Actual source code: snesj.c


  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: +  snes - the SNES context
 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:    This routine ignores the maximum number of function evaluations set with SNESSetTolerances() and the function
 36:    evaluations it performs are not counted in what is returned by of SNESGetNumberFunctionEvals().

 38:    Level: intermediate

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

 60:   snes->max_funcs = PETSC_MAX_INT;
 61:   /* Since this Jacobian will possibly have "extra" nonzero locations just turn off errors for these locations */
 62:   MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
 63:   PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,NULL);

 65:   PetscObjectGetComm((PetscObject)x1,&comm);
 66:   MPI_Comm_size(comm,&size);
 67:   MatAssembled(B,&assembled);
 68:   if (assembled) {
 69:     MatZeroEntries(B);
 70:   }
 71:   if (!snes->nvwork) {
 72:     if (snes->dm) {
 73:       DMGetGlobalVector(snes->dm,&j1a);
 74:       DMGetGlobalVector(snes->dm,&j2a);
 75:       DMGetGlobalVector(snes->dm,&x2);
 76:     } else {
 77:       snes->nvwork = 3;
 78:       VecDuplicateVecs(x1,snes->nvwork,&snes->vwork);
 79:       PetscLogObjectParents(snes,snes->nvwork,snes->vwork);
 80:       j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2];
 81:     }
 82:   }

 84:   VecGetSize(x1,&N);
 85:   VecGetOwnershipRange(x1,&start,&end);
 86:   SNESGetDM(snes,&dm);
 87:   DMGetDMSNES(dm,&dms);
 88:   if (dms->ops->computemffunction) {
 89:     SNESComputeMFFunction(snes,x1,j1a);
 90:   } else {
 91:     SNESComputeFunction(snes,x1,j1a);
 92:   }

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

 99:   if (use_wp) {
100:     VecNorm(x1,NORM_2,&unorm);
101:   }
102:   /* Compute Jacobian approximation, 1 column at a time.
103:       x1 = current iterate, j1a = F(x1)
104:       x2 = perturbed iterate, j2a = F(x2)
105:    */
106:   for (i=0; i<N; i++) {
107:     VecCopy(x1,x2);
108:     if (i>= start && i<end) {
109:       VecGetArrayRead(x1,&xx);
110:       if (use_wp) dx = PetscSqrtReal(1.0 + unorm);
111:       else        dx = xx[i-start];
112:       VecRestoreArrayRead(x1,&xx);
113:       if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
114:       dx    *= epsilon;
115:       wscale = 1.0/dx;
116:       VecSetValues(x2,1,&i,&dx,ADD_VALUES);
117:     } else {
118:       wscale = 0.0;
119:     }
120:     VecAssemblyBegin(x2);
121:     VecAssemblyEnd(x2);
122:     if (dms->ops->computemffunction) {
123:       SNESComputeMFFunction(snes,x2,j2a);
124:     } else {
125:       SNESComputeFunction(snes,x2,j2a);
126:     }
127:     VecAXPY(j2a,-1.0,j1a);
128:     /* Communicate scale=1/dx_i to all processors */
129:     VecGetOwnershipRanges(x1,&ranges);
130:     root = size;
131:     for (j=size-1; j>-1; j--) {
132:       root--;
133:       if (i>=ranges[j]) break;
134:     }
135:     MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);
136:     VecScale(j2a,wscale);
137:     VecNorm(j2a,NORM_INFINITY,&amax); amax *= 1.e-14;
138:     VecGetArray(j2a,&y);
139:     for (j=start; j<end; j++) {
140:       if (PetscAbsScalar(y[j-start]) > amax || j == i) {
141:         MatSetValues(B,1,&j,1,&i,y+j-start,INSERT_VALUES);
142:       }
143:     }
144:     VecRestoreArray(j2a,&y);
145:   }
146:   if (snes->dm) {
147:     DMRestoreGlobalVector(snes->dm,&j1a);
148:     DMRestoreGlobalVector(snes->dm,&j2a);
149:     DMRestoreGlobalVector(snes->dm,&x2);
150:   }
151:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
152:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
153:   if (B != J) {
154:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
155:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
156:   }
157:   snes->max_funcs = max_funcs;
158:   snes->nfuncs    -= N;
159:   return(0);
160: }