 1; i__ <= i__1; ++i__) {
302 /* code for both increments equal to 1 */
313 for (i__ = 1; i__ <= i__1; ++i__) {
323 for (i__ = mp1; i__ <= i__1; i__ += 7) {
325 dy[i__ + 1] = dx[i__ + 1];
326 dy[i__ + 2] = dx[i__ + 2];
327 dy[i__ + 3] = dx[i__ + 3];
328 dy[i__ + 4] = dx[i__ + 4];
329 dy[i__ + 5] = dx[i__ + 5];
330 dy[i__ + 6] = dx[i__ + 6];
336 /* dscal.f -- translated by f2c (version 19991025).
337 You must link the resulting object file with the libraries:
338 -lf2c -lm (in that order)
341 static int dscal_(integer *n, doublereal *da, doublereal *dx,
344 /* System generated locals */
347 /* Local variables */
348 integer i__, m, ix, mp1;
351 /* scales a vector by a constant. */
352 /* uses unrolled loops for increment equal to one. */
353 /* jack dongarra, linpack, 3/11/78. */
354 /* modified to correct problem with negative increment, 8/21/90. */
357 /* Parameter adjustments */
368 /* code for increment not equal to 1 */
372 ix = (-(*n) + 1) * *incx + 1;
375 for (i__ = 1; i__ <= i__1; ++i__) {
376 dx[ix] = *da * dx[ix];
382 /* code for increment equal to 1 */
393 for (i__ = 1; i__ <= i__1; ++i__) {
394 dx[i__] = *da * dx[i__];
403 for (i__ = mp1; i__ <= i__1; i__ += 5) {
404 dx[i__] = *da * dx[i__];
405 dx[i__ + 1] = *da * dx[i__ + 1];
406 dx[i__ + 2] = *da * dx[i__ + 2];
407 dx[i__ + 3] = *da * dx[i__ + 3];
408 dx[i__ + 4] = *da * dx[i__ + 4];
414 /* dist.f -- translated by f2c (version 19991025).
415 You must link the resulting object file with the libraries:
416 -lf2c -lm (in that order)
419 static doublereal dist_(integer *n, doublereal *x, doublereal *y)
421 /* System generated locals */
423 doublereal ret_val, d__1;
425 /* Local variables */
427 doublereal scale, absxmy, sum;
431 /* Coded by Tom Rowan */
432 /* Department of Computer Sciences */
433 /* University of Texas at Austin */
435 /* dist calculates the distance between the points x,y. */
439 /* n - number of components */
441 /* x - point in n-space */
443 /* y - point in n-space */
445 /* local variables */
448 /* subroutines and functions */
452 /* ----------------------------------------------------------- */
454 /* Parameter adjustments */
459 absxmy = (d__1 = x[1] - y[1], fabs(d__1));
461 sum = absxmy * absxmy;
468 for (i__ = 2; i__ <= i__1; ++i__) {
469 absxmy = (d__1 = x[i__] - y[i__], fabs(d__1));
470 if (absxmy <= scale) {
471 /* Computing 2nd power */
472 d__1 = absxmy / scale;
475 /* Computing 2nd power */
476 d__1 = scale / absxmy;
477 sum = sum * (d__1 * d__1) + 1.;
482 ret_val = scale * sqrt(sum);
486 /* calcc.f -- translated by f2c (version 19991025).
487 You must link the resulting object file with the libraries:
488 -lf2c -lm (in that order)
491 /* Table of constant values */
493 static doublereal c_b3 = 0.;
494 static integer c__0 = 0;
495 static integer c__1 = 1;
496 static doublereal c_b7 = 1.;
498 static int calcc_(integer *ns, doublereal *s, integer *ih, integer *
499 inew, logical *updatc, doublereal *c__)
501 /* System generated locals */
502 integer s_dim1, s_offset, i__1;
505 /* Local variables */
508 /* Coded by Tom Rowan */
509 /* Department of Computer Sciences */
510 /* University of Texas at Austin */
512 /* calcc calculates the centroid of the simplex without the */
513 /* vertex with highest function value. */
517 /* ns - subspace dimension */
519 /* s - double precision work space of dimension .ge. */
520 /* ns*(ns+3) used to store simplex */
522 /* ih - index to vertex with highest function value */
524 /* inew - index to new point */
526 /* updatc - logical switch */
527 /* = .true. : update centroid */
528 /* = .false. : calculate centroid from scratch */
530 /* c - centroid of the simplex without vertex with */
531 /* highest function value */
535 /* c - new centroid */
537 /* local variables */
540 /* subroutines and functions */
544 /* ----------------------------------------------------------- */
546 /* Parameter adjustments */
549 s_offset = 1 + s_dim1 * 1;
558 for (i__ = 1; i__ <= i__1; ++i__) {
559 c__[i__] += (s[i__ + *inew * s_dim1] - s[i__ + *ih * s_dim1]) / *
564 dcopy_(ns, &c_b3, &c__0, &c__[1], &c__1);
566 for (j = 1; j <= i__1; ++j) {
568 daxpy_(ns, &c_b7, &s[j * s_dim1 + 1], &c__1, &c__[1], &c__1);
573 dscal_(ns, &d__1, &c__[1], &c__1);
578 /* order.f -- translated by f2c (version 19991025).
