| 1 |
#include <stdio.h> |
| 2 |
#include <stdlib.h> |
| 3 |
#include <math.h> |
| 4 |
// #include "rdutil.h" |
| 5 |
|
| 6 |
int read_fit_v(FILE *fpt, int *npts, int **n, double **l, double **f, |
| 7 |
double **ef, double **ux, double **eux, double **uy, double **euy) { |
| 8 |
/* |
| 9 |
Function - read_fit |
| 10 |
Takes an open file pointer, and reads n, l, frequencies, and velocities |
| 11 |
*/ |
| 12 |
int i, nlines; |
| 13 |
char buffer[8192]; |
| 14 |
if( ferror(fpt) ) { |
| 15 |
//perror(fpt); |
| 16 |
return -1; |
| 17 |
} |
| 18 |
if( feof(fpt)) rewind(fpt); |
| 19 |
|
| 20 |
nlines = 0; |
| 21 |
while(!feof(fpt)) { |
| 22 |
fgets(buffer, 8192, fpt); |
| 23 |
if(buffer[0] != '#' && !feof(fpt)) nlines++; |
| 24 |
} |
| 25 |
if(nlines == 0) return 1; |
| 26 |
nlines++; |
| 27 |
*n = (int*) malloc(nlines*sizeof(int)); |
| 28 |
*l = (double *)calloc(nlines, sizeof(double)); |
| 29 |
*f = (double*) malloc(nlines*sizeof(double)); |
| 30 |
*ef = (double*) malloc(nlines*sizeof(double)); |
| 31 |
*ux = (double*) malloc(nlines*sizeof(double)); |
| 32 |
*eux = (double*) malloc(nlines*sizeof(double)); |
| 33 |
*uy = (double*) malloc(nlines*sizeof(double)); |
| 34 |
*euy = (double*) malloc(nlines*sizeof(double)); |
| 35 |
nlines--; |
| 36 |
rewind(fpt); |
| 37 |
|
| 38 |
for(i=0; i<nlines; i++) { |
| 39 |
fgets(buffer, 8192, fpt); |
| 40 |
while(buffer[0] == '#') fgets(buffer, 8192, fpt); |
| 41 |
sscanf(buffer, "%i %lf %*f %lf %lf %lf %lf %lf %lf", &(*n)[i], &(*l)[i], &(*f)[i], |
| 42 |
&(*ef)[i], &(*ux)[i], &(*eux)[i], &(*uy)[i], &(*euy)[i]); |
| 43 |
} |
| 44 |
*npts = nlines; |
| 45 |
//fprintf (stderr, "read_fit_v(): returning npts = %d\n", nlines); |
| 46 |
|
| 47 |
return 0; |
| 48 |
} |
| 49 |
|
| 50 |
int nearst(double xb, double x[], int ntab) { |
| 51 |
int low, igh, mid; |
| 52 |
|
| 53 |
low=0; igh=ntab-1; |
| 54 |
if((xb < x[low]) != (xb < x[igh]) ) { |
| 55 |
|
| 56 |
/* If the point is within the range of table, then locate it by bisection */ |
| 57 |
|
| 58 |
while(igh-low > 1) { |
| 59 |
mid=(low+igh)/2; |
| 60 |
if((xb < x[mid]) == (xb < x[low])) low=mid; |
| 61 |
else igh=mid; |
| 62 |
} |
| 63 |
} |
| 64 |
|
| 65 |
if(fabs(xb-x[low]) < fabs(xb-x[igh])) return low; |
| 66 |
else return igh; |
| 67 |
} |
| 68 |
|
| 69 |
int read_fit(FILE *fpt, int *npts, int **n, double **l, double **f, double **ef) { |
| 70 |
/* |
| 71 |
Function - read_fit |
| 72 |
Takes an open file pointer, and reads n, l, frequencies, and velocities |
| 73 |
*/ |
| 74 |
int i, nlines; |
| 75 |
char buffer[8192]; |
| 76 |
if( ferror(fpt) ) { |
| 77 |
//perror(fpt); |
| 78 |
return -1; |
| 79 |
} |
| 80 |
if( feof(fpt)) rewind(fpt); |
| 81 |
|
| 82 |
nlines = 0; |
| 83 |
while(!feof(fpt)) { |
| 84 |
fgets(buffer, 8192, fpt); |
| 85 |
if(buffer[0] != '#' && !feof(fpt)) nlines++; |
| 86 |
} |
| 87 |
if(nlines == 0) return 1; |
| 88 |
|
| 89 |
*n = (int*) malloc(nlines*sizeof(int)); |
| 90 |
*l = (double*) malloc(nlines*sizeof(double)); |
| 91 |
*f = (double*) malloc(nlines*sizeof(double)); |
| 92 |
*ef = (double*) malloc(nlines*sizeof(double)); |
| 93 |
|
| 94 |
rewind(fpt); |
| 95 |
|
| 96 |
for(i=0; i<nlines; i++) { |
| 97 |
fgets(buffer, 8192, fpt); |
| 98 |
while(buffer[0] == '#') fgets(buffer, 8192, fpt); |
| 99 |
sscanf(buffer, "%i %lf %*f %lf %lf", &(*n)[i], &(*l)[i], &(*f)[i], |
