Actual source code: eptorsion2f.F90
1: ! Program usage: mpiexec -n <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: !
12: ! ----------------------------------------------------------------------
13: !
14: ! Elastic-plastic torsion problem.
15: !
16: ! The elastic plastic torsion problem arises from the deconverged
17: ! of the stress field on an infinitely long cylindrical bar, which is
18: ! equivalent to the solution of the following problem:
19: ! min{ .5 * integral(||gradient(v(x))||^2 dx) - C * integral(v(x) dx)}
20: ! where C is the torsion angle per unit length.
21: !
22: ! The C version of this code is eptorsion2.c
23: !
24: ! ----------------------------------------------------------------------
26: module eptorsion2fmodule
27: #include "petsc/finclude/petsctao.h"
28: use petscdmda
29: use petsctao
30: implicit none
32: type(tVec) localX
33: type(tDM) dm
34: PetscReal param
35: PetscInt mx, my
36: end module
38: use eptorsion2fmodule
39: implicit none
40: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: ! Variable declarations
42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
43: !
44: ! See additional variable declarations in the file eptorsion2f.h
45: !
46: PetscErrorCode ierr ! used to check for functions returning nonzeros
47: type(tVec) x ! solution vector
48: type(tMat) H ! hessian matrix
49: PetscInt Nx, Ny ! number of processes in x- and y- directions
50: type(tTao) tao ! Tao solver context
51: PetscBool flg
52: PetscInt i1
53: PetscInt dummy
55: ! Note: Any user-defined Fortran routines (such as FormGradient)
56: ! MUST be declared as external.
58: external FormInitialGuess,FormFunctionGradient,ComputeHessian
59: external Monitor,ConvergenceTest
61: i1 = 1
63: ! Initialize TAO, PETSc contexts
64: PetscCallA(PetscInitialize(ierr))
66: ! Specify default parameters
67: param = 5.0
68: mx = 10
69: my = 10
70: Nx = PETSC_DECIDE
71: Ny = PETSC_DECIDE
73: ! Check for any command line arguments that might override defaults
74: PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-mx',mx,flg,ierr))
75: PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-my',my,flg,ierr))
76: PetscCallA(PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-par',param,flg,ierr))
78: ! Set up distributed array and vectors
79: PetscCallA(DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx,my,Nx,Ny,i1,i1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,dm,ierr))
80: PetscCallA(DMSetFromOptions(dm,ierr))
81: PetscCallA(DMSetUp(dm,ierr))
83: ! Create vectors
84: PetscCallA(DMCreateGlobalVector(dm,x,ierr))
85: PetscCallA(DMCreateLocalVector(dm,localX,ierr))
87: ! Create Hessian
88: PetscCallA(DMCreateMatrix(dm,H,ierr))
89: PetscCallA(MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr))
91: ! The TAO code begins here
93: ! Create TAO solver
94: PetscCallA(TaoCreate(PETSC_COMM_WORLD,tao,ierr))
95: PetscCallA(TaoSetType(tao,TAOCG,ierr))
97: ! Set routines for function and gradient evaluation
99: PetscCallA(TaoSetObjectiveAndGradient(tao,PETSC_NULL_VEC,FormFunctionGradient,0,ierr))
100: PetscCallA(TaoSetHessian(tao,H,H,ComputeHessian,0,ierr))
102: ! Set initial guess
103: PetscCallA(FormInitialGuess(x,ierr))
104: PetscCallA(TaoSetSolution(tao,x,ierr))
106: PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-testmonitor',flg,ierr))
107: if (flg) then
108: PetscCallA(TaoSetMonitor(tao,Monitor,dummy,PETSC_NULL_FUNCTION,ierr))
109: endif
111: PetscCallA(PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-testconvergence',flg, ierr))
112: if (flg) then
113: PetscCallA(TaoSetConvergenceTest(tao,ConvergenceTest,dummy,ierr))
114: endif
116: ! Check for any TAO command line options
117: PetscCallA(TaoSetFromOptions(tao,ierr))
119: ! SOLVE THE APPLICATION
120: PetscCallA(TaoSolve(tao,ierr))
122: ! Free TAO data structures
123: PetscCallA(TaoDestroy(tao,ierr))
125: ! Free PETSc data structures
126: PetscCallA(VecDestroy(x,ierr))
127: PetscCallA(VecDestroy(localX,ierr))
128: PetscCallA(MatDestroy(H,ierr))
129: PetscCallA(DMDestroy(dm,ierr))
131: ! Finalize TAO and PETSc
132: PetscCallA(PetscFinalize(ierr))
133: end
135: ! ---------------------------------------------------------------------
136: !
