Actual source code: eptorsion2f.F
1: ! Program usage: mpirun -np <proc> eptorsion2f [all TAO options]
2: !
3: ! Description: This example demonstrates use of the TAO package to solve
4: ! unconstrained minimization problems in parallel. This example is based
5: ! on the Elastic-Plastic Torsion (dept) problem from the MINPACK-2 test suite.
6: ! The command line options are:
7: ! -mx <xg>, where <xg> = number of grid points in the 1st coordinate direction
8: ! -my <yg>, where <yg> = number of grid points in the 2nd coordinate direction
9: ! -par <param>, where <param> = angle of twist per unit length
10: !
11: !/*T
12: ! Concepts: TAO - Solving an unconstrained minimization problem
13: ! Routines: TaoInitialize(); TaoFinalize();
14: ! Routines: TaoCreate(); TaoSetType();
15: ! Routines: TaoSetInitialVector();
16: ! Routines: TaoSetObjectiveAndGradientRoutine();
17: ! Routines: TaoSetHessianRoutine(); TaoSetFromOptions();
18: ! Routines: TaoSetMonitor(); TaoSetConvergenceTest()
19: ! Routines: TaoSolve(); TaoGetSolutionStatus()
20: ! Routines: TaoGetTerminationReason(); TaoDestroy();
22: ! Processors: n
23: !T*/
24: !
25: ! ----------------------------------------------------------------------
26: !
27: ! Elastic-plastic torsion problem.
28: !
29: ! The elastic plastic torsion problem arises from the determination
30: ! of the stress field on an infinitely long cylindrical bar, which is
31: ! equivalent to the solution of the following problem:
32: ! min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
33: ! where C is the torsion angle per unit length.
34: !
35: ! The C version of this code is eptorsion2.c
36: !
37: ! ----------------------------------------------------------------------
39: implicit none
40: #include "eptorsion2f.h"
42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: ! Variable declarations
44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: !
46: ! See additional variable declarations in the file eptorsion2f.h
47: !
48: PetscErrorCode ierr ! used to check for functions returning nonzeros
49: Vec x ! solution vector
50: Mat H ! hessian matrix
51: PetscInt Nx, Ny ! number of processes in x- and y- directions
52: TaoSolver tao ! TaoSolver solver context
53: TaoSolverTerminationReason reason
54: PetscBool flg
55: PetscInt iter ! iteration information
56: PetscReal ff,gnorm,cnorm,xdiff
57: PetscInt i1
58: PetscInt dummy
59:
61: ! Note: Any user-defined Fortran routines (such as FormGradient)
62: ! MUST be declared as external.
64: external FormInitialGuess,FormFunctionGradient,ComputeHessian
65: external Monitor,ConvergenceTest
67: i1 = 1
69: ! Initialize TAO, PETSc contexts
70: call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
71: call TaoInitialize(PETSC_NULL_CHARACTER,ierr)
73: ! Specify default parameters
74: param = 5.0d0
75: mx = 10
76: my = 10
77: Nx = PETSC_DECIDE
78: Ny = PETSC_DECIDE
80: ! Check for any command line arguments that might override defaults
81: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-mx",mx,flg,ierr)
82: call PetscOptionsGetInt(PETSC_NULL_CHARACTER,"-my",my,flg,ierr)
83: call PetscOptionsGetReal(PETSC_NULL_CHARACTER,"-par", &
84: & param,flg,ierr)
86:
87: ! Set up distributed array and vectors
88: call DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE, &
89: & DMDA_BOUNDARY_NONE, &
90: & DMDA_STENCIL_BOX,mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER, &
91: & PETSC_NULL_INTEGER,dm,ierr)
93: ! Create vectors
94: call DMCreateGlobalVector(dm,x,ierr)
95: call DMCreateLocalVector(dm,localX,ierr)
97: ! Create Hessian
98: call DMGetMatrix(dm,MATAIJ,H,ierr)
99: call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)
101: ! The TAO code begins here
103: ! Create TAO solver
104: call TaoCreate(PETSC_COMM_WORLD,tao,ierr)
105: call TaoSetType(tao,"tao_cg",ierr)
107: ! Set routines for function and gradient evaluation
109: call TaoSetObjectiveAndGradientRoutine(tao, &
