Actual source code: rosenbrock1f.F

petsc-3.7.4 2016-10-02
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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:       implicit none

 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,rank    ! number of processes running
 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)

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

 65: !  Initialize problem parameters
 66:       n     = 2
 67:       alpha = 99.0d0



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

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

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

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


 87: !  The TAO code begins here

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

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


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


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

114: !  SOLVE THE APPLICATION
115:       call TaoSolve(tao,ierr)

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


123: !  Free TAO data structures
124:       call TaoDestroy(tao,ierr)

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

130:       call PetscFinalize(ierr)
131:       end


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

146:       subroutine FormFunctionGradient(tao, X, f, G, dummy, ierr)
147:       implicit none

149: ! n,alpha defined in rosenbrock1f.h
150: #include "rosenbrock1f.h"

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


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

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

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

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


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

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

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

195:       return
196:       end

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

218:       subroutine FormHessian(tao,X,H,PrecH,dummy,ierr)
219:       implicit none

221: #include "rosenbrock1f.h"

223: !  Input/output variables:
224:       Tao        tao
225:       Vec              X
226:       Mat              H, PrecH
227:       PetscErrorCode   ierr
228:       PetscInt         dummy

230:       PetscReal        v(0:1,0:1)
231:       PetscBool assembled

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


243:       0
244:       nn= n/2
245:       i2 = 2

247: !  Zero existing matrix entries
248:       call MatAssembled(H,assembled,ierr)
249:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(H,ierr)

251: !  Get a pointer to vector data

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

255: !  Compute Hessian entries

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

268: !  Restore vector

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

272: !  Assemble matrix

274:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
275:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)

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

279:       return
280:       end