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:   PetscOptionsGetReal(((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,0);

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

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

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

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

 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:       VecGetArrayRead(x1,&xx);
 93:       if (use_wp) dx = PetscSqrtReal(1.0 + unorm);
 94:       else        dx = xx[i-start];
 95:       VecRestoreArrayRead(x1,&xx);
 96:       if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
 97:       dx    *= epsilon;
 98:       wscale = 1.0/dx;
 99:       VecSetValues(x2,1,&i,&dx,ADD_VALUES);
100:     } else {
101:       wscale = 0.0;
102:     }
103:     VecAssemblyBegin(x2);
104:     VecAssemblyEnd(x2);
105:     SNESComputeFunction(snes,x2,j2a);
106:     VecAXPY(j2a,-1.0,j1a);
107:     /* Communicate scale=1/dx_i to all processors */
108:     VecGetOwnershipRanges(x1,&ranges);
109:     root = size;
110:     for (j=size-1; j>-1; j--) {
111:       root--;
112:       if (i>=ranges[j]) break;
113:     }
114:     MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);

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