[2] | 1 | /* GLoBES -- General LOng Baseline Experiment Simulator |
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| 2 | * (C) 2002 - 2004, The GLoBES Team |
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| 3 | * |
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| 4 | * GLoBES is mainly intended for academic purposes. Proper |
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| 5 | * credit must be given if you use GLoBES or parts of it. Please |
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| 6 | * read the section 'Credit' in the README file. |
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| 7 | * |
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| 8 | * This program is free software; you can redistribute it and/or modify |
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| 9 | * it under the terms of the GNU General Public License as published by |
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| 10 | * the Free Software Foundation; either version 2 of the License, or |
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| 11 | * (at your option) any later version. |
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| 12 | * |
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| 13 | * This program is distributed in the hope that it will be useful, |
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| 14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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| 16 | * GNU General Public License for more details. |
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| 17 | * |
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| 18 | * You should have received a copy of the GNU General Public License |
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| 19 | * along with this program; if not, write to the Free Software |
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| 20 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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| 21 | */ |
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| 22 | |
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| 23 | |
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| 24 | |
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| 25 | #include <math.h> |
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| 26 | #include <stdio.h> |
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| 27 | |
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| 28 | /* new */ |
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| 29 | /*#include <stdlib.h> |
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| 30 | #include <math.h> |
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| 31 | #include <string.h> */ |
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| 32 | |
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| 33 | #include "glb_error.h" |
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| 34 | #include "glb_min_sup.h" |
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| 35 | |
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| 36 | static void glb_minimizer_error(char error_text[]) |
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| 37 | { |
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| 38 | glb_fatal(error_text); |
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| 39 | } |
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| 40 | |
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| 41 | double *glb_alloc_vec(int nl,int nh) |
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| 42 | { |
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| 43 | double *v; |
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| 44 | v=(double *)glb_malloc((unsigned) (nh-nl+1)*sizeof(double)); |
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| 45 | return v-nl; |
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| 46 | } |
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| 47 | |
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| 48 | double **glb_alloc_mat(int nrl,int nrh, int ncl,int nch) |
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| 49 | { |
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| 50 | int i; |
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| 51 | double **m; |
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| 52 | |
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| 53 | m=(double **) glb_malloc((unsigned) (nrh-nrl+1)*sizeof(double*)); |
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| 54 | m -= nrl; |
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| 55 | for(i=nrl;i<=nrh;i++) |
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| 56 | { |
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| 57 | m[i]=(double *) glb_malloc((unsigned) |
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| 58 | (nch-ncl+1)*sizeof(double)); |
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| 59 | m[i] -= ncl; |
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| 60 | } |
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| 61 | return m; |
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| 62 | } |
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| 63 | |
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| 64 | void glb_free_vec(double *v,int nl,int nh) |
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| 65 | { |
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| 66 | glb_free((char*) (v+nl)); |
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| 67 | } |
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| 68 | |
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| 69 | void glb_free_mat(double **m,int nrl,int nrh,int ncl,int nch) |
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| 70 | { |
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| 71 | int i; |
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| 72 | for(i=nrh;i>=nrl;i--) glb_free((char*) (m[i]+ncl)); |
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| 73 | glb_free((char*) (m+nrl)); |
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| 74 | } |
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| 75 | |
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| 76 | |
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| 77 | |
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| 78 | |
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| 79 | #define TOL 2.0e-4 |
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| 80 | |
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| 81 | |
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| 82 | typedef struct { |
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| 83 | int ncom; |
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| 84 | double *pcom; |
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| 85 | double *xicom; |