579 You must link the resulting object file with the libraries:
580 -lf2c -lm (in that order)
583 static int order_(integer *npts, doublereal *fs, integer *il,
584 integer *is, integer *ih)
586 /* System generated locals */
589 /* Local variables */
594 /* Coded by Tom Rowan */
595 /* Department of Computer Sciences */
596 /* University of Texas at Austin */
598 /* order determines the indices of the vertices with the */
599 /* lowest, second highest, and highest function values. */
603 /* npts - number of points in simplex */
605 /* fs - double precision vector of function values of */
608 /* il - index to vertex with lowest function value */
612 /* il - new index to vertex with lowest function value */
614 /* is - new index to vertex with second highest */
617 /* ih - new index to vertex with highest function value */
619 /* local variables */
622 /* subroutines and functions */
626 /* ----------------------------------------------------------- */
628 /* Parameter adjustments */
634 if (fs[j] >= fs[*il]) {
642 i__1 = il0 + *npts - 2;
643 for (i__ = il0 + 1; i__ <= i__1; ++i__) {
645 if (fs[j] >= fs[*ih]) {
648 } else if (fs[j] > fs[*is]) {
650 } else if (fs[j] < fs[*il]) {
658 /* partx.f -- translated by f2c (version 19991025).
659 You must link the resulting object file with the libraries:
660 -lf2c -lm (in that order)
663 /* Common Block Declarations */
666 doublereal alpha, beta, gamma, delta, psi, omega;
667 integer nsmin, nsmax, irepl, ifxsw;
668 doublereal bonus, fstop;
669 integer nfstop, nfxe;
670 doublereal fxstat[4], ftest;
671 logical minf, initx, newx;
674 #define usubc_1 usubc_
676 static int partx_(integer *n, integer *ip, doublereal *absdx,
677 integer *nsubs, integer *nsvals)
679 /* System generated locals */
682 /* Local variables */
683 static integer i__, nleft, nused;
684 static doublereal as1max, gapmax, asleft, as1, as2;
685 static integer ns1, ns2;
686 static doublereal gap;
690 /* Coded by Tom Rowan */
691 /* Department of Computer Sciences */
692 /* University of Texas at Austin */
694 /* partx partitions the vector x by grouping components of */
695 /* similar magnitude of change. */
699 /* n - number of components (problem dimension) */
701 /* ip - permutation vector */
703 /* absdx - vector of magnitude of change in x */
705 /* nsvals - integer array dimensioned .ge. int(n/nsmin) */
709 /* nsubs - number of subspaces */
711 /* nsvals - integer array of subspace dimensions */
717 /* local variables */
721 /* subroutines and functions */
725 /* ----------------------------------------------------------- */
727 /* Parameter adjustments */
738 for (i__ = 2; i__ <= i__1; ++i__) {
739 asleft += absdx[i__];
746 i__1 = usubc_1.nsmin - 1;
747 for (i__ = 1; i__ <= i__1; ++i__) {
748 as1 += absdx[ip[nused + i__]];
752 i__1 = MIN2(usubc_1.nsmax,nleft);
753 for (ns1 = usubc_1.nsmin; ns1 <= i__1; ++ns1) {
754 as1 += absdx[ip[nused + ns1]];
757 if (ns2 >= ((ns2 - 1) / usubc_1.nsmax + 1) * usubc_1.nsmin) {
759 gap = as1 / ns1 - as2 / ns2;
762 nsvals[*nsubs] = ns1;
767 if (as1 / ns1 > gapmax) {
768 nsvals[*nsubs] = ns1;
774 nused += nsvals[*nsubs];
782 /* sortd.f -- translated by f2c (version 19991025).
783 You must link the resulting object file with the libraries:
784 -lf2c -lm (in that order)
787 static int sortd_(integer *n, doublereal *xkey, integer *ix)
789 /* System generated locals */
792 /* Local variables */
793 integer ixip1, i__, ilast, iswap, ifirst, ixi;
797 /* Coded by Tom Rowan */
798 /* Department of Computer Sciences */
799 /* University of Texas at Austin */
801 /* sortd uses the shakersort method to sort an array of keys */
802 /* in decreasing order. The sort is performed implicitly by */
803 /* modifying a vector of indices. */
805 /* For nearly sorted arrays, sortd requires O(n) comparisons. */
806 /* for completely unsorted arrays, sortd requires O(n**2) */
807 /* comparisons and will be inefficient unless n is small. */
811 /* n - number of components */
813 /* xkey - double precision vector of keys */
815 /* ix - integer vector of indices */
819 /* ix - indices satisfy xkey(ix(i)) .ge. xkey(ix(i+1)) */
820 /* for i = 1,...,n-1 */
822 /* local variables */
825 /* ----------------------------------------------------------- */
827 /* Parameter adjustments */
836 if (ifirst <= ilast) {
838 for (i__ = ifirst; i__ <= i__1; ++i__) {
841 if (xkey[ixi] < xkey[ixip1]) {
850 for (i__ = ilast; i__ >= i__1; --i__) {
853 if (xkey[ixi] < xkey[ixip1]) {
866 /* newpt.f -- translated by f2c (version 19991025).