| 100 |
&(*ef)[i]); |
| 101 |
} |
| 102 |
*npts = nlines; |
| 103 |
|
| 104 |
return 0; |
| 105 |
} |
| 106 |
|
| 107 |
int divdif(double xb, double x[], double f[], int *nuse, int ntab, |
| 108 |
double fb[], double aeps, double *dfb, double *ddfb) { |
| 109 |
int i,j,k,next,in,ip,nit,ier, nmax=10; |
| 110 |
double err,px,dpx,ddpx,xn[11],xd[11]; |
| 111 |
|
| 112 |
/* Find the nearest point */ |
| 113 |
|
| 114 |
next=nearst(xb,x,ntab); |
| 115 |
fb[1]=f[next]; |
| 116 |
xd[1]=f[next]; |
| 117 |
xn[1]=x[next]; |
| 118 |
ier=0; |
| 119 |
px=1.0; |
| 120 |
|
| 121 |
/* Initialisation for the derivatives */ |
| 122 |
|
| 123 |
*dfb=0.0; *ddfb=0.0; |
| 124 |
dpx=0.0; ddpx=0.0; |
| 125 |
|
| 126 |
/* Points between IN and IP are used for interpolation */ |
| 127 |
|
| 128 |
ip=next; in=next; |
| 129 |
|
| 130 |
/* Maximum number of points to be used for interpolation */ |
| 131 |
nit=*nuse; if(nmax<nit) nit=nmax; if(ntab<nit) nit=ntab; |
| 132 |
if(*nuse>nmax || *nuse>ntab) ier=22; |
| 133 |
if(*nuse<1) { |
| 134 |
ier=21; |
| 135 |
nit=6; if(nmax<nit) nit=nmax; if(ntab<nit) nit=ntab; |
| 136 |
} |
| 137 |
*nuse=1; |
| 138 |
|
| 139 |
/* Calculate successive interpolation polynomial */ |
| 140 |
for(j=2; j<=nit; ++j) { |
| 141 |
/* Choose the next nearest point to XB */ |
| 142 |
if(in<=0 ) { |
| 143 |
ip=ip+1; next=ip; |
| 144 |
} |
| 145 |
else if(ip >= ntab-1) { |
| 146 |
in=in-1; next=in; |
| 147 |
} |
| 148 |
else if(fabs(xb-x[ip+1]) < fabs(xb-x[in-1]) ) { |
| 149 |
ip=ip+1; next=ip; |
| 150 |
} |
| 151 |
else { |
| 152 |
in=in-1; next=in; |
| 153 |
} |
| 154 |
|
| 155 |
/* Calculating the divided differences */ |
| 156 |
xd[j]=f[next]; |
| 157 |
xn[j]=x[next]; |
| 158 |
for(k=j-1; k>=1; --k) xd[k]=(xd[k+1]-xd[k])/(xn[j]-xn[k]); |
| 159 |
|
| 160 |
/* Calculating the derivatives */ |
| 161 |
ddpx=ddpx*(xb-xn[j-1])+2.*dpx; |
| 162 |
dpx=dpx*(xb-xn[j-1])+px; |
| 163 |
*dfb = *dfb+dpx*xd[1]; |
| 164 |
*ddfb = *ddfb+ddpx*xd[1]; |
| 165 |
|
| 166 |
px=px*(xb-xn[j-1]); |
| 167 |
err=xd[1]*px; |
| 168 |
fb[j]=fb[j-1]+err; |
| 169 |
*nuse=j; |
| 170 |
|
| 171 |
if(fabs(err) < aeps) return ier; |
| 172 |
} |
| 173 |
return 23; |
| 174 |
} |
| 175 |
|
| 176 |
int interp_vel(int *n, double *l, double *f, double *ef, double *ux, |
| 177 |
double *eux, double *uy, double *euy, int npts) { |
| 178 |
/* |
| 179 |
Function - interp |
| 180 |
Takes power spectra fit parameters, and interpolates them to integer l. |
| 181 |
Data are returned in the input arrays - **data is overwritten!** |
| 182 |
*/ |
| 183 |
int i, j, nuse, ierr, offset=0; |
| 184 |
int n_num[13]; |
| 185 |
double fb[10], ll; |
| 186 |
double dfb, ddfb, aeps=1e-7; |
| 187 |
double *inp_l, *inp_f, *inp_ef, *inp_ux, *inp_uy, *inp_eux, *inp_euy; |
| 188 |
FILE * outBug; |
| 189 |
|
| 190 |
// count number of frequencies for each n |
| 191 |
// note that it is assumed that all frequencies for each |
| 192 |
// n are grouped together in the arrays |
| 193 |
for(i=0; i<13; i++) n_num[i]=0; |
| 194 |
for(i=0; i < npts; i++) { |
| 195 |
n_num[n[i]] ++; |
| 196 |
} |
| 197 |
|
| 198 |
inp_l=(double*) malloc(npts*sizeof(double)); |
| 199 |
inp_f=(double*) malloc(npts*sizeof(double)); |
| 200 |
inp_ef=(double*) malloc(npts*sizeof(double)); |
| 201 |
inp_ux=(double*) malloc(npts*sizeof(double)); |
