2: #include <petsc-private/snesimpl.h>    /*I  "petscsnes.h"  I*/

  6: /*@C
  7:    SNESDefaultComputeJacobian - 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)
 18: -  flag - flag indicating whether the matrix sparsity structure has changed

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

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

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

 36:    Level: intermediate

 38: .keywords: SNES, finite differences, Jacobian

 40: .seealso: SNESSetJacobian(), SNESDefaultComputeJacobianColor(), MatCreateSNESMF()
 41: @*/
 42: PetscErrorCode  SNESDefaultComputeJacobian(SNES snes,Vec x1,Mat *J,Mat *B,MatStructure *flag,void *ctx)
 43: {
 44:   Vec            j1a,j2a,x2;
 46:   PetscInt       i,N,start,end,j,value,root;
 47:   PetscScalar    dx,*y,*xx,wscale;
 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:   PetscErrorCode (*eval_fct)(SNES,Vec,Vec)=0;
 52:   PetscBool      assembled,use_wp = PETSC_TRUE,flg;
 53:   const char     *list[2] = {"ds","wp"};
 54:   PetscMPIInt    size;
 55:   const PetscInt *ranges;

 58:   PetscOptionsGetReal(((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,0);
 59:   eval_fct = SNESComputeFunction;

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

 74:   VecGetSize(x1,&N);
 75:   VecGetOwnershipRange(x1,&start,&end);
 76:   (*eval_fct)(snes,x1,j1a);

 78:   PetscOptionsEList("-mat_fd_type","Algorithm to compute difference parameter","SNESDefaultComputeJacobian",list,2,"wp",&value,&flg);
 79:   if (flg && !value) {
 80:     use_wp = PETSC_FALSE;
 81:   }
 82:   if (use_wp) {
 83:     VecNorm(x1,NORM_2,&unorm);
 84:   }
 85:   /* Compute Jacobian approximation, 1 column at a time. 
 86:       x1 = current iterate, j1a = F(x1)
 87:       x2 = perturbed iterate, j2a = F(x2)
 88:    */
 89:   for (i=0; i<N; i++) {
 90:     VecCopy(x1,x2);
 91:     if (i>= start && i<end) {
 92:       VecGetArray(x1,&xx);
 93:       if (use_wp) {
 94:         dx = 1.0 + unorm;
 95:       } else {
 96:         dx = xx[i-start];
 97:       }
 98:       VecRestoreArray(x1,&xx);
 99:       if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
100:       dx *= epsilon;
101:       wscale = 1.0/dx;
102:       VecSetValues(x2,1,&i,&dx,ADD_VALUES);
103:     } else {
104:       wscale = 0.0;
105:     }
106:     VecAssemblyBegin(x2);
107:     VecAssemblyEnd(x2);
108:     (*eval_fct)(snes,x2,j2a);
109:     VecAXPY(j2a,-1.0,j1a);
110:     /* Communicate scale=1/dx_i to all processors */
111:     VecGetOwnershipRanges(x1,&ranges);
112:     root = size;
113:     for (j=size-1; j>-1; j--){
114:       root--;
115:       if (i>=ranges[j]) break;
116:     }
117:     MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);

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