110: & FormFunctionGradient,PETSC_NULL_OBJECT,ierr)
111: call TaoSetHessianRoutine(tao,H,H,ComputeHessian, &
112: & PETSC_NULL_OBJECT,ierr)
114: ! Set initial guess
115: call FormInitialGuess(x,ierr)
116: call TaoSetInitialVector(tao,x,ierr)
118: call PetscOptionsHasName(PETSC_NULL_CHARACTER,"-testmonitor",flg, &
119: & ierr)
120: if (flg) then
121: call TaoSetMonitor(tao,Monitor,dummy,PETSC_NULL_FUNCTION, &
122: & ierr)
123: endif
125: call PetscOptionsHasName(PETSC_NULL_CHARACTER,"-testconvergence", &
126: & flg, ierr)
127: if (flg) then
128: call TaoSetConvergenceTest(tao,ConvergenceTest,dummy, &
129: & ierr)
130: endif
132: ! Check for any TAO command line options
133: call TaoSetFromOptions(tao,ierr)
136: ! SOLVE THE APPLICATION
137: call TaoSolve(tao,ierr)
139: ! Get information on termination
140: call TaoGetTerminationReason(tao,reason,ierr)
141: if (reason .lt. 0) then
142: call PetscPrintF(PETSC_COMM_WORLD, &
143: & 'TAO did not terminate successfully\n',ierr)
144: endif
146:
147: ! Free TAO data structures
148: call TaoDestroy(tao,ierr)
150:
151: ! Free PETSc data structures
152: call VecDestroy(x,ierr)
153: call VecDestroy(localX,ierr)
154: call MatDestroy(H,ierr)
155: call DMDestroy(dm,ierr)
158: ! Finalize TAO and PETSc
159: call PetscFinalize(ierr)
160: call TaoFinalize(ierr)
162: end
165: ! ---------------------------------------------------------------------
166: !
167: ! FormInitialGuess - Computes an initial approximation to the solution.
168: !
169: ! Input Parameters:
170: ! X - vector
171: !
172: ! Output Parameters:
173: ! X - vector
174: ! ierr - error code
175: !
176: subroutine FormInitialGuess(X,ierr)
177: implicit none
179: ! mx, my are defined in eptorsion2f.h
180: #include "eptorsion2f.h"
182: ! Input/output variables:
183: Vec X
184: PetscErrorCode ierr
186: ! Local variables:
187: PetscInt i, j, k, xe, ye
188: PetscReal temp, val, hx, hy
189: PetscInt xs, ys, xm, ym
190: PetscInt gxm, gym, gxs, gys
191: PetscInt i1
193: i1 = 1
194: hx = 1.0d0/(mx + 1)
195: hy = 1.0d0/(my + 1)
197: ! Get corner information
198: call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym, &
199: & PETSC_NULL_INTEGER,ierr)
200: call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER, &
201: & gxm,gym,PETSC_NULL_INTEGER,ierr)
205: ! Compute initial guess over locally owned part of mesh
206: xe = xs+xm
207: ye = ys+ym
208: do j=ys,ye-1
209: temp = min(j+1,my-j)*hy
210: do i=xs,xe-1
211: k = (j-gys)*gxm + i-gxs
212: val = min((min(i+1,mx-i))*hx,temp)
213: call VecSetValuesLocal(X,i1,k,val,ADD_VALUES,ierr)
214: end do
215: end do
216: call VecAssemblyBegin(X,ierr)
217: call VecAssemblyEnd(X,ierr)
218: return
219: end
222: ! ---------------------------------------------------------------------
223: !
224: ! FormFunctionGradient - Evaluates gradient G(X).
225: !
226: ! Input Parameters:
227: ! tao - the TaoSolver context
228: ! X - input vector
229: ! dummy - optional user-defined context (not used here)
230: !
231: ! Output Parameters:
232: ! f - the function value at X
233: ! G - vector containing the newly evaluated gradient
234: ! ierr - error code
235: !
236: ! Notes:
237: ! This routine serves as a wrapper for the lower-level routine
238: ! "ApplicationGradient", where the actual computations are
239: ! done using the standard Fortran style of treating the local
240: ! input vector data as an array over the local mesh.
241: !
242: subroutine FormFunctionGradient(tao,X,f,G,dummy,ierr)
243: implicit none
245: ! dm, mx, my, param, localX declared in eptorsion2f.h
246: #include "eptorsion2f.h"
248: ! Input/output variables:
249: TaoSolver tao
250: Vec X, G
251: PetscReal f
252: PetscErrorCode ierr
253: PetscInt dummy
255: ! Declarations for use with local array:
258: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
259: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
260: ! will return an array of doubles referenced by x_array offset by x_index.
