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/** R : A Computer Language for Statistical Data Analysis* Copyright (C) 1999-2001 the R Development Core Team** This program is free software; you can redistribute it and/or modify* it under the terms of the GNU General Public License as published by* the Free Software Foundation; either version 2 of the License, or* (at your option) any later version.** This program is distributed in the hope that it will be useful,* but WITHOUT ANY WARRANTY; without even the implied warranty of* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the* GNU General Public License for more details.** You should have received a copy of the GNU General Public License* along with this program; if not, write to the Free Software* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA*/#include <Defn.h>#include <Rdefines.h> /* for CREATE_STRING_VECTOR */#include <R_ext/Random.h> /* for the random number generation insamin() */#include <R_ext/Applic.h> /* setulb() */static SEXP getListElement(SEXP list, char *str){SEXP elmt = R_NilValue, names = getAttrib(list, R_NamesSymbol);int i;for (i = 0; i < length(list); i++)if (strcmp(CHAR(STRING_ELT(names, i)), str) == 0) {elmt = VECTOR_ELT(list, i);break;}return elmt;}static double * vect(int n){return (double *)R_alloc(n, sizeof(double));}typedef struct opt_struct{SEXP R_fcall; /* function */SEXP R_gcall; /* gradient */SEXP R_env; /* where to evaluate the calls */double* ndeps; /* tolerances for numerical derivatives */double fnscale; /* scaling for objective */double* parscale;/* scaling for parameters */int usebounds;double* lower, *upper;} opt_struct, *OptStruct;static void vmmin(int n, double *b, double *Fmin, int maxit, int trace,int *mask, double abstol, double reltol, int nREPORT,OptStruct OS, int *fncount, int *grcount, int *fail);static void nmmin(int n, double *Bvec, double *X, double *Fmin,int *fail, double abstol, double intol, OptStruct OS,double alpha, double beta, double gamm, int trace,int *fncount, int maxit);static void cgmin(int n, double *Bvec, double *X, double *Fmin,int *fail, double abstol, double intol, OptStruct OS,int type, int trace, int *fncount, int *grcount, int maxit);static void lbfgsb(int n, int m, double *x, double *l, double *u, int *nbd,double *Fmin, int *fail, OptStruct OS,double factr, double pgtol, int *fncount, int *grcount,int maxit, char *msg, int trace, int nREPORT);static void samin(int n, double *pb, double *yb, int maxit, int tmax,double ti, int trace, OptStruct OS);static double fminfn(int n, double *p, OptStruct OS){SEXP s, x;int i;double val;PROTECT_INDEX ipx;PROTECT(x = allocVector(REALSXP, n));for (i = 0; i < n; i++) {if (!R_FINITE(p[i])) error("non-finite value supplied by optim");REAL(x)[i] = p[i] * (OS->parscale[i]);}SETCADR(OS->R_fcall, x);PROTECT_WITH_INDEX(s = eval(OS->R_fcall, OS->R_env), &ipx);REPROTECT(s = coerceVector(s, REALSXP), ipx);val = REAL(s)[0]/(OS->fnscale);UNPROTECT(2);return val;}static void fmingr(int n, double *p, double *df, OptStruct OS){SEXP s, x;int i;double val1, val2, eps, epsused, tmp;PROTECT_INDEX ipx;if (!isNull(OS->R_gcall)) { /* analytical derivatives */PROTECT(x = allocVector(REALSXP, n));for (i = 0; i < n; i++) {if (!R_FINITE(p[i])) error("non-finite value supplied by optim");REAL(x)[i] = p[i] * (OS->parscale[i]);}SETCADR(OS->R_gcall, x);PROTECT_WITH_INDEX(s = eval(OS->R_gcall, OS->R_env), &ipx);REPROTECT(s = coerceVector(s, REALSXP), ipx);if(LENGTH(s) != n)error("gradient in optim evaluated to length %d not %d",LENGTH(s), n);for (i = 0; i < n; i++)df[i] = REAL(s)[i] * (OS->parscale[i])/(OS->fnscale);UNPROTECT(2);} else { /* numerical derivatives */PROTECT(x = allocVector(REALSXP, n));for (i = 0; i < n; i++) REAL(x)[i] = p[i] * (OS->parscale[i]);SETCADR(OS->R_fcall, x);if(OS->usebounds == 0) {for (i = 0; i < n; i++) {eps = OS->ndeps[i];REAL(x)[i] = (p[i] + eps) * (OS->parscale[i]);SETCADR(OS->R_fcall, x);PROTECT_WITH_INDEX(s = eval(OS->R_fcall, OS->R_env), &ipx);REPROTECT(s = coerceVector(s, REALSXP), ipx);val1 = REAL(s)[0]/(OS->fnscale);REAL(x)[i] = (p[i] - eps) * (OS->parscale[i]);SETCADR(OS->R_fcall, x);REPROTECT(s = eval(OS->R_fcall, OS->R_env), ipx);REPROTECT(s = coerceVector(s, REALSXP), ipx);val2 = REAL(s)[0]/(OS->fnscale);df[i] = (val1 - val2)/(2 * eps);#define DO_df_x \if(!R_FINITE(df[i])) \error("non-finite finite-difference value [%d]", i);\REAL(x)[i] = p[i] * (OS->parscale[i])DO_df_x;UNPROTECT(1);}} else { /* usebounds */for (i = 0; i < n; i++) {epsused = eps = OS->ndeps[i];tmp = p[i] + eps;if (tmp > OS->upper[i]) {tmp = OS->upper[i];epsused = tmp - p[i] ;}REAL(x)[i] = tmp * (OS->parscale[i]);SETCADR(OS->R_fcall, x);PROTECT_WITH_INDEX(s = eval(OS->R_fcall, OS->R_env), &ipx);REPROTECT(s = coerceVector(s, REALSXP), ipx);val1 = REAL(s)[0]/(OS->fnscale);tmp = p[i] - eps;if (tmp < OS->lower[i]) {tmp = OS->lower[i];eps = p[i] - tmp;}REAL(x)[i] = tmp * (OS->parscale[i]);SETCADR(OS->R_fcall, x);REPROTECT(s = eval(OS->R_fcall, OS->R_env), ipx);REPROTECT(s = coerceVector(s, REALSXP), ipx);val2 = REAL(s)[0]/(OS->fnscale);df[i] = (val1 - val2)/(epsused + eps);DO_df_x;UNPROTECT(1);}}UNPROTECT(1); /* x */}}/* par fn gr method options */SEXP do_optim(SEXP call, SEXP op, SEXP args, SEXP rho){SEXP par, fn, gr, method, options, tmp, slower, supper;SEXP res, value, counts, conv;int i, npar=0, *mask, trace, maxit, fncount, grcount, nREPORT, tmax;int ifail = 0;double *dpar, *opar, val, abstol, reltol, temp;char *tn;OptStruct OS;char *vmax;checkArity(op, args);vmax = vmaxget();OS = (OptStruct) R_alloc(1, sizeof(opt_struct));OS->usebounds = 0;OS->R_env = rho;par = CAR(args);args = CDR(args); fn = CAR(args);if (!isFunction(fn)) errorcall(call, "fn is not a function");args = CDR(args); gr = CAR(args);args = CDR(args); method = CAR(args);if (!isString(method)|| LENGTH(method) != 1)errorcall(call, "invalid method argument");tn = CHAR(STRING_ELT(method, 0));args = CDR(args); options = CAR(args);PROTECT(OS->R_fcall = lang2(fn, R_NilValue));PROTECT(par = coerceVector(duplicate(par), REALSXP));npar = LENGTH(par);dpar = vect(npar);opar = vect(npar);trace = asInteger(getListElement(options, "trace"));OS->fnscale = asReal(getListElement(options, "fnscale"));tmp = getListElement(options, "parscale");if (LENGTH(tmp) != npar)errorcall(call, "parscale is of the wrong length");PROTECT(tmp = coerceVector(tmp, REALSXP));OS->parscale = vect(npar);for (i = 0; i < npar; i++) OS->parscale[i] = REAL(tmp)[i];UNPROTECT(1);for (i = 0; i < npar; i++)dpar[i] = REAL(par)[i] / (OS->parscale[i]);PROTECT(res = allocVector(VECSXP, 5));PROTECT(value = allocVector(REALSXP, 1));PROTECT(counts = allocVector(INTSXP, 2));PROTECT(conv = allocVector(INTSXP, 