867 You must link the resulting object file with the libraries:
868 -lf2c -lm (in that order)
871 static int newpt_(integer *ns, doublereal *coef, doublereal *xbase,
872 doublereal *xold, logical *new__, doublereal *xnew, logical *small)
874 /* System generated locals */
877 /* Local variables */
885 /* Coded by Tom Rowan */
886 /* Department of Computer Sciences */
887 /* University of Texas at Austin */
889 /* newpt performs reflections, expansions, contractions, and */
890 /* shrinkages (massive contractions) by computing: */
892 /* xbase + coef * (xbase - xold) */
894 /* The result is stored in xnew if new .eq. .true., */
895 /* in xold otherwise. */
897 /* use : coef .gt. 0 to reflect */
898 /* coef .lt. 0 to expand, contract, or shrink */
902 /* ns - number of components (subspace dimension) */
904 /* coef - one of four simplex method coefficients */
906 /* xbase - double precision ns-vector representing base */
909 /* xold - double precision ns-vector representing old */
912 /* new - logical switch */
913 /* = .true. : store result in xnew */
914 /* = .false. : store result in xold, xnew is not */
919 /* xold - unchanged if new .eq. .true., contains new */
920 /* point otherwise */
922 /* xnew - double precision ns-vector representing new */
923 /* point if new .eq. .true., not referenced */
926 /* small - logical flag */
927 /* = .true. : coincident points */
928 /* = .false. : otherwise */
930 /* local variables */
933 /* subroutines and functions */
937 /* ----------------------------------------------------------- */
939 /* Parameter adjustments */
949 for (i__ = 1; i__ <= i__1; ++i__) {
950 xnew[i__] = xbase[i__] + *coef * (xbase[i__] - xold[i__]);
951 eqbase = eqbase && xnew[i__] == xbase[i__];
952 eqold = eqold && xnew[i__] == xold[i__];
957 for (i__ = 1; i__ <= i__1; ++i__) {
959 xold[i__] = xbase[i__] + *coef * (xbase[i__] - xold[i__]);
960 eqbase = eqbase && xold[i__] == xbase[i__];
961 eqold = eqold && xold[i__] == xoldi;
965 *small = eqbase || eqold;
969 /* start.f -- translated by f2c (version 19991025).
970 You must link the resulting object file with the libraries:
971 -lf2c -lm (in that order)
974 static int start_(integer *n, doublereal *x, doublereal *step,
975 integer *ns, integer *ips, doublereal *s, logical *small)
977 /* System generated locals */
978 integer s_dim1, s_offset, i__1;
980 /* Local variables */
984 /* Coded by Tom Rowan */
985 /* Department of Computer Sciences */
986 /* University of Texas at Austin */
988 /* start creates the initial simplex for simplx minimization. */
992 /* n - problem dimension */
994 /* x - current best point */
996 /* step - stepsizes for corresponding components of x */
998 /* ns - subspace dimension */
1000 /* ips - permutation vector */
1005 /* s - first ns+1 columns contain initial simplex */
1007 /* small - logical flag */
1008 /* = .true. : coincident points */
1009 /* = .false. : otherwise */
1011 /* local variables */
1014 /* subroutines and functions */
1019 /* ----------------------------------------------------------- */
1021 /* Parameter adjustments */
1026 s_offset = 1 + s_dim1 * 1;
1031 for (i__ = 1; i__ <= i__1; ++i__) {
1032 s[i__ + s_dim1] = x[ips[i__]];
1036 for (j = 2; j <= i__1; ++j) {
1037 dcopy_(ns, &s[s_dim1 + 1], &c__1, &s[j * s_dim1 + 1], &c__1);
1038 s[j - 1 + j * s_dim1] = s[j - 1 + s_dim1] + step[ips[j - 1]];
1042 /* check for coincident points */
1045 for (j = 2; j <= i__1; ++j) {
1046 if (s[j - 1 + j * s_dim1] == s[j - 1 + s_dim1]) {
1054 /* coincident points */
1061 /* fstats.f -- translated by f2c (version 19991025).
1062 You must link the resulting object file with the libraries:
1063 -lf2c -lm (in that order)
1066 static int fstats_(doublereal *fx, integer *ifxwt, logical *reset)
1068 /* System generated locals */
1069 doublereal d__1, d__2, d__3;
1071 /* Local variables */
1072 static doublereal fscale;
1074 static doublereal f1sv;
1078 /* Coded by Tom Rowan */
1079 /* Department of Computer Sciences */
1080 /* University of Texas at Austin */
1082 /* fstats modifies the common /usubc/ variables nfxe,fxstat. */
1086 /* fx - most recent evaluation of f at best x */
1088 /* ifxwt - integer weight for fx */
1090 /* reset - logical switch */
1091 /* = .true. : initialize nfxe,fxstat */
1092 /* = .false. : update nfxe,fxstat */
1098 /* local variables */
1102 /* subroutines and functions */
1106 /* ----------------------------------------------------------- */
1109 usubc_1.nfxe = *ifxwt;
1110 usubc_1.fxstat[0] = *fx;
1111 usubc_1.fxstat[1] = *fx;
1112 usubc_1.fxstat[2] = *fx;
1113 usubc_1.fxstat[3] = 0.;
1116 f1sv = usubc_1.fxstat[0];
1117 usubc_1.nfxe += *ifxwt;
1118 usubc_1.fxstat[0] += *ifxwt * (*fx - usubc_1.fxstat[0]) /
1120 usubc_1.fxstat[1] = MAX2(usubc_1.fxstat[1],*fx);
1121 usubc_1.fxstat[2] = MIN2(usubc_1.fxstat[2],*fx);
1123 d__1 = fabs(usubc_1.fxstat[1]), d__2 = fabs(usubc_1.fxstat[2]), d__1 =
1125 fscale = MAX2(d__1,1.);
1126 /* Computing 2nd power */
1127 d__1 = usubc_1.fxstat[3] / fscale;
1128 /* Computing 2nd power */
1129 d__2 = (usubc_1.fxstat[0] - f1sv) / fscale;
1130 /* Computing 2nd power */
1131 d__3 = (*fx - usubc_1.fxstat[0]) / fscale;
1132 usubc_1.fxstat[3] = fscale * sqrt(((nsv - 1) * (d__1 * d__1) + nsv * (
1133 d__2 * d__2) + *ifxwt * (d__3 * d__3)) / (usubc_1.nfxe - 1));
1138 /* evalf.f -- translated by f2c (version 19991025).