| 202 |
inp_uy=(double*) malloc(npts*sizeof(double)); |
| 203 |
inp_eux=(double*) malloc(npts*sizeof(double)); |
| 204 |
inp_euy=(double*) malloc(npts*sizeof(double)); |
| 205 |
// loop over n |
| 206 |
// outBug=fopen("tesbug","w"); |
| 207 |
for(i=0; i < 10; i++) { |
| 208 |
for(j=0;j<npts;j++) { |
| 209 |
inp_l[j]=0.0; |
| 210 |
inp_f[j]=0.0; |
| 211 |
inp_ef[j]=0.0; |
| 212 |
inp_ux[j]=0.0; |
| 213 |
inp_uy[j]=0.0; |
| 214 |
inp_eux[j]=0.0; |
| 215 |
inp_euy[j]=0.0; |
| 216 |
} |
| 217 |
for(j=0;j<n_num[i];j++) { |
| 218 |
inp_l[j]=l[j+offset]; |
| 219 |
inp_f[j]=f[j+offset]; |
| 220 |
inp_ef[j]=ef[j+offset]; |
| 221 |
inp_ux[j]=ux[j+offset]; |
| 222 |
inp_uy[j]=uy[j+offset]; |
| 223 |
inp_eux[j]=eux[j+offset]; |
| 224 |
inp_euy[j]=euy[j+offset]; |
| 225 |
} |
| 226 |
for(j=0;j<n_num[i];j++) { |
| 227 |
ll=(int)(inp_l[j]+0.5); |
| 228 |
nuse=3; |
| 229 |
ierr=divdif(ll, inp_l, inp_f, &nuse, |
| 230 |
n_num[i], fb, aeps, &dfb, &ddfb); |
| 231 |
f[j+offset]=fb[nuse]; |
| 232 |
nuse=3; |
| 233 |
ierr=divdif(ll, inp_l, inp_ef, &nuse, |
| 234 |
n_num[i], fb, aeps, &dfb, &ddfb); |
| 235 |
ef[j+offset]=fb[nuse]; |
| 236 |
nuse=3; |
| 237 |
ierr=divdif(ll, inp_l, inp_ux, &nuse, |
| 238 |
n_num[i], fb, aeps, &dfb, &ddfb); |
| 239 |
ux[j+offset]=fb[nuse]; |
| 240 |
nuse=3; |
| 241 |
ierr=divdif(ll, inp_l, inp_uy, &nuse, |
| 242 |
n_num[i], fb, aeps, &dfb, &ddfb); |
| 243 |
uy[j+offset]=fb[nuse]; |
| 244 |
nuse=3; |
| 245 |
ierr=divdif(ll, inp_l, inp_eux, &nuse, |
| 246 |
n_num[i], fb, aeps, &dfb, &ddfb); |
| 247 |
eux[j+offset]=fb[nuse]; |
| 248 |
nuse=3; |
| 249 |
ierr=divdif(ll, inp_l, inp_euy, &nuse, |
| 250 |
n_num[i], fb, aeps, &dfb, &ddfb); |
| 251 |
euy[j+offset]=fb[nuse]; |
| 252 |
l[j+offset]=ll; |
| 253 |
} |
| 254 |
offset+=n_num[i]; |
| 255 |
} |
| 256 |
|
| 257 |
return 0; |
| 258 |
} |
| 259 |
|
| 260 |
int interp_freq(int *n, double *l, double *f, double *ef, int npts, |
| 261 |
int *ni, int *li, double *fi, double *efi, int *npts_out) { |
| 262 |
int i, j, nn, ll, nmin, nmax, this_npts, nuse; |
| 263 |
double *this_l, *this_f, *this_ef, all, fb[5]; |
| 264 |
double reps, dfb, ddfb, ff, error; |
| 265 |
|
| 266 |
this_l = (double*) malloc(npts*sizeof(double)); |
| 267 |
this_f = (double*) malloc(npts*sizeof(double)); |
| 268 |
this_ef = (double*) malloc(npts*sizeof(double)); |
| 269 |
|
| 270 |
*npts_out = 0; |
| 271 |
nmin = 100; |
| 272 |
nmax = 0; |
| 273 |
for(i=0; i<npts; i++) { |
| 274 |
if(n[i] < nmin) nmin = n[i]; |
| 275 |
if(n[i] > nmax) nmax = n[i]; |
| 276 |
} |
| 277 |
for(nn=nmin; nn<=nmax; nn++) { |
| 278 |
j = 0; |
| 279 |
for(i=0; i<npts; i++) { |
| 280 |
if(n[i]==nn) { |
| 281 |
this_l[j] = l[i]; |
| 282 |
this_f[j] = f[i]; |
| 283 |
this_ef[j] = ef[i]; |
| 284 |
j++; |
| 285 |
} |
| 286 |
} |
| 287 |
this_npts = j; |
| 288 |
j = *npts_out; |
| 289 |
//printf("%i %i\n",this_npts, *npts_out); |
| 290 |
for(i=0; i<this_npts; i++) { |
| 291 |
ll = (int) this_l[i] + 0.5; |
| 292 |
all = (double) ll; // cast back to double for function argument |
| 293 |
nuse = 3; |
| 294 |
reps = 1.0e-7; |
| 295 |
//printf("got here\n"); |
| 296 |
divdif(all, this_l, this_f, &nuse, this_npts, fb, reps, &dfb, &ddfb); |
| 297 |
ff = fb[nuse]; |
| 298 |
nuse = 3; |
| 299 |
divdif(all, this_l, this_ef, &nuse, this_npts, fb, reps, &dfb, &ddfb); |