1));abstol = asReal(getListElement(options, "abstol"));reltol = asReal(getListElement(options, "reltol"));maxit = asInteger(getListElement(options, "maxit"));if (maxit == NA_INTEGER) error("maxit is not an integer");if (strcmp(tn, "Nelder-Mead") == 0) {double alpha, beta, gamm;alpha = asReal(getListElement(options, "alpha"));beta = asReal(getListElement(options, "beta"));gamm = asReal(getListElement(options, "gamma"));nmmin(npar, dpar, opar, &val, &ifail, abstol, reltol, OS,alpha, beta, gamm, trace, &fncount, maxit);for (i = 0; i < npar; i++)REAL(par)[i] = opar[i] * (OS->parscale[i]);grcount = NA_INTEGER;}else if (strcmp(tn, "SANN") == 0) {tmax = asInteger(getListElement(options, "tmax"));temp = asReal(getListElement(options, "temp"));if (tmax == NA_INTEGER) error("tmax is not an integer");samin (npar, dpar, &val, maxit, tmax, temp, trace, OS);for (i = 0; i < npar; i++)REAL(par)[i] = dpar[i] * (OS->parscale[i]);fncount = maxit;grcount = NA_INTEGER;} else if (strcmp(tn, "BFGS") == 0) {SEXP ndeps;nREPORT = asInteger(getListElement(options, "REPORT"));if (!isNull(gr)) {if (!isFunction(gr)) error("gr is not a function");PROTECT(OS->R_gcall = lang2(gr, R_NilValue));} else {PROTECT(OS->R_gcall = R_NilValue); /* for balance */ndeps = getListElement(options, "ndeps");if (LENGTH(ndeps) != npar) error("ndeps is of the wrong length");OS->ndeps = vect(npar);PROTECT(ndeps = coerceVector(ndeps, REALSXP));for (i = 0; i < npar; i++) OS->ndeps[i] = REAL(ndeps)[i];UNPROTECT(1);}mask = (int *) R_alloc(npar, sizeof(int));for (i = 0; i < npar; i++) mask[i] = 1;vmmin(npar, dpar, &val, maxit, trace, mask, abstol, reltol,nREPORT, OS, &fncount, &grcount, &ifail);for (i = 0; i < npar; i++)REAL(par)[i] = dpar[i] * (OS->parscale[i]);UNPROTECT(1); /* OS->R_gcall */} else if (strcmp(tn, "CG") == 0) {int type;SEXP ndeps;type = asInteger(getListElement(options, "type"));if (!isNull(gr)) {if (!isFunction(gr)) error("gr is not a function");PROTECT(OS->R_gcall = lang2(gr, R_NilValue));} else {PROTECT(OS->R_gcall = R_NilValue); /* for balance */ndeps = getListElement(options, "ndeps");if (LENGTH(ndeps) != npar) error("ndeps is of the wrong length");OS->ndeps = vect(npar);PROTECT(ndeps = coerceVector(ndeps, REALSXP));for (i = 0; i < npar; i++) OS->ndeps[i] = REAL(ndeps)[i];UNPROTECT(1);}cgmin(npar, dpar, opar, &val, &ifail, abstol, reltol, OS, type, trace,&fncount, &grcount, maxit);for (i = 0; i < npar; i++)REAL(par)[i] = opar[i] * (OS->parscale[i]);UNPROTECT(1); /* OS->R_gcall */} else if (strcmp(tn, "L-BFGS-B") == 0) {SEXP ndeps, smsg;double *lower = vect(npar), *upper = vect(npar);int lmm, *nbd = (int *) R_alloc(npar, sizeof(int));double factr, pgtol;char msg[60];nREPORT = asInteger(getListElement(options, "REPORT"));factr = asReal(getListElement(options, "factr"));pgtol = asReal(getListElement(options, "pgtol"));lmm = asInteger(getListElement(options, "lmm"));if (!isNull(gr)) {if (!isFunction(gr)) error("gr is not a function");PROTECT(OS->R_gcall = lang2(gr, R_NilValue));} else {PROTECT(OS->R_gcall = R_NilValue); /* for balance */ndeps = getListElement(options, "ndeps");if (LENGTH(ndeps) != npar) error("ndeps is of the wrong length");OS->ndeps = vect(npar);PROTECT(ndeps = coerceVector(ndeps, REALSXP));for (i = 0; i < npar; i++) OS->ndeps[i] = REAL(ndeps)[i];UNPROTECT(1);}args = CDR(args); slower = CAR(args); /* coerce in