File: trans.c

package info (click to toggle)
yorick 2.2.03+dfsg-3
  • links: PTS, VCS
  • area: main
  • in suites: jessie, jessie-kfreebsd
  • size: 9,620 kB
  • ctags: 9,317
  • sloc: ansic: 85,521; sh: 1,665; cpp: 1,282; lisp: 1,234; makefile: 1,034; fortran: 19
file content (473 lines) | stat: -rw-r--r-- 16,793 bytes parent folder | download | duplicates (6)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
/*
 * $Id: trans.c,v 1.1 2005-09-18 22:04:57 dhmunro Exp $
 * Routines for transporting a ray through a cylindrical mesh.
 */
/* Copyright (c) 2005, The Regents of the University of California.
 * All rights reserved.
 * This file is part of yorick (http://yorick.sourceforge.net).
 * Read the accompanying LICENSE file for details.
 */

#include "trans.h"
/* includes track.h and bound.h as well */

extern double exp(double);
extern double sqrt(double);
extern double fabs(double);
#define SQ(x) ((x)*(x))
#define FUZZ 1.0e-99

#ifdef NLTSS
/* Let Hybrid-C compiler find vector versions of exp, sqrt, etc. */
#include <lcc.h>
#endif
/* Also a CYCRED switch below, originally intended for Crays, but
   optimized incorrectly there when last checked.  */

/* 1-exp(-x) != x for small x.  For x<ONE_MINUS_EXP, just use x. */
#define ONE_MINUS_EXP 1.0e-4

/* ---------------------------------------------------------------------- */

/* Solve the transport equation assuming that both the opacity and
 * source function are constant within each zone.  Return the overall
 * absorption and self-emission along the ray.
 */
void
FlatSource(double *opac, double *source,        /* opacity, emissivity */
           long kxlm, long ngroup,              /* opac, source dimens */
           RayPath *path,                       /* ray path through mesh */
           double *absorb, double *selfem,      /* attenuation factor and
                                                 * self-emission for
                                                 * entire path */
           double *work)                        /* scratch space */
{
    /* Formulas:
     *   The transport equation is  d(inu)/ds= (knu)(jnu - inu), or
     *          d(inu)/d(tau)= jnu - inu.
     * In a region where knu and jnu are constant, the solution is
     *          inu= exp(-tau)*inu0 + (1-exp(-tau))*jnu.
     *
     * Thus, integrating inu along the path requires solving the
     * first order recurrence:
     *          x[i+1]= a[i]*x[i] + b[i]
     * where x is inu, a is exp(-tau), and b is (1-exp(-tau))*jnu.
     *
     * The solution to this recurrence is:
     *          inu= (absorb)*inu0 + (selfem)
     * where absorb is the product of all a[i], and selfem is x[last]
     * with x[0]=0.  This total attenuation factor and self-emission
     * specific intensity (in same units as input source function) are
     * the outputs of FlatSource.
     */

   long nzones= path->ncuts-1;
   long *zone= path->zone;
   double *ds= path->ds;
   double *tau= work;
   double *atten= tau+nzones;
   double *jnu= atten+nzones;
   long n,i;
   register long j;

   if (nzones<1) {
     if (absorb && selfem) {
       for (n=0 ; n<ngroup ; n++) {
         *absorb++= 1.0;
         *selfem++= 0.0;
       }
     }
     return;
   }

    /* Eventually, may want to branch to a separate algorithm if the
     * number of groups is very large, but the number of edge crossings
     * is small...
     * For now, the slightly less efficient inner loop on crossings
     * is a better choice, since the number of groups is often quite
     * small, while the number of crossings is rarely small.
     */
   for (n=0 ; n<ngroup ; n++) {

       /* Gather the opacity and source function along the ray path.
        * Assume that opac[0]==0 and source[0]==0, so no special coding
        * required for non-contiguous sections of the path.
        */
/* #pragma nohazard */
      for (i=0 ; i<nzones ; i++) {
         j= zone[i];
         tau[i]= opac[j]*ds[i];
         atten[i]= exp(-tau[i]);
         jnu[i]= source[j];
      }

