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

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

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

 67:   PetscCall(PetscObjectGetComm((PetscObject)x1, &comm));
 68:   PetscCallMPI(MPI_Comm_size(comm, &size));
 69:   PetscCall(MatAssembled(B, &assembled));
 70:   if (assembled) PetscCall(MatZeroEntries(B));
 71:   if (!snes->nvwork) {
 72:     if (snes->dm) {
 73:       PetscCall(DMGetGlobalVector(snes->dm, &j1a));
 74:       PetscCall(DMGetGlobalVector(snes->dm, &j2a));
 75:       PetscCall(DMGetGlobalVector(snes->dm, &x2));
 76:     } else {
 77:       snes->nvwork = 3;
 78:       PetscCall(VecDuplicateVecs(x1, snes->nvwork, &snes->vwork));
 79:       j1a = snes->vwork[0];
 80:       j2a = snes->vwork[1];
 81:       x2  = snes->vwork[2];
 82:     }
 83:   }

 85:   PetscCall(VecGetSize(x1, &N));
 86:   PetscCall(VecGetOwnershipRange(x1, &start, &end));
 87:   PetscCall(SNESGetDM(snes, &dm));
 88:   PetscCall(DMGetDMSNES(dm, &dms));
 89:   if (dms->ops->computemffunction) {
 90:     PetscCall(SNESComputeMFFunction(snes, x1, j1a));
 91:   } else {
 92:     PetscCall(SNESComputeFunction(snes, x1, j1a));
 93:   }

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

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