calling code */args = CDR(args); supper = CAR(args);for (i = 0; i < npar; i++) {lower[i] = REAL(slower)[i] / (OS->parscale[i]);upper[i] = REAL(supper)[i] / (OS->parscale[i]);if (!R_FINITE(lower[i])) {if (!R_FINITE(upper[i])) nbd[i] = 0; else nbd[i] = 3;} else {if (!R_FINITE(upper[i])) nbd[i] = 1; else nbd[i] = 2;}}OS->usebounds = 1;OS->lower = lower;OS->upper = upper;lbfgsb(npar, lmm, dpar, lower, upper, nbd, &val, &ifail, OS,factr, pgtol, &fncount, &grcount, maxit, msg, trace, nREPORT);for (i = 0; i < npar; i++)REAL(par)[i] = dpar[i] * (OS->parscale[i]);UNPROTECT(1); /* OS->R_gcall */PROTECT(smsg = allocVector(STRSXP, 1));SET_STRING_ELT(smsg, 0, CREATE_STRING_VECTOR(msg));SET_VECTOR_ELT(res, 4, smsg);UNPROTECT(1);} elseerrorcall(call, "unknown method");REAL(value)[0] = val * (OS->fnscale);SET_VECTOR_ELT(res, 0, par); SET_VECTOR_ELT(res, 1, value);INTEGER(counts)[0] = fncount; INTEGER(counts)[1] = grcount;SET_VECTOR_ELT(res, 2, counts);INTEGER(conv)[0] = ifail;SET_VECTOR_ELT(res, 3, conv);vmaxset(vmax);UNPROTECT(6);return res;}/* par fn gr options */SEXP do_optimhess(SEXP call, SEXP op, SEXP args, SEXP rho){SEXP par, fn, gr, options, tmp, ndeps, ans;OptStruct OS;int npar, i , j;double *dpar, *df1, *df2, eps;char *vmax;checkArity(op, args);vmax = vmaxget();OS = (OptStruct) R_alloc(1, sizeof(opt_struct));OS->usebounds = 0;OS->R_env = rho;par = CAR(args);npar = LENGTH(par);args = CDR(args); fn = CAR(args);if (!isFunction(fn)) errorcall(call, "fn is not a function");args = CDR(args); gr = CAR(args);args = CDR(args); options = CAR(args);OS->fnscale = asReal(getListElement(options, "fnscale"));tmp = getListElement(options, "parscale");if (LENGTH(tmp) != npar)errorcall(call, "parscale is of the wrong length");PROTECT(tmp = coerceVector(tmp, REALSXP));OS->parscale = vect(npar);for (i = 0; i < npar; i++) OS->parscale[i] = REAL(tmp)[i];UNPROTECT(1);PROTECT(OS->R_fcall = lang2(fn, R_NilValue));PROTECT(par = coerceVector(par, REALSXP));if (!isNull(gr)) {if (!isFunction(gr)) error("gr is not a function");PROTECT(OS->R_gcall = lang2(gr, R_NilValue));} else {PROTECT(OS->R_gcall = R_NilValue); /* for balance */}ndeps = getListElement(options, "ndeps");if (LENGTH(ndeps) != npar) error("ndeps is of the wrong length");OS->ndeps = vect(npar);PROTECT(ndeps = coerceVector(ndeps, REALSXP));for (i = 0; i < npar; i++) OS->ndeps[i] = REAL(ndeps)[i];UNPROTECT(1);PROTECT(ans = allocMatrix(REALSXP, npar, npar));dpar = vect(npar);for (i = 0; i < npar; i++)dpar[i] = REAL(par)[i] / (OS->parscale[i]);df1 = vect(npar);df2 = vect(npar);for (i = 0; i < npar; i++) {eps = OS->ndeps[i]/(OS->parscale[i]);dpar[i] = dpar[i] + eps;fmingr(npar, dpar, df1, OS);dpar[i] = dpar[i] - 2 * eps;fmingr(npar, dpar, df2, OS);for (j = 0; j < npar; j++)REAL(ans)[i * npar + j] = (OS->fnscale) * (df1[j] - df2[j])/(2 * eps * (OS->parscale[i]) * (OS->parscale[j]));dpar[i] = dpar[i] + eps;}vmaxset(vmax);UNPROTECT(4);return ans;}static double ** matrix(int nrh, int nch){int i;double **m;m = (double **) R_alloc((nrh + 1), sizeof(double *));for (i = 0; i <= nrh; i++)m[i] = (double*) R_alloc((nch + 1), sizeof(double));return m;}static double ** Lmatrix(int n){int i;double **m;m = (double **) R_alloc(n, sizeof(double *));for (i = 0; i < n; i++)m[i] = (double *) R_alloc((i + 1), sizeof(double));return m;}#define stepredn 0.2#define acctol 0.0001#define