| 300 |
error = fb[nuse]; |
| 301 |
//printf("%i %i %f %f\n",nn,ll,ff,error); |
| 302 |
if(error>0) { |
| 303 |
ni[j] = nn; |
| 304 |
li[j] = ll; |
| 305 |
fi[j] = ff; |
| 306 |
efi[j] = error; |
| 307 |
j++; |
| 308 |
} |
| 309 |
} |
| 310 |
//printf("%i\n",j); |
| 311 |
*npts_out = j; |
| 312 |
} |
| 313 |
|
| 314 |
return 0; |
| 315 |
} |
| 316 |
|
| 317 |
int freqdif(int *n1, int *n2, int *l1, double *l2, double *f1, double *f2, |
| 318 |
double *ef1, double *ef2, int npts1, int npts2, int *n, int *l, double *f, |
| 319 |
double *df, double *edf, int *npts) { |
| 320 |
int i, j, nn, ll, *index, nmin, nmax, lmin, lmax, this_npts, ind; |
| 321 |
int nuse; |
| 322 |
double *this_l, *this_f, *this_ef, all, fb[5], dfb, ddfb, reps; |
| 323 |
double ff, error; |
| 324 |
|
| 325 |
*npts = 0; |
| 326 |
|
| 327 |
this_l = (double*) malloc(npts2*sizeof(double)); |
| 328 |
this_f = (double*) malloc(npts2*sizeof(double)); |
| 329 |
this_ef = (double*) malloc(npts2*sizeof(double)); |
| 330 |
|
| 331 |
nmin = n1[0]; |
| 332 |
nmax = n1[0]; |
| 333 |
// lmin = (int) l2[0]+0.5; |
| 334 |
// lmax = (int) l2[0]+0.5; |
| 335 |
for(i=1; i<npts1; i++) { |
| 336 |
if(n1[i] < nmin) nmin = n1[i]; |
| 337 |
if(n1[i] > nmax) nmax = n1[i]; |
| 338 |
// if(l2[i] < lmin) lmin = (int) l2[i]+0.5; |
| 339 |
// if(l2[i] > lmax) lmax = (int) l2[i]+0.5; |
| 340 |
} |
| 341 |
|
| 342 |
// index = (int*) malloc((nmax-nmin)*(lmax-lmin)*sizeof(int)); |
| 343 |
// for(i=0; i<(nmax-nmin)*(lmax-lmin); i++) index[i] = -1; |
| 344 |
// for(i=0; i<npts2; i++) { |
| 345 |
// ll = (int) l2[i]+0.5; |
| 346 |
// index[n2[i]*(lmax-lmin)+ll-lmin] = i; |
| 347 |
// } |
| 348 |
|
| 349 |
for(nn=nmin; nn<=nmax; nn++) { |
| 350 |
j = 0; |
| 351 |
lmin = 10000; |
| 352 |
lmax = 0; |
| 353 |
for(i=0; i<npts2; i++) { |
| 354 |
if(n2[i] == nn) { |
| 355 |
this_l[j] = l2[i]; |
| 356 |
this_f[j] = f2[i]; |
| 357 |
this_ef[j] = ef2[i]; |
| 358 |
if(lmin > l2[i]) lmin = (int) l2[i]+0.5; |
| 359 |
if(lmax < l2[i]) lmax = (int) l2[i]+0.5; |
| 360 |
j++; |
| 361 |
} |
| 362 |
} |
| 363 |
this_npts = j; |
| 364 |
//printf("this_npts = %i\n", this_npts); |
| 365 |
j = *npts; |
| 366 |
for(i=0; i<npts1; i++) { |
| 367 |
// ind = index[n1[i]*(lmax-lmin)+l1[i]-lmin]; |
| 368 |
// if(ind>=0) { |
| 369 |
if(n1[i] == nn && l1[i] >= lmin && l1[i] <= lmax) { |
| 370 |
//ll = (int) this_l[i] + 0.5; |
| 371 |
ll = l1[i]; |
| 372 |
all = (double) ll; // cast back to double for function argument |
| 373 |
nuse = 3; |
| 374 |
reps = 1.0e-7; |
| 375 |
divdif(all, this_l, this_f, &nuse, this_npts, fb, reps, &dfb, &ddfb); |
| 376 |
ff = fb[nuse]; |
| 377 |
nuse = 3; |
| 378 |
divdif(all, this_l, this_ef, &nuse, this_npts, fb, reps, &dfb, &ddfb); |
| 379 |
error = fb[nuse]; |
| 380 |
if(error>0.0) { |
| 381 |
n[j] = nn; |
| 382 |
l[j] = ll; |
| 383 |
f[j] = f1[i]; |
| 384 |
df[j] = f1[i] - ff; |
| 385 |
edf[j] = sqrt(ef1[i]*ef1[i]+error*error); |
| 386 |
//printf("%i %i %i %f %f %f\n",j, n[j], l[j], f[j], df[j], edf[j]); |
| 387 |
j++; |
| 388 |
} |
| 389 |
} |
| 390 |
} |
| 391 |
*npts = j; |
| 392 |
//printf("%i\n",*npts); |
| 393 |
} |
| 394 |
|
| 395 |
return 0; |
| 396 |
} |
| 397 |
|
| 398 |
int autoweed_vel(int* n, double* l, double *ux, double *uy, |
| 399 |
int *mask, int npts) { |
| 400 |
/* |
| 401 |