       /* Replace jnu by appropriate "b" function.
        * Note that (1-exp(-tau))*jnu --> tau*jnu as tau-->0 may be
        * important even for very small tau... */
/* #pragma nohazard */
      for (i=0 ; i<nzones ; i++) {
         if (fabs(tau[i]) > ONE_MINUS_EXP) jnu[i]*= (1.0-atten[i]);
         else jnu[i]*= tau[i];
      }

       /* Solve the first order recurrence. */
      Reduce(atten,jnu,nzones); /* clobbers atten, jnu arrays... */
      *absorb= atten[0];
      *selfem= jnu[0];

      absorb++;
      selfem++;
      opac+= kxlm;
      source+= kxlm;
   }

}

/* ---------------------------------------------------------------------- */

/* Solve the transport equation assuming that the source function
 * varies linearly with optical depth across a zone.  The opacity is
 * assumed to be constant within each zone.  (Hence, opac must be zone
 * centered, while source is point centered.)  Return the overall
 * absorption and self-emission along the ray.
 */
void
LinearSource(double *opac, double *source,      /* opacity, emissivity */
             long kxlm, long ngroup,            /* opac, source dimens */
             RayPath *path,                     /* ray path through mesh */
             double *absorb, double *selfem,    /* attenuation factor and
                                                 * self-emission for
                                                 * entire path */
             double *work)                      /* scratch space */
{
    /* Formulas:
     *   The transport equation is  d(inu)/ds= (knu)(jnu - inu), or
     *          d(inu)/d(tau)= jnu - inu.
     * In a region where knu is constant and jnu linear, the solution is
     *          inu1= exp(-tau)*inu0 + (1-exp(-tau))*jnu0 +
     *                      (1-(1-exp(-tau))/tau)*(jnu1-jnu0).
     *
     * Thus, integrating inu along the path requires solving the
     * first order recurrence:
     *          x[i+1]= a[i]*x[i] + b[i]
     * where x is inu, a is exp(-tau), and b is (1-exp(-tau))*jnu0+
     *                            (1-(1-exp(-tau))/tau)*(jnu1-jnu0).
     *
     * The solution to this recurrence is:
     *          inu= (absorb)*inu0 + (selfem)
     * where absorb is the product of all a[i], and selfem is x[last]
     * with x[0]=0.  This total attenuation factor and self-emission
     * specific intensity (in same units as input source function) are
     * the outputs of LinearSource.
     */

   long nzones= path->ncuts-1;
   long *zone= path->zone;
   double *ds= path->ds;
   long *pt1= path->pt1;
   long *pt2= path->pt2;
   double *f= path->f;
   double fi= path->fi;
   double ff= path->ff;
   double *tau= work;
   double *atten= tau+nzones;
   double *jnu= atten+nzones;   /* jnu has nzones+1 elements! */
   long n,i;
   register long j,k;
   register double f1,f2;

   if (nzones<1) {
     if (absorb && selfem) {
       for (n=0 ; n<ngroup ; n++) {
         *absorb++= 1.0;
         *selfem++= 0.0;
       }
     }
     return;
   }

    /* Eventually, may want to branch to a separate algorithm if the
     * number of groups is very large, but the number of edge crossings
     * is small...
     * For now, the slightly less efficient inner loop on crossings
     * is a better choice, since the number of groups is often quite
     * small, while the number of crossings is rarely small.
     */
   for (n=0 ; n<ngroup ; n++) {

