1 |
************************************************************************* |
2 |
* |
3 |
* Subroutine inter_B.f |
4 |
* |
5 |
* it computes the magnetic field in a chosen point x,y,z inside or |
6 |
* outside the magnetic cavity, using a trilinear interpolation of |
7 |
* B field measurements (read before by means of ./read_B.f) |
8 |
* if the point falls outside the interpolation volume, set the field to 0 |
9 |
* |
10 |
* needs: |
11 |
* - common_B_inner.f common file for the inner magnetic field map |
12 |
* - ./inter_B_inner.f common file for the inner magnetic field map |
13 |
* - common_B_outer.f common file for the outer magnetic field map |
14 |
* - ./inter_B_outer.f common file for the outer magnetic field map |
15 |
* |
16 |
* to be called after ./read_B.f (magnetic field map reading subroutine) |
17 |
* |
18 |
* input: coordinates in m |
19 |
* output: magnetic field in T |
20 |
* |
21 |
************************************************************************* |
22 |
|
23 |
subroutine inter_B(x,y,z,res) !coordinates in m, magnetic field in T |
24 |
|
25 |
implicit double precision (a-h,o-z) |
26 |
include 'common_B.f' |
27 |
|
28 |
|
29 |
c------------------------------------------------------------------------ |
30 |
c |
31 |
c local variables |
32 |
c |
33 |
c------------------------------------------------------------------------ |
34 |
|
35 |
real*8 x,y,z !point of interest |
36 |
real*8 res(3) !interpolated B components: res = (Bx, By, Bz) |
37 |
|
38 |
real*8 zl,zu |
39 |
real*8 resu(3),resl(3) |
40 |
|
41 |
c------------------------------------------------------------------------ |
42 |
c |
43 |
c set the field outside the interpolation volume to be 0 |
44 |
c |
45 |
c------------------------------------------------------------------------ |
46 |
|
47 |
do ip=1,3 |
48 |
res(ip)=0. |
49 |
enddo |
50 |
|
51 |
|
52 |
c------------------------------------------------------------------------ |
53 |
c |
54 |
c check if the point falls inside the interpolation volumes |
55 |
c |
56 |
c------------------------------------------------------------------------ |
57 |
|
58 |
* ----------------------- |
59 |
* INNER MAP |
60 |
* ----------------------- |
61 |
if( |
62 |
$ (x.ge.edgexmin).and.(x.le.edgexmax) |
63 |
$ .and.(y.ge.edgeymin).and.(y.le.edgeymax) |
64 |
$ .and.(z.ge.edgezmin).and.(z.le.edgezmax) |
65 |
$ ) then |
66 |
|
67 |
call inter_B_inner(x,y,z,res) |
68 |
c print*,'INNER - ',z,res |
69 |
|
70 |
endif |
71 |
|
72 |
* ----------------------- |
73 |
* OUTER MAP |
74 |
* ----------------------- |
75 |
if( |
76 |
$ ((x.ge.edgeuxmin).and.(x.le.edgeuxmax) |
77 |
$ .and.(y.ge.edgeuymin).and.(y.le.edgeuymax) |
78 |
$ .and.(z.ge.edgeuzmin).and.(z.le.edgeuzmax)) |
79 |
$ .or. |
80 |
$ ((x.ge.edgelxmin).and.(x.le.edgelxmax) |
81 |
$ .and.(y.ge.edgelymin).and.(y.le.edgelymax) |
82 |
$ .and.(z.ge.edgelzmin).and.(z.le.edgelzmax)) |
83 |
$ ) then |
84 |
|
85 |
call inter_B_outer(x,y,z,res) |
86 |
c res(2)=res(2)*10 |