Function - autoweed_vel |
| 402 |
Function to automatically weed velocities. An int array |
| 403 |
'mask' is returned of length npts - mask[i] is False for |
| 404 |
rejected modes. Ux and Uy are weeded together. |
| 405 |
*/ |
| 406 |
const int maxn=8; |
| 407 |
const double tol=5.0; |
| 408 |
|
| 409 |
int i, j, offset; |
| 410 |
int n_num[maxn]; |
| 411 |
double num; |
| 412 |
double sumx, sumxx, sumy, sumyy, meanx, meany, stdx, stdy; |
| 413 |
double range, uxmin, uxmax, uymin, uymax; |
| 414 |
double lmin,lmax; |
| 415 |
|
| 416 |
for(i=0; i<maxn; i++) { |
| 417 |
n_num[i]=0; |
| 418 |
} |
| 419 |
for(i=0; i<npts; i++) { |
| 420 |
if(n[i] < maxn) n_num[n[i]]++; |
| 421 |
} |
| 422 |
|
| 423 |
offset=0; |
| 424 |
for(i=0; i<maxn; i++) { |
| 425 |
num=0.0; |
| 426 |
sumx=0.0; |
| 427 |
sumy=0.0; |
| 428 |
sumxx=0.0; |
| 429 |
sumyy=0.0; |
| 430 |
// get l limits |
| 431 |
//fprintf (stderr, "autoweed_vel(): i = %d: lmin = lmax = l[%d] = %f\n", |
| 432 |
//i, offset, l[offset]); |
| 433 |
lmin=lmax=l[offset]; |
| 434 |
for(j=offset; j<n_num[i]+offset; j++) { |
| 435 |
if(l[j] < lmin) lmin=l[j]; |
| 436 |
if(l[j] > lmax) lmax= l[j]; |
| 437 |
} |
| 438 |
range=(lmax-lmin)/5.0; |
| 439 |
//printf("%f %f %f",lmin,lmax,range); |
| 440 |
lmin+=2.0*range; |
| 441 |
lmax-=2.0*range; |
| 442 |
for(j=offset; j<n_num[i]+offset; j++) { |
| 443 |
if(l[j] <= lmax && l[j] >= lmin) { |
| 444 |
sumx+=ux[j]; |
| 445 |
sumxx+=ux[j]*ux[j]; |
| 446 |
sumy+=uy[j]; |
| 447 |
sumyy+=uy[j]*uy[j]; |
| 448 |
num++; |
| 449 |
} |
| 450 |
} |
| 451 |
meanx=sumx/num; |
| 452 |
meany=sumy/num; |
| 453 |
stdx=num*sumxx-sumx*sumx; |
| 454 |
stdy=num*sumyy-sumy*sumy; |
| 455 |
stdx/=(num*(num-1)); |
| 456 |
stdy/=(num*(num-1)); |
| 457 |
stdx=sqrt(stdx); |
| 458 |
stdy=sqrt(stdy); |
| 459 |
//printf("%f %f %f %f\n",stdx,stdy,lmin,lmax); |
| 460 |
uxmin=meanx-5.0*stdx; |
| 461 |
uxmax=meanx+5.0*stdx; |
| 462 |
uymin=meany-5.0*stdy; |
| 463 |
uymax=meany+5.0*stdy; |
| 464 |
//printf("%f %f %f %f\n",uxmin,uxmax,uymin,uymax); |
| 465 |
|
| 466 |
for(j=offset; j<n_num[i]+offset; j++) { |
| 467 |
if(ux[j] <= uxmax && ux[j] >= uxmin && |
| 468 |
uy[j] <= uymax && uy[j] >= uymin) mask[j]=1; |
| 469 |
else mask[j]=0; |
| 470 |
} |
| 471 |
offset+=n_num[i]; |
| 472 |
} |
| 473 |
return 0; |
| 474 |
} |
| 475 |
|
| 476 |
void line(int m, double *x, double *y) { |
| 477 |
y[0] = x[0]; |
| 478 |
y[1] = 1.0; |
| 479 |
return; |
| 480 |
} |
| 481 |
|
| 482 |
int svd(int n, int m, double *a, double *v, double sigma[], int la, int lv) |
| 483 |
|
| 484 |
{ |
| 485 |
int i,j,k,l,itr,ier, itmax=30; |
| 486 |
double f, g, h, rmax, s, r1, r2, c, x, y, z, aeps, eps=1.e-16; |
| 487 |
// double *e; |
| 488 |
double e[2]; |
| 489 |
|
| 490 |
if(n>m || n<=0 || m<=0 || n>la || n>lv) return 105; |
| 491 |
ier=0; |
| 492 |
|
| 493 |
/* Reduction to Bidiagonal form using Householder transformations */ |
| 494 |
g=0.0; rmax=0.0; |
| 495 |
// e=(double *) calloc(n, sizeof(double)); |
| 496 |
|
| 497 |
for(i=0; i<n; ++i) { |
| 498 |
/* Off-diagonal elements of bidiagonal form */ |
| 499 |
e[i]=g; |
| 500 |
s=0.0; |
| 501 |
for(j=i; j<m; ++j) s=s+a[i+j*la]*a[i+j*la]; |
| 502 |
if(s <= 0.0) { |
| 503 |
/* transformation not required */ |
| 504 |
g=0.0; |
| 505 |
} |
| 506 |
else { |
| 507 |
f= a[i+i*la]; |
| 508 |
