1 #define PETSCSNES_DLL 2 3 #include "private/snesimpl.h" /*I "petscsnes.h" I*/ 4 5 #undef __FUNCT__ 6 #define __FUNCT__ "SNESDefaultComputeJacobian" 7 /*@C 8 SNESDefaultComputeJacobian - Computes the Jacobian using finite differences. 9 10 Collective on SNES 11 12 Input Parameters: 13 + x1 - compute Jacobian at this point 14 - ctx - application's function context, as set with SNESSetFunction() 15 16 Output Parameters: 17 + J - Jacobian matrix (not altered in this routine) 18 . B - newly computed Jacobian matrix to use with preconditioner (generally the same as J) 19 - flag - flag indicating whether the matrix sparsity structure has changed 20 21 Options Database Key: 22 + -snes_fd - Activates SNESDefaultComputeJacobian() 23 . -snes_test_err - Square root of function error tolerance, default square root of machine 24 epsilon (1.e-8 in double, 3.e-4 in single) 25 - -mat_fd_type - Either wp or ds (see MATMFFD_WP or MATMFFD_DS) 26 27 Notes: 28 This routine is slow and expensive, and is not currently optimized 29 to take advantage of sparsity in the problem. Although 30 SNESDefaultComputeJacobian() is not recommended for general use 31 in large-scale applications, It can be useful in checking the 32 correctness of a user-provided Jacobian. 33 34 An alternative routine that uses coloring to exploit matrix sparsity is 35 SNESDefaultComputeJacobianColor(). 36 37 Level: intermediate 38 39 .keywords: SNES, finite differences, Jacobian 40 41 .seealso: SNESSetJacobian(), SNESDefaultComputeJacobianColor(), MatCreateSNESMF() 42 @*/ 43 PetscErrorCode SNESDefaultComputeJacobian(SNES snes,Vec x1,Mat *J,Mat *B,MatStructure *flag,void *ctx) 44 { 45 Vec j1a,j2a,x2; 46 PetscErrorCode ierr; 47 PetscInt i,N,start,end,j,value,root; 48 PetscScalar dx,*y,*xx,wscale; 49 PetscReal amax,epsilon = PETSC_SQRT_MACHINE_EPSILON; 50 PetscReal dx_min = 1.e-16,dx_par = 1.e-1,unorm; 51 MPI_Comm comm; 52 PetscErrorCode (*eval_fct)(SNES,Vec,Vec)=0; 53 PetscBool assembled,use_wp = PETSC_TRUE,flg; 54 const char *list[2] = {"ds","wp"}; 55 PetscMPIInt size; 56 const PetscInt *ranges; 57 58 PetscFunctionBegin; 59 ierr = PetscOptionsGetReal(((PetscObject)snes)->prefix,"-snes_test_err",&epsilon,0);CHKERRQ(ierr); 60 eval_fct = SNESComputeFunction; 61 62 ierr = PetscObjectGetComm((PetscObject)x1,&comm);CHKERRQ(ierr); 63 ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr); 64 ierr = MatAssembled(*B,&assembled);CHKERRQ(ierr); 65 if (assembled) { 66 ierr = MatZeroEntries(*B);CHKERRQ(ierr); 67 } 68 if (!snes->nvwork) { 69 snes->nvwork = 3; 70 ierr = VecDuplicateVecs(x1,snes->nvwork,&snes->vwork);CHKERRQ(ierr); 71 ierr = PetscLogObjectParents(snes,snes->nvwork,snes->vwork);CHKERRQ(ierr); 72 } 73 j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2]; 74 75 ierr = VecGetSize(x1,&N);CHKERRQ(ierr); 76 ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr); 77 ierr = (*eval_fct)(snes,x1,j1a);CHKERRQ(ierr); 78 79 ierr = PetscOptionsEList("-mat_fd_type","Algorithm to compute difference parameter","SNESDefaultComputeJacobian",list,2,"wp",&value,&flg);CHKERRQ(ierr); 80 if (flg && !value) { 81 use_wp = PETSC_FALSE; 82 } 83 if (use_wp) { 84 ierr = VecNorm(x1,NORM_2,&unorm);CHKERRQ(ierr); 85 } 86 /* Compute Jacobian approximation, 1 column at a time. 87 x1 = current iterate, j1a = F(x1) 88 x2 = perturbed iterate, j2a = F(x2) 89 */ 90 for (i=0; i<N; i++) { 91 ierr = VecCopy(x1,x2);CHKERRQ(ierr); 92 if (i>= start && i<end) { 93 ierr = VecGetArray(x1,&xx);CHKERRQ(ierr); 94 if (use_wp) { 95 dx = 1.0 + unorm; 96 } else { 97 dx = xx[i-start]; 98 } 99 ierr = VecRestoreArray(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 = (*eval_fct)(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 ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 131 ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 132 if (*B != *J) { 133 ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 134 ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 135 } 136 *flag = DIFFERENT_NONZERO_PATTERN; 137 PetscFunctionReturn(0); 138 } 139 140 141