Actual source code: snesj.c
petsc-3.13.6 2020-09-29
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      2:  #include <petsc/private/snesimpl.h>
      3:  #include <petscdm.h>

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

      8:    Collective on SNES

     10:    Input Parameters:
     11: +  x1 - compute Jacobian at this point
     12: -  ctx - Section 1.5 Writing Application Codes with PETSc's function context, as set with SNESSetFunction()

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

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

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

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

     34:    Level: intermediate

     36: .seealso: SNESSetJacobian(), SNESComputeJacobianDefaultColor(), MatCreateSNESMF()
     37: @*/
     38: PetscErrorCode  SNESComputeJacobianDefault(SNES snes,Vec x1,Mat J,Mat B,void *ctx)
     39: {
     40:   Vec               j1a,j2a,x2;
     41:   PetscErrorCode    ierr;
     42:   PetscInt          i,N,start,end,j,value,root;
     43:   PetscScalar       dx,*y,wscale;
     44:   const PetscScalar *xx;
     45:   PetscReal         amax,epsilon = PETSC_SQRT_MACHINE_EPSILON;
     46:   PetscReal         dx_min = 1.e-16,dx_par = 1.e-1,unorm;
     47:   MPI_Comm          comm;
     48:   PetscBool         assembled,use_wp = PETSC_TRUE,flg;
     49:   const char        *list[2] = {"ds","wp"};
     50:   PetscMPIInt       size;
     51:   const PetscInt    *ranges;

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

     58:   PetscObjectGetComm((PetscObject)x1,&comm);
     59:   MPI_Comm_size(comm,&size);
     60:   MatAssembled(B,&assembled);
     61:   if (assembled) {
     62:     MatZeroEntries(B);
     63:   }
     64:   if (!snes->nvwork) {
     65:     if (snes->dm) {
     66:       DMGetGlobalVector(snes->dm,&j1a);
     67:       DMGetGlobalVector(snes->dm,&j2a);
     68:       DMGetGlobalVector(snes->dm,&x2);
     69:     } else {
     70:       snes->nvwork = 3;
     71:       VecDuplicateVecs(x1,snes->nvwork,&snes->vwork);
     72:       PetscLogObjectParents(snes,snes->nvwork,snes->vwork);
     73:       j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2];
     74:     }
     75:   }

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

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

     86:   if (use_wp) {
     87:     VecNorm(x1,NORM_2,&unorm);
     88:   }
     89:   /* Compute Jacobian approximation, 1 column at a time.
     90:       x1 = current iterate, j1a = F(x1)
     91:       x2 = perturbed iterate, j2a = F(x2)
     92:    */
     93:   for (i=0; i<N; i++) {
     94:     VecCopy(x1,x2);
     95:     if (i>= start && i<end) {
     96:       VecGetArrayRead(x1,&xx);
     97:       if (use_wp) dx = PetscSqrtReal(1.0 + unorm);
     98:       else        dx = xx[i-start];
     99:       VecRestoreArrayRead(x1,&xx);
    100:       if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
    101:       dx    *= epsilon;
    102:       wscale = 1.0/dx;
    103:       VecSetValues(x2,1,&i,&dx,ADD_VALUES);
    104:     } else {
    105:       wscale = 0.0;
    106:     }
    107:     VecAssemblyBegin(x2);
    108:     VecAssemblyEnd(x2);
    109:     SNESComputeFunction(snes,x2,j2a);
    110:     VecAXPY(j2a,-1.0,j1a);
    111:     /* Communicate scale=1/dx_i to all processors */
    112:     VecGetOwnershipRanges(x1,&ranges);
    113:     root = size;
    114:     for (j=size-1; j>-1; j--) {
    115:       root--;
    116:       if (i>=ranges[j]) break;
    117:     }
    118:     MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);

    120:     VecScale(j2a,wscale);
    121:     VecNorm(j2a,NORM_INFINITY,&amax); amax *= 1.e-14;
    122:     VecGetArray(j2a,&y);
    123:     for (j=start; j<end; j++) {
    124:       if (PetscAbsScalar(y[j-start]) > amax || j == i) {
    125:         MatSetValues(B,1,&j,1,&i,y+j-start,INSERT_VALUES);
    126:       }
    127:     }
    128:     VecRestoreArray(j2a,&y);
    129:   }
    130:   if (snes->dm) {
    131:     DMRestoreGlobalVector(snes->dm,&j1a);
    132:     DMRestoreGlobalVector(snes->dm,&j2a);
    133:     DMRestoreGlobalVector(snes->dm,&x2);
    134:   }
    135:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    136:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    137:   if (B != J) {
    138:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    139:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    140:   }
    141:   return(0);
    142: }