137: ! FormInitialGuess - Computes an initial approximation to the solution.
138: !
139: ! Input Parameters:
140: ! X - vector
141: !
142: ! Output Parameters:
143: ! X - vector
144: ! ierr - error code
145: !
146: subroutine FormInitialGuess(X,ierr)
147: use eptorsion2fmodule
148: implicit none
150: ! Input/output variables:
151: Vec X
152: PetscErrorCode ierr
154: ! Local variables:
155: PetscInt i, j, k, xe, ye
156: PetscReal temp, val, hx, hy
157: PetscInt xs, ys, xm, ym
158: PetscInt gxm, gym, gxs, gys
159: PetscInt i1
161: i1 = 1
162: hx = 1.0/real(mx + 1)
163: hy = 1.0/real(my + 1)
165: ! Get corner information
166: PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
167: PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))
169: ! Compute initial guess over locally owned part of mesh
170: xe = xs+xm
171: ye = ys+ym
172: do j=ys,ye-1
173: temp = min(j+1,my-j)*hy
174: do i=xs,xe-1
175: k = (j-gys)*gxm + i-gxs
176: val = min((min(i+1,mx-i))*hx,temp)
177: PetscCall(VecSetValuesLocal(X,i1,k,val,ADD_VALUES,ierr))
178: end do
179: end do
180: PetscCall(VecAssemblyBegin(X,ierr))
181: PetscCall(VecAssemblyEnd(X,ierr))
182: return
183: end
185: ! ---------------------------------------------------------------------
186: !
187: ! FormFunctionGradient - Evaluates gradient G(X).
188: !
189: ! Input Parameters:
190: ! tao - the Tao context
191: ! X - input vector
192: ! dummy - optional user-defined context (not used here)
193: !
194: ! Output Parameters:
195: ! f - the function value at X
196: ! G - vector containing the newly evaluated gradient
197: ! ierr - error code
198: !
199: ! Notes:
200: ! This routine serves as a wrapper for the lower-level routine
201: ! "ApplicationGradient", where the actual computations are
202: ! done using the standard Fortran style of treating the local
203: ! input vector data as an array over the local mesh.
204: !
205: subroutine FormFunctionGradient(tao,X,f,G,dummy,ierr)
206: use eptorsion2fmodule
207: implicit none
209: ! Input/output variables:
210: type(tTao) tao
211: type(tVec) X, G
212: PetscReal f
213: PetscErrorCode ierr
214: PetscInt dummy
216: ! Declarations for use with local array:
218: PetscReal, pointer :: lx_v(:)
220: ! Local variables:
221: PetscReal zero, p5, area, cdiv3
222: PetscReal val, flin, fquad,floc
223: PetscReal v, vb, vl, vr, vt, dvdx
224: PetscReal dvdy, hx, hy
225: PetscInt xe, ye, xsm, ysm
226: PetscInt xep, yep, i, j, k, ind
227: PetscInt xs, ys, xm, ym
228: PetscInt gxs, gys, gxm, gym
229: PetscInt i1
231: i1 = 1
232: ierr = 0
233: cdiv3 = param/3.0
234: zero = 0.0
235: p5 = 0.5
236: hx = 1.0/real(mx + 1)
237: hy = 1.0/real(my + 1)
238: fquad = zero
239: flin = zero
241: ! Initialize gradient to zero
242: PetscCall(VecSet(G,zero,ierr))
244: ! Scatter ghost points to local vector
245: PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,localX,ierr))
246: PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,localX,ierr))
248: ! Get corner information
249: PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
250: PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))
252: ! Get pointer to vector data.
