Actual source code: chwirut1f.F

tao-2.1-p0 2012-07-24
  1: !  Program usage: mpirun -np 1 chwirut1f [-help] [all TAO options] 
  2: !
  3: !  Description:  This example demonstrates use of the TAO package to solve a
  4: !  nonlinear least-squares problem on a single processor.  We minimize the 
  5: !  Chwirut function: 
  6: !       sum_{i=0}^{n/2-1} ( alpha*(x_{2i+1}-x_{2i}^2)^2 + (1-x_{2i})^2 )
  7: !
  8: !  The C version of this code is test_chwirut1.c
  9: !
 10: !/*T
 11: !  Concepts: TAO - Solving an unconstrained minimization problem
 12: !  Routines: TaoInitialize(); TaoFinalize(); 
 13: !  Routines: TaoCreate();
 14: !  Routines: TaoSetType(); 
 15: !  Routines: TaoSetInitialVector();
 16: !  Routines: TaoSetSeparableObjectiveRoutine();
 17: !  Routines: TaoSetMonitor();
 18: !  Routines: TaoSetFromOptions();
 19: !  Routines: TaoSolve();
 20: !  Routines: TaoDestroy(); 
 21: !  Processors: 1
 22: !T*/ 
 23: !
 24: ! ---------------------------------------------------------------------- 
 25: !
 26:       implicit none

 28: #include "chwirut1f.h"

 30: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 31: !                   Variable declarations
 32: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 33: !
 34: !  See additional variable declarations in the file chwirut1f.h

 36:       PetscErrorCode   ierr    ! used to check for functions returning nonzeros
 37:       Vec              x       ! solution vector
 38:       Vec              f       ! vector of functions
 39:       TaoSolver        tao     ! TaoSolver context
 40:       PetscBool       flg     
 41:       PetscInt         i,nhist
 42:       integer          size,rank    ! number of processes running
 43:       PetscReal      zero
 44:       PetscReal      hist(100) ! objective value history
 45:       PetscReal      resid(100)! residual history
 46:       PetscReal      cnorm(100)! cnorm history
 47:       TaoSolverTerminationReason reason

 49:       


 52: !  Note: Any user-defined Fortran routines (such as FormGradient)
 53: !  MUST be declared as external.

 55:       external FormFunction

 57:       zero = 0.0d0

 59: !  Initialize TAO and PETSc
 60:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 61:       call TaoInitialize(PETSC_NULL_CHARACTER,ierr)

 63:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
 64:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
 65:       if (size .ne. 1) then
 66:          if (rank .eq. 0) then
 67:             write(6,*) 'This is a uniprocessor example only!'
 68:          endif
 69:          SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
 70:       endif

 72: !  Initialize problem parameters
 73:       m = 214
 74:       n = 3


 77: !  Allocate vectors for the solution and gradient
 78:       call VecCreateSeq(PETSC_COMM_SELF,n,x,ierr)
 79:       call VecCreateSeq(PETSC_COMM_SELF,m,f,ierr)


 82: !  The TAO code begins here 

 84: !  Create TAO solver
 85:       call TaoCreate(PETSC_COMM_SELF,tao,ierr)
 86:       CHKERRQ(ierr)
 87:       call TaoSetType(tao,'tao_pounders',ierr)
 88:       CHKERRQ(ierr)
 89: !  Set routines for function, gradient, and hessian evaluation 

 91:       call TaoSetSeparableObjectiveRoutine(tao,f,                       &
 92:      &      FormFunction,PETSC_NULL_OBJECT,ierr)
 93:       CHKERRQ(ierr)

 95: !  Optional: Set initial guess
 96:       call InitializeData()
 97:       call FormStartingPoint(x)
 98:       call TaoSetInitialVector(tao, x, ierr)
 99:       CHKERRQ(ierr)