87 |
c print*,'OUTER - ',z,res |
88 |
|
89 |
endif |
90 |
|
91 |
* -------------------------------- |
92 |
* GAP between INNER and OUTER MAPS |
93 |
* -------------------------------- |
94 |
if( |
95 |
$ (x.gt.edgexmin).and.(x.lt.edgexmax) |
96 |
$ .and.(y.gt.edgeymin).and.(y.lt.edgeymax) |
97 |
$ .and.(z.gt.edgezmax).and.(z.lt.edgeuzmin) |
98 |
$ )then |
99 |
|
100 |
zu = edgeuzmin |
101 |
zl = edgezmax |
102 |
call inter_B_inner(x,y,zl,resu) |
103 |
call inter_B_outer(x,y,zu,resl) |
104 |
|
105 |
do i=1,3 |
106 |
res(i) = z * ((resu(i)-resl(i))/(zu-zl)) |
107 |
$ + resu(i) |
108 |
$ - zu * ((resu(i)-resl(i))/(zu-zl)) |
109 |
enddo |
110 |
c print*,'GAP U - ',z,res |
111 |
|
112 |
elseif( |
113 |
$ (x.gt.edgexmin).and.(x.lt.edgexmax) |
114 |
$ .and.(y.gt.edgeymin).and.(y.lt.edgeymax) |
115 |
$ .and.(z.gt.edgelzmax).and.(z.lt.edgezmin) |
116 |
$ ) then |
117 |
|
118 |
|
119 |
zu = edgezmin |
120 |
zl = edgelzmax |
121 |
call inter_B_inner(x,y,zu,resu) |
122 |
call inter_B_outer(x,y,zl,resl) |
123 |
|
124 |
do i=1,3 |
125 |
res(i) = z * ((resu(i)-resl(i))/(zu-zl)) |
126 |
$ + resu(i) |
127 |
$ - zu * ((resu(i)-resl(i))/(zu-zl)) |
128 |
enddo |
129 |
c print*,'GAP D - ',z,res |
130 |
|
131 |
endif |
132 |
|
133 |
return |
134 |
end |
135 |
|
136 |
|
137 |
************************************************************************* |
138 |
* |
139 |
* Subroutine inter_B_inner.f |
140 |
* |
141 |
* it computes the magnetic field in a chosen point x,y,z inside the |
142 |
* magnetic cavity, using a trilinear interpolation of |
143 |
* B field measurements (read before by means of ./read_B.f) |
144 |
* the value is computed for two different inner maps and then averaged |
145 |
* |
146 |
* needs: |
147 |
* - ../common/common_B_inner.f |
148 |
* |
149 |
* input: coordinates in m |
150 |
* output: magnetic field in T |
151 |
* |
152 |
************************************************************************* |
153 |
|
154 |
subroutine inter_B_inner(x,y,z,res) !coordinates in m, magnetic field in T |
155 |
|
156 |
implicit double precision (a-h,o-z) |
157 |
include 'common_B.f' |
158 |
|
159 |
|
160 |
c------------------------------------------------------------------------ |
161 |
c |
162 |
c local variables |
163 |
c |
164 |
c------------------------------------------------------------------------ |
165 |
|
166 |
real*8 x,y,z !point of interpolation |
167 |
real*8 res(3) !interpolated B components: res = (Bx, By, Bz) |
168 |
real*8 res1(3),res2(3) !interpolated B components for the two maps |
169 |
|
170 |
integer ic !index for B components: |
171 |
! ic=1 ---> Bx |
172 |
! ic=2 ---> By |
173 |
! ic=3 ---> Bz |
174 |
|
175 |
integer cube(3) !vector of indexes identifying the cube |
176 |
! containing the point of interpolation |
177 |
! (see later...) |
178 |
|
179 |
real*8 xl,xh,yl,yh,zl,zh !cube vertexes coordinates |
180 |
|
181 |
real*8 xr,yr,zr !reduced variables (coordinates of the |
182 |
! point of interpolation inside the cube) |