253: PetscCall(VecGetArrayReadF90(localX,lx_v,ierr))
255: ! Set local loop dimensions
256: xe = xs+xm
257: ye = ys+ym
258: if (xs .eq. 0) then
259: xsm = xs-1
260: else
261: xsm = xs
262: endif
263: if (ys .eq. 0) then
264: ysm = ys-1
265: else
266: ysm = ys
267: endif
268: if (xe .eq. mx) then
269: xep = xe+1
270: else
271: xep = xe
272: endif
273: if (ye .eq. my) then
274: yep = ye+1
275: else
276: yep = ye
277: endif
279: ! Compute local gradient contributions over the lower triangular elements
281: do j = ysm, ye-1
282: do i = xsm, xe-1
283: k = (j-gys)*gxm + i-gxs
284: v = zero
285: vr = zero
286: vt = zero
287: if (i .ge. 0 .and. j .ge. 0) v = lx_v(k+1)
288: if (i .lt. mx-1 .and. j .gt. -1) vr = lx_v(k+2)
289: if (i .gt. -1 .and. j .lt. my-1) vt = lx_v(k+1+gxm)
290: dvdx = (vr-v)/hx
291: dvdy = (vt-v)/hy
292: if (i .ne. -1 .and. j .ne. -1) then
293: ind = k
294: val = - dvdx/hx - dvdy/hy - cdiv3
295: PetscCall(VecSetValuesLocal(G,i1,k,val,ADD_VALUES,ierr))
296: endif
297: if (i .ne. mx-1 .and. j .ne. -1) then
298: ind = k+1
299: val = dvdx/hx - cdiv3
300: PetscCall(VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr))
301: endif
302: if (i .ne. -1 .and. j .ne. my-1) then
303: ind = k+gxm
304: val = dvdy/hy - cdiv3
305: PetscCall(VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr))
306: endif
307: fquad = fquad + dvdx*dvdx + dvdy*dvdy
308: flin = flin - cdiv3 * (v+vr+vt)
309: end do
310: end do
312: ! Compute local gradient contributions over the upper triangular elements
314: do j = ys, yep-1
315: do i = xs, xep-1
316: k = (j-gys)*gxm + i-gxs
317: vb = zero
318: vl = zero
319: v = zero
320: if (i .lt. mx .and. j .gt. 0) vb = lx_v(k+1-gxm)
321: if (i .gt. 0 .and. j .lt. my) vl = lx_v(k)
322: if (i .lt. mx .and. j .lt. my) v = lx_v(1+k)
323: dvdx = (v-vl)/hx
324: dvdy = (v-vb)/hy
325: if (i .ne. mx .and. j .ne. 0) then
326: ind = k-gxm
327: val = - dvdy/hy - cdiv3
328: PetscCall(VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr))
329: endif
330: if (i .ne. 0 .and. j .ne. my) then
331: ind = k-1
332: val = - dvdx/hx - cdiv3
333: PetscCall(VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr))
334: endif
335: if (i .ne. mx .and. j .ne. my) then
336: ind = k
337: val = dvdx/hx + dvdy/hy - cdiv3
338: PetscCall(VecSetValuesLocal(G,i1,ind,val,ADD_VALUES,ierr))
339: endif
340: fquad = fquad + dvdx*dvdx + dvdy*dvdy
341: flin = flin - cdiv3*(vb + vl + v)
342: end do
343: end do
345: ! Restore vector
346: PetscCall(VecRestoreArrayReadF90(localX,lx_v,ierr))
348: ! Assemble gradient vector
349: PetscCall(VecAssemblyBegin(G,ierr))
350: PetscCall(VecAssemblyEnd(G,ierr))
352: ! Scale the gradient
353: area = p5*hx*hy
354: floc = area *(p5*fquad+flin)
355: PetscCall(VecScale(G,area,ierr))
357: ! Sum function contributions from all processes
358: PetscCallMPI(MPI_Allreduce(floc,f,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD,ierr))
359: PetscCall(PetscLogFlops(20.0d0*(ye-ysm)*(xe-xsm)+16.0d0*(xep-xs)*(yep-ys),ierr))
360: return
361: end