102: !  Check for TAO command line options
103:       call TaoSetFromOptions(tao,ierr)
104:       CHKERRQ(ierr)
105:       call TaoSetHistory(tao,hist,resid,cnorm,                          &
106:      &     100,PETSC_TRUE,ierr)
107:       CHKERRQ(ierr)
108: !  SOLVE THE APPLICATION
109:       call TaoSolve(tao,ierr)
110:       CHKERRQ(ierr)
111:       call TaoGetHistory(tao,nhist,ierr)
112:       CHKERRQ(ierr)
113:       do i=1,nhist
114:          print *,hist(i),resid(i)
115:       enddo
116:       call TaoGetTerminationReason(tao, reason, ierr)
117:       if (reason .le. 0) then
118:          print *,'Try a different TAO method, adjust some parameters,'
119:          print *,'or check the function evaluation routines.'
120:       endif
121: !  TaoView() prints ierr about the TAO solver; the option
122: !      -tao_view 
123: !  can alternatively be used to activate this at runtime.
124:       call TaoView(tao,PETSC_VIEWER_STDOUT_SELF,ierr)
125:       

127: !  Free TAO data structures
128:       call TaoDestroy(tao,ierr)

130: !  Free PETSc data structures 
131:       call VecDestroy(x,ierr)
132:       call VecDestroy(f,ierr)

134: !  Finalize TAO 
135:       call TaoFinalize(ierr)
136:       call PetscFinalize(ierr)

138:       end


141: ! --------------------------------------------------------------------
142: !  FormFunction - Evaluates the function f(X) and gradient G(X)
143: !
144: !  Input Parameters:
145: !  tao - the TaoSolver context
146: !  X   - input vector
147: !  dummy - not used
148: !
149: !  Output Parameters:
150: !  f - function vector
151:       
152:       subroutine FormFunction(tao, x, f, dummy, ierr)
153:       implicit none

155: ! n,alpha defined in chwirut1f.h
156: #include "chwirut1f.h"

158:       TaoSolver        tao
159:       Vec              x,f
160:       PetscErrorCode   ierr
161:       PetscInt         dummy

163:       PetscInt         i

165: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
166: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
167: ! will return an array of doubles referenced by x_array offset by x_index.
168: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
169: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
170:       PetscReal        f_v(0:1),x_v(0:1)
171:       PetscOffset      f_i,x_i

173:       0

175: !     Get pointers to vector data
176:       call VecGetArray(x,x_v,x_i,ierr)
177:       CHKERRQ(ierr)
178:       call VecGetArray(f,f_v,f_i,ierr)
179:       CHKERRQ(ierr)


182: !     Compute F(X)
183:       do i=0,m-1
184:          f_v(f_i+i) = y(i) - exp(-x_v(x_i+0)*t(i))/                      &
185:      &    (x_v(x_i+1) + x_v(x_i+2)*t(i))

187:       enddo


190: !     Restore vectors
191:       call VecRestoreArray(X,x_v,x_i,ierr)
192:       CHKERRQ(ierr)
193:       call VecRestoreArray(F,f_v,f_i,ierr)
194:       CHKERRQ(ierr)
195:       
196:       
197:       return
198:       end





204:       subroutine FormStartingPoint(x)
205:       implicit none

207: ! n,alpha defined in chwirut1f.h
208: #include "chwirut1f.h"
209:       Vec             x
210:       PetscReal       x_v(0:1)
211:       PetscOffset     x_i
212:       PetscErrorCode  ierr
213:       
214:       call VecGetArray(x,x_v,x_i,ierr)
215:       x_v(x_i) = 0.15d0
216:       x_v(x_i+1) = 0.008d0
217:       x_v(x_i+2) = 0.01d0
218:       call VecRestoreArray(x,x_v,x_i,ierr)
219:       return
220:       end