261: ! i.e., to reference the kth element of X, use x_array(k + x_index).
262: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
263: PetscReal lx_v(0:1)
264: PetscOffset lx_i
266: ! Local variables:
267: PetscReal zero, p5, area, cdiv3
268: PetscReal val, flin, fquad,floc
269: PetscReal v, vb, vl, vr, vt, dvdx
270: PetscReal dvdy, hx, hy
271: PetscInt xe, ye, xsm, ysm
272: PetscInt xep, yep, i, j, k, ind
273: PetscInt xs, ys, xm, ym
274: PetscInt gxs, gys, gxm, gym
275: PetscInt i1
277: i1 = 1
278: 0
279: cdiv3 = param/3.0d0
280: zero = 0.0d0
281: p5 = 0.5d0
282: hx = 1.0d0/(mx + 1)
283: hy = 1.0d0/(my + 1)
284: fquad = zero
285: flin = zero
287: ! Initialize gradient to zero
288: call VecSet(G,zero,ierr)
290: ! Scatter ghost points to local vector
291: call DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr)
292: call DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr)
295: ! Get corner information
296: call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym, &
297: & PETSC_NULL_INTEGER,ierr)
298: call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER, &
299: & gxm,gym,PETSC_NULL_INTEGER,ierr)
301: ! Get pointer to vector data.
302: call VecGetArray(localX,lx_v,lx_i,ierr)
305: ! Set local loop dimensions
306: xe = xs+xm
307: ye = ys+ym
308: if (xs .eq. 0) then
309: xsm = xs-1
310: else
311: xsm = xs
312: endif
313: if (ys .eq. 0) then
314: ysm = ys-1
315: else
316: ysm = ys
317: endif
318: if (xe .eq. mx) then
319: xep = xe+1
320: else
321: xep = xe
322: endif
323: if (ye .eq. my) then
324: yep = ye+1
325: else
326: yep = ye
327: endif
329: ! Compute local gradient contributions over the lower triangular elements
330:
331: do j = ysm, ye-1
332: do i = xsm, xe-1
333: k = (j-gys)*gxm + i-gxs
334: v = zero
335: vr = zero
336: vt = zero
337: if (i .ge. 0 .and. j .ge. 0) v = lx_v(lx_i+k)
338: if (i .lt. mx-1 .and. j .gt. -1) vr = lx_v(lx_i+k+1)
339: if (i .gt. -1 .and. j .lt. my-1) vt = lx_v(lx_i+k+gxm)
340: dvdx = (vr-v)/hx
341: dvdy = (vt-v)/hy
342: if (i .ne. -1 .and. j .ne. -1) then
343: ind = k
344: val = - dvdx/hx - dvdy/hy - cdiv3
345: call VecSetValuesLocal(G,i1,k,val,ADD_VALUES,ierr)
346: endif
347: if (i .ne. mx-1 .and. j .ne. -1) then
348: ind = k+1
349: val = dvdx/hx - cdiv3
350: call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
351: endif
352: if (i .ne. -1 .and. j .ne. my-1) then
353: ind = k+gxm
354: val = dvdy/hy - cdiv3
355: call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
356: endif
357: fquad = fquad + dvdx*dvdx + dvdy*dvdy
358: flin = flin - cdiv3 * (v+vr+vt)
359: end do
360: end do
362: ! Compute local gradient contributions over the upper triangular elements
364: do j = ys, yep-1
365: do i = xs, xep-1
366: k = (j-gys)*gxm + i-gxs
367: vb = zero
368: vl = zero
369: v = zero
370: if (i .lt. mx .and. j .gt. 0) vb = lx_v(lx_i+k-gxm)
371: if (i .gt. 0 .and. j .lt. my) vl = lx_v(lx_i+k-1)
372: if (i .lt. mx .and. j .lt. my) v = lx_v(lx_i+k)
373: dvdx = (v-vl)/hx
374: dvdy = (v-vb)/hy
375: if (i .ne. mx .and. j .ne. 0) then
376: ind = k-gxm
377: val = - dvdy/hy - cdiv3
378: call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
379: endif
380: if (i .ne. 0 .and. j .ne. my) then
381: ind = k-1
382: val = - dvdx/hx - cdiv3
383: call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
384: endif
385: if (i .ne. mx .and. j .ne. my) then
386: ind = k
387: val = dvdx/hx + dvdy/hy - cdiv3
388: call VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr)