363: subroutine ComputeHessian(tao, X, H, Hpre, dummy, ierr)
364: use eptorsion2fmodule
365: implicit none
367: type(tTao) tao
368: type(tVec) X
369: type(tMat) H,Hpre
370: PetscErrorCode ierr
371: PetscInt dummy
373: PetscInt i,j,k
374: PetscInt col(0:4),row
375: PetscInt xs,xm,gxs,gxm
376: PetscInt ys,ym,gys,gym
377: PetscReal v(0:4)
378: PetscInt i1
380: i1 = 1
382: ! Get local grid boundaries
383: PetscCall(DMDAGetCorners(dm,xs,ys,PETSC_NULL_INTEGER,xm,ym,PETSC_NULL_INTEGER,ierr))
384: PetscCall(DMDAGetGhostCorners(dm,gxs,gys,PETSC_NULL_INTEGER,gxm,gym,PETSC_NULL_INTEGER,ierr))
386: do j=ys,ys+ym-1
387: do i=xs,xs+xm-1
388: row = (j-gys)*gxm + (i-gxs)
390: k = 0
391: if (j .gt. gys) then
392: v(k) = -1.0
393: col(k) = row-gxm
394: k = k + 1
395: endif
397: if (i .gt. gxs) then
398: v(k) = -1.0
399: col(k) = row - 1
400: k = k +1
401: endif
403: v(k) = 4.0
404: col(k) = row
405: k = k + 1
407: if (i+1 .lt. gxs + gxm) then
408: v(k) = -1.0
409: col(k) = row + 1
410: k = k + 1
411: endif
413: if (j+1 .lt. gys + gym) then
414: v(k) = -1.0
415: col(k) = row + gxm
416: k = k + 1
417: endif
419: PetscCall(MatSetValuesLocal(H,i1,row,k,col,v,INSERT_VALUES,ierr))
420: enddo
421: enddo
423: ! Assemble matrix
424: PetscCall(MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr))
425: PetscCall(MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr))
427: ! Tell the matrix we will never add a new nonzero location to the
428: ! matrix. If we do it will generate an error.
430: PetscCall(MatSetOption(H,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE,ierr))
431: PetscCall(MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr))
433: PetscCall(PetscLogFlops(9.0d0*xm*ym + 49.0d0*xm,ierr))
435: ierr = 0
436: return
437: end
439: subroutine Monitor(tao, dummy, ierr)
440: use eptorsion2fmodule
441: implicit none
443: type(tTao) tao
444: PetscInt dummy
445: PetscErrorCode ierr
447: PetscInt its
448: PetscReal f,gnorm,cnorm,xdiff
449: TaoConvergedReason reason
451: PetscCall(TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff,reason,ierr))
452: if (mod(its,5) .ne. 0) then
453: PetscCall(PetscPrintf(PETSC_COMM_WORLD,'iteration multiple of 5\n',ierr))
454: endif
456: ierr = 0
458: return
459: end
461: subroutine ConvergenceTest(tao, dummy, ierr)
462: use eptorsion2fmodule
463: implicit none
465: type(tTao) tao
466: PetscInt dummy
467: PetscErrorCode ierr
469: PetscInt its
470: PetscReal f,gnorm,cnorm,xdiff
471: TaoConvergedReason reason
473: PetscCall(TaoGetSolutionStatus(tao,its,f,gnorm,cnorm,xdiff,reason,ierr))
474: if (its .eq. 7) then
475: PetscCall(TaoSetConvergedReason(tao,TAO_DIVERGED_MAXITS,ierr))
476: endif
478: ierr = 0
480: return
481: end
483: !/*TEST
484: !
485: ! build:
486: ! requires: !complex
487: !
488: ! test:
489: ! args: -tao_smonitor -tao_type nls -tao_gttol 1.e-2
490: !
491: ! test:
492: ! suffix: 2
493: ! nsize: 2
494: ! args: -tao_smonitor -tao_type lmvm -tao_gttol 1.e-2
495: !
496: ! test:
497: ! suffix: 3
498: ! args: -testmonitor -tao_type lmvm -tao_gttol 1.e-2
499: !TEST*/