223:       subroutine InitializeData()
224:       implicit none

226: ! n,alpha defined in chwirut1f.h
227: #include "chwirut1f.h"
228:       integer i
229:       i=0
230:       y(i) =    92.9000;  t(i) =  0.5000; i=i+1
231:       y(i) =    78.7000;  t(i) =   0.6250; i=i+1
232:       y(i) =    64.2000;  t(i) =   0.7500; i=i+1
233:       y(i) =    64.9000;  t(i) =   0.8750; i=i+1
234:       y(i) =    57.1000;  t(i) =   1.0000; i=i+1
235:       y(i) =    43.3000;  t(i) =   1.2500; i=i+1
236:       y(i) =    31.1000;  t(i) =  1.7500; i=i+1
237:       y(i) =    23.6000;  t(i) =  2.2500; i=i+1
238:       y(i) =    31.0500;  t(i) =  1.7500; i=i+1
239:       y(i) =    23.7750;  t(i) =  2.2500; i=i+1
240:       y(i) =    17.7375;  t(i) =  2.7500; i=i+1
241:       y(i) =    13.8000;  t(i) =  3.2500; i=i+1
242:       y(i) =    11.5875;  t(i) =  3.7500; i=i+1
243:       y(i) =     9.4125;  t(i) =  4.2500; i=i+1
244:       y(i) =     7.7250;  t(i) =  4.7500; i=i+1
245:       y(i) =     7.3500;  t(i) =  5.2500; i=i+1
246:       y(i) =     8.0250;  t(i) =  5.7500; i=i+1
247:       y(i) =    90.6000;  t(i) =  0.5000; i=i+1
248:       y(i) =    76.9000;  t(i) =  0.6250; i=i+1
249:       y(i) =    71.6000;  t(i) = 0.7500; i=i+1
250:       y(i) =    63.6000;  t(i) =  0.8750; i=i+1
251:       y(i) =    54.0000;  t(i) =  1.0000; i=i+1
252:       y(i) =    39.2000;  t(i) =  1.2500; i=i+1
253:       y(i) =    29.3000;  t(i) = 1.7500; i=i+1
254:       y(i) =    21.4000;  t(i) =  2.2500; i=i+1
255:       y(i) =    29.1750;  t(i) =  1.7500; i=i+1
256:       y(i) =    22.1250;  t(i) =  2.2500; i=i+1
257:       y(i) =    17.5125;  t(i) =  2.7500; i=i+1
258:       y(i) =    14.2500;  t(i) =  3.2500; i=i+1
259:       y(i) =     9.4500;  t(i) =  3.7500; i=i+1
260:       y(i) =     9.1500;  t(i) =  4.2500; i=i+1
261:       y(i) =     7.9125;  t(i) =  4.7500; i=i+1
262:       y(i) =     8.4750;  t(i) =  5.2500; i=i+1
263:       y(i) =     6.1125;  t(i) =  5.7500; i=i+1
264:       y(i) =    80.0000;  t(i) =  0.5000; i=i+1
265:       y(i) =    79.0000;  t(i) =  0.6250; i=i+1
266:       y(i) =    63.8000;  t(i) =  0.7500; i=i+1
267:       y(i) =    57.2000;  t(i) =  0.8750; i=i+1
268:       y(i) =    53.2000;  t(i) =  1.0000; i=i+1
269:       y(i) =    42.5000;  t(i) =  1.2500; i=i+1
270:       y(i) =    26.8000;  t(i) =  1.7500; i=i+1
271:       y(i) =    20.4000;  t(i) =  2.2500; i=i+1
272:       y(i) =    26.8500;  t(i) =   1.7500; i=i+1
273:       y(i) =    21.0000;  t(i) =   2.2500; i=i+1
274:       y(i) =    16.4625;  t(i) =   2.7500; i=i+1
275:       y(i) =    12.5250;  t(i) =   3.2500; i=i+1
276:       y(i) =    10.5375;  t(i) =   3.7500; i=i+1
277:       y(i) =     8.5875;  t(i) =   4.2500; i=i+1
278:       y(i) =     7.1250;  t(i) =   4.7500; i=i+1
279:       y(i) =     6.1125;  t(i) =   5.2500; i=i+1
280:       y(i) =     5.9625;  t(i) =   5.7500; i=i+1
281:       y(i) =    74.1000;  t(i) =   0.5000; i=i+1