183 |
|
184 |
real*8 Bp(8) !vector of values of B component |
185 |
! being computed, on the eight cube vertexes |
186 |
|
187 |
|
188 |
c------------------------------------------------------------------------ |
189 |
c |
190 |
c *** FIRST MAP *** |
191 |
c |
192 |
c------------------------------------------------------------------------ |
193 |
|
194 |
do ic=1,3 !loops on the three B components |
195 |
|
196 |
c------------------------------------------------------------------------ |
197 |
c |
198 |
c chooses the coordinates interval containing the input point |
199 |
c |
200 |
c------------------------------------------------------------------------ |
201 |
c e.g.: |
202 |
c |
203 |
c x1 x2 x3 x4 x5... |
204 |
c |-----|-+---|-----|-----|---- |
205 |
c ~~~~~~~~x |
206 |
c |
207 |
c in this case the right interval is identified by indexes 2-3, so the |
208 |
c value assigned to cube variable is 2 |
209 |
|
210 |
cube(1)=INT((nx-1)*(x-px1min(ic))/(px1max(ic)-px1min(ic))) +1 |
211 |
cube(2)=INT((ny-1)*(y-py1min(ic))/(py1max(ic)-py1min(ic))) +1 |
212 |
cube(3)=INT((nz-1)*(z-pz1min(ic))/(pz1max(ic)-pz1min(ic))) +1 |
213 |
|
214 |
c------------------------------------------------------------------------ |
215 |
c |
216 |
c if the point falls beyond the extremes of the grid... |
217 |
c |
218 |
c------------------------------------------------------------------------ |
219 |
c |
220 |
c ~~~~~~~~~~x1 x2 x3... |
221 |
c - - + - - |-----|-----|---- |
222 |
c ~~~~x |
223 |
c |
224 |
c in the case cube = 1 |
225 |
c |
226 |
c |
227 |
c ...nx-2 nx-1 nx |
228 |
c ----|-----|-----| - - - + - - |
229 |
c ~~~~~~~~~~~~~~~~~~~~~~~~x |
230 |
c |
231 |
c in this case cube = nx-1 |
232 |
|
233 |
if (cube(1).le.0) cube(1) = 1 |
234 |
if (cube(2).le.0) cube(2) = 1 |
235 |
if (cube(3).le.0) cube(3) = 1 |
236 |
if (cube(1).ge.nx) cube(1) = nx-1 |
237 |
if (cube(2).ge.ny) cube(2) = ny-1 |
238 |
if (cube(3).ge.nz) cube(3) = nz-1 |
239 |
|
240 |
|
241 |
c------------------------------------------------------------------------ |
242 |
c |
243 |
c temporary variables definition for field computation |
244 |
c |
245 |
c------------------------------------------------------------------------ |
246 |
|
247 |
xl = px1(cube(1),ic) !X coordinates of cube vertexes |
248 |
xh = px1(cube(1)+1,ic) |
249 |
|
250 |
yl = py1(cube(2),ic) !Y coordinates of cube vertexes |
251 |
yh = py1(cube(2)+1,ic) |
252 |
|
253 |
zl = pz1(cube(3),ic) !Z coordinates of cube vertexes |
254 |
zh = pz1(cube(3)+1,ic) |
255 |
|
256 |
xr = (x-xl) / (xh-xl) !reduced variables |
257 |
yr = (y-yl) / (yh-yl) |
258 |
zr = (z-zl) / (zh-zl) |
259 |
|
260 |
Bp(1) = b1(cube(1) ,cube(2) ,cube(3) ,ic) !ic-th component of B |
261 |
Bp(2) = b1(cube(1)+1,cube(2) ,cube(3) ,ic) ! on the eight cube |
262 |
Bp(3) = b1(cube(1) ,cube(2)+1,cube(3) ,ic) ! vertexes |
263 |
Bp(4) = b1(cube(1)+1,cube(2)+1,cube(3) ,ic) |
264 |
Bp(5) = b1(cube(1) ,cube(2) ,cube(3)+1,ic) |
265 |
Bp(6) = b1(cube(1)+1,cube(2) ,cube(3)+1,ic) |
