Actual source code: snesj.c
petsc-3.7.3 2016-08-01
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: }