g=sqrt(s); |
| 509 |
if(f>=0.0) g=-g; |
| 510 |
h=f*g-s; |
| 511 |
a[i+i*la] = f-g; |
| 512 |
|
| 513 |
for(j=i+1; j<n; ++j) { |
| 514 |
s=0.0; |
| 515 |
for(k=i; k<m; ++k) s=s+a[i+k*la]*a[j+k*la]; |
| 516 |
f=s/h; |
| 517 |
for(k=i; k<m; ++k) a[j+k*la]= a[j+k*la]+f*a[i+k*la]; |
| 518 |
} |
| 519 |
} |
| 520 |
|
| 521 |
/* Diagonal elements of bidiagonal form */ |
| 522 |
sigma[i]=g; |
| 523 |
s=0.0; |
| 524 |
for(j=i+1; j<n; ++j) s=s+a[j+i*la]*a[j+i*la]; |
| 525 |
|
| 526 |
if(s<= 0.0) g=0.0; |
| 527 |
else { |
| 528 |
f= a[i*la+(i+1)]; |
| 529 |
g=sqrt(s); |
| 530 |
if(f>= 0.0) g=-g; |
| 531 |
h=f*g-s; |
| 532 |
a[i*la+(i+1)]=f-g; |
| 533 |
for(j=i+1; j<n; ++j) e[j]=a[j+i*la]/h; |
| 534 |
|
| 535 |
for(j=i+1; j<m; ++j) { |
| 536 |
s=0.0; |
| 537 |
for(k=i+1; k<n; ++k) s=s+a[k+j*la]*a[k+i*la]; |
| 538 |
for(k=i+1; k<n; ++k) a[k+j*la] = a[k+j*la]+s*e[k]; |
| 539 |
} |
| 540 |
} |
| 541 |
r1=fabs(sigma[i])+fabs(e[i]); |
| 542 |
if(r1 > rmax) rmax=r1; |
| 543 |
} |
| 544 |
|
| 545 |
/* Accumulation of right hand transformation in array V */ |
| 546 |
for(i=n-1; i>=0; --i) { |
| 547 |
if(g != 0.0) { |
| 548 |
h=g*a[i*la+(i+1)]; |
| 549 |
for(j=i+1; j<n; ++j) v[i+j*lv]=a[j+i*la]/h; |
| 550 |
|
| 551 |
for(j=i+1; j<n; ++j) { |
| 552 |
s=0.0; |
| 553 |
for(k=i+1; k<n; ++k) s=s+a[k+i*la]*v[j+k*lv]; |
| 554 |
for(k=i+1; k<n; ++k) v[j+k*lv]=v[j+k*lv]+s*v[i+k*lv]; |
| 555 |
} |
| 556 |
} |
| 557 |
|
| 558 |
for(j=i+1; j<n; ++j) { |
| 559 |
v[j+i*lv]=0.0; v[i+j*lv]=0.0; |
| 560 |
} |
| 561 |
v[i+i*lv]=1; |
| 562 |
g= e[i]; |
| 563 |
} |
| 564 |
|
| 565 |
/* Accumulation of left hand transformation overwritten on matrix A */ |
| 566 |
for(i=n-1; i>=0; --i) { |
| 567 |
g=sigma[i]; |
| 568 |
for(j=i+1; j<n; ++j) a[j+i*la]=0.0; |
| 569 |
if(g != 0.0) { |
| 570 |
h=g*a[i+i*la]; |
| 571 |
|
| 572 |
for(j=i+1; j<n; ++j) { |
| 573 |
s=0.0; |
| 574 |
for(k=i+1; k<m; ++k) s=s+a[i+k*la]*a[j+k*la]; |
| 575 |
f=s/h; |
| 576 |
for(k=i; k<m; ++k) a[j+k*la]=a[j+k*la]+f*a[i+k*la]; |
| 577 |
} |
| 578 |
|
| 579 |
for(j=i; j<m; ++j) a[i+j*la]=a[i+j*la]/g; |
| 580 |
} |
| 581 |
else { |
| 582 |
for(j=i; j<m; ++j) a[i+j*la]=0.0; |
| 583 |
} |
| 584 |
a[i+i*la] = a[i+i*la]+1; |
| 585 |
} |
| 586 |
|
| 587 |
/* Diagonalisation of the bidiagonal form */ |
| 588 |
aeps=eps*rmax; |
| 589 |
/* Loop over the singular values */ |
| 590 |
for(k=n-1; k>=0; --k) { |
| 591 |
/* The QR transformation */ |
| 592 |
for(itr=1; itr<=itmax; ++itr) { |
| 593 |
|
| 594 |
/* Test for splitting */ |
| 595 |
for(l=k; l>=0; --l) { |
| 596 |
if(fabs(e[l]) < aeps) goto split; |
| 597 |
if(fabs(sigma[l-1]) < aeps) break; |
| 598 |
} |
| 599 |
|
| 600 |
/* cancellation of E[L] if L>1 */ |
| 601 |
c=0.0; s=1.0; |
| 602 |
for(i=l; i<=k; ++i) { |
| 603 |
f=s*e[i]; |
| 604 |
e[i] = c*e[i]; |
| 605 |
if(fabs(f) < aeps) goto split; |
| 606 |
g=sigma[i]; |
| 607 |
sigma[i]=sqrt(f*f+g*g); |
| 608 |
c=g/sigma[i]; |
| 609 |
s=-f/sigma[i]; |
| 610 |
|
| 611 |
for(j=0; j<m; ++j) { |
| 612 |
r1= a[j*la+(l-1)]; |
| 613 |
r2= a[i+j*la]; |
| 614 |
a[j*la+(l-1)]=r1*c+r2*s; |
| 615 |
a[i+j*la]=c*r2-s*r1; |
| 616 |
} |
| 617 |
} |
| 618 |
|
| 619 |
split: z=sigma[k]; |
| 620 |
if(l == k) { |
| 621 |
/* QR iteration has converged */ |
| 622 |
if(z < 0.0) { |
| 623 |
sigma[k] = -z; |
| 624 |
for(j=0; j<n; ++j) v[k+j*lv]=-v[k+j*lv]; |