266 |
Bp(7) = b1(cube(1) ,cube(2)+1,cube(3)+1,ic) |
267 |
Bp(8) = b1(cube(1)+1,cube(2)+1,cube(3)+1,ic) |
268 |
|
269 |
c------------------------------------------------------------------------ |
270 |
c |
271 |
c computes interpolated ic-th component of B in (x,y,z) |
272 |
c |
273 |
c------------------------------------------------------------------------ |
274 |
|
275 |
res1(ic) = |
276 |
+ Bp(1)*(1-xr)*(1-yr)*(1-zr) + |
277 |
+ Bp(2)*xr*(1-yr)*(1-zr) + |
278 |
+ Bp(3)*(1-xr)*yr*(1-zr) + |
279 |
+ Bp(4)*xr*yr*(1-zr) + |
280 |
+ Bp(5)*(1-xr)*(1-yr)*zr + |
281 |
+ Bp(6)*xr*(1-yr)*zr + |
282 |
+ Bp(7)*(1-xr)*yr*zr + |
283 |
+ Bp(8)*xr*yr*zr |
284 |
|
285 |
|
286 |
enddo |
287 |
|
288 |
c------------------------------------------------------------------------ |
289 |
c |
290 |
c *** SECOND MAP *** |
291 |
c |
292 |
c------------------------------------------------------------------------ |
293 |
|
294 |
c second map is rotated by 180 degree along the Z axis. so change sign |
295 |
c of x and y coordinates and then change sign to Bx and By components |
296 |
c to obtain the correct result |
297 |
|
298 |
x=-x |
299 |
y=-y |
300 |
|
301 |
do ic=1,3 |
302 |
|
303 |
cube(1)=INT((nx-1)*(x-px2min(ic))/(px2max(ic)-px2min(ic))) +1 |
304 |
cube(2)=INT((ny-1)*(y-py2min(ic))/(py2max(ic)-py2min(ic))) +1 |
305 |
cube(3)=INT((nz-1)*(z-pz2min(ic))/(pz2max(ic)-pz2min(ic))) +1 |
306 |
|
307 |
if (cube(1).le.0) cube(1) = 1 |
308 |
if (cube(2).le.0) cube(2) = 1 |
309 |
if (cube(3).le.0) cube(3) = 1 |
310 |
if (cube(1).ge.nx) cube(1) = nx-1 |
311 |
if (cube(2).ge.ny) cube(2) = ny-1 |
312 |
if (cube(3).ge.nz) cube(3) = nz-1 |
313 |
|
314 |
xl = px2(cube(1),ic) |
315 |
xh = px2(cube(1)+1,ic) |
316 |
|
317 |
yl = py2(cube(2),ic) |
318 |
yh = py2(cube(2)+1,ic) |
319 |
|
320 |
zl = pz2(cube(3),ic) |
321 |
zh = pz2(cube(3)+1,ic) |
322 |
|
323 |
xr = (x-xl) / (xh-xl) |
324 |
yr = (y-yl) / (yh-yl) |
325 |
zr = (z-zl) / (zh-zl) |
326 |
|
327 |
Bp(1) = b2(cube(1) ,cube(2) ,cube(3) ,ic) |
328 |
Bp(2) = b2(cube(1)+1,cube(2) ,cube(3) ,ic) |
329 |
Bp(3) = b2(cube(1) ,cube(2)+1,cube(3) ,ic) |
330 |
Bp(4) = b2(cube(1)+1,cube(2)+1,cube(3) ,ic) |
331 |
Bp(5) = b2(cube(1) ,cube(2) ,cube(3)+1,ic) |
332 |
Bp(6) = b2(cube(1)+1,cube(2) ,cube(3)+1,ic) |
333 |
Bp(7) = b2(cube(1) ,cube(2)+1,cube(3)+1,ic) |
334 |
Bp(8) = b2(cube(1)+1,cube(2)+1,cube(3)+1,ic) |
335 |
|
336 |
res2(ic) = |
337 |
+ Bp(1)*(1-xr)*(1-yr)*(1-zr) + |
338 |
+ Bp(2)*xr*(1-yr)*(1-zr) + |
339 |
+ Bp(3)*(1-xr)*yr*(1-zr) + |
340 |
+ Bp(4)*xr*yr*(1-zr) + |
341 |
+ Bp(5)*(1-xr)*(1-yr)*zr + |
342 |
+ Bp(6)*xr*(1-yr)*zr + |
343 |
+ Bp(7)*(1-xr)*yr*zr + |
344 |
+ Bp(8)*xr*yr*zr |
345 |
|
346 |
enddo |
347 |
|
348 |
c change Bx and By components sign |
349 |
res2(1)=-res2(1) |
350 |
res2(2)=-res2(2) |
351 |
|
352 |
c change back the x and y coordinate signs |
353 |
x=-x |
354 |
y=-y |
355 |
|
356 |
|
357 |
c------------------------------------------------------------------------ |
358 |
c |
359 |