1139 You must link the resulting object file with the libraries:
1140 -lf2c -lm (in that order)
1143 /* Common Block Declarations */
1146 doublereal fbonus, sfstop, sfbest;
1150 #define isubc_1 isubc_
1152 static logical c_true = TRUE_;
1153 static logical c_false = FALSE_;
1155 static int evalf_(D_fp f,void*fdata, integer *ns, integer *ips, doublereal *xs,
1156 integer *n, doublereal *x, doublereal *sfx, integer *nfe)
1158 /* System generated locals */
1161 /* Local variables */
1163 static doublereal fx;
1164 static logical newbst;
1166 /* Coded by Tom Rowan */
1167 /* Department of Computer Sciences */
1168 /* University of Texas at Austin */
1170 /* evalf evaluates the function f at a point defined by x */
1171 /* with ns of its components replaced by those in xs. */
1175 /* f - user supplied function f(n,x) to be optimized */
1177 /* ns - subspace dimension */
1179 /* ips - permutation vector */
1181 /* xs - double precision ns-vector to be mapped to x */
1183 /* n - problem dimension */
1185 /* x - double precision n-vector */
1187 /* nfe - number of function evaluations */
1191 /* sfx - signed value of f evaluated at x */
1193 /* nfe - incremented number of function evaluations */
1201 /* local variables */
1205 /* subroutines and functions */
1208 /* ----------------------------------------------------------- */
1210 /* Parameter adjustments */
1217 for (i__ = 1; i__ <= i__1; ++i__) {
1218 x[ips[i__]] = xs[i__];
1221 usubc_1.newx = isubc_1.new__ || usubc_1.irepl != 2;
1222 fx = (*f)(*n, &x[1], fdata);
1223 if (usubc_1.irepl == 0) {
1229 } else if (isubc_1.new__) {
1232 newbst = fx < usubc_1.ftest;
1235 newbst = fx > usubc_1.ftest;
1237 if (usubc_1.initx || newbst) {
1238 if (usubc_1.irepl == 1) {
1239 fstats_(&fx, &c__1, &c_true);
1242 isubc_1.sfbest = *sfx;
1245 if (usubc_1.irepl == 1) {
1246 fstats_(&fx, &c__1, &c_false);
1247 fx = usubc_1.fxstat[usubc_1.ifxsw - 1];
1249 usubc_1.ftest = fx + isubc_1.fbonus * usubc_1.fxstat[3];
1251 *sfx = usubc_1.ftest;
1252 isubc_1.sfbest = fx;
1254 *sfx = -usubc_1.ftest;
1255 isubc_1.sfbest = -fx;
1262 /* simplx.f -- translated by f2c (version 19991025).
1263 You must link the resulting object file with the libraries:
1264 -lf2c -lm (in that order)
1267 static int simplx_(D_fp f, void *fdata, integer *n, doublereal *step, integer *
1268 ns, integer *ips, nlopt_stopping *stop, logical *cmode, doublereal *x,
1269 doublereal *fx, integer *nfe, doublereal *s, doublereal *fs, integer *
1272 /* System generated locals */
1273 integer s_dim1, s_offset, i__1;
1274 doublereal d__1, d__2;
1276 /* Local variables */
1277 static integer inew;
1278 static integer npts;
1279 static integer i__, j;
1280 static integer icent;
1281 static logical small;
1282 static integer itemp;
1283 static doublereal fc, fe;
1284 static integer ih, il;
1285 static doublereal fr;
1287 static logical updatc;
1288 static doublereal dum, tol;
1292 /* Coded by Tom Rowan */
1293 /* Department of Computer Sciences */
1294 /* University of Texas at Austin */
1296 /* simplx uses the Nelder-Mead simplex method to minimize the */
1297 /* function f on a subspace. */
1301 /* f - function to be minimized, declared external in */
1302 /* calling routine */
1304 /* n - problem dimension */
1306 /* step - stepsizes for corresponding components of x */
1308 /* ns - subspace dimension */
1310 /* ips - permutation vector */
1312 /* maxnfe - maximum number of function evaluations */