389: endif
390: fquad = fquad + dvdx*dvdx + dvdy*dvdy
391: flin = flin - cdiv3*(vb + vl + v)
392: end do
393: end do
395: ! Restore vector
396: call VecRestoreArray(localX,lx_v,lx_i,ierr)
398: ! Assemble gradient vector
399: call VecAssemblyBegin(G,ierr)
400: call VecAssemblyEnd(G,ierr)
402: ! Scale the gradient
403: area = p5*hx*hy
404: floc = area *(p5*fquad+flin)
405: call VecScale(G,area,ierr)
408: ! Sum function contributions from all processes
409: call MPI_Allreduce(floc,f,1,MPIU_SCALAR,MPI_SUM, &
410: & PETSC_COMM_WORLD,ierr)
411: call PetscLogFlops((ye-ysm)*(xe-xsm)*20+(xep-xs)*(yep-ys)*16.0d0, &
412: & ierr)
416: return
417: end
422: subroutine ComputeHessian(tao, X, H, Hpre, flag, dummy, ierr)
423: implicit none
424: #include "eptorsion2f.h"
425: TaoSolver tao
426: Vec X
427: Mat H,Hpre
428: MatStructure flag
429: PetscErrorCode ierr
430: PetscInt dummy
432:
433: PetscInt i,j,k
434: PetscInt col(0:4),row
435: PetscInt xs,xm,gxs,gxm
436: PetscInt ys,ym,gys,gym
437: PetscReal v(0:4)
438: PetscInt i1
440: i1 = 1
442: ! Get local grid boundaries
443: call DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym, &
444: & PETSC_NULL_INTEGER,ierr)
445: call DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym, &
446: & PETSC_NULL_INTEGER,ierr)
448: do j=ys,ys+ym-1
449: do i=xs,xs+xm-1
450: row = (j-gys)*gxm + (i-gxs)
452: k = 0
453: if (j .gt. gys) then
454: v(k) = -1.0d0
455: col(k) = row-gxm
456: k = k + 1
457: endif
459: if (i .gt. gxs) then
460: v(k) = -1.0d0
461: col(k) = row - 1
462: k = k +1
463: endif
465: v(k) = 4.0d0
466: col(k) = row
467: k = k + 1
469: if (i+1 .lt. gxs + gxm) then
470: v(k) = -1.0d0
471: col(k) = row + 1
472: k = k + 1
473: endif
475: if (j+1 .lt. gys + gym) then
476: v(k) = -1.0d0
477: col(k) = row + gxm
478: k = k + 1
479: endif
481: call MatSetValuesLocal(H,i1,row,k,col,v,INSERT_VALUES,ierr)
482: enddo
483: enddo
485:
486: ! Assemble matrix
487: call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
488: call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)
491: ! Tell the matrix we will never add a new nonzero location to the
492: ! matrix. If we do it will generate an error.
494: call MatSetOption(H,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr)
495: call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)
498: call PetscLogFlops(9.0d0*xm*ym + 49.0d0*xm,ierr)
500: 0
501: return
502: end
503:
504:
505:
506: subroutine Monitor(tao, dummy, ierr)
507: implicit none
508: #include "eptorsion2f.h"
509: TaoSolver tao
510: PetscInt dummy
511: PetscErrorCode ierr
513: PetscInt its
514: PetscReal f,gnorm,cnorm,xdiff
515: TaoSolverTerminationReason reason
516:
517: call TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff, &
518: & reason,ierr)
519: if (mod(its,5) .ne. 0) then
520: call PetscPrintf(PETSC_COMM_WORLD,"iteration multiple of 5\n", &
521: & ierr)
522: endif
523:
524: 0
526: return
527: end
529: subroutine ConvergenceTest(tao, dummy, ierr)
530: implicit none
531: #include "eptorsion2f.h"
532: TaoSolver tao
533: PetscInt dummy
534: PetscErrorCode ierr
536: PetscInt its
537: PetscReal f,gnorm,cnorm,xdiff
538: TaoSolverTerminationReason reason
539:
540: call TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff, &
541: & reason,ierr)
542: if (its .eq. 7) then
543: call TaoSetTerminationReason(tao,TAO_DIVERGED_MAXITS, &
544: & ierr)
545: endif
546:
547: 0
549: return
550: end