| 625 |
} |
| 626 |
break; |
| 627 |
} |
| 628 |
|
| 629 |
if(itr==itmax) {ier=12; break;} |
| 630 |
|
| 631 |
/* calculating shift from bottom 2x2 minor */ |
| 632 |
x=sigma[l]; |
| 633 |
y=sigma[k-1]; |
| 634 |
g=e[k-1]; |
| 635 |
h=e[k]; |
| 636 |
f=((y-z)*(y+z)+(g-h)*(g+h))/(2.*h*y); |
| 637 |
g=sqrt(1.+f*f); |
| 638 |
if(f < 0.0) g=-g; |
| 639 |
f=((x-z)*(x+z)+h*(y/(f+g)-h))/x; |
| 640 |
|
| 641 |
/* next QR transformation */ |
| 642 |
c=1.0; s=1.0; |
| 643 |
/* Given's rotation */ |
| 644 |
for(i=l+1; i<=k; ++i) { |
| 645 |
g=e[i]; |
| 646 |
y=sigma[i]; |
| 647 |
h=s*g; |
| 648 |
g=c*g; |
| 649 |
e[i-1]=sqrt(f*f+h*h); |
| 650 |
c=f/e[i-1]; |
| 651 |
s=h/e[i-1]; |
| 652 |
f=c*x+s*g; |
| 653 |
g=c*g-s*x; |
| 654 |
h=s*y; |
| 655 |
y=c*y; |
| 656 |
|
| 657 |
for(j=0; j<n; ++j) { |
| 658 |
x=v[j*lv+(i-1)]; |
| 659 |
z=v[i+j*lv]; |
| 660 |
v[j*lv+(i-1)]=c*x+s*z; |
| 661 |
v[i+j*lv]=c*z-s*x; |
| 662 |
} |
| 663 |
|
| 664 |
sigma[i-1]=sqrt(f*f+h*h); |
| 665 |
if(sigma[i-1] != 0.0) { |
| 666 |
c=f/sigma[i-1]; |
| 667 |
s=h/sigma[i-1]; |
| 668 |
} |
| 669 |
f=c*g+s*y; |
| 670 |
x=c*y-s*g; |
| 671 |
for(j=0; j<m; ++j) { |
| 672 |
y= a[j*la+(i-1)]; |
| 673 |
z= a[i+j*la]; |
| 674 |
a[j*la+(i-1)] = c*y+s*z; |
| 675 |
a[i+j*la] = c*z-s*y; |
| 676 |
} |
| 677 |
} |
| 678 |
|
| 679 |
e[l]=0.0; |
| 680 |
e[k]=f; |
| 681 |
sigma[k]=x; |
| 682 |
} |
| 683 |
} |
| 684 |
// free(e); |
| 685 |
return ier; |
| 686 |
} |
| 687 |
|
| 688 |
int svdevl(int n, int m, double *u, double *v, double sigma[], int lu, |
| 689 |
int lv, double b[], double reps) |
| 690 |
|
| 691 |
{ |
| 692 |
int i,j; |
| 693 |
double smax, aeps, s; |
| 694 |
double *wk; |
| 695 |
|
| 696 |
/* Finding the largest singular value */ |
| 697 |
smax=0.0; |
| 698 |
for(i=0; i<n; ++i) |
| 699 |
if(sigma[i] > smax) smax=sigma[i]; |
| 700 |
|
| 701 |
aeps=smax*reps; |
| 702 |
wk=(double *)calloc(n, sizeof(double)); |
| 703 |
for(i=0; i<n; ++i) { |
| 704 |
s=0.0; |
| 705 |
/* Only SIGMA[I] > AEPS contribute to the solution */ |
| 706 |
if(sigma[i] > aeps) { |
| 707 |
for(j=0; j<m; ++j) s=s+b[j]*u[i+j*lu]; |
| 708 |
s=s/sigma[i]; |
| 709 |
} |
| 710 |
wk[i]=s; |
| 711 |
} |
| 712 |
|
| 713 |
for(i=0; i<n; ++i) { |
| 714 |
s=0.0; |
| 715 |
for(j=0; j<n; ++j) s=s+v[j+i*lv]*wk[j]; |
| 716 |
b[i]=s; |
| 717 |
} |
| 718 |
free(wk); |
| 719 |
return 0; |
| 720 |
} |
| 721 |
|
| 722 |
int llsq(int n, int m, int k, double *x, int ix, double f[], double ef[], |
| 723 |
double a[], double *u, double *v, int iu, int iv, double sigma[], |
| 724 |
double y[], void (* phi) (int , double * , double * ), double reps, |
| 725 |
double *chisq) |
| 726 |
|
| 727 |
{ |
| 728 |
int i,j,ier; |
| 729 |
double s1; |
| 730 |
// double *wk; |
| 731 |
double wk[2]; |
| 732 |
|
| 733 |
if(m>n || m<=0 || n<=0 || k>ix) return 606; |
| 734 |
|
| 735 |
// wk=(double *) calloc(m, sizeof(double)); |
| 736 |
/* Setting up the design matrix and the RHS */ |
| 737 |
for(i=0; i<n; ++i) { |
| 738 |
if(ef[i]<=0.0) {/*free(wk); */return 607;} |
| 739 |
a[i]=f[i]/ef[i]; |
| 740 |
phi(m,&x[i*ix],wk); |
| 741 |
for(j=0; j<m; ++j) u[j+i*iu]=wk[j]/ef[i]; |
| 742 |
} |
| 743 |
|
| 744 |
ier=svd(m,n,u,v,sigma,iu,iv); |
| 745 |
if(ier>100) {/*free(wk);*/ return ier;} |
| 746 |
|
| 747 |
/* Calculate the least squares solution */ |
| 748 |