1314 /* cmode - logical switch */
1315 /* = .true. : continuation of previous call */
1316 /* = .false. : first call */
1318 /* x - starting guess for minimum */
1320 /* fx - value of f at x */
1322 /* nfe - number of function evaluations */
1324 /* s - double precision work array of dimension .ge. */
1325 /* ns*(ns+3) used to store simplex */
1327 /* fs - double precision work array of dimension .ge. */
1328 /* ns+1 used to store function values of simplex */
1333 /* x - computed minimum */
1335 /* fx - value of f at x */
1337 /* nfe - incremented number of function evaluations */
1339 /* iflag - error flag */
1340 /* = -1 : maxnfe exceeded */
1341 /* = 0 : simplex reduced by factor of psi */
1342 /* = 1 : limit of machine precision */
1343 /* = 2 : reached fstop */
1351 /* local variables */
1355 /* subroutines and functions */
1360 /* ----------------------------------------------------------- */
1362 /* Parameter adjustments */
1367 s_offset = 1 + s_dim1 * 1;
1379 start_(n, &x[1], &step[1], ns, &ips[1], &s[s_offset], &small);
1384 if (usubc_1.irepl > 0) {
1385 isubc_1.new__ = FALSE_;
1386 evalf_((D_fp)f,fdata, ns, &ips[1], &s[s_dim1 + 1], n, &x[1], &fs[1], nfe);
1391 isubc_1.new__ = TRUE_;
1393 for (j = 2; j <= i__1; ++j) {
1394 evalf_((D_fp)f, fdata,ns, &ips[1], &s[j * s_dim1 + 1], n, &x[1], &fs[j],
1400 order_(&npts, &fs[1], &il, &is, &ih);
1401 tol = usubc_1.psi * dist_(ns, &s[ih * s_dim1 + 1], &s[il * s_dim1 + 1]);
1406 calcc_(ns, &s[s_offset], &ih, &inew, &updatc, &s[icent * s_dim1 + 1]);
1412 newpt_(ns, &usubc_1.alpha, &s[icent * s_dim1 + 1], &s[ih * s_dim1 + 1], &
1413 c_true, &s[itemp * s_dim1 + 1], &small);
1417 evalf_((D_fp)f,fdata, ns, &ips[1], &s[itemp * s_dim1 + 1], n, &x[1], &fr, nfe);
1423 d__1 = -usubc_1.gamma;
1424 newpt_(ns, &d__1, &s[icent * s_dim1 + 1], &s[itemp * s_dim1 + 1], &
1425 c_true, &s[ih * s_dim1 + 1], &small);
1429 evalf_((D_fp)f,fdata, ns, &ips[1], &s[ih * s_dim1 + 1], n, &x[1], &fe, nfe);
1434 dcopy_(ns, &s[itemp * s_dim1 + 1], &c__1, &s[ih * s_dim1 + 1], &
1438 } else if (fr < fs[is]) {
1440 /* accept reflected point */
1442 dcopy_(ns, &s[itemp * s_dim1 + 1], &c__1, &s[ih * s_dim1 + 1], &c__1);
1449 d__1 = -usubc_1.beta;
1450 newpt_(ns, &d__1, &s[icent * s_dim1 + 1], &s[ih * s_dim1 + 1], &
1451 c_true, &s[itemp * s_dim1 + 1], &small);
1453 d__1 = -usubc_1.beta;
1454 newpt_(ns, &d__1, &s[icent * s_dim1 + 1], &s[itemp * s_dim1 + 1],
1455 &c_false, &dum, &small);
1460 evalf_((D_fp)f,fdata, ns, &ips[1], &s[itemp * s_dim1 + 1], n, &x[1], &fc,
1464 d__1 = fr, d__2 = fs[ih];
1465 if (fc < MIN2(d__1,d__2)) {
1466 dcopy_(ns, &s[itemp * s_dim1 + 1], &c__1, &s[ih * s_dim1 + 1], &
1471 /* shrink simplex */
1474 for (j = 1; j <= i__1; ++j) {
1476 d__1 = -usubc_1.delta;
1477 newpt_(ns, &d__1, &s[il * s_dim1 + 1], &s[j * s_dim1 + 1],
1478 &c_false, &dum, &small);
1482 evalf_((D_fp)f,fdata, ns, &ips[1], &s[j * s_dim1 + 1], n, &x[1],
1491 order_(&npts, &fs[1], &il, &is, &ih);
1493 /* check termination */
1496 if (usubc_1.irepl == 0) {
1499 *fx = isubc_1.sfbest;
1502 if (nlopt_stop_forced(stop))
1504 else if (*fx < stop->minf_max)
1506 else if (nlopt_stop_evals(stop))
1508 else if (nlopt_stop_time(stop))
1510 else if (dist_(ns, &s[ih * s_dim1 + 1], &s[il * s_dim1 + 1]) <= tol
1516 /* end main loop, return best point */
1519 for (i__ = 1; i__ <= i__1; ++i__) {
1520 x[ips[i__]] = s[i__ + il * s_dim1];
1526 /* subopt.f -- translated by f2c (version 19991025).
