Date: 2021-03-03T22:28:09+00:00

Actual source code: rosenbrock1f.F90
petsc-3.14.5 2021-03-03
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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:       PetscMPIInt     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,PETSC_ERR_WRONG_MPI_SIZE,'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*/