Actual source code: rosenbrock1f.F90

  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*/

 22: !

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

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

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

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

 46:       external FormFunctionGradient,FormHessian

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

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

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

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

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

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

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

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

 81: !  The TAO code begins here

 83: !  Create TAO solver
 84:       call TaoCreate(PETSC_COMM_SELF,tao,ierr)
 85:       CHKERRA(ierr)
 86:       call TaoSetType(tao,TAOLMVM,ierr)
 87:       CHKERRA(ierr)

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

 97: !  Optional: Set initial guess
 98:       call VecSet(x, zero, ierr)
 99:       call TaoSetInitialVector(tao, x, ierr)
100:       CHKERRA(ierr)

102: !  Check for TAO command line options
103:       call TaoSetFromOptions(tao,ierr)
104:       CHKERRA(ierr)

106: !  SOLVE THE APPLICATION
107:       call TaoSolve(tao,ierr)

109: !  TaoView() prints ierr about the TAO solver; the option
110: !      -tao_view
111: !  can alternatively be used to activate this at runtime.
112: !      call TaoView(tao,PETSC_VIEWER_STDOUT_SELF,ierr)

114: !  Free TAO data structures
115:       call TaoDestroy(tao,ierr)

117: !  Free PETSc data structures
118:       call VecDestroy(x,ierr)
119:       call MatDestroy(H,ierr)

121:       call PetscFinalize(ierr)
122:       end

124: ! --------------------------------------------------------------------
125: !  FormFunctionGradient - Evaluates the function f(X) and gradient G(X)
126: !
127: !  Input Parameters:
128: !  tao - the Tao context
129: !  X   - input vector
130: !  dummy - not used
131: !
132: !  Output Parameters:
133: !  G - vector containing the newly evaluated gradient
134: !  f - function value

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

139:       Tao        tao
140:       Vec              X,G
141:       PetscReal        f
142:       PetscErrorCode   ierr
143:       PetscInt         dummy

145:       PetscReal        ff,t1,t2
146:       PetscInt         i,nn

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

156:       0
157:       nn = n/2
158:       ff = 0

160: !     Get pointers to vector data
161:       call VecGetArrayRead(X,x_v,x_i,ierr)
162:       call VecGetArray(G,g_v,g_i,ierr)

164: !     Compute G(X)
165:       do i=0,nn-1
166:          t1 = x_v(x_i+2*i+1) - x_v(x_i+2*i)*x_v(x_i+2*i)
167:          t2 = 1.0 - x_v(x_i + 2*i)
168:          ff = ff + alpha*t1*t1 + t2*t2
169:          g_v(g_i + 2*i) = -4*alpha*t1*x_v(x_i + 2*i) - 2.0*t2
170:          g_v(g_i + 2*i + 1) = 2.0*alpha*t1
171:       enddo

173: !     Restore vectors
174:       call VecRestoreArrayRead(X,x_v,x_i,ierr)
175:       call VecRestoreArray(G,g_v,g_i,ierr)

177:       f = ff
178:       call PetscLogFlops(15.0d0*nn,ierr)

180:       return
181:       end

183: !
184: ! ---------------------------------------------------------------------
185: !
186: !  FormHessian - Evaluates Hessian matrix.
187: !
188: !  Input Parameters:
189: !  tao     - the Tao context
190: !  X       - input vector
191: !  dummy   - optional user-defined context, as set by SNESSetHessian()
192: !            (not used here)
193: !
194: !  Output Parameters:
195: !  H      - Hessian matrix
196: !  PrecH  - optionally different preconditioning matrix (not used here)
197: !  flag   - flag indicating matrix structure
198: !  ierr   - error code
199: !
200: !  Note: Providing the Hessian may not be necessary.  Only some solvers
201: !  require this matrix.

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

206: !  Input/output variables:
207:       Tao        tao
208:       Vec              X
209:       Mat              H, PrecH
210:       PetscErrorCode   ierr
211:       PetscInt         dummy

213:       PetscReal        v(0:1,0:1)
214:       PetscBool assembled

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

225:       0
226:       nn= n/2
227:       i2 = 2

229: !  Zero existing matrix entries
230:       call MatAssembled(H,assembled,ierr)
231:       if (assembled .eqv. PETSC_TRUE) call MatZeroEntries(H,ierr)

233: !  Get a pointer to vector data

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

237: !  Compute Hessian entries

239:       do i=0,nn-1
240:          v(1,1) = 2.0*alpha
241:          v(0,0) = -4.0*alpha*(x_v(x_i+2*i+1) -                          &
242:      &                3*x_v(x_i+2*i)*x_v(x_i+2*i))+2
243:          v(1,0) = -4.0*alpha*x_v(x_i+2*i)
244:          v(0,1) = v(1,0)
245:          ind(0) = 2*i
246:          ind(1) = 2*i + 1
247:          call MatSetValues(H,i2,ind,i2,ind,v,INSERT_VALUES,ierr)
248:       enddo

250: !  Restore vector

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

254: !  Assemble matrix

256:       call MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY,ierr)
257:       call MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY,ierr)

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

261:       return
262:       end

264: !
265: !/*TEST
266: !
267: !   build:
268: !      requires: !complex
269: !
270: !   test:
271: !      args: -tao_smonitor -tao_type ntr -tao_gatol 1.e-5
272: !      requires: !single
273: !
274: !TEST*/