c average the two maps results |
360 |
c |
361 |
c------------------------------------------------------------------------ |
362 |
|
363 |
do ic=1,3 |
364 |
res(ic)=(res1(ic)+res2(ic))/2 |
365 |
enddo |
366 |
|
367 |
|
368 |
return |
369 |
end |
370 |
************************************************************************* |
371 |
* |
372 |
* Subroutine inter_B_outer.f |
373 |
* |
374 |
* it computes the magnetic field in a chosen point x,y,z OUTSIDE the |
375 |
* magnetic cavity, using a trilinear interpolation of |
376 |
* B field measurements (read before by means of ./read_B.f) |
377 |
* the value is computed for the outer map |
378 |
* |
379 |
* needs: |
380 |
* - ../common/common_B_outer.f |
381 |
* |
382 |
* input: coordinates in m |
383 |
* output: magnetic field in T |
384 |
* |
385 |
************************************************************************* |
386 |
|
387 |
subroutine inter_B_outer(x,y,z,res) !coordinates in m, magnetic field in T |
388 |
|
389 |
implicit double precision (a-h,o-z) |
390 |
include 'common_B.f' |
391 |
|
392 |
|
393 |
c------------------------------------------------------------------------ |
394 |
c |
395 |
c local variables |
396 |
c |
397 |
c------------------------------------------------------------------------ |
398 |
|
399 |
real*8 x,y,z !point of interpolation |
400 |
real*8 res(3) !interpolated B components: res = (Bx, By, Bz) |
401 |
real*8 zin |
402 |
|
403 |
integer ic |
404 |
c !index for B components: |
405 |
c ! ic=1 ---> Bx |
406 |
c ! ic=2 ---> By |
407 |
c ! ic=3 ---> Bz |
408 |
|
409 |
integer cube(3) |
410 |
c !vector of indexes identifying the cube |
411 |
c ! containing the point of interpolation |
412 |
c ! (see later...) |
413 |
|
414 |
real*8 xl,xh,yl,yh,zl,zh !cube vertexes coordinates |
415 |
|
416 |
real*8 xr,yr,zr |
417 |
c !reduced variables (coordinates of the |
418 |
c ! point of interpolation inside the cube) |
419 |
|
420 |
real*8 Bp(8) |
421 |
c !vector of values of B component |
422 |
c ! being computed, on the eight cube vertexes |
423 |
|
424 |
|
425 |
c LOWER MAP |
426 |
c ---> up/down simmetry |
427 |
zin=z |
428 |
if(zin.le.edgelzmax)z=-z |
429 |
|
430 |
c------------------------------------------------------------------------ |
431 |
c |
432 |
c *** MAP *** |
433 |
c |
434 |
c------------------------------------------------------------------------ |
435 |
|
436 |
do ic=1,3 !loops on the three B components |
437 |
|
438 |
c------------------------------------------------------------------------ |
439 |
c |
440 |
c chooses the coordinates interval containing the input point |
441 |
c |
442 |
c------------------------------------------------------------------------ |
443 |
c e.g.: |
444 |
c |
445 |
c x1 x2 x3 x4 x5... xN |
446 |
c |-----|-+---|-----|-----|---- ... ----|-----| |
447 |
c ~~~~~~~~x |
448 |
c |
449 |
c in this case the right interval is identified by indexes 2-3, so the |
450 |
c value assigned to cube variable is 2 |
451 |
|
452 |
