1 /*$Id: snesj.c,v 1.75 2001/09/11 18:06:40 bsmith Exp $*/ 2 3 #include "src/snes/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 26 Notes: 27 This routine is slow and expensive, and is not currently optimized 28 to take advantage of sparsity in the problem. Although 29 SNESDefaultComputeJacobian() is not recommended for general use 30 in large-scale applications, It can be useful in checking the 31 correctness of a user-provided Jacobian. 32 33 An alternative routine that uses coloring to explot matrix sparsity is 34 SNESDefaultComputeJacobianColor(). 35 36 Level: intermediate 37 38 .keywords: SNES, finite differences, Jacobian 39 40 .seealso: SNESSetJacobian(), SNESDefaultComputeJacobianColor() 41 @*/ 42 int SNESDefaultComputeJacobian(SNES snes,Vec x1,Mat *J,Mat *B,MatStructure *flag,void *ctx) 43 { 44 Vec j1a,j2a,x2; 45 int i,ierr,N,start,end,j; 46 PetscScalar dx,mone = -1.0,*y,scale,*xx,wscale; 47 PetscReal amax,epsilon = PETSC_SQRT_MACHINE_EPSILON; 48 PetscReal dx_min = 1.e-16,dx_par = 1.e-1; 49 MPI_Comm comm; 50 int (*eval_fct)(SNES,Vec,Vec)=0; 51 52 PetscFunctionBegin; 53 ierr = PetscOptionsGetReal(snes->prefix,"-snes_test_err",&epsilon,0);CHKERRQ(ierr); 54 eval_fct = SNESComputeFunction; 55 56 ierr = PetscObjectGetComm((PetscObject)x1,&comm);CHKERRQ(ierr); 57 ierr = MatZeroEntries(*B);CHKERRQ(ierr); 58 if (!snes->nvwork) { 59 ierr = VecDuplicateVecs(x1,3,&snes->vwork);CHKERRQ(ierr); 60 snes->nvwork = 3; 61 PetscLogObjectParents(snes,3,snes->vwork); 62 } 63 j1a = snes->vwork[0]; j2a = snes->vwork[1]; x2 = snes->vwork[2]; 64 65 ierr = VecGetSize(x1,&N);CHKERRQ(ierr); 66 ierr = VecGetOwnershipRange(x1,&start,&end);CHKERRQ(ierr); 67 ierr = (*eval_fct)(snes,x1,j1a);CHKERRQ(ierr); 68 69 /* Compute Jacobian approximation, 1 column at a time. 70 x1 = current iterate, j1a = F(x1) 71 x2 = perturbed iterate, j2a = F(x2) 72 */ 73 for (i=0; i<N; i++) { 74 ierr = VecCopy(x1,x2);CHKERRQ(ierr); 75 if (i>= start && i<end) { 76 ierr = VecGetArray(x1,&xx);CHKERRQ(ierr); 77 dx = xx[i-start]; 78 ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr); 79 #if !defined(PETSC_USE_COMPLEX) 80 if (dx < dx_min && dx >= 0.0) dx = dx_par; 81 else if (dx < 0.0 && dx > -dx_min) dx = -dx_par; 82 #else 83 if (PetscAbsScalar(dx) < dx_min && PetscRealPart(dx) >= 0.0) dx = dx_par; 84 else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < dx_min) dx = -dx_par; 85 #endif 86 dx *= epsilon; 87 wscale = 1.0/dx; 88 ierr = VecSetValues(x2,1,&i,&dx,ADD_VALUES);CHKERRQ(ierr); 89 } else { 90 wscale = 0.0; 91 } 92 ierr = (*eval_fct)(snes,x2,j2a);CHKERRQ(ierr); 93 ierr = VecAXPY(&mone,j1a,j2a);CHKERRQ(ierr); 94 /* Communicate scale to all processors */ 95 ierr = MPI_Allreduce(&wscale,&scale,1,MPIU_SCALAR,PetscSum_Op,comm);CHKERRQ(ierr); 96 ierr = VecScale(&scale,j2a);CHKERRQ(ierr); 97 ierr = VecNorm(j2a,NORM_INFINITY,&amax);CHKERRQ(ierr); amax *= 1.e-14; 98 ierr = VecGetArray(j2a,&y);CHKERRQ(ierr); 99 for (j=start; j<end; j++) { 100 if (PetscAbsScalar(y[j-start]) > amax) { 101 ierr = MatSetValues(*B,1,&j,1,&i,y+j-start,INSERT_VALUES);CHKERRQ(ierr); 102 } 103 } 104 ierr = VecRestoreArray(j2a,&y);CHKERRQ(ierr); 105 } 106 ierr = MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 107 ierr = MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 108 *flag = DIFFERENT_NONZERO_PATTERN; 109 PetscFunctionReturn(0); 110 } 111 112 113