1527 You must link the resulting object file with the libraries:
1528 -lf2c -lm (in that order)
1531 static int subopt_(integer *n)
1535 /* Coded by Tom Rowan */
1536 /* Department of Computer Sciences */
1537 /* University of Texas at Austin */
1539 /* subopt sets options for subplx. */
1543 /* n - problem dimension */
1550 /* subroutines and functions */
1554 /* ----------------------------------------------------------- */
1556 /* *********************************************************** */
1557 /* simplex method strategy parameters */
1558 /* *********************************************************** */
1560 /* alpha - reflection coefficient */
1565 /* beta - contraction coefficient */
1566 /* 0 .lt. beta .lt. 1 */
1570 /* gamma - expansion coefficient */
1575 /* delta - shrinkage (massive contraction) coefficient */
1576 /* 0 .lt. delta .lt. 1 */
1580 /* *********************************************************** */
1581 /* subplex method strategy parameters */
1582 /* *********************************************************** */
1584 /* psi - simplex reduction coefficient */
1585 /* 0 .lt. psi .lt. 1 */
1589 /* omega - step reduction coefficient */
1590 /* 0 .lt. omega .lt. 1 */
1594 /* nsmin and nsmax specify a range of subspace dimensions. */
1595 /* In addition to satisfying 1 .le. nsmin .le. nsmax .le. n, */
1596 /* nsmin and nsmax must be chosen so that n can be expressed */
1597 /* as a sum of positive integers where each of these integers */
1598 /* ns(i) satisfies nsmin .le. ns(i) .ge. nsmax. */
1600 /* nsmin*ceil(n/nsmax) .le. n must be true. */
1602 /* nsmin - subspace dimension minimum */
1604 usubc_1.nsmin = MIN2(2,*n);
1606 /* nsmax - subspace dimension maximum */
1608 usubc_1.nsmax = MIN2(5,*n);
1610 /* *********************************************************** */
1611 /* subplex method special cases */
1612 /* *********************************************************** */
1613 /* nelder-mead simplex method with periodic restarts */
1614 /* nsmin = nsmax = n */
1615 /* *********************************************************** */
1616 /* nelder-mead simplex method */
1617 /* nsmin = nsmax = n, psi = small positive */
1618 /* *********************************************************** */
1620 /* irepl, ifxsw, and bonus deal with measurement replication. */
1621 /* Objective functions subject to large amounts of noise can */
1622 /* cause an optimization method to halt at a false optimum. */
1623 /* An expensive solution to this problem is to evaluate f */
1624 /* several times at each point and return the average (or max */
1625 /* or min) of these trials as the function value. subplx */
1626 /* performs measurement replication only at the current best */
1627 /* point. The longer a point is retained as best, the more */
1628 /* accurate its function value becomes. */
1630 /* The common variable nfxe contains the number of function */
1631 /* evaluations at the current best point. fxstat contains the */
1632 /* mean, max, min, and standard deviation of these trials. */
1634 /* irepl - measurement replication switch */
1635 /* irepl = 0, 1, or 2 */
1636 /* = 0 : no measurement replication */
1637 /* = 1 : subplx performs measurement replication */
1638 /* = 2 : user performs measurement replication */
1639 /* (This is useful when optimizing on the mean, */
1640 /* max, or min of trials is insufficient. Common */
1641 /* variable initx is true for first function */
1642 /* evaluation. newx is true for first trial at */
1643 /* this point. The user uses subroutine fstats */
1644 /* within his objective function to maintain */
1645 /* fxstat. By monitoring newx, the user can tell */
1646 /* whether to return the function evaluation */
1647 /* (newx = .true.) or to use the new function */
1648 /* evaluation to refine the function evaluation */
1649 /* of the current best point (newx = .false.). */
1650 /* The common variable ftest gives the function */
1651 /* value that a new point must beat to be */
1652 /* considered the new best point.) */
1656 /* ifxsw - measurement replication optimization switch */
1657 /* ifxsw = 1, 2, or 3 */
1658 /* = 1 : retain mean of trials as best function value */
1659 /* = 2 : retain max */
1660 /* = 3 : retain min */
1664 /* Since the current best point will also be the most */
1665 /* accurately evaluated point whenever irepl .gt. 0, a bonus */
1666 /* should be added to the function value of the best point */
1667 /* so that the best point is not replaced by a new point */
1668 /* that only appears better because of noise. */
1669 /* subplx uses bonus to determine how many multiples of */
1670 /* fxstat(4) should be added as a bonus to the function */
1671 /* evaluation. (The bonus is adjusted automatically by */
1672 /* subplx when ifxsw or minf is changed.) */
1674 /* bonus - measurement replication bonus coefficient */
1675 /* bonus .ge. 0 (normally, bonus = 0 or 1) */
1676 /* = 0 : bonus not used */
1677 /* = 1 : bonus used */
1681 /* nfstop = 0 : f(x) is not tested against fstop */
1682 /* = 1 : if f(x) has reached fstop, subplx returns */
1684 /* = 2 : (only valid when irepl .gt. 0) */
1685 /* if f(x) has reached fstop and */
1686 /* nfxe .gt. nfstop, subplx returns iflag = 2 */
1690 /* fstop - f target value */
1691 /* Its usage is determined by the value of nfstop. */
1693 /* minf - logical switch */
1694 /* = .true. : subplx performs minimization */
1695 /* = .false. : subplx performs maximization */
1697 usubc_1.minf = TRUE_;
1701 /* setstp.f -- translated by f2c (version 19991025).
1702 You must link the resulting object file with the libraries:
1703 -lf2c -lm (in that order)
1706 static double d_sign(doublereal *x, doublereal *y)
1708 return copysign(*x, *y);
1711 static int setstp_(integer *nsubs, integer *n, doublereal *deltax,
1714 /* System generated locals */
1716 doublereal d__1, d__2, d__3;
1718 /* Builtin functions */
1719 /* double d_sign(doublereal *, doublereal *); */
1721 /* Local variables */
1723 static doublereal stpfac;
1727 /* Coded by Tom Rowan */
1728 /* Department of Computer Sciences */
1729 /* University of Texas at Austin */
1731 /* setstp sets the stepsizes for the corresponding components */
1732 /* of the solution vector. */
1736 /* nsubs - number of subspaces */
1738 /* n - number of components (problem dimension) */
1740 /* deltax - vector of change in solution vector */
1742 /* step - stepsizes for corresponding components of */
1743 /* solution vector */
1747 /* step - new stepsizes */
1753 /* local variables */
1757 /* subroutines and functions */
1762 /* ----------------------------------------------------------- */
1766 /* Parameter adjustments */
1774 d__3 = dasum_(n, &deltax[1], &c__1) / dasum_(n, &step[1], &c__1);
1775 d__1 = MAX2(d__3,usubc_1.omega), d__2 = 1. / usubc_1.omega;
1776 stpfac = MIN2(d__1,d__2);
1778 stpfac = usubc_1.psi;
1780 dscal_(n, &stpfac, &step[1], &c__1);
1782 /* reorient simplex */
1785 for (i__ = 1; i__ <= i__1; ++i__) {
1786 if (deltax[i__] != 0.) {
1787 step[i__] = d_sign(&step[i__], &deltax[i__]);
1789 step[i__] = -step[i__];
1796 /* subplx.f -- translated by f2c (version 19991025).
