Actual source code: snesj.c
1: #include <petsc/private/snesimpl.h>
2: #include <petsc/private/vecimpl.h>
3: #include <petscdm.h>
5: /*@
6: SNESComputeJacobianDefault - Computes the Jacobian using finite differences.
8: Collective
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 Keys:
20: + -snes_fd - Activates `SNESComputeJacobianDefault()`
21: . -snes_fd_coloring - Activates a faster computation that uses a graph coloring of the matrix
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: Level: intermediate
28: Notes:
29: This routine is slow and expensive, and is not currently optimized
30: to take advantage of sparsity in the problem. Although
31: `SNESComputeJacobianDefault()` is not recommended for general use
32: in large-scale applications, It can be useful in checking the
33: correctness of a user-provided Jacobian.
35: An alternative routine that uses coloring to exploit matrix sparsity is
36: `SNESComputeJacobianDefaultColor()`.
38: This routine ignores the maximum number of function evaluations set with `SNESSetTolerances()` and the function
39: evaluations it performs are not counted in what is returned by of `SNESGetNumberFunctionEvals()`.
41: This function can be provided to `SNESSetJacobian()` along with a dense matrix to hold the Jacobian
43: Developer Note:
44: The function has a poorly chosen name since it does not mention the use of finite differences
46: .seealso: [](ch_snes), `SNES`, `SNESSetJacobian()`, `SNESComputeJacobianDefaultColor()`, `MatCreateSNESMF()`
47: @*/
48: PetscErrorCode SNESComputeJacobianDefault(SNES snes, Vec x1, Mat J, Mat B, void *ctx)
49: {
50: Vec j1a, j2a, x2;
51: PetscInt i, N, start, end, j, value, max_funcs = snes->max_funcs;
52: PetscScalar dx, *y, wscale;
53: const PetscScalar *xx;
54: PetscReal amax, epsilon = PETSC_SQRT_MACHINE_EPSILON;
55: PetscReal dx_min = 1.e-16, dx_par = 1.e-1, unorm;
56: MPI_Comm comm;
57: PetscBool assembled, use_wp = PETSC_TRUE, flg;
58: const char *list[2] = {"ds", "wp"};
59: PetscMPIInt size, root;
60: const PetscInt *ranges;
61: DM dm;
62: DMSNES dms;
64: PetscFunctionBegin;
65: snes->max_funcs = PETSC_INT_MAX;
66: /* Since this Jacobian will possibly have "extra" nonzero locations just turn off errors for these locations */
67: PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
68: PetscCall(PetscOptionsGetReal(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_test_err", &epsilon, NULL));
70: PetscCall(PetscObjectGetComm((PetscObject)x1, &comm));
71: PetscCallMPI(MPI_Comm_size(comm, &size));
72: PetscCall(MatAssembled(B, &assembled));
73: if (assembled) PetscCall(MatZeroEntries(B));
74: if (!snes->nvwork) {
75: if (snes->dm) {
76: PetscCall(DMGetGlobalVector(snes->dm, &j1a));
77: PetscCall(DMGetGlobalVector(snes->dm, &j2a));
78: PetscCall(DMGetGlobalVector(snes->dm, &x2));
79: } else {
80: snes->nvwork = 3;
81: PetscCall(VecDuplicateVecs(x1, snes->nvwork, &snes->vwork));
82: j1a = snes->vwork[0];
83: j2a = snes->vwork[1];
84: x2 = snes->vwork[2];
85: }
86: }
88: PetscCall(VecGetSize(x1, &N));
89: PetscCall(VecGetOwnershipRange(x1, &start, &end));
90: PetscCall(SNESGetDM(snes, &dm));
91: PetscCall(DMGetDMSNES(dm, &dms));
92: if (dms->ops->computemffunction) {
93: PetscCall(SNESComputeMFFunction(snes, x1, j1a));
94: } else {
95: PetscCall(SNESComputeFunction(snes, x1, j1a));
96: }
98: PetscOptionsBegin(PetscObjectComm((PetscObject)snes), ((PetscObject)snes)->prefix, "Differencing options", "SNES");
99: PetscCall(PetscOptionsEList("-mat_fd_type", "Algorithm to compute difference parameter", "SNESComputeJacobianDefault", list, 2, "wp", &value, &flg));
100: PetscOptionsEnd();
101: if (flg && !value) use_wp = PETSC_FALSE;
103: if (use_wp) PetscCall(VecNorm(x1, NORM_2, &unorm));
104: /* Compute Jacobian approximation, 1 column at a time.
105: x1 = current iterate, j1a = F(x1)
106: x2 = perturbed iterate, j2a = F(x2)
107: */
108: for (i = 0; i < N; i++) {
109: PetscCall(VecCopy(x1, x2));
110: if (i >= start && i < end) {
111: PetscCall(VecGetArrayRead(x1, &xx));
112: if (use_wp) dx = PetscSqrtReal(1.0 + unorm);
113: else dx = xx[i - start];
114: PetscCall(VecRestoreArrayRead(x1, &xx));
115: if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par;
116: dx *= epsilon;
117: wscale = 1.0 / dx;
118: if (x2->ops->setvalues) PetscCall(VecSetValues(x2, 1, &i, &dx, ADD_VALUES));
119: else {
120: PetscCall(VecGetArray(x2, &y));
121: y[i - start] += dx;
122: PetscCall(VecRestoreArray(x2, &y));
123: }
124: } else {
125: wscale = 0.0;
126: }
127: PetscCall(VecAssemblyBegin(x2));
128: PetscCall(VecAssemblyEnd(x2));
129: if (dms->ops->computemffunction) {
130: PetscCall(SNESComputeMFFunction(snes, x2, j2a));
131: } else {
132: PetscCall(SNESComputeFunction(snes, x2, j2a));
133: }
134: PetscCall(VecAXPY(j2a, -1.0, j1a));
135: /* Communicate scale=1/dx_i to all processors */
136: PetscCall(VecGetOwnershipRanges(x1, &ranges));
137: root = size;
138: for (j = size - 1; j > -1; j--) {
139: root--;
140: if (i >= ranges[j]) break;
141: }
142: PetscCallMPI(MPI_Bcast(&wscale, 1, MPIU_SCALAR, root, comm));
143: PetscCall(VecScale(j2a, wscale));
144: PetscCall(VecNorm(j2a, NORM_INFINITY, &amax));
145: amax *= 1.e-14;
146: PetscCall(VecGetArray(j2a, &y));
147: for (j = start; j < end; j++) {
148: if (PetscAbsScalar(y[j - start]) > amax || j == i) PetscCall(MatSetValues(B, 1, &j, 1, &i, y + j - start, INSERT_VALUES));
149: }
150: PetscCall(VecRestoreArray(j2a, &y));
151: }
152: if (snes->dm) {
153: PetscCall(DMRestoreGlobalVector(snes->dm, &j1a));
154: PetscCall(DMRestoreGlobalVector(snes->dm, &j2a));
155: PetscCall(DMRestoreGlobalVector(snes->dm, &x2));
156: }
157: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
158: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
159: if (B != J) {
160: PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
161: PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
162: }
163: snes->max_funcs = max_funcs;
164: snes->nfuncs -= N;
165: PetscFunctionReturn(PETSC_SUCCESS);
166: }