       /* Gather the opacity and source function along the ray path.
        * Assume that opac[0]==0 and source[0]==0, so no special coding
        * required for non-contiguous sections of the path.
        */
/* #pragma nohazard */
      for (i=0 ; i<nzones ; i++) {
         j= zone[i];
         tau[i]= opac[j]*ds[i];
         atten[i]= exp(-tau[i]);
      }
       /* Interpolate source to crossing point on each edge */
/* #pragma nohazard */
      for (i=0 ; i<=nzones ; i++) {
         j= pt1[i];   k= pt2[i];
         jnu[i]= (0.5-f[i])*source[j] + (0.5+f[i])*source[k];
      }
       /* Interpolate source into interior of first and last zone */
      f1= (1.0-fi)*jnu[0]+fi*jnu[1];    /* nzones=1 is possible... */
      jnu[nzones]= ff*jnu[nzones-1]+(1.0-ff)*jnu[nzones];
      jnu[0]= f1;

       /* Replace jnu by appropriate "b" function.
        * Note that (1-exp(-tau)-tau)*jnu --> (tau^2/2)*jnu as tau-->0
        * may be important even for very small tau...
        * Vectorizing algorithm requires small positive random number
        * in order to make zero divide very unlikely.  Magnitude is
        * chosen in order to have sub-roundoff effect on
        * tau > ONE_MINUS_EXP. */
#define RANDOM_SMALL_TAU (1.5261614e-20*ONE_MINUS_EXP)
       /* Note: this vectorizes on Cray as of 3/jul/90 */
/* #pragma nohazard */
      for (i=0 ; i<nzones ; i++) {
         f1= -atten[i]+(1-atten[i])/(tau[i]+RANDOM_SMALL_TAU);
         f2=  1.0     -(1-atten[i])/(tau[i]+RANDOM_SMALL_TAU);
         if (fabs(tau[i]) > ONE_MINUS_EXP) {
            jnu[i]= f1*jnu[i]+f2*jnu[i+1];
         } else {
            jnu[i]= 0.5*tau[i]*(jnu[i]+jnu[i+1]);
         }
      }

       /* Solve the first order recurrence. */
      Reduce(atten,jnu,nzones); /* clobbers atten, jnu arrays... */
      *absorb= atten[0];
      *selfem= jnu[0];

      absorb++;
      selfem++;
      opac+= kxlm;
      source+= kxlm;
   }

}

/* ---------------------------------------------------------------------- */

/* Reduce x[i+1]= a[i]*x[i]+b[i] for i=0,...,n-1 to
 *          x[n]= a[0]*x[0]+b[0]     -i.e.- return a[0], b[0]
 * May use an algorithm which clobbers a[1:n-1], b[1:n-1] as well.
 */
void Reduce(double *a, double *b, long n)
{
   long i;

#ifndef CYCRED
    /* on a non-vector machine, use the straightforward algorithm */
   register double tmpa,tmpb;

   tmpa= a[0];   tmpb= b[0];   /* miscoded tmpa*b[0] originally?? */
   for (i=1 ; i<n ; i++) {
      tmpa*= a[i];
      tmpb= tmpb*a[i]+b[i];
   }
   a[0]= tmpa;   b[0]= tmpb;

#else
    /* on vector machine, a cyclic reduction algorithm is faster */
   while (n > 2) {      /* log2(n) reduction passes */
/* #pragma nohazard */
      for (i=0 ; i<n/2 ; i++) {
         a[i]= a[2*i]*a[2*i+1];
         b[i]= b[2*i]*a[2*i+1]+b[2*i+1];
      }
      if (n & 01) {     /* keep final odd point if present */
         a[i]= a[2*i];
         b[i]= b[2*i];
         n= i+1;
      } else n= i;
   }
   if (n == 2) {
      a[0]= a[0]*a[1];
      b[0]= b[0]*a[1]+b[1];
   }
#endif
}

