1 2 #include <petsc-private/snesimpl.h> /*I "petscsnes.h" I*/ 3 4 #undef __FUNCT__ 5 #define __FUNCT__ "SNESComputeJacobianDefault" 6 /*@C 7 SNESComputeJacobianDefault - Computes the Jacobian using finite differences. 8 9 Collective on SNES 10 11 Input Parameters: 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 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) 24 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. 31 32 An alternative routine that uses coloring to exploit matrix sparsity is 33 SNESComputeJacobianDefaultColor(). 34 35 Level: intermediate 36 37 .keywords: SNES, finite differences, Jacobian 38 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,*xx,wscale; 47 PetscReal amax,epsilon = PETSC_SQRT_MACHINE_EPSILON; 48 PetscReal dx_min = 1.e-16,dx_par = 1.e-1,unorm; 49 MPI_Comm comm; 50 PetscErrorCode (*eval_fct)(SNES,Vec,Vec)=0; 51 PetscBool assembled,use_wp = PETSC_TRUE,flg; 52 const char *list[2] = {"ds","wp"}; 53 PetscMPIInt size; 54 const PetscInt *ranges; 55 56 PetscFunctionBegin; 57 ierr = PetscOptionsGetReal(((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,0);CHKERRQ(ierr); 58 eval_fct = SNESComputeFunction; 59 60 ierr = PetscObjectGetComm((PetscObject)x1,&comm);CHKERRQ(ierr); 61 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 62 ierr = MatAssembled(B,&assembled);CHKERRQ(ierr); 63 if (assembled) { 64 ierr = MatZeroEntries(B);CHKERRQ(ierr); 65 } 66 if (!snes->nvwork) { 67 snes->nvwork = 3; 68 69 ierr = VecDuplicateVecs(x1,snes->nvwork,&snes->vwork);CHKERRQ(ierr); 70 ierr = PetscLogObjectParents(snes,snes->nvwork,snes->vwork);CHKERRQ(ierr); 71 } 72 j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2]; 73 74 ierr = VecGetSize(x1,&N);CHKERRQ(ierr); 75 ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr); 76 ierr = (*eval_fct)(snes,x1,j1a);CHKERRQ(ierr); 77 78 ierr = PetscOptionsEList("-mat_fd_type","Algorithm to compute difference parameter","SNESComputeJacobianDefault",list,2,"wp",&value,&flg);CHKERRQ(ierr); 79 if (flg && !value) use_wp = PETSC_FALSE; 80 81 if (use_wp) { 82 ierr = VecNorm(x1,NORM_2,&unorm);CHKERRQ(ierr); 83 } 84 /* Compute Jacobian approximation, 1 column at a time. 85 x1 = current iterate, j1a = F(x1) 86 x2 = perturbed iterate, j2a = F(x2) 87 */ 88 for (i=0; i<N; i++) { 89 ierr = VecCopy(x1,x2);CHKERRQ(ierr); 90 if (i>= start && i<end) { 91 ierr = VecGetArray(x1,&xx);CHKERRQ(ierr); 92 if (use_wp) dx = 1.0 + unorm; 93 else dx = xx[i-start]; 94 ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr); 95 if (PetscAbsScalar(dx) < dx_min) dx = (PetscRealPart(dx) < 0. ? -1. : 1.) * dx_par; 96 dx *= epsilon; 97 wscale = 1.0/dx; 98 ierr = VecSetValues(x2,1,&i,&dx,ADD_VALUES);CHKERRQ(ierr); 99 } else { 100 wscale = 0.0; 101 } 102 ierr = VecAssemblyBegin(x2);CHKERRQ(ierr); 103 ierr = VecAssemblyEnd(x2);CHKERRQ(ierr); 104 ierr = (*eval_fct)(snes,x2,j2a);CHKERRQ(ierr); 105 ierr = VecAXPY(j2a,-1.0,j1a);CHKERRQ(ierr); 106 /* Communicate scale=1/dx_i to all processors */ 107 ierr = VecGetOwnershipRanges(x1,&ranges);CHKERRQ(ierr); 108 root = size; 109 for (j=size-1; j>-1; j--) { 110 root--; 111 if (i>=ranges[j]) break; 112 } 113 ierr = MPI_Bcast(&wscale,1,MPIU_SCALAR,root,comm);CHKERRQ(ierr); 114 115 ierr = VecScale(j2a,wscale);CHKERRQ(ierr); 116 ierr = VecNorm(j2a,NORM_INFINITY,&amax);CHKERRQ(ierr); amax *= 1.e-14; 117 ierr = VecGetArray(j2a,&y);CHKERRQ(ierr); 118 for (j=start; j<end; j++) { 119 if (PetscAbsScalar(y[j-start]) > amax || j == i) { 120 ierr = MatSetValues(B,1,&j,1,&i,y+j-start,INSERT_VALUES);CHKERRQ(ierr); 121 } 122 } 123 ierr = VecRestoreArray(j2a,&y);CHKERRQ(ierr); 124 } 125 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 126 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 127 if (B != J) { 128 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 129 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 130 } 131 PetscFunctionReturn(0); 132 } 133 134 135