282:       y(i) =    67.3000;  t(i) =   0.6250; i=i+1
283:       y(i) =    60.8000;  t(i) =   0.7500; i=i+1
284:       y(i) =    55.5000;  t(i) =   0.8750; i=i+1
285:       y(i) =    50.3000;  t(i) =   1.0000; i=i+1
286:       y(i) =    41.0000;  t(i) =   1.2500; i=i+1
287:       y(i) =    29.4000;  t(i) =   1.7500; i=i+1
288:       y(i) =    20.4000;  t(i) =   2.2500; i=i+1
289:       y(i) =    29.3625;  t(i) =   1.7500; i=i+1
290:       y(i) =    21.1500;  t(i) =   2.2500; i=i+1
291:       y(i) =    16.7625;  t(i) =   2.7500; i=i+1
292:       y(i) =    13.2000;  t(i) =   3.2500; i=i+1
293:       y(i) =    10.8750;  t(i) =   3.7500; i=i+1
294:       y(i) =     8.1750;  t(i) =   4.2500; i=i+1
295:       y(i) =     7.3500;  t(i) =   4.7500; i=i+1
296:       y(i) =     5.9625;  t(i) =  5.2500; i=i+1
297:       y(i) =     5.6250;  t(i) =   5.7500; i=i+1
298:       y(i) =    81.5000;  t(i) =    .5000; i=i+1
299:       y(i) =    62.4000;  t(i) =    .7500; i=i+1
300:       y(i) =    32.5000;  t(i) =   1.5000; i=i+1
301:       y(i) =    12.4100;  t(i) =   3.0000; i=i+1
302:       y(i) =    13.1200;  t(i) =   3.0000; i=i+1
303:       y(i) =    15.5600;  t(i) =   3.0000; i=i+1
304:       y(i) =     5.6300;  t(i) =   6.0000; i=i+1
305:       y(i) =    78.0000;  t(i) =   .5000; i=i+1
306:       y(i) =    59.9000;  t(i) =    .7500; i=i+1
307:       y(i) =    33.2000;  t(i) =   1.5000; i=i+1
308:       y(i) =    13.8400;  t(i) =   3.0000; i=i+1
309:       y(i) =    12.7500;  t(i) =   3.0000; i=i+1
310:       y(i) =    14.6200;  t(i) =   3.0000; i=i+1
311:       y(i) =     3.9400;  t(i) =   6.0000; i=i+1
312:       y(i) =    76.8000;  t(i) =    .5000; i=i+1
313:       y(i) =    61.0000;  t(i) =    .7500; i=i+1
314:       y(i) =    32.9000;  t(i) =   1.5000; i=i+1
315:       y(i) =    13.8700;  t(i) = 3.0000; i=i+1
316:       y(i) =    11.8100;  t(i) =   3.0000; i=i+1
317:       y(i) =    13.3100;  t(i) =   3.0000; i=i+1
318:       y(i) =     5.4400;  t(i) =   6.0000; i=i+1
319:       y(i) =    78.0000;  t(i) =    .5000; i=i+1
320:       y(i) =    63.5000;  t(i) =    .7500; i=i+1
321:       y(i) =    33.8000;  t(i) =   1.5000; i=i+1
322:       y(i) =    12.5600;  t(i) =   3.0000; i=i+1
323:       y(i) =     5.6300;  t(i) =   6.0000; i=i+1
324:       y(i) =    12.7500;  t(i) =   3.0000; i=i+1
325:       y(i) =    13.1200;  t(i) =   3.0000; i=i+1
326:       y(i) =     5.4400;  t(i) =   6.0000; i=i+1
327:       y(i) =    76.8000;  t(i) =    .5000; i=i+1
328:       y(i) =    60.0000;  t(i) =    .7500; i=i+1
329:       y(i) =    47.8000;  t(i) =   1.0000; i=i+1
330:       y(i) =    32.0000;  t(i) =   1.5000; i=i+1
331:       y(i) =    22.2000;  t(i) =   2.0000; i=i+1
332:       y(i) =    22.5700;  t(i) =   2.0000; i=i+1
333:       y(i) =    18.8200;  t(i) =   2.5000; i=i+1
334:       y(i) =    13.9500;  t(i) =   3.0000; i=i+1
335:       y(i) =    11.2500;  t(i) =   4.0000; i=i+1