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| 86 | double (*nrfunc)(double*); |
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| 87 | } glb_min_data; |
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| 88 | |
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| 89 | |
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| 90 | static double one_dim_projection(double x,glb_min_data *in) |
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| 91 | { |
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| 92 | int j; |
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| 93 | double f,*xt; |
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| 94 | |
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| 95 | xt=glb_alloc_vec(1,in->ncom); |
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| 96 | for (j=1;j<=in->ncom;j++) xt[j]=in->pcom[j]+x*in->xicom[j]; |
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| 97 | f=in->nrfunc(xt); |
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| 98 | glb_free_vec(xt,1,in->ncom); |
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| 99 | return f; |
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| 100 | } |
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| 101 | |
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| 102 | |
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| 103 | |
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| 104 | #define ITMAX 100 |
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| 105 | #define CGOLD 0.3819660 |
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| 106 | #define ZEPS 1.0e-10 |
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| 107 | #define SIGN(a,b) ((b) > 0.0 ? fabs(a) : -fabs(a)) |
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| 108 | #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); |
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| 109 | |
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| 110 | static double glb_brent_min(double ax,double bx,double cx, |
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| 111 | double (*f)(double,glb_min_data*), |
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| 112 | double tol,double *xmin,glb_min_data *in) |
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| 113 | { |
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| 114 | int iter; |
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| 115 | double a,b,d,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm; |
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| 116 | double e=0.0; |
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| 117 | |
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| 118 | a=((ax < cx) ? ax : cx); |
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| 119 | b=((ax > cx) ? ax : cx); |
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| 120 | x=w=v=bx; |
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| 121 | fw=fv=fx=(*f)(x,in); |
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| 122 | for (iter=1;iter<=ITMAX;iter++) { |
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| 123 | xm=0.5*(a+b); |
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| 124 | tol2=2.0*(tol1=tol*fabs(x)+ZEPS); |
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| 125 | if (fabs(x-xm) <= (tol2-0.5*(b-a))) { |
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| 126 | *xmin=x; |
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| 127 | return fx; |
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| 128 | } |
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| 129 | if (fabs(e) > tol1) { |
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| 130 | r=(x-w)*(fx-fv); |
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| 131 | q=(x-v)*(fx-fw); |
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| 132 | p=(x-v)*q-(x-w)*r; |
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| 133 | q=2.0*(q-r); |
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| 134 | if (q > 0.0) p = -p; |
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| 135 | q=fabs(q); |
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| 136 | etemp=e; |
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| 137 | e=d; |
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| 138 | if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) |
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| 139 | d=CGOLD*(e=(x >= xm ? a-x : b-x)); |
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| 140 | else { |
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| 141 | d=p/q; |
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| 142 | u=x+d; |
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| 143 | if (u-a < tol2 || b-u < tol2) |
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| 144 | d=SIGN(tol1,xm-x); |
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| 145 | } |
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| 146 | } else { |
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| 147 | d=CGOLD*(e=(x >= xm ? a-x : b-x)); |
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| 148 | } |
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| 149 | u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); |
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| 150 | fu=(*f)(u,in); |
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| 151 | if (fu <= fx) { |
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| 152 | if (u >= x) a=x; else b=x; |
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| 153 | SHFT(v,w,x,u) |
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| 154 | SHFT(fv,fw,fx,fu) |
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| 155 | } else { |
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| 156 | if (u < x) a=u; else b=u; |
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| 157 | if (fu <= fw || w == x) { |
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| 158 | v=w; |
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| 159 | w=u; |
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| 160 | fv=fw; |
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| 161 | fw=fu; |
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| 162 | } else if (fu <= fv || v == x || v == w) { |
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| 163 | v=u; |
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| 164 | fv=fu; |
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| 165 | } |
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| 166 | } |
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| 167 | } |
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| 168 | glb_minimizer_error("glb_brent_min"); |
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| 169 | *xmin=x; |