reltest 10.0/* BFGS variable-metric method, based on Pascal codein J.C. Nash, `Compact Numerical Methods for Computers', 2nd edition,converted by p2c then re-crafted by B.D. Ripley */static voidvmmin(int n0, double *b, double *Fmin, int maxit, int trace, int *mask,double abstol, double reltol, int nREPORT, OptStruct OS,int *fncount, int *grcount, int *fail){Rboolean accpoint, enough;double *g, *t, *X, *c, **B;int count, funcount, gradcount;double f, gradproj;int i, j, ilast, iter = 0;double s, steplength;double D1, D2;int n, *l;if (nREPORT <= 0)error("REPORT must be > 0 (method = \"BFGS\")");l = (int *) R_alloc(n0, sizeof(int));n = 0;for (i = 0; i < n0; i++) if (mask[i]) l[n++] = i;g = vect(n0);t = vect(n);X = vect(n);c = vect(n);B = Lmatrix(n);f = fminfn(n, b, OS);if (!R_FINITE(f))error("initial value in vmmin is not finite");if (trace) Rprintf("initial value %f \n", f);*Fmin = f;funcount = gradcount = 1;fmingr(n, b, g, OS);iter++;ilast = gradcount;do {if (ilast == gradcount) {for (i = 0; i < n; i++) {for (j = 0; j < i; j++) B[i][j] = 0.0;B[i][i] = 1.0;}}for (i = 0; i < n; i++) {X[i] = b[l[i]];c[i] = g[l[i]];}gradproj = 0.0;for (i = 0; i < n; i++) {s = 0.0;for (j = 0; j <= i; j++) s -= B[i][j] * g[l[j]];for (j = i + 1; j < n; j++) s -= B[j][i] * g[l[j]];t[i] = s;gradproj += s * g[l[i]];}if (gradproj < 0.0) { /* search direction is downhill */steplength = 1.0;accpoint = FALSE;do {count = 0;for (i = 0; i < n; i++) {b[l[i]] = X[i] + steplength * t[i];if (reltest + X[i] == reltest + b[l[i]]) /* no change */count++;}if (count < n) {f = fminfn(n, b, OS);funcount++;accpoint = R_FINITE(f) &&(f <= *Fmin + gradproj * steplength * acctol);if (!accpoint) {steplength *= stepredn;}}} while (!(count == n || accpoint));enough = (f > abstol) &&fabs(f - *Fmin) > reltol * (fabs(*Fmin) + reltol);/* stop if value if small or if relative change is low */if (!enough) {count = n;*Fmin = f;}if (count < n) {/* making progress */*Fmin = f;fmingr(n, b, g, OS);gradcount++;iter++;D1 = 0.0;for (i = 0; i < n; i++) {t[i] = steplength * t[i];c[i] = g[l[i]] - c[i];D1 += t[i] * c[i];}if (D1 > 0) {D2 = 0.0;for (i = 0; i < n; i++) {s = 0.0;for (j = 0; j <= i; j++)s += B[i][j] * c[j];for (j = i + 1; j < n; j++)s += B[j][i] * c[j];X[i] = s;D2 += s * c[i];}D2 = 1.0 + D2 / D1;for (i = 0; i < n; i++) {for (j = 0; j <= i; j++)B[i][j] += (D2 * t[i] * t[j]- X[i] * t[j] - t[i] * X[j]) / D1;}} else { /* D1 < 0 */ilast = gradcount;}} else { /* no progress */if (ilast < gradcount) {count = 0;ilast = gradcount;}}} else { /* uphill search */count = 0;if (ilast == gradcount) count = n;else ilast = gradcount;/* Resets unless has just been reset */}if (trace && (iter % nREPORT == 0))Rprintf("iter%4d value %f\n", iter, f);if (iter >= maxit) break;if (gradcount - ilast > 2 * n)ilast = gradcount; /* periodic restart */} while (count != n || ilast != gradcount);if (trace) {Rprintf("final value %f \n", *Fmin);if (iter < maxit) Rprintf("converged\n");else Rprintf("stopped after %i iterations\n", iter);}*fncount = funcount;*grcount = gradcount;}#define big 1.0e+35 /*a very large number*//* Nelder-Mead */staticvoid nmmin(int n, double *Bvec, double *X, double *Fmin,int *fail, double abstol, double intol, OptStruct OS,double alpha, double beta, double gamm, int trace,int *fncount, int maxit){char action[50];int C;Rboolean calcvert, shrinkfail = FALSE;double convtol, f;int funcount=0, H, i, j, L=0;int n1=0;double oldsize;double **P;double size, step, temp, trystep;char tstr[6];double VH, VL, VR;if (trace)Rprintf(" Nelder-Mead direct search function minimizer\n");P = matrix(n, n+1);*fail = FALSE;f = fminfn(n, Bvec, OS);if (!R_FINITE(f)) {error("Function cannot be evaluated at initial parameters");*fail = TRUE;} else {if (trace) Rprintf("Function value for initial parameters = %f\n", f);funcount = 1;convtol = intol * (fabs(f) + intol);if (trace) Rprintf(" Scaled convergence tolerance is %g\n", convtol);n1 = n + 1;C = n + 2;P[n1 - 1][0] = f;for (i = 0; i < n; i++)P[i][0] = Bvec[i];L = 1;size = 0.0;step = 0.0;for (i = 0; i < n; i++) {if (0.1 * fabs(Bvec[i]) > step)step = 0.1 * fabs(Bvec[i]);}if (step == 0.0) step = 0.1;if (trace) Rprintf("Stepsize computed as %f\n", step);for (j = 2; j <= n1; j++) {strcpy(action, "BUILD ");for (i = 0; i < n; i++)P[i][j - 1] = Bvec[i];trystep = step;while (P[j - 2][j - 1] == Bvec[j - 2]) {P[j - 2][j - 1] = Bvec[j - 2] + trystep;trystep *= 10;}size += trystep;}oldsize = size;calcvert = TRUE;shrinkfail = FALSE;do {if (calcvert) {for (j = 0; j < n1; j++) {if (j + 1 != L) {for (i = 0; i < n; i++)Bvec[i] = P[i][j];f = fminfn(n, Bvec, OS);if (!R_FINITE(f)) f = big;funcount++;P[n1 - 1][j] = f;}}calcvert = FALSE;}VL = P[n1 - 1][L - 1];VH = VL;H = L;for (j = 1; j <= n1; j++) {if (j != L) {f = P[n1 - 1][j - 1];if (f < VL) {L = j;VL = f;}if (f > VH) {H = j;VH = f;}}}if (VH > VL + convtol && VL > abstol) {sprintf(tstr, "%5d", funcount);if (trace) Rprintf("%s%s %f %f\n", action, tstr, VH, VL);for (i = 0; i < n; i++) {temp = -P[i][H - 1];for (j = 0; j < n1; j++)temp += P[i][j];P[i][C - 1] = temp / n;}for (i = 0; i < n; i++)Bvec[i] = (1.0 + alpha) * P[i][C - 1] - alpha * P[i][H - 1];f = fminfn(n, Bvec, OS);if (!R_FINITE(f)) f = big;funcount++;strcpy(action, "REFLECTION ");VR = f;if (VR < VL) {P[n1 - 1][C - 1] = f;for (i = 0; i < n; i++) {f = gamm * Bvec[i] + (1 - gamm) * P[i][C - 1];P[i][C - 1] = Bvec[i];Bvec[i] = f;}f = fminfn(n, Bvec, OS);if (!R_FINITE(f)) f = big;funcount++;if (f < VR) {for (i = 0; i < n; i++)P[i][H - 1] = Bvec[i];P[n1 - 1][H - 1] = f;strcpy(action, "EXTENSION ");} else {for (i = 0; i < n; i++)P[i][H - 1] = P[i][C - 1];P[n1 - 1][H - 1] = VR;}} else {strcpy(action, "HI-REDUCTION ");if (VR < VH) {for (i = 0; i < n; i++)P[i][H - 1] = Bvec[i];P[n1 - 1][H - 1] = VR;strcpy(action, "LO-REDUCTION ");}for (i = 0; i < n; i++)Bvec[i] = (1 - beta) * P[i][H - 1] + beta * P[i][C - 1];f = fminfn(n, Bvec, OS);if (!R_FINITE(f)) f = big;funcount++;if (f < P[n1 - 1][H - 1]) {for (i = 0; i < n; i++)P[i][H - 1] = Bvec[i];P[n1 - 1][H - 1] = f;} else {if (VR >= VH) {strcpy(action, "SHRINK ");calcvert = TRUE;size = 0.0;for (j = 0; j < n1; j++) {if (j + 1 != L) {for (i = 0; i < n; i++) {P[i][j] = beta * (P[i][j] - P[i][L - 1]) + P[i][L - 1];size += fabs(P[i][j] - P[i][L - 1]);}}}if (size < oldsize) {shrinkfail = FALSE;oldsize = size;} else {if (trace)Rprintf("Polytope size measure not decreased in shrink\n");shrinkfail = TRUE;}}}}}} while (!(VH <= VL + convtol || VL <= abstol ||shrinkfail || funcount > maxit));}if (trace) {Rprintf("Exiting from Nelder Mead minimizer\n");Rprintf(" %d function evaluations used\n", funcount);}*Fmin = P[n1 - 1][L - 1];for (i = 0; i < n; i++) X[i] = P[i][L - 1];if (shrinkfail) *fail = 10;if (funcount > maxit) *fail = 1;*fncount = funcount;}staticvoid cgmin(int n, double *Bvec, double *X, double *Fmin, int *fail,double abstol, double intol, OptStruct OS, int type, int trace,int *fncount, int *grcount, int maxit){Rboolean accpoint;double *c, *g, *t;int count, cycle, cyclimit;double f;double G1, G2, G3, gradproj;int funcount=0, gradcount=0, i;double newstep, oldstep, setstep, steplength=1.0;double tol;if (trace) {Rprintf(" Conjugate gradients function minimiser\n");switch (type) {case 1: Rprintf("Method: Fletcher Reeves\n"); break;case 2: Rprintf("Method: Polak Ribiere\n"); break;case 3: Rprintf("Method: Beale Sorenson\n"); break;default:error("unknown type in CG method of optim");}}c = vect(n); g = vect(n); t = vect(n);setstep = 1.7;*fail = 0;cyclimit = n;tol = intol * n * sqrt(intol);if (trace) Rprintf("tolerance used in gradient test=%g\n", tol);f = fminfn(n, Bvec, OS);if (!R_FINITE(f)) {error("Function cannot be evaluated at initial parameters");} else {*Fmin = f;funcount = 1;gradcount = 0;do {for (i = 0; i < n; i++) {t[i] = 0.0;c[i] = 0.0;}cycle = 0;oldstep = 1.0;count = 0;do {cycle++;if (trace) {Rprintf("%d %d %f\n", gradcount, funcount, *Fmin);Rprintf("parameters ");for (i = 1; i <= n; i++) {Rprintf("%10.5f ", Bvec[i - 1]);if (i / 7 * 7 == i && i < n)Rprintf("\n");}Rprintf("\n");}gradcount++;if (gradcount > maxit) {*fncount = funcount;*grcount = gradcount;*fail = 1;return;}fmingr(n, Bvec, g, OS);G1 = 0.0;G2 = 0.0;for (i = 0; i < n; i++) {X[i] = Bvec[i];switch (type) {case 1: /* Fletcher-Reeves */G1 += g[i] * g[i];G2 += c[i] * c[i];break;case 2: /* Polak-Ribiere */G1 += g[i] * (g[i] - c[i]);G2 += c[i] * c[i];break;case 3: /* Beale-Sorenson */G1 += g[i] * (g[i] - c[i]);G2 += t[i] * (g[i] - c[i]);break;default:error("unknown type in CG method of optim");}c[i] = g[i];}if (G1 > tol) {if (G2 > 0.0)G3 = G1 / G2;elseG3 = 1.0;gradproj = 0.0;for (i = 0; i < n; i++) {t[i] = t[i] * G3 - g[i];gradproj += t[i] * g[i];}steplength = oldstep;accpoint = FALSE;do {count = 0;for (i = 0; i < n; i++) {Bvec[i] = X[i] + steplength * t[i];if (reltest + X[i] == reltest + Bvec[i])count++;}if (count < n) {f = fminfn(n, Bvec, OS);funcount++;accpoint = (R_FINITE(f) &&f <= *Fmin + gradproj * steplength * acctol);if (!accpoint) {steplength *= stepredn;if (trace) Rprintf("*");}}} while (!(count == n || accpoint));if (count < n) {newstep = 2 * (f - *Fmin - gradproj * steplength);if (newstep > 0) {newstep = -(gradproj * steplength * steplength / newstep);for (i = 0; i < n; i++)Bvec[i] = X[i] + newstep * t[i];*Fmin = f;f = fminfn(n, Bvec, OS);funcount++;if (f < *Fmin) {*Fmin = f;if (trace) Rprintf(" i< ");} else {if (trace) Rprintf(" i> ");for (i = 0; i < n; i++)Bvec[i] = X[i] + steplength * t[i];}}}}oldstep = setstep * steplength;if (oldstep > 1.0)oldstep = 1.0;} while ((count != n) && (G1 > tol) && (cycle != cyclimit));} while ((cycle != 1) ||((count != n) && (G1 > tol) && *Fmin > abstol));}if (trace) {Rprintf("Exiting from conjugate gradients minimizer\n");Rprintf(" %d function evaluations used\n", funcount);Rprintf(" %d gradient evaluations used\n", gradcount);}*fncount = funcount;*grcount = gradcount;}staticvoid lbfgsb(int n, int m, double *x, double *l, double *u, int *nbd,double *Fmin, int *fail, OptStruct OS,double factr, double pgtol,int *fncount, int *grcount, int maxit, char *msg,int trace, int