336:       y(i) =     9.0000;  t(i) =   5.0000; i=i+1
337:       y(i) =     6.6700;  t(i) =   6.0000; i=i+1
338:       y(i) =    75.8000;  t(i) =    .5000; i=i+1
339:       y(i) =    62.0000;  t(i) =    .7500; i=i+1
340:       y(i) =    48.8000;  t(i) =   1.0000; i=i+1
341:       y(i) =    35.2000;  t(i) =   1.5000; i=i+1
342:       y(i) =    20.0000;  t(i) =   2.0000; i=i+1
343:       y(i) =    20.3200;  t(i) =   2.0000; i=i+1
344:       y(i) =    19.3100;  t(i) =   2.5000; i=i+1
345:       y(i) =    12.7500;  t(i) =   3.0000; i=i+1
346:       y(i) =    10.4200;  t(i) =   4.0000; i=i+1
347:       y(i) =     7.3100;  t(i) =   5.0000; i=i+1
348:       y(i) =     7.4200;  t(i) =   6.0000; i=i+1
349:       y(i) =    70.5000;  t(i) =    .5000; i=i+1
350:       y(i) =    59.5000;  t(i) =    .7500; i=i+1
351:       y(i) =    48.5000;  t(i) =   1.0000; i=i+1
352:       y(i) =    35.8000;  t(i) =   1.5000; i=i+1
353:       y(i) =    21.0000;  t(i) =   2.0000; i=i+1
354:       y(i) =    21.6700;  t(i) =   2.0000; i=i+1
355:       y(i) =    21.0000;  t(i) =   2.5000; i=i+1
356:       y(i) =    15.6400;  t(i) =   3.0000; i=i+1
357:       y(i) =     8.1700;  t(i) =   4.0000; i=i+1
358:       y(i) =     8.5500;  t(i) =   5.0000; i=i+1
359:       y(i) =    10.1200;  t(i) =   6.0000; i=i+1
360:       y(i) =    78.0000;  t(i) =    .5000; i=i+1
361:       y(i) =    66.0000;  t(i) =    .6250; i=i+1
362:       y(i) =    62.0000;  t(i) =    .7500; i=i+1
363:       y(i) =    58.0000;  t(i) =    .8750; i=i+1
364:       y(i) =    47.7000;  t(i) =   1.0000; i=i+1
365:       y(i) =    37.8000;  t(i) =   1.2500; i=i+1
366:       y(i) =    20.2000;  t(i) =   2.2500; i=i+1
367:       y(i) =    21.0700;  t(i) =   2.2500; i=i+1
368:       y(i) =    13.8700;  t(i) =   2.7500; i=i+1
369:       y(i) =     9.6700;  t(i) =   3.2500; i=i+1
370:       y(i) =     7.7600;  t(i) =   3.7500; i=i+1
371:       y(i) =     5.4400;  t(i) =  4.2500; i=i+1
372:       y(i) =     4.8700;  t(i) =  4.7500; i=i+1
373:       y(i) =     4.0100;  t(i) =   5.2500; i=i+1
374:       y(i) =     3.7500;  t(i) =   5.7500; i=i+1
375:       y(i) =    24.1900;  t(i) =   3.0000; i=i+1
376:       y(i) =    25.7600;  t(i) =   3.0000; i=i+1
377:       y(i) =    18.0700;  t(i) =   3.0000; i=i+1
378:       y(i) =    11.8100;  t(i) =   3.0000; i=i+1
379:       y(i) =    12.0700;  t(i) =   3.0000; i=i+1
380:       y(i) =    16.1200;  t(i) =   3.0000; i=i+1
381:       y(i) =    70.8000;  t(i) =    .5000; i=i+1
382:       y(i) =    54.7000;  t(i) =    .7500; i=i+1
383:       y(i) =    48.0000;  t(i) =   1.0000; i=i+1
384:       y(i) =    39.8000;  t(i) =   1.5000; i=i+1
385:       y(i) =    29.8000;  t(i) =   2.0000; i=i+1
386:       y(i) =    23.7000;  t(i) =   2.5000; i=i+1
387:       y(i) =    29.6200;  t(i) =   2.0000; i=i+1
388:       y(i) =    23.8100;  t(i) =   2.5000; i=i+1
389:       y(i) =    17.7000;  t(i) =   3.0000; i=i+1
390:       y(i) =    11.5500;  t(i) =   4.0000; i=i+1
