1 2 #include <petsc/private/snesimpl.h> /*I "petscsnes.h" I*/ 3 #include <petscdm.h> 4 5 /*@C 6 SNESComputeJacobianDefault - Computes the Jacobian using finite differences. 7 8 Collective 9 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()` 14 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 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`) 25 26 Level: intermediate 27 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. 34 35 An alternative routine that uses coloring to exploit matrix sparsity is 36 `SNESComputeJacobianDefaultColor()`. 37 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()`. 40 41 This function can be provided to `SNESSetJacobian()` along with a dense matrix to hold the Jacobian 42 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; 60 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)); 66 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 } 84 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 } 94 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; 99 100 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 } 159