1797 You must link the resulting object file with the libraries:
1798 -lf2c -lm (in that order)
1801 static int subplx_(D_fp f, void *fdata, integer *n,
1802 nlopt_stopping *stop, integer *mode,
1803 const doublereal *scale, doublereal *x, doublereal *fx,
1804 integer *nfe, doublereal *work, integer *iwork,
1807 /* Initialized data */
1809 static doublereal bnsfac[6] /* was [3][2] */ = { -1.,-2.,0.,1.,0.,2. };
1811 /* System generated locals */
1813 doublereal d__1, d__2, d__3, d__4, d__5, d__6;
1815 /* Local variables */
1817 static logical cmode;
1818 static integer istep;
1819 static doublereal xpscl;
1820 static integer nsubs, ipptr;
1821 static integer isptr;
1822 static integer ns, insfnl, ifsptr;
1823 static integer insptr;
1824 static integer istptr;
1825 static doublereal scl, dum;
1827 static doublereal sfx, sfx_old, *x_old;
1831 /* Coded by Tom Rowan */
1832 /* Department of Computer Sciences */
1833 /* University of Texas at Austin */
1835 /* subplx uses the subplex method to solve unconstrained */
1836 /* optimization problems. The method is well suited for */
1837 /* optimizing objective functions that are noisy or are */
1838 /* discontinuous at the solution. */
1840 /* subplx sets default optimization options by calling the */
1841 /* subroutine subopt. The user can override these defaults */
1842 /* by calling subopt prior to calling subplx, changing the */
1843 /* appropriate common variables, and setting the value of */
1844 /* mode as indicated below. */
1846 /* By default, subplx performs minimization. */
1850 /* f - user supplied function f(n,x) to be optimized, */
1851 /* declared external in calling routine */
1853 /* n - problem dimension */
1855 /* tol - relative error tolerance for x (tol .ge. 0.) */
1857 /* maxnfe - maximum number of function evaluations */
1859 /* mode - integer mode switch with binary expansion */
1860 /* (bit 1) (bit 0) : */
1861 /* bit 0 = 0 : first call to subplx */
1862 /* = 1 : continuation of previous call */
1863 /* bit 1 = 0 : use default options */
1864 /* = 1 : user set options */
1866 /* scale - scale and initial stepsizes for corresponding */
1867 /* components of x */
1868 /* (If scale(1) .lt. 0., */
1869 /* abs(scale(1)) is used for all components of x, */
1870 /* and scale(2),...,scale(n) are not referenced.) */
1872 /* x - starting guess for optimum */
1874 /* work - double precision work array of dimension .ge. */
1875 /* 2*n + nsmax*(nsmax+4) + 1 */
1876 /* (nsmax is set in subroutine subopt. */
1877 /* default: nsmax = min(5,n)) */
1879 /* iwork - integer work array of dimension .ge. */
1880 /* n + int(n/nsmin) */
1881 /* (nsmin is set in subroutine subopt. */
1882 /* default: nsmin = min(2,n)) */
1886 /* x - computed optimum */
1888 /* fx - value of f at x */
1890 /* nfe - number of function evaluations */
1892 /* iflag - error flag */
1893 /* = -2 : invalid input */
1894 /* = -1 : maxnfe exceeded */
1895 /* = 0 : tol satisfied */
1896 /* = 1 : limit of machine precision */
1897 /* = 2 : fstop reached (fstop usage is determined */
1898 /* by values of options minf, nfstop, and */
1899 /* irepl. default: f(x) not tested against */
1901 /* iflag should not be reset between calls to */
1910 /* local variables */
1914 /* subroutines and functions */
1921 /* Parameter adjustments */
1930 /* ----------------------------------------------------------- */
1932 if (*mode % 2 == 0) {
1934 /* first call, check input */
1939 if (scale[1] >= 0.) {
1941 for (i__ = 1; i__ <= i__1; ++i__) {
1942 xpscl = x[i__] + scale[i__];
1943 if (xpscl == x[i__]) {
1949 scl = fabs(scale[1]);
1951 for (i__ = 1; i__ <= i__1; ++i__) {
1952 xpscl = x[i__] + scl;
1953 if (xpscl == x[i__]) {
1959 if (*mode / 2 % 2 == 0) {
1962 if (usubc_1.alpha <= 0.) {
1965 if (usubc_1.beta <= 0. || usubc_1.beta >= 1.) {
1968 if (usubc_1.gamma <= 1.) {
1971 if (usubc_1.delta <= 0. || usubc_1.delta >= 1.) {
1974 if (usubc_1.psi <= 0. || usubc_1.psi >= 1.) {
1977 if (usubc_1.omega <= 0. || usubc_1.omega >= 1.) {