391:       y(i) =    12.0700;  t(i) =   5.0000; i=i+1
392:       y(i) =     8.7400;  t(i) =   6.0000; i=i+1
393:       y(i) =    80.7000;  t(i) =    .5000; i=i+1
394:       y(i) =    61.3000;  t(i) =    .7500; i=i+1
395:       y(i) =    47.5000;  t(i) =   1.0000; i=i+1
396:       y(i) =    29.0000;  t(i) =   1.5000; i=i+1
397:       y(i) =    24.0000;  t(i) =   2.0000; i=i+1
398:       y(i) =    17.7000;  t(i) =   2.5000; i=i+1
399:       y(i) =    24.5600;  t(i) =   2.0000; i=i+1
400:       y(i) =    18.6700;  t(i) =   2.5000; i=i+1
401:       y(i) =    16.2400;  t(i) =   3.0000; i=i+1
402:       y(i) =     8.7400;  t(i) =   4.0000; i=i+1
403:       y(i) =     7.8700;  t(i) =   5.0000; i=i+1
404:       y(i) =     8.5100;  t(i) =   6.0000; i=i+1
405:       y(i) =    66.7000;  t(i) =    .5000; i=i+1
406:       y(i) =    59.2000;  t(i) =    .7500; i=i+1
407:       y(i) =    40.8000;  t(i) =   1.0000; i=i+1
408:       y(i) =    30.7000;  t(i) =   1.5000; i=i+1
409:       y(i) =    25.7000;  t(i) =   2.0000; i=i+1
410:       y(i) =    16.3000;  t(i) =   2.5000; i=i+1
411:       y(i) =    25.9900;  t(i) =   2.0000; i=i+1
412:       y(i) =    16.9500;  t(i) =   2.5000; i=i+1
413:       y(i) =    13.3500;  t(i) =   3.0000; i=i+1
414:       y(i) =     8.6200;  t(i) =   4.0000; i=i+1
415:       y(i) =     7.2000;  t(i) =   5.0000; i=i+1
416:       y(i) =     6.6400;  t(i) =   6.0000; i=i+1
417:       y(i) =    13.6900;  t(i) =   3.0000; i=i+1
418:       y(i) =    81.0000;  t(i) =    .5000; i=i+1
419:       y(i) =    64.5000;  t(i) =    .7500; i=i+1
420:       y(i) =    35.5000;  t(i) =   1.5000; i=i+1
421:       y(i) =    13.3100;  t(i) =   3.0000; i=i+1
422:       y(i) =     4.8700;  t(i) =   6.0000; i=i+1
423:       y(i) =    12.9400;  t(i) =   3.0000; i=i+1
424:       y(i) =     5.0600;  t(i) =   6.0000; i=i+1
425:       y(i) =    15.1900;  t(i) =   3.0000; i=i+1
426:       y(i) =    14.6200;  t(i) =   3.0000; i=i+1
427:       y(i) =    15.6400;  t(i) =   3.0000; i=i+1
428:       y(i) =    25.5000;  t(i) =   1.7500; i=i+1
429:       y(i) =    25.9500;  t(i) =   1.7500; i=i+1
430:       y(i) =    81.7000;  t(i) =    .5000; i=i+1
431:       y(i) =    61.6000;  t(i) =    .7500; i=i+1
432:       y(i) =    29.8000;  t(i) =   1.7500; i=i+1
433:       y(i) =    29.8100;  t(i) =   1.7500; i=i+1
434:       y(i) =    17.1700;  t(i) =   2.7500; i=i+1
435:       y(i) =    10.3900;  t(i) =   3.7500; i=i+1
436:       y(i) =    28.4000;  t(i) =   1.7500; i=i+1
437:       y(i) =    28.6900;  t(i) =   1.7500; i=i+1
438:       y(i) =    81.3000;  t(i) =    .5000; i=i+1
439:       y(i) =    60.9000;  t(i) =    .7500; i=i+1
440:       y(i) =    16.6500;  t(i) =   2.7500; i=i+1
441:       y(i) =    10.0500;  t(i) =   3.7500; i=i+1
442:       y(i) =    28.9000;  t(i) =   1.7500; i=i+1
443:       y(i) =    28.9500;  t(i) =   1.7500; i=i+1
444:       
445:       return
446:       end

448: