Actual source code: fdiff.c

  1: #include <petsctao.h>
  2: #include <petsc/private/taoimpl.h>
  3: #include <petscsnes.h>
  4: #include <petscdmshell.h>

  6: /*
  7:    For finite difference computations of the Hessian, we use PETSc's SNESComputeJacobianDefault
  8: */
  9: static PetscErrorCode Fsnes(SNES snes, Vec X, Vec G, PetscCtx ctx)
 10: {
 11:   Tao tao = (Tao)ctx;

 13:   PetscFunctionBegin;
 15:   PetscCall(TaoComputeGradient(tao, X, G));
 16:   PetscFunctionReturn(PETSC_SUCCESS);
 17: }

 19: /*@C
 20:   TaoDefaultComputeGradient - computes the gradient using finite differences.

 22:   Collective

 24:   Input Parameters:
 25: + tao   - the Tao context
 26: . Xin   - compute gradient at this point
 27: - dummy - not used

 29:   Output Parameter:
 30: . G - Gradient Vector

 32:   Options Database Key:
 33: + -tao_fd_gradient    - activates TaoDefaultComputeGradient()
 34: - -tao_fd_delta delta - change in X used to calculate finite differences

 36:   Level: advanced

 38:   Notes:
 39:   This routine is slow and expensive, and is not optimized
 40:   to take advantage of sparsity in the problem.  Although
 41:   not recommended for general use
 42:   in large-scale applications, it can be useful in checking the
 43:   correctness of a user-provided gradient using the command-line option `-tao_test_gradient`
 44:   This finite difference gradient evaluation can be set using the routine `TaoSetGradient()` or by using the command line option -tao_fd_gradient

 46: .seealso: `Tao`, `TaoSetGradient()`, `TaoTermComputeGradientFD()`
 47: @*/
 48: PetscErrorCode TaoDefaultComputeGradient(Tao tao, Vec Xin, Vec G, void *dummy)
 49: {
 50:   Vec          X;
 51:   PetscScalar *g;
 52:   PetscReal    f, f2;
 53:   PetscInt     low, high, N, i;
 54:   PetscBool    flg;
 55:   PetscReal    h = .5 * PETSC_SQRT_MACHINE_EPSILON;

 57:   PetscFunctionBegin;
 58:   PetscCall(PetscOptionsGetReal(((PetscObject)tao)->options, ((PetscObject)tao)->prefix, "-tao_fd_delta", &h, &flg));
 59:   PetscCall(VecDuplicate(Xin, &X));
 60:   PetscCall(VecCopy(Xin, X));
 61:   PetscCall(VecGetSize(X, &N));
 62:   PetscCall(VecGetOwnershipRange(X, &low, &high));
 63:   PetscCall(VecSetOption(X, VEC_IGNORE_OFF_PROC_ENTRIES, PETSC_TRUE));
 64:   PetscCall(VecGetArray(G, &g));
 65:   for (i = 0; i < N; i++) {
 66:     PetscCall(VecSetValue(X, i, -h, ADD_VALUES));
 67:     PetscCall(VecAssemblyBegin(X));
 68:     PetscCall(VecAssemblyEnd(X));
 69:     PetscCall(TaoComputeObjective(tao, X, &f));
 70:     PetscCall(VecSetValue(X, i, 2.0 * h, ADD_VALUES));
 71:     PetscCall(VecAssemblyBegin(X));
 72:     PetscCall(VecAssemblyEnd(X));
 73:     PetscCall(TaoComputeObjective(tao, X, &f2));
 74:     PetscCall(VecSetValue(X, i, -h, ADD_VALUES));
 75:     PetscCall(VecAssemblyBegin(X));
 76:     PetscCall(VecAssemblyEnd(X));
 77:     if (i >= low && i < high) g[i - low] = (f2 - f) / (2.0 * h);
 78:   }
 79:   PetscCall(VecRestoreArray(G, &g));
 80:   PetscCall(VecDestroy(&X));
 81:   PetscFunctionReturn(PETSC_SUCCESS);
 82: }

 84: /*@C
 85:   TaoDefaultComputeHessian - Computes the Hessian using finite differences.