nREPORT){char task[60];double f, *g, dsave[29], *wa;int tr = -1, iter = 0, *iwa, isave[44], lsave[4];if (nREPORT <= 0)error("REPORT must be > 0 (method = \"L-BFGS-B\")");switch(trace) {case 2: tr = 0; break;case 3: tr = nREPORT; break;case 4: tr = 99; break;case 5: tr = 100; break;case 6: tr = 101; break;default: tr = -1; break;}*fail = 0;g = vect(n);wa = vect(2*m*n+4*n+11*m*m+8*m);iwa = (int *) R_alloc(3*n, sizeof(int));strcpy(task, "START");while(1) {/* Main workhorse setulb() from ../appl/lbfgsb.c : */setulb(n, m, x, l, u, nbd, &f, g, factr, &pgtol, wa, iwa, task,tr, lsave, isave, dsave);/* Rprintf("in lbfgsb - %s\n", task);*/if (strncmp(task, "FG", 2) == 0) {f = fminfn(n, x, OS);if (!R_FINITE(f))error("L-BFGS-B needs finite values of fn");fmingr(n, x, g, OS);} else if (strncmp(task, "NEW_X", 5) == 0) {if(trace == 1 && (iter % nREPORT == 0)) {Rprintf("iter %4d value %f\n", iter, f);}if (++iter > maxit) {*fail = 1;break;}} else if (strncmp(task, "WARN", 4) == 0) {*fail = 51;break;} else if (strncmp(task, "CONV", 4) == 0) {break;} else if (strncmp(task, "ERROR", 5) == 0) {*fail = 52;break;} else { /* some other condition that is not supposed to happen */*fail = 52;break;}}*Fmin = f;*fncount = *grcount = isave[33];if (trace) {Rprintf("final value %f \n", *Fmin);if (iter < maxit && *fail == 0) Rprintf("converged\n");else Rprintf("stopped after %i iterations\n", iter);}strcpy(msg, task);}#define E1 1.7182818 /* exp(1.0)-1.0 */#define STEPS 100static void samin(int n, double *pb, double *yb, int maxit, int tmax,double ti, int trace, OptStruct OS)/* Given a starting point pb[0..n-1], simulated annealing minimizationis performed on the function fminfn. The starting temperatureis input as ti. To make sann work silently set trace to zero.sann makes in total maxit function evaluations, tmaxevaluations at each temperature. Returned quantities are pb(the location of the minimum), and yb (the minimum value ofthe function func). Author: Adrian Trapletti*/{long i, j;int k, its, itdoc;double t, y, dy, ytry, scale;double *p, *dp, *ptry;p = vect (n); dp = vect (n); ptry = vect (n);GetRNGstate();*yb = fminfn (n, pb, OS); /* init best system state pb, *yb */if (!R_FINITE(*yb)) *yb = big;for (j = 0; j < n; j++) p[j] = pb[j];y = *yb; /* init system state p, y */if (trace){Rprintf ("sann objective function values\n");Rprintf ("initial value %f\n", *yb);}scale = 1.0/ti;its = itdoc = 1;while (its < maxit) { /* cool down system */t = ti/log((double)its + E1); /* temperature annealing schedule */k = 1;while ((k <= tmax) && (its < maxit)) /* iterate at constant temperature */{for (i = 0; i < n; i++)dp[i] = scale * t * norm_rand(); /* random perturbation */for (i = 0; i < n; i++)ptry[i] = p[i] + dp[i]; /* new candidate point */ytry = fminfn (n, ptry, OS);if (!R_FINITE(ytry)) ytry = big;dy = ytry - y;if ((dy <= 0.0) || (unif_rand() < exp(-dy/t))) { /* accept new point? */for (j = 0; j < n; j++) p[j] = ptry[j];y = ytry; /* update system state p, y */if (y <= *yb) /* if system state is best, then update best system state pb, *yb */{for (j = 0; j < n; j++) pb[j] = p[j];*yb = y;}}its++; k++;}if ((trace) && ((itdoc % STEPS) == 0))Rprintf("iter %8d value %f\n", its - 1, *yb);itdoc++;}if (trace){Rprintf ("final value %f\n", *yb);Rprintf ("sann stopped after %d iterations\n", its - 1);}PutRNGstate();}#undef E1#undef STEPS