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| 170 | return fx; |
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| 171 | } |
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| 172 | |
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| 173 | #undef ITMAX |
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| 174 | #undef CGOLD |
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| 175 | #undef ZEPS |
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| 176 | #undef SIGN |
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| 177 | |
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| 178 | |
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| 179 | |
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| 180 | |
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| 181 | #define GOLD 1.618034 |
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| 182 | #define GLIMIT 100.0 |
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| 183 | #define TINY 1.0e-20 |
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| 184 | #define MAX(a,b) ((a) > (b) ? (a) : (b)) |
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| 185 | #define SIGN(a,b) ((b) > 0.0 ? fabs(a) : -fabs(a)) |
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| 186 | #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); |
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| 187 | |
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| 188 | static void bracket(double *ax,double *bx,double *cx,double *fa,double *fb, |
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| 189 | double *fc, double (*func)(double,glb_min_data*),glb_min_data *in) |
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| 190 | { |
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| 191 | double ulim,u,r,q,fu,dum; |
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| 192 | |
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| 193 | *fa=(*func)(*ax,in); |
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| 194 | *fb=(*func)(*bx,in); |
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| 195 | if (*fb > *fa) { |
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| 196 | SHFT(dum,*ax,*bx,dum) |
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| 197 | SHFT(dum,*fb,*fa,dum) |
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| 198 | } |
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| 199 | *cx=(*bx)+GOLD*(*bx-*ax); |
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| 200 | *fc=(*func)(*cx,in); |
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| 201 | while (*fb > *fc) { |
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| 202 | r=(*bx-*ax)*(*fb-*fc); |
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| 203 | q=(*bx-*cx)*(*fb-*fa); |
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| 204 | u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ |
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| 205 | (2.0*SIGN(MAX(fabs(q-r),TINY),q-r)); |
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| 206 | ulim=(*bx)+GLIMIT*(*cx-*bx); |
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| 207 | if ((*bx-u)*(u-*cx) > 0.0) { |
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| 208 | fu=(*func)(u,in); |
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| 209 | if (fu < *fc) { |
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| 210 | *ax=(*bx); |
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| 211 | *bx=u; |
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| 212 | *fa=(*fb); |
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| 213 | *fb=fu; |
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| 214 | return; |
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| 215 | } else if (fu > *fb) { |
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| 216 | *cx=u; |
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| 217 | *fc=fu; |
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| 218 | return; |
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| 219 | } |
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| 220 | u=(*cx)+GOLD*(*cx-*bx); |
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| 221 | fu=(*func)(u,in); |
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| 222 | } else if ((*cx-u)*(u-ulim) > 0.0) { |
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| 223 | fu=(*func)(u,in); |
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| 224 | if (fu < *fc) { |
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| 225 | SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) |
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| 226 | SHFT(*fb,*fc,fu,(*func)(u,in)) |
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| 227 | } |
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| 228 | } else if ((u-ulim)*(ulim-*cx) >= 0.0) { |
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| 229 | u=ulim; |
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| 230 | fu=(*func)(u,in); |
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| 231 | } else { |
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| 232 | u=(*cx)+GOLD*(*cx-*bx); |
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| 233 | fu=(*func)(u,in); |
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| 234 | } |
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| 235 | SHFT(*ax,*bx,*cx,u) |
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| 236 | SHFT(*fa,*fb,*fc,fu) |
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| 237 | } |
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| 238 | } |
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| 239 | |
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| 240 | |
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| 241 | |
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| 242 | #undef GOLD |
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| 243 | #undef GLIMIT |
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| 244 | #undef TINY |
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| 245 | #undef MAX |
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| 246 | #undef SIGN |
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| 247 | #undef SHFT |
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| 248 | |
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| 249 | |
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| 250 | static void line_minimization(double p[],double xi[],int n,double *fret, |
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| 251 | double (*func)(double*), |
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| 252 | glb_min_data *in) |
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| 253 | { |
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| 254 | int j; |
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| 255 | double xx,xmin,fx,fb,fa,bx,ax; |