/* ---------------------------------------------------------------------- */

/* The LinearSource transport solver requires a point centered source
 * function; the given source function is zone centered.
 * This point centering scheme is local to the four zones surrounding
 * the point, with weights which are large for zones whose optical
 * depth (along either k or l) is near 1.
 * The algorithm requires 4*(kmax*(lmax+1)+1) doubles as working space.
 *
 * An unrelated Milne condition is applied for points which lie on
 * the vacuum boundary of the problem.
 */
void PtCenterSource(double *opac, double *source, long kxlm, long ngroup,
                    Mesh *mesh, Boundary *boundary, double *work)
/* Historical note: This algorithm should be algebraically equivalent
 * to the algorithm used in DIRT or TDG, excepting a case in the
 * boundary correction involving a boundary between non-void zones,
 * which can, in fact, never occur.
 */
{
  long klmax= mesh->klmax;
  long kmax= mesh->kmax;
  double *z= mesh->z;
  double *r= mesh->r;
  int *ireg= mesh->ireg;

  /* partition the working space */
  double *wp= work;                     /* wp only needs kmax*lmax... */
  double *wk= wp+klmax+kmax+1;
  double *wl= wk+klmax+kmax+1;
  double *b=  wl+klmax+kmax+1;

  long i,n;
  register double area,dddk,dddl;
  register double w00,w01,w10,w11;

  /* applying of Milne condition at boundaries logically complex... */
  long npoints= boundary->npoints;
  long *zone= boundary->zone;
  int *side= boundary->side;
  /* zone+pt1[side] --> zone+pt2[side] is boundary edge */
  long pt1index[4]= { -1L, -1L /* -kmax */, 0L /* -kmax */, 0L };
  long pt2index[4]= { 0L, -1L, -1L /* -kmax */, 0L /* -kmax */ };
  /* zone+zon[side] is zone interior to boundary by one more than zone */
  long zonindex[4]= { 0L /* -kmax */, +1L, 0L /* +kmax */, -1L };
  double b1,w1,milne1,b2,w2,milne2,dx,dtau,bx,dtaux,b1b,w1b,milne1b;
  long j1,j2,jz,jx,j1b;
  int beginSection;

  /* without this, not obvious that these are initialized */
  b1= w1= milne1= b2= w2= milne2= b1b= w1b= milne1b= 0.0;
  j2= j1b= 0;

  pt1index[1]-= kmax;
  pt1index[2]-= kmax;
  pt2index[2]-= kmax;
  pt2index[3]-= kmax;
  zonindex[0]-= kmax;
  zonindex[2]+= kmax;

  /* zero workspace in guard zones */
  for (i=0 ; i<=kmax ; i++) wk[i]= wl[i]= 0.0;
  for (i=klmax ; i<klmax+kmax+1 ; i++) wk[i]= wl[i]= b[i]= 0.0;

  for (n=0 ; n<ngroup ; n++) {

    /* Compute weighting factors -- zone centered, but separate
     * values wk, wl for the delta-k and delta-l directions. */
/* #pragma nohazard */
    for (i=kmax+1 ; i<klmax ; i++) {
      /* area is actually twice zonal area */
      area= (z[i]-z[i-kmax-1])*(r[i-1]-r[i-kmax]) -
        (z[i-1]-z[i-kmax])*(r[i]-r[i-kmax-1]);
      /* dddk, dddl actually twice median lengths */
      dddk= sqrt( SQ(z[i]-z[i-1] + z[i-kmax]-z[i-kmax-1]) +
                 SQ(r[i]-r[i-1] + r[i-kmax]-r[i-kmax-1]));
      dddl= sqrt( SQ(z[i]-z[i-kmax] + z[i-1]-z[i-kmax-1]) +
                 SQ(r[i]-r[i-kmax] + r[i-1]-r[i-kmax-1]));
      if (ireg[i]) {
        wp[i]= 1.0/(opac[i]*area+FUZZ);
        wk[i]= wp[i]*SQ(1.0-exp(-0.5*opac[i]*dddk));
        wl[i]= wp[i]*SQ(1.0-exp(-0.5*opac[i]*dddl));
      } else {
        wp[i]= wk[i]= wl[i]= 0.0;
      }
    }

    /* Copy source to temporary to add guard zones */
/* #pragma nohazard */
    for (i=0 ; i<klmax ; i++) b[i]= source[i];