cube(1)=INT((nox-1)*(x-poxmin(ic))/(poxmax(ic)-poxmin(ic))) +1 |
453 |
cube(2)=INT((noy-1)*(y-poymin(ic))/(poymax(ic)-poymin(ic))) +1 |
454 |
cube(3)=INT((noz-1)*(z-pozmin(ic))/(pozmax(ic)-pozmin(ic))) +1 |
455 |
|
456 |
c------------------------------------------------------------------------ |
457 |
c |
458 |
c if the point falls beyond the extremes of the grid... |
459 |
c |
460 |
c------------------------------------------------------------------------ |
461 |
c |
462 |
c ~~~~~~~~~~x1 x2 x3... |
463 |
c - - + - - |-----|-----|---- |
464 |
c ~~~~x |
465 |
c |
466 |
c in the case cube = 1 |
467 |
c |
468 |
c |
469 |
c ...nx-2 nx-1 nx |
470 |
c ----|-----|-----| - - - + - - |
471 |
c ~~~~~~~~~~~~~~~~~~~~~~~~x |
472 |
c |
473 |
c in this case cube = nx-1 |
474 |
|
475 |
if (cube(1).le.0) cube(1) = 1 |
476 |
if (cube(2).le.0) cube(2) = 1 |
477 |
if (cube(3).le.0) cube(3) = 1 |
478 |
if (cube(1).ge.nox) cube(1) = nox-1 |
479 |
if (cube(2).ge.noy) cube(2) = noy-1 |
480 |
if (cube(3).ge.noz) cube(3) = noz-1 |
481 |
|
482 |
|
483 |
c------------------------------------------------------------------------ |
484 |
c |
485 |
c temporary variables definition for field computation |
486 |
c |
487 |
c------------------------------------------------------------------------ |
488 |
|
489 |
xl = pox(cube(1),ic) !X coordinates of cube vertexes |
490 |
xh = pox(cube(1)+1,ic) |
491 |
|
492 |
yl = poy(cube(2),ic) !Y coordinates of cube vertexes |
493 |
yh = poy(cube(2)+1,ic) |
494 |
|
495 |
zl = poz(cube(3),ic) !Z coordinates of cube vertexes |
496 |
zh = poz(cube(3)+1,ic) |
497 |
|
498 |
xr = (x-xl) / (xh-xl) !reduced variables |
499 |
yr = (y-yl) / (yh-yl) |
500 |
zr = (z-zl) / (zh-zl) |
501 |
|
502 |
Bp(1) = bo(cube(1) ,cube(2) ,cube(3) ,ic) !ic-th component of B |
503 |
Bp(2) = bo(cube(1)+1,cube(2) ,cube(3) ,ic) ! on the eight cube |
504 |
Bp(3) = bo(cube(1) ,cube(2)+1,cube(3) ,ic) ! vertexes |
505 |
Bp(4) = bo(cube(1)+1,cube(2)+1,cube(3) ,ic) |
506 |
Bp(5) = bo(cube(1) ,cube(2) ,cube(3)+1,ic) |
507 |
Bp(6) = bo(cube(1)+1,cube(2) ,cube(3)+1,ic) |
508 |
Bp(7) = bo(cube(1) ,cube(2)+1,cube(3)+1,ic) |
509 |
Bp(8) = bo(cube(1)+1,cube(2)+1,cube(3)+1,ic) |
510 |
|
511 |
c------------------------------------------------------------------------ |
512 |
c |
513 |
c computes interpolated ic-th component of B in (x,y,z) |
514 |
c |
515 |
c------------------------------------------------------------------------ |
516 |
|
517 |
res(ic) = |
518 |
+ Bp(1)*(1-xr)*(1-yr)*(1-zr) + |
519 |
+ Bp(2)*xr*(1-yr)*(1-zr) + |
520 |
+ Bp(3)*(1-xr)*yr*(1-zr) + |
521 |
+ Bp(4)*xr*yr*(1-zr) + |
522 |
+ Bp(5)*(1-xr)*(1-yr)*zr + |
523 |
+ Bp(6)*xr*(1-yr)*zr + |
524 |
+ Bp(7)*(1-xr)*yr*zr + |
525 |
+ Bp(8)*xr*yr*zr |
526 |
|
527 |
|
528 |
enddo |
529 |
|
530 |
c LOWER MAP |
531 |
c ---> up/down simmetry |
532 |
if(zin.le.edgelzmax)then |
533 |
z=-z !back to initial ccoordinate |
534 |
res(3)=-res(3) !invert BZ component |
535 |
endif |
536 |
|
537 |
return |
538 |
end |