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| 256 | int ncom=0; |
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| 257 | double *pcom=0,*xicom=0,(*nrfunc)(double*); |
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| 258 | |
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| 259 | ncom=n; |
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| 260 | pcom=glb_alloc_vec(1,n); |
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| 261 | xicom=glb_alloc_vec(1,n); |
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| 262 | nrfunc=func; |
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| 263 | for (j=1;j<=n;j++) { |
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| 264 | pcom[j]=p[j]; |
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| 265 | xicom[j]=xi[j]; |
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| 266 | } |
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| 267 | |
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| 268 | in->ncom=n; |
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| 269 | in->pcom=pcom; |
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| 270 | in->xicom=xicom; |
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| 271 | in->nrfunc=func; |
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| 272 | ax=0.0; |
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| 273 | xx=1.0; |
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| 274 | bx=2.0; |
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| 275 | bracket(&ax,&xx,&bx,&fa,&fx,&fb,one_dim_projection,in); |
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| 276 | *fret=glb_brent_min(ax,xx,bx,one_dim_projection,TOL,&xmin,in); |
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| 277 | for (j=1;j<=n;j++) { |
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| 278 | xi[j] *= xmin; |
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| 279 | p[j] += xi[j]; |
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| 280 | } |
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| 281 | glb_free_vec(xicom,1,n); |
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| 282 | glb_free_vec(pcom,1,n); |
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| 283 | } |
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| 284 | |
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| 285 | |
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| 286 | |
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| 287 | |
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| 288 | |
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| 289 | |
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| 290 | |
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| 291 | #define ITMAX 10000 /* was 500 */ |
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| 292 | static double sqrarg; |
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| 293 | #define SQR(a) (sqrarg=(a),sqrarg*sqrarg) |
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| 294 | |
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| 295 | void glb_powell(double p[],double **xi,int n, |
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| 296 | double ftol,int *iter,double *fret, |
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| 297 | double (*func)(double*)) |
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| 298 | { |
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| 299 | int i,ibig,j; |
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| 300 | double t,fptt,fp,del; |
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| 301 | double *pt,*ptt,*xit; |
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| 302 | glb_min_data in; |
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| 303 | pt=glb_alloc_vec(1,n); |
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| 304 | ptt=glb_alloc_vec(1,n); |
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| 305 | xit=glb_alloc_vec(1,n); |
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| 306 | *fret=(*func)(p); |
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| 307 | for (j=1;j<=n;j++) pt[j]=p[j]; |
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| 308 | for (*iter=1;;(*iter)++) { |
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| 309 | fp=(*fret); |
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| 310 | ibig=0; |
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| 311 | del=0.0; |
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| 312 | for (i=1;i<=n;i++) { |
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| 313 | for (j=1;j<=n;j++) xit[j]=xi[j][i]; |
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| 314 | fptt=(*fret); |
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| 315 | line_minimization(p,xit,n,fret,func,&in); |
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| 316 | if (fabs(fptt-(*fret)) > del) { |
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| 317 | del=fabs(fptt-(*fret)); |
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| 318 | ibig=i; |
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| 319 | } |
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| 320 | } |
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| 321 | if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) { |
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| 322 | glb_free_vec(xit,1,n); |
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| 323 | glb_free_vec(ptt,1,n); |
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| 324 | glb_free_vec(pt,1,n); |
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| 325 | return; |
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| 326 | } |
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| 327 | if (*iter == ITMAX) |
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| 328 | { /* modified by WW */ |
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| 329 | /* glb_minimizer_error("empty (1)"); */ |
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| 330 | glb_free_vec(xit,1,n); |
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| 331 | glb_free_vec(ptt,1,n); |
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| 332 | glb_free_vec(pt,1,n); |
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| 333 | (*fret) = 999999.0; |
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| 334 | printf("At Point: "); |
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| 335 | for (j=1;j<=n;j++) printf("%g ",p[j]); |
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| 336 | printf("\n"); |
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| 337 | glb_error("Minimizer error: no convergence (1)"); |
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| 338 | return; |
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| 339 | } |
