Actual source code: rosenbrock1f.F

petsc-master 2016-12-08
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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*/
 21: !

 23: ! ----------------------------------------------------------------------
 24: !
 25: #include "rosenbrock1f.h"

 27: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 28: !                   Variable declarations
 29: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 30: !
 31: !  See additional variable declarations in the file rosenbrock1f.h

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

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

 45:       external FormFunctionGradient,FormHessian

 47:       zero = 0.0d0
 48:       i2 = 2
 49:       i1 = 1

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

 58:       call MPI_Comm_size(PETSC_COMM_WORLD,size,ierr)
 59:       call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr)
 60:       if (size .ne. 1) then
 61:          if (rank .eq. 0) then
 62:             write(6,*) 'This is a uniprocessor example only!'
 63:          endif
 64:          SETERRQ(PETSC_COMM_SELF,1,' ',ierr)
 65:       endif

 67: !  Initialize problem parameters
 68:       n     = 2
 69:       alpha = 99.0d0



 73: ! Check for command line arguments to override defaults
 74:       call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,    &
 75:      &                        '-n',n,flg,ierr)
 76:       call PetscOptionsGetReal(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,   &
 77:      &                         '-alpha',alpha,flg,ierr)

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

 82: !  Allocate storage space for Hessian;
 83:       call MatCreateSeqBAIJ(PETSC_COMM_SELF,i2,n,n,i1,                   &
 84:      &     PETSC_NULL_INTEGER, H,ierr)

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


 89: !  The TAO code begins here

 91: !  Create TAO solver
 92:       call TaoCreate(PETSC_COMM_SELF,tao,ierr)
 93:       CHKERRQ(ierr)
 94:       call TaoSetType(tao,TAOLMVM,ierr)
 95:       CHKERRQ(ierr)

 97: !  Set routines for function, gradient, and hessian evaluation
 98:       call TaoSetObjectiveAndGradientRoutine(tao,                       &
 99:      &      FormFunctionGradient,0,ierr)
100:       CHKERRQ(ierr)
101:       call TaoSetHessianRoutine(tao,H,H,FormHessian,                    &
102:      &     0,ierr)
103:       CHKERRQ(ierr)


106: !  Optional: Set initial guess
107:       call VecSet(x, zero, ierr)
108:       call TaoSetInitialVector(tao, x, ierr)
109:       CHKERRQ(ierr)


112: !  Check for TAO command line options
113:       call TaoSetFromOptions(tao,ierr)
114:       CHKERRQ(ierr)

116: !  SOLVE THE APPLICATION
117:       call TaoSolve(tao,ierr)

119: !  TaoView() prints ierr about the TAO solver; the option
120: !      -tao_view
121: !  can alternatively be used to activate this at runtime.
122: !      call TaoView(tao,PETSC_VIEWER_STDOUT_SELF,ierr)


125: !  Free TAO data structures
126:       call TaoDestroy(tao,ierr)

128: !  Free PETSc data structures
129:       call VecDestroy(x,ierr)
130:       call MatDestroy(H,ierr)

132:       call PetscFinalize(ierr)
133:       end


136: ! --------------------------------------------------------------------
137: !  FormFunctionGradient - Evaluates the function f(X) and gradient G(X)
138: !
139: !  Input Parameters:
140: !  tao - the Tao context
141: !  X   - input vector
142: !  dummy - not used
143: !
144: !  Output Parameters:
145: !  G - vector containing the newly evaluated gradient
146: !  f - function value

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

151:       Tao        tao
152:       Vec              X,G
153:       PetscReal        f
154:       PetscErrorCode   ierr
155:       PetscInt         dummy


158:       PetscReal        ff,t1,t2
159:       PetscInt         i,nn

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

169:       0
170:       nn = n/2
171:       ff = 0

173: !     Get pointers to vector data
174:       call VecGetArray(X,x_v,x_i,ierr)
175:       call VecGetArray(G,g_v,g_i,ierr)


178: !     Compute G(X)
179:       do i=0,nn-1
180:          t1 = x_v(x_i+2*i+1) - x_v(x_i+2*i)*x_v(x_i+2*i)
181:          t2 = 1.0 - x_v(x_i + 2*i)
182:          ff = ff + alpha*t1*t1 + t2*t2
183:          g_v(g_i + 2*i) = -4*alpha*t1*x_v(x_i + 2*i) - 2.0*t2
184:          g_v(g_i + 2*i + 1) = 2.0*alpha*t1
185:       enddo

187: !     Restore vectors
188:       call VecRestoreArray(X,x_v,x_i,ierr)
189:       call VecRestoreArray(G,g_v,g_i,ierr)

191:       f = ff
192:       call PetscLogFlops(15.0d0*nn,ierr)

194:       return
195:       end

197: !
198: ! ---------------------------------------------------------------------
199: !
200: !  FormHessian - Evaluates Hessian matrix.
201: !
202: !  Input Parameters:
203: !  tao     - the Tao context
204: !  X       - input vector
205: !  dummy   - optional user-defined context, as set by SNESSetHessian()
206: !            (not used here)
207: !
208: !  Output Parameters:
209: !  H      - Hessian matrix
210: !  PrecH  - optionally different preconditioning matrix (not used here)
211: !  flag   - flag indicating matrix structure
212: !  ierr   - error code
213: !
214: !  Note: Providing the Hessian may not be necessary.  Only some solvers
215: !  require this matrix.

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

220: !  Input/output variables:
221:       Tao        tao
222:       Vec              X
223:       Mat              H, PrecH
224:       PetscErrorCode   ierr
225:       PetscInt         dummy

227:       PetscReal        v(0:1,0:1)
228:       PetscBool assembled

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


240:       0
241:       nn= n/2
242:       i2 = 2

244: !  Zero existing matrix entries
245:       call MatAssembled(H,assembled,ierr)
246:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(H,ierr)

248: !  Get a pointer to vector data

250:       call VecGetArray(X,x_v,x_i,ierr)

252: !  Compute Hessian entries

254:       do i=0,nn-1
255:          v(1,1) = 2.0*alpha
256:          v(0,0) = -4.0*alpha*(x_v(x_i+2*i+1) -                          &
257:      &                3*x_v(x_i+2*i)*x_v(x_i+2*i))+2
258:          v(1,0) = -4.0*alpha*x_v(x_i+2*i)
259:          v(0,1) = v(1,0)
260:          ind(0) = 2*i
261:          ind(1) = 2*i + 1
262:          call MatSetValues(H,i2,ind,i2,ind,v,INSERT_VALUES,ierr)
263:       enddo

265: !  Restore vector

267:       call VecRestoreArray(X,x_v,x_i,ierr)

269: !  Assemble matrix

271:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
272:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)

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

276:       return
277:       end