Actual source code: snesj.c
petsc-3.7.1 2016-05-15
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      2: #include <petsc/private/snesimpl.h>    /*I  "petscsnes.h"  I*/

      6: /*@C
      7:    SNESComputeJacobianDefault - Computes the Jacobian using finite differences.

      9:    Collective on SNES

     11:    Input Parameters:
     12: +  x1 - compute Jacobian at this point
     13: -  ctx - application's function context, as set with SNESSetFunction()

     15:    Output Parameters:
     16: +  J - Jacobian matrix (not altered in this routine)
     17: -  B - newly computed Jacobian matrix to use with preconditioner (generally the same as J)

     19:    Options Database Key:
     20: +  -snes_fd - Activates SNESComputeJacobianDefault()
     21: .  -snes_test_err - Square root of function error tolerance, default square root of machine
     22:                     epsilon (1.e-8 in double, 3.e-4 in single)
     23: -  -mat_fd_type - Either wp or ds (see MATMFFD_WP or MATMFFD_DS)

     25:    Notes:
     26:    This routine is slow and expensive, and is not currently optimized
     27:    to take advantage of sparsity in the problem.  Although
     28:    SNESComputeJacobianDefault() is not recommended for general use
     29:    in large-scale applications, It can be useful in checking the
     30:    correctness of a user-provided Jacobian.

     32:    An alternative routine that uses coloring to exploit matrix sparsity is
     33:    SNESComputeJacobianDefaultColor().

     35:    Level: intermediate

     37: .keywords: SNES, finite differences, Jacobian

     39: .seealso: SNESSetJacobian(), SNESComputeJacobianDefaultColor(), MatCreateSNESMF()
     40: @*/
     41: PetscErrorCode  SNESComputeJacobianDefault(SNES snes,Vec x1,Mat J,Mat B,void *ctx)
     42: {
     43:   Vec               j1a,j2a,x2;
     44:   PetscErrorCode    ierr;
     45:   PetscInt          i,N,start,end,j,value,root;
     46:   PetscScalar       dx,*y,wscale;
     47:   const PetscScalar *xx;
     48:   PetscReal         amax,epsilon = PETSC_SQRT_MACHINE_EPSILON;
     49:   PetscReal         dx_min = 1.e-16,dx_par = 1.e-1,unorm;
     50:   MPI_Comm          comm;
     51:   PetscBool         assembled,use_wp = PETSC_TRUE,flg;
     52:   const char        *list[2] = {"ds","wp"};
     53:   PetscMPIInt       size;
     54:   const PetscInt    *ranges;

     57:   /* Since this Jacobian will possibly have "extra" nonzero locations just turn off errors for these locations */
     58:   MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
     59:   PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,0);

     61:   PetscObjectGetComm((PetscObject)x1,&comm);
     62:   MPI_Comm_size(comm,&size);
     63:   MatAssembled(B,&assembled);
     64:   if (assembled) {
     65:     MatZeroEntries(B);
     66:   }
     67:   if (!snes->nvwork) {
     68:     snes->nvwork = 3;

     70:     VecDuplicateVecs(x1,snes->nvwork,&snes->vwork);
     71:     PetscLogObjectParents(snes,snes->nvwork,snes->vwork);
     72:   }
     73:   j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2];

     75:   VecGetSize(x1,&N);
     76:   VecGetOwnershipRange(x1,&start,&end);
     77:   SNESComputeFunction(snes,x1,j1a);

     79:   PetscOptionsBegin(PetscObjectComm((PetscObject)snes),((PetscObject)snes)->prefix,"Differencing options","SNES");
     80:   PetscOptionsEList("-mat_fd_type","Algorithm to compute difference parameter","SNESComputeJacobianDefault",list,2,"wp",&value,&flg);
     81:   PetscOptionsEnd();
     82:   if (flg && !value) use_wp = PETSC_FALSE;

     84:   if (use_wp) {
     85:     VecNorm(x1,NORM_2,&unorm);
     86:   }
     87:   /* Compute Jacobian approximation, 1 column at a time.
     88:       x1 = current iterate, j1a = F(x1)
     89:       x2 = perturbed iterate, j2a = F(x2)
     90:    */
     91:   for (i=0; i<N; i++) {
     92:     VecCopy(x1,x2);
     93:     if (i>= start && i<end) {
     94:       VecGetArrayRead(x1,&xx);
     95:       if (use_wp) dx = PetscSqrtReal(1.0 + unorm);
     96:       else        dx = xx[i-start];
     97:       VecRestoreArrayRead(x1,&xx);
     98:       if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
     99:       dx    *= epsilon;
    100:       wscale = 1.0/dx;
    101:       VecSetValues(x2,1,&i,&dx,ADD_VALUES);
    102:     } else {
    103:       wscale = 0.0;
    104:     }
    105:     VecAssemblyBegin(x2);
    106:     VecAssemblyEnd(x2);
    107:     SNESComputeFunction(snes,x2,j2a);
    108:     VecAXPY(j2a,-1.0,j1a);
    109:     /* Communicate scale=1/dx_i to all processors */
    110:     VecGetOwnershipRanges(x1,&ranges);
    111:     root = size;
    112:     for (j=size-1; j>-1; j--) {
    113:       root--;
    114:       if (i>=ranges[j]) break;
    115:     }
    116:     MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);

    118:     VecScale(j2a,wscale);
    119:     VecNorm(j2a,NORM_INFINITY,&amax); amax *= 1.e-14;
    120:     VecGetArray(j2a,&y);
    121:     for (j=start; j<end; j++) {
    122:       if (PetscAbsScalar(y[j-start]) > amax || j == i) {
    123:         MatSetValues(B,1,&j,1,&i,y+j-start,INSERT_VALUES);
    124:       }
    125:     }
    126:     VecRestoreArray(j2a,&y);
    127:   }
    128:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    129:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    130:   if (B != J) {
    131:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    132:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    133:   }
    134:   return(0);
    135: }