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| 340 | for (j=1;j<=n;j++) { |
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| 341 | ptt[j]=2.0*p[j]-pt[j]; |
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| 342 | xit[j]=p[j]-pt[j]; |
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| 343 | pt[j]=p[j]; |
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| 344 | } |
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| 345 | fptt=(*func)(ptt); |
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| 346 | if (fptt < fp) { |
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| 347 | t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); |
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| 348 | if (t < 0.0) { |
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| 349 | line_minimization(p,xit,n,fret,func,&in); |
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| 350 | for (j=1;j<=n;j++) xi[j][ibig]=xit[j]; |
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| 351 | } |
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| 352 | } |
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| 353 | } |
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| 354 | } |
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| 355 | |
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| 356 | |
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| 357 | void glb_powell2(double p[],double **xi,int n,double ftol, |
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| 358 | int *iter,double *fret, |
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| 359 | double (*func)(double*)) |
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| 360 | { |
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| 361 | int i,ibig,j; |
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| 362 | double t,fptt,fp,del; |
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| 363 | double *pt,*ptt,*xit; |
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| 364 | glb_min_data in; |
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| 365 | pt=glb_alloc_vec(1,n); |
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| 366 | ptt=glb_alloc_vec(1,n); |
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| 367 | xit=glb_alloc_vec(1,n); |
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| 368 | *fret=(*func)(p); |
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| 369 | for (j=1;j<=n;j++) pt[j]=p[j]; |
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| 370 | for (*iter=1;;(*iter)++) { |
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| 371 | fp=(*fret); |
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| 372 | ibig=0; |
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| 373 | del=0.0; |
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| 374 | for (i=1;i<=n;i++) { |
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| 375 | for (j=1;j<=n;j++) xit[j]=xi[j][i]; |
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| 376 | fptt=(*fret); |
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| 377 | line_minimization(p,xit,n,fret,func,&in); |
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| 378 | if (fabs(fptt-(*fret)) > del) { |
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| 379 | del=fabs(fptt-(*fret)); |
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| 380 | ibig=i; |
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| 381 | } |
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| 382 | } |
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| 383 | if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) { |
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| 384 | glb_free_vec(xit,1,n); |
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| 385 | glb_free_vec(ptt,1,n); |
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| 386 | glb_free_vec(pt,1,n); |
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| 387 | return; |
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| 388 | } |
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| 389 | if (*iter == ITMAX) |
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| 390 | { /* modified by WW */ |
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| 391 | /* glb_minimizer_error("empty (2)"); */ |
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| 392 | glb_free_vec(xit,1,n); |
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| 393 | glb_free_vec(ptt,1,n); |
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| 394 | glb_free_vec(pt,1,n); |
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| 395 | (*fret) = 999999.0; |
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| 396 | printf("At Point: "); |
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| 397 | for (j=1;j<=n;j++) printf("%g ",p[j]); |
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| 398 | printf("\n"); |
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| 399 | glb_error("Minimizer error: no convergence (2)"); |
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| 400 | return; |
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| 401 | } |
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| 402 | |
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| 403 | for (j=1;j<=n;j++) { |
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| 404 | ptt[j]=2.0*p[j]-pt[j]; |
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| 405 | xit[j]=p[j]-pt[j]; |
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| 406 | pt[j]=p[j]; |
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| 407 | } |
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| 408 | fptt=(*func)(ptt); |
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| 409 | if (fptt < fp) { |
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| 410 | t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); |
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| 411 | if (t < 0.0) { |
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| 412 | line_minimization(p,xit,n,fret,func,&in); |
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| 413 | for (j=1;j<=n;j++) xi[j][ibig]=xit[j]; |
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| 414 | } |
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| 415 | } |
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| 416 | } |
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| 417 | } |
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| 418 | |
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| 419 | |
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| 420 | |
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| 421 | #undef ITMAX |
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| 422 | #undef SQR |
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| 423 | #undef TOL |
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