    /* Point centered source is weighted average over
     * the four surrounding edges, each of which is centered
     * between its two bounding zones. */
/* #pragma nohazard */
    for (i=0 ; i<klmax ; i++) {
      w00= wk[i]+       wl[i];
      w10= wk[i+1]+     wl[i+1];
      w01= wk[i+kmax]+  wl[i+kmax];
      w11= wk[i+kmax+1]+wl[i+kmax+1];
      b[i]= (b[i]*w00+b[i+1]*w10+b[i+kmax]*w01+b[i+kmax+1]*w11) /
        (w00+w01+w10+w11+FUZZ);
    }

    /* Instead of interior weighting, use Milne condition at
     * (vacuum) boundaries.
     * Note that r=0 or z=0 symmetry boundaries are not in the list,
     * because FindBoundaryPoints will not find them.  TrimBoundary
     * must be used to eliminate khold, lhold, and norad boundaries. */
    /* Note that this loop is usually much shorter than the others. */
    beginSection= 1;
    for (i=0 ; i<npoints ; i++) {
      /* Get point indices j1, j2, zone index jz */
      jz= zone[i];
      if (jz) {
        if (beginSection) {
          j1= jz + pt1index[side[i]];
        } else {
          j1= j2;
          b1= b2;   w1= w2;   milne1= milne2;
        }
        j2= jz + pt2index[side[i]];
        b2= source[jz];
        if (side[i]&01) w2= wk[jz];
        else            w2= wl[jz];

        /* dtau is half the optical depth of the zone perpendicular
         * to the boundary edge -- i.e.- the optical depth from
         * zone center to boundary.  The Milne factor reduces the
         * source so a linear extrapolation reaches 0.0 at
         * optical depth 2/3 beyond the zone boundary.  If dtau>1
         * and the source function is decreasing toward the boundary,
         * then extrapolate the source function to optical depth 1
         * before applying the Milne reduction. */
        dx= sqrt(SQ(z[j2]-z[j1])+SQ(r[j2]-r[j1]));
        dtau= 0.25/(dx*wp[jz]+FUZZ);
        if (dtau>1.0 && ireg[jx= jz+zonindex[side[i]]]) {
          bx= source[jx];
          dtaux= 0.25/(dx*wp[jx]+FUZZ);
          if (bx > b2) {  /* flux (gradient) out of boundary */
            if (b2*(dtau+dtaux) > (bx-b2)*(dtau+(2./3.)))
              /* effectively extrapolate to optical depth 1 first */
              dtau= 1.0+(5./3.)*(bx-b2)*(dtau-1.0)/
                (b2*(dtau+dtaux)-(bx-b2)*(dtau-1.0));
          } else dtau= 1.0; /* Huh? At least this is continuous... */
        }
        milne2= 1.0+1.5*dtau;

        /* Source at boundary point is weighted mean between the
         * two adjacent boundary edges. */
        if (beginSection) {
          beginSection= 0;
          j1b= j1;
          b1b= b2;   w1b= w2;   milne1b= milne2;
          b[j1]= b2 / (milne2+FUZZ);  /* if closed boundary, changed later */
        } else {
          b[j1]= (b1*w1+b2*w2) / (w1*milne1+w2*milne2+FUZZ);
        }

      } else if (!beginSection) {       /* final point of boundary section */
        beginSection= 1;
        if (j2 == j1b) {  /* handle closed boundary */
          b[j2]= (b1b*w1b+b2*w2) / (w1b*milne1b+w2*milne2+FUZZ);
        } else {  /* open boundary */
          b[j2]= b2 / (milne2+FUZZ);
        }
      }

    }

    /* Copy point centered source over zone centered input */
/* #pragma nohazard */
    for (i=0 ; i<klmax ; i++) source[i]= b[i];

    source+= kxlm;
    opac+= kxlm;
  }
}

/* ---------------------------------------------------------------------- */