Actual source code: rosenbrock1f.F90

petsc-master 2019-10-21
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  1: !  Program usage: mpiexec -n 1 rosenbrock1f [-help] [all TAO options]
  2: !
  3: !  Description:  This example demonstrates use of the TAO package to solve an
  4: !  unconstrained minimization problem on a single processor.  We minimize the
  5: !  extended Rosenbrock 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 rosenbrock1.c
  9: !
 10: !!/*T
 11: !  Concepts: TAO^Solving an unconstrained minimization problem
 12: !  Routines: TaoCreate();
 13: !  Routines: TaoSetType(); TaoSetObjectiveAndGradientRoutine();
 14: !  Routines: TaoSetHessianRoutine();
 15: !  Routines: TaoSetInitialVector();
 16: !  Routines: TaoSetFromOptions();
 17: !  Routines: TaoSolve();
 18: !  Routines: TaoDestroy();
 19: !  Processors: 1
 20: !T*/


 23: !

 25: ! ----------------------------------------------------------------------
 26: !
 27: #include "rosenbrock1f.h"

 29: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 30: !                   Variable declarations
 31: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 32: !
 33: !  See additional variable declarations in the file rosenbrock1f.h

 35:       PetscErrorCode   ierr    ! used to check for functions returning nonzeros
 36:       Vec              x       ! solution vector
 37:       Mat              H       ! hessian matrix
 38:       Tao        tao     ! TAO_SOVER context
 39:       PetscBool       flg
 40:       PetscInt         i2,i1
 41:       integer          size
 42:       PetscReal      zero

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

 47:       external FormFunctionGradient,FormHessian

 49:       zero = 0.0d0
 50:       i2 = 2
 51:       i1 = 1

 53: !  Initialize TAO and PETSc
 54:       call PetscInitialize(PETSC_NULL_CHARACTER,ierr)
 55:       if (ierr .ne. 0) then
 56:          print*,'Unable to initialize PETSc'
 57:          stop
 58:       endif

 60:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
 61:       if (size .ne. 1) then; SETERRA(PETSC_COMM_SELF,1,'This is a uniprocessor example only'); endif

 63: !  Initialize problem parameters
 64:       n     = 2
 65:       alpha = 99.0d0


 68: ! Check for command line arguments to override defaults
 69:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
 70:      &                        '-n',n,flg,ierr)
 71:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,   &
 72:      &                         '-alpha',alpha,flg,ierr)

 74: !  Allocate vectors for the solution and gradient
 75:       call VecCreateSeq(PETSC_COMM_SELF,n,x,ierr)

 77: !  Allocate storage space for Hessian;
 78:       call MatCreateSeqBAIJ(PETSC_COMM_SELF,i2,n,n,i1,                   &
 79:      &     PETSC_NULL_INTEGER, H,ierr)

 81:       call MatSetOption(H,MAT_SYMMETRIC,PETSC_TRUE,ierr)


 84: !  The TAO code begins here

 86: !  Create TAO solver
 87:       call TaoCreate(PETSC_COMM_SELF,tao,ierr)
 88:       CHKERRA(ierr)
 89:       call TaoSetType(tao,TAOLMVM,ierr)
 90:       CHKERRA(ierr)

 92: !  Set routines for function, gradient, and hessian evaluation
 93:       call TaoSetObjectiveAndGradientRoutine(tao,                       &
 94:      &      FormFunctionGradient,0,ierr)
 95:       CHKERRA(ierr)
 96:       call TaoSetHessianRoutine(tao,H,H,FormHessian,                    &
 97:      &     0,ierr)
 98:       CHKERRA(ierr)


101: !  Optional: Set initial guess
102:       call VecSet(x, zero, ierr)
103:       call TaoSetInitialVector(tao, x, ierr)
104:       CHKERRA(ierr)


107: !  Check for TAO command line options
108:       call TaoSetFromOptions(tao,ierr)
109:       CHKERRA(ierr)

111: !  SOLVE THE APPLICATION
112:       call TaoSolve(tao,ierr)

114: !  TaoView() prints ierr about the TAO solver; the option
115: !      -tao_view
116: !  can alternatively be used to activate this at runtime.
117: !      call TaoView(tao,PETSC_VIEWER_STDOUT_SELF,ierr)


120: !  Free TAO data structures
121:       call TaoDestroy(tao,ierr)

123: !  Free PETSc data structures
124:       call VecDestroy(x,ierr)
125:       call MatDestroy(H,ierr)

127:       call PetscFinalize(ierr)
128:       end


131: ! --------------------------------------------------------------------
132: !  FormFunctionGradient - Evaluates the function f(X) and gradient G(X)
133: !
134: !  Input Parameters:
135: !  tao - the Tao context
136: !  X   - input vector
137: !  dummy - not used
138: !
139: !  Output Parameters:
140: !  G - vector containing the newly evaluated gradient
141: !  f - function value

143:       subroutine FormFunctionGradient(tao, X, f, G, dummy, ierr)
144: #include "rosenbrock1f.h"

146:       Tao        tao
147:       Vec              X,G
148:       PetscReal        f
149:       PetscErrorCode   ierr
150:       PetscInt         dummy


153:       PetscReal        ff,t1,t2
154:       PetscInt         i,nn

156: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
157: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
158: ! will return an array of doubles referenced by x_array offset by x_index.
159: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
160: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
161:       PetscReal        g_v(0:1),x_v(0:1)
162:       PetscOffset      g_i,x_i

164:       0
165:       nn = n/2
166:       ff = 0

168: !     Get pointers to vector data
169:       call VecGetArrayRead(X,x_v,x_i,ierr)
170:       call VecGetArray(G,g_v,g_i,ierr)


173: !     Compute G(X)
174:       do i=0,nn-1
175:          t1 = x_v(x_i+2*i+1) - x_v(x_i+2*i)*x_v(x_i+2*i)
176:          t2 = 1.0 - x_v(x_i + 2*i)
177:          ff = ff + alpha*t1*t1 + t2*t2
178:          g_v(g_i + 2*i) = -4*alpha*t1*x_v(x_i + 2*i) - 2.0*t2
179:          g_v(g_i + 2*i + 1) = 2.0*alpha*t1
180:       enddo

182: !     Restore vectors
183:       call VecRestoreArrayRead(X,x_v,x_i,ierr)
184:       call VecRestoreArray(G,g_v,g_i,ierr)

186:       f = ff
187:       call PetscLogFlops(15.0d0*nn,ierr)

189:       return
190:       end

192: !
193: ! ---------------------------------------------------------------------
194: !
195: !  FormHessian - Evaluates Hessian matrix.
196: !
197: !  Input Parameters:
198: !  tao     - the Tao context
199: !  X       - input vector
200: !  dummy   - optional user-defined context, as set by SNESSetHessian()
201: !            (not used here)
202: !
203: !  Output Parameters:
204: !  H      - Hessian matrix
205: !  PrecH  - optionally different preconditioning matrix (not used here)
206: !  flag   - flag indicating matrix structure
207: !  ierr   - error code
208: !
209: !  Note: Providing the Hessian may not be necessary.  Only some solvers
210: !  require this matrix.

212:       subroutine FormHessian(tao,X,H,PrecH,dummy,ierr)
213: #include "rosenbrock1f.h"

215: !  Input/output variables:
216:       Tao        tao
217:       Vec              X
218:       Mat              H, PrecH
219:       PetscErrorCode   ierr
220:       PetscInt         dummy

222:       PetscReal        v(0:1,0:1)
223:       PetscBool assembled

225: ! PETSc's VecGetArray acts differently in Fortran than it does in C.
226: ! Calling VecGetArray((Vec) X, (PetscReal) x_array(0:1), (PetscOffset) x_index, ierr)
227: ! will return an array of doubles referenced by x_array offset by x_index.
228: !  i.e.,  to reference the kth element of X, use x_array(k + x_index).
229: ! Notice that by declaring the arrays with range (0:1), we are using the C 0-indexing practice.
230:       PetscReal        x_v(0:1)
231:       PetscOffset      x_i
232:       PetscInt         i,nn,ind(0:1),i2


235:       0
236:       nn= n/2
237:       i2 = 2

239: !  Zero existing matrix entries
240:       call MatAssembled(H,assembled,ierr)
241:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(H,ierr)

243: !  Get a pointer to vector data

245:       call VecGetArrayRead(X,x_v,x_i,ierr)

247: !  Compute Hessian entries

249:       do i=0,nn-1
250:          v(1,1) = 2.0*alpha
251:          v(0,0) = -4.0*alpha*(x_v(x_i+2*i+1) -                          &
252:      &                3*x_v(x_i+2*i)*x_v(x_i+2*i))+2
253:          v(1,0) = -4.0*alpha*x_v(x_i+2*i)
254:          v(0,1) = v(1,0)
255:          ind(0) = 2*i
256:          ind(1) = 2*i + 1
257:          call MatSetValues(H,i2,ind,i2,ind,v,INSERT_VALUES,ierr)
258:       enddo

260: !  Restore vector

262:       call VecRestoreArrayRead(X,x_v,x_i,ierr)

264: !  Assemble matrix

266:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
267:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)

269:       call PetscLogFlops(9.0d0*nn,ierr)

271:       return
272:       end





278: !
279: !/*TEST
280: !
281: !   build:
282: !      requires: !complex
283: !
284: !   test:
285: !      args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-5
286: !      requires: !single
287: !
288: !TEST*/