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 on SNES 9 10 Input Parameters: 11 + x1 - compute Jacobian at this point 12 - ctx - application's function context, as set with SNESSetFunction() 13 14 Output Parameters: 15 + J - Jacobian matrix (not altered in this routine) 16 - B - newly computed Jacobian matrix to use with preconditioner (generally the same as J) 17 18 Options Database Key: 19 + -snes_fd - Activates SNESComputeJacobianDefault() 20 . -snes_test_err - Square root of function error tolerance, default square root of machine 21 epsilon (1.e-8 in double, 3.e-4 in single) 22 - -mat_fd_type - Either wp or ds (see MATMFFD_WP or MATMFFD_DS) 23 24 Notes: 25 This routine is slow and expensive, and is not currently optimized 26 to take advantage of sparsity in the problem. Although 27 SNESComputeJacobianDefault() is not recommended for general use 28 in large-scale applications, It can be useful in checking the 29 correctness of a user-provided Jacobian. 30 31 An alternative routine that uses coloring to exploit matrix sparsity is 32 SNESComputeJacobianDefaultColor(). 33 34 Level: intermediate 35 36 .seealso: SNESSetJacobian(), SNESComputeJacobianDefaultColor(), MatCreateSNESMF() 37 @*/ 38 PetscErrorCode SNESComputeJacobianDefault(SNES snes,Vec x1,Mat J,Mat B,void *ctx) 39 { 40 Vec j1a,j2a,x2; 41 PetscErrorCode ierr; 42 PetscInt i,N,start,end,j,value,root; 43 PetscScalar dx,*y,wscale; 44 const PetscScalar *xx; 45 PetscReal amax,epsilon = PETSC_SQRT_MACHINE_EPSILON; 46 PetscReal dx_min = 1.e-16,dx_par = 1.e-1,unorm; 47 MPI_Comm comm; 48 PetscBool assembled,use_wp = PETSC_TRUE,flg; 49 const char *list[2] = {"ds","wp"}; 50 PetscMPIInt size; 51 const PetscInt *ranges; 52 53 PetscFunctionBegin; 54 /* Since this Jacobian will possibly have "extra" nonzero locations just turn off errors for these locations */ 55 ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);CHKERRQ(ierr); 56 ierr = PetscOptionsGetReal(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,NULL);CHKERRQ(ierr); 57 58 ierr = PetscObjectGetComm((PetscObject)x1,&comm);CHKERRQ(ierr); 59 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 60 ierr = MatAssembled(B,&assembled);CHKERRQ(ierr); 61 if (assembled) { 62 ierr = MatZeroEntries(B);CHKERRQ(ierr); 63 } 64 if (!snes->nvwork) { 65 if (snes->dm) { 66 ierr = DMGetGlobalVector(snes->dm,&j1a);CHKERRQ(ierr); 67 ierr = DMGetGlobalVector(snes->dm,&j2a);CHKERRQ(ierr); 68 ierr = DMGetGlobalVector(snes->dm,&x2);CHKERRQ(ierr); 69 } else { 70 snes->nvwork = 3; 71 ierr = VecDuplicateVecs(x1,snes->nvwork,&snes->vwork);CHKERRQ(ierr); 72 ierr = PetscLogObjectParents(snes,snes->nvwork,snes->vwork);CHKERRQ(ierr); 73 j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2]; 74 } 75 } 76 77 ierr = VecGetSize(x1,&N);CHKERRQ(ierr); 78 ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr); 79 ierr = SNESComputeFunction(snes,x1,j1a);CHKERRQ(ierr); 80 81 ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)snes),((PetscObject)snes)->prefix,"Differencing options","SNES");CHKERRQ(ierr); 82 ierr = PetscOptionsEList("-mat_fd_type","Algorithm to compute difference parameter","SNESComputeJacobianDefault",list,2,"wp",&value,&flg);CHKERRQ(ierr); 83 ierr = PetscOptionsEnd();CHKERRQ(ierr); 84 if (flg && !value) use_wp = PETSC_FALSE; 85 86 if (use_wp) { 87 ierr = VecNorm(x1,NORM_2,&unorm);CHKERRQ(ierr); 88 } 89 /* Compute Jacobian approximation, 1 column at a time. 90 x1 = current iterate, j1a = F(x1) 91 x2 = perturbed iterate, j2a = F(x2) 92 */ 93 for (i=0; i<N; i++) { 94 ierr = VecCopy(x1,x2);CHKERRQ(ierr); 95 if (i>= start && i<end) { 96 ierr = VecGetArrayRead(x1,&xx);CHKERRQ(ierr); 97 if (use_wp) dx = PetscSqrtReal(1.0 + unorm); 98 else dx = xx[i-start]; 99 ierr = VecRestoreArrayRead(x1,&xx);CHKERRQ(ierr); 100 if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par; 101 dx *= epsilon; 102 wscale = 1.0/dx; 103 ierr = VecSetValues(x2,1,&i,&dx,ADD_VALUES);CHKERRQ(ierr); 104 } else { 105 wscale = 0.0; 106 } 107 ierr = VecAssemblyBegin(x2);CHKERRQ(ierr); 108 ierr = VecAssemblyEnd(x2);CHKERRQ(ierr); 109 ierr = SNESComputeFunction(snes,x2,j2a);CHKERRQ(ierr); 110 ierr = VecAXPY(j2a,-1.0,j1a);CHKERRQ(ierr); 111 /* Communicate scale=1/dx_i to all processors */ 112 ierr = VecGetOwnershipRanges(x1,&ranges);CHKERRQ(ierr); 113 root = size; 114 for (j=size-1; j>-1; j--) { 115 root--; 116 if (i>=ranges[j]) break; 117 } 118 ierr = MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);CHKERRQ(ierr); 119 120 ierr = VecScale(j2a,wscale);CHKERRQ(ierr); 121 ierr = VecNorm(j2a,NORM_INFINITY,&amax);CHKERRQ(ierr); amax *= 1.e-14; 122 ierr = VecGetArray(j2a,&y);CHKERRQ(ierr); 123 for (j=start; j<end; j++) { 124 if (PetscAbsScalar(y[j-start]) > amax || j == i) { 125 ierr = MatSetValues(B,1,&j,1,&i,y+j-start,INSERT_VALUES);CHKERRQ(ierr); 126 } 127 } 128 ierr = VecRestoreArray(j2a,&y);CHKERRQ(ierr); 129 } 130 if (snes->dm) { 131 ierr = DMRestoreGlobalVector(snes->dm,&j1a);CHKERRQ(ierr); 132 ierr = DMRestoreGlobalVector(snes->dm,&j2a);CHKERRQ(ierr); 133 ierr = DMRestoreGlobalVector(snes->dm,&x2);CHKERRQ(ierr); 134 } 135 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 136 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 137 if (B != J) { 138 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 139 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 140 } 141 PetscFunctionReturn(0); 142 } 143 144 145