1980 if (usubc_1.nsmin < 1 || usubc_1.nsmax < usubc_1.nsmin || *n <
1984 if (*n < ((*n - 1) / usubc_1.nsmax + 1) * usubc_1.nsmin) {
1987 if (usubc_1.irepl < 0 || usubc_1.irepl > 2) {
1990 if (usubc_1.ifxsw < 1 || usubc_1.ifxsw > 3) {
1993 if (usubc_1.bonus < 0.) {
1996 if (usubc_1.nfstop < 0) {
2001 /* initialization */
2004 isptr = istptr + *n;
2005 ifsptr = isptr + usubc_1.nsmax * (usubc_1.nsmax + 3);
2007 if (scale[1] > 0.) {
2008 dcopy_(n, &scale[1], &c__1, &work[1], &c__1);
2009 dcopy_(n, &scale[1], &c__1, &work[istptr], &c__1);
2011 dcopy_(n, &scl, &c__0, &work[1], &c__1);
2012 dcopy_(n, &scl, &c__0, &work[istptr], &c__1);
2015 for (i__ = 1; i__ <= i__1; ++i__) {
2021 if (usubc_1.irepl == 0) {
2022 isubc_1.fbonus = 0.;
2023 } else if (usubc_1.minf) {
2024 isubc_1.fbonus = bnsfac[usubc_1.ifxsw - 1] * usubc_1.bonus;
2026 isubc_1.fbonus = bnsfac[usubc_1.ifxsw + 2] * usubc_1.bonus;
2028 if (usubc_1.nfstop == 0) {
2029 isubc_1.sfstop = 0.;
2030 } else if (usubc_1.minf) {
2031 isubc_1.sfstop = usubc_1.fstop;
2033 isubc_1.sfstop = -usubc_1.fstop;
2037 isubc_1.new__ = TRUE_;
2038 usubc_1.initx = TRUE_;
2039 evalf_((D_fp)f, fdata, &c__0, &iwork[1], &dum, n, &x[1], &sfx, nfe);
2041 usubc_1.initx = FALSE_;
2044 /* continuation of previous call */
2048 isubc_1.sfstop = usubc_1.fstop;
2050 isubc_1.sfstop = -usubc_1.fstop;
2054 } else if (*iflag == -1) {
2057 } else if (*iflag == 0) {
2069 for (i__ = 1; i__ <= i__1; ++i__) {
2070 work[i__] = (d__1 = work[i__], fabs(d__1));
2073 sortd_(n, &work[1], &iwork[1]);
2074 partx_(n, &iwork[1], &work[1], &nsubs, &iwork[insptr]);
2075 dcopy_(n, &x[1], &c__1, &work[1], &c__1);
2077 insfnl = insptr + nsubs - 1;
2082 memcpy(&x_old[1], &x[1], sizeof(doublereal) * *n);
2086 simplx_((D_fp)f, fdata, n, &work[istptr], &ns, &iwork[ipptr], stop, &cmode, &x[1], &sfx, nfe, &work[isptr], &work[ifsptr], iflag);
2097 /* end simplex loop */
2100 for (i__ = 1; i__ <= i__1; ++i__) {
2101 work[i__] = x[i__] - work[i__];
2105 /* check termination */
2107 if (nlopt_stop_ftol(stop, sfx, sfx_old)) {
2111 if (nlopt_stop_x(stop, &x[1], &x_old[1])) {
2119 for (i__ = 1; i__ <= i__1; ++i__) {
2121 d__4 = (d__2 = work[i__], fabs(d__2)), d__5 = (d__1 = work[istep], fabs(
2122 d__1)) * usubc_1.psi;
2124 d__6 = (d__3 = x[i__], fabs(d__3));
2125 if (MAX2(d__4,d__5) / MAX2(d__6,1.) > stop->xtol_rel) {
2126 setstp_(&nsubs, n, &work[1], &work[istptr]);
2133 /* end subplex loop */
2151 /****************************************************************************/
2152 /****************************************************************************/
2154 /* front-end for subplex routines */
2156 /* Wrapper around f2c'ed subplx_ routine, for multidimensinal
2157 unconstrained optimization:
2161 f: function f(n,x,fdata) to be optimized
2162 n: problem dimension
2163 minf: (output) value of f at minimum
2164 x[n]: (input) starting guess position, (output) computed minimum
2165 fdata: data pointer passed to f
2168 tol: relative error tolerance for x
2169 maxnfe: maximum number of function evaluations
2170 minf_max, use_minf_max: if use_minf_max, stop when f <= minf_max
2172 new args: nlopt_stopping *stop (stopping criteria)
2174 scale[n]: (input) scale & initial stepsizes for components of x
2175 (if *scale < 0, |*scale| is used for all components)
2178 = -2 : invalid input
2179 = -10 : maxtime exceeded
2180 = -1 : maxevals exceeded
2182 = 1 : limit of machine precision
2183 = 2 : fstop reached (fstop usage is determined by values of
2184 options minf, nfstop, and irepl. default: f(x) not
2185 tested against fstop)
2187 = -200 : out of memory
2189 int nlopt_subplex(subplex_func f, double *minf, double *x, int n, void *fdata,
2190 nlopt_stopping *stop,
2191 const double *scale)
2193 int mode = 0, *iwork, nsmax, nsmin, errflag, nfe;
2198 work = (double*) malloc(sizeof(double) * (3*n + nsmax*(nsmax+4) + 1));
2201 iwork = (int*) malloc(sizeof(int) * (n + n/nsmin + 1));
2207 subplx_(f,fdata, &n,
2211 work, iwork, &errflag);