 87:   Collective

 89:   Input Parameters:
 90: + tao   - the Tao context
 91: . V     - compute Hessian at this point
 92: - dummy - not used

 94:   Output Parameters:
 95: + H - Hessian matrix (not altered in this routine)
 96: - B - newly computed Hessian matrix to use with preconditioner (generally the same as H)

 98:   Options Database Key:
 99: . -tao_fd_hessian - activates TaoDefaultComputeHessian()

101:   Level: advanced

103:   Notes:
104:   This routine is slow and expensive, and is not optimized
105:   to take advantage of sparsity in the problem.  Although
106:   it is not recommended for general use
107:   in large-scale applications, It can be useful in checking the
108:   correctness of a user-provided Hessian.

110: .seealso: `Tao`, `TaoSetHessian()`, `TaoDefaultComputeHessianColor()`, `SNESComputeJacobianDefault()`, `TaoSetGradient()`, `TaoDefaultComputeGradient()`
111: @*/
112: PetscErrorCode TaoDefaultComputeHessian(Tao tao, Vec V, Mat H, Mat B, void *dummy)
113: {
114:   SNES snes;
115:   DM   dm;

117:   PetscFunctionBegin;
118:   PetscCall(PetscInfo(tao, "TAO Using finite differences w/o coloring to compute Hessian matrix\n"));
119:   PetscCall(SNESCreate(PetscObjectComm((PetscObject)H), &snes));
120:   PetscCall(SNESSetFunction(snes, NULL, Fsnes, tao));
121:   PetscCall(SNESGetDM(snes, &dm));
122:   PetscCall(DMShellSetGlobalVector(dm, V));
123:   PetscCall(SNESSetUp(snes));
124:   if (H) {
125:     PetscInt n, N;

127:     PetscCall(VecGetSize(V, &N));
128:     PetscCall(VecGetLocalSize(V, &n));
129:     PetscCall(MatSetSizes(H, n, n, N, N));
130:     PetscCall(MatSetUp(H));
131:   }
132:   if (B && B != H) {
133:     PetscInt n, N;

135:     PetscCall(VecGetSize(V, &N));
136:     PetscCall(VecGetLocalSize(V, &n));
137:     PetscCall(MatSetSizes(B, n, n, N, N));
138:     PetscCall(MatSetUp(B));
139:   }
140:   PetscCall(SNESComputeJacobianDefault(snes, V, H, B, NULL));
141:   PetscCall(SNESDestroy(&snes));
142:   PetscFunctionReturn(PETSC_SUCCESS);
143: }

145: /*@C
146:   TaoDefaultComputeHessianColor - Computes the Hessian using colored finite differences.

148:   Collective

150:   Input Parameters:
151: + tao - the Tao context
152: . V   - compute Hessian at this point
153: - ctx - the color object of type `MatFDColoring`

155:   Output Parameters:
156: + H - Hessian matrix (not altered in this routine)
157: - B - newly computed Hessian matrix to use with preconditioner (generally the same as H)

159:   Level: advanced

161: .seealso: `Tao`, `MatColoring`, `TaoSetHessian()`, `TaoDefaultComputeHessian()`, `SNESComputeJacobianDefaultColor()`, `TaoSetGradient()`
162: @*/
163: PetscErrorCode TaoDefaultComputeHessianColor(Tao tao, Vec V, Mat H, Mat B, PetscCtx ctx)
164: {
165:   MatFDColoring coloring = (MatFDColoring)ctx;

167:   PetscFunctionBegin;
169:   PetscCall(PetscInfo(tao, "TAO computing matrix using finite differences Hessian and coloring\n"));
170:   PetscCall(MatFDColoringApply(B, coloring, V, ctx));
171:   if (H != B) {
172:     PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
173:     PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
174:   }
175:   PetscFunctionReturn(PETSC_SUCCESS);
176: }

178: /*@
179:   TaoDefaultComputeHessianMFFD - Computes the Hessian using finite differences with `MATMFFD`.

181:   Collective

183:   Input Parameters:
184: + tao - the