ier=svdevl(m,n,u,v,sigma,iu,iv,a,reps); |
| 749 |
|
| 750 |
/* Computing the \chi^2 from fitted coefficients */ |
| 751 |
*chisq=0.0; |
| 752 |
for(i=0; i<n; ++i) { |
| 753 |
phi(m,&x[i*ix],wk); |
| 754 |
s1=0.0; |
| 755 |
for(j=0; j<m; ++j) s1=s1+a[j]*wk[j]; |
| 756 |
y[i]=s1; |
| 757 |
s1=(f[i]-y[i])/ef[i]; |
| 758 |
*chisq=(*chisq)+s1*s1; |
| 759 |
} |
| 760 |
|
| 761 |
// free(wk); |
| 762 |
return 0; |
| 763 |
} |
| 764 |
|
| 765 |
int autoweed(int *l, int *n, double *f, double *df, double *edf, int *msk, |
| 766 |
int npts) { |
| 767 |
int avglen = 4; |
| 768 |
double tol = 4.0; |
| 769 |
double delnu = 50.0; |
| 770 |
int i, j, nn, this_npts, llim, ulim, offset; |
| 771 |
int data_range[2], *this_l; |
| 772 |
double *this_f, *this_df, *this_edf, *slopes, *a, *u, *y; |
| 773 |
double v[4], sigma[2], chisq; |
| 774 |
double mean, std; |
| 775 |
|
| 776 |
this_l = (int*) malloc(npts*sizeof(int)); |
| 777 |
this_f = (double*) malloc(npts*sizeof(double)); |
| 778 |
this_df = (double*) malloc(npts*sizeof(double)); |
| 779 |
this_edf = (double*) malloc(npts*sizeof(double)); |
| 780 |
slopes = (double*) malloc(npts*sizeof(double)); |
| 781 |
a = (double*) malloc(avglen*sizeof(double)); |
| 782 |
u = (double*) malloc(2*avglen*sizeof(double)); |
| 783 |
y = (double*) malloc(avglen*sizeof(double)); |
| 784 |
offset = 0; |
| 785 |
for(i=0; i<npts; i++) msk[i] = 0; |
| 786 |
for(nn=0; nn<7; nn++) { |
| 787 |
j = 0; |
| 788 |
mean = 0.0; |
| 789 |
std = 0.0; |
| 790 |
for(i=0; i<npts; i++) { |
| 791 |
if(n[i] == nn) { |
| 792 |
this_l[j] = l[i]; |
| 793 |
this_f[j] = f[i]; |
| 794 |
this_df[j] = df[i]; |
| 795 |
this_edf[j] = edf[i]; |
| 796 |
j++; |
| 797 |
} |
| 798 |
} |
| 799 |
this_npts = j; |
| 800 |
if(this_npts > avglen + 5) { |
| 801 |
data_range[0] = (int) 2*this_npts/10.; |
| 802 |
data_range[1] = (int) 8*this_npts/10.; |
| 803 |
for(i=0; i<this_npts-avglen; i++) { |
| 804 |
llsq(avglen, 2, 1, &this_f[i], 1, &this_df[i], &this_edf[i], a, u, |
| 805 |
v, 2, 2, sigma, y, *line, 1.0e-6, &chisq); |
| 806 |
slopes[i] = a[0]; |
| 807 |
//printf("%i %f\n",nn,a[0]); |
| 808 |
mean += a[0]; |
| 809 |
} |
| 810 |
mean /= (double) this_npts; |
| 811 |
for(i=0; i<this_npts-avglen; i++) std += (slopes[i]-mean)*(slopes[i]-mean); |
| 812 |
std /= (double) this_npts; |
| 813 |
std = sqrt(std); |
| 814 |
// printf("%i %i %i\n",data_range[0], data_range[1], this_npts/2); |
| 815 |
llim = data_range[0]; |
| 816 |
ulim = data_range[1]; |
| 817 |
while(llim > 0) { |
| 818 |
if( fabs(slopes[llim]-mean)/std > tol) break; |
| 819 |
llim--; |
| 820 |
} |
| 821 |
while(ulim<this_npts-avglen-1) { |
| 822 |
if( fabs(slopes[ulim]-mean)/std > tol) break; |
| 823 |
ulim++; |
| 824 |
} |
| 825 |
i = this_npts/2; |
| 826 |
while(i>0) { |
| 827 |
if(this_f[i]-this_f[i-1] > delnu) break; |
| 828 |
i--; |
| 829 |
} |
| 830 |
if(i > llim) llim = i; |
| 831 |
i = this_npts/2; |
| 832 |
while(i<this_npts) { |
| 833 |
if(this_f[i]-this_f[i-1] > delnu) break; |
| 834 |
i++; |
| 835 |
} |
| 836 |
if(i < ulim) ulim = i; |
| 837 |
printf("%i %i %i %i\n",nn,this_npts,llim,ulim); |
| 838 |
for(i=offset+llim; i<offset+ulim; i++) msk[i] = 1;//i<this_npts+offset-ulim; i++) msk[i] = 1; |
| 839 |
offset += this_npts; |
| 840 |
} |
| 841 |
} |
| 842 |
|
| 843 |
return 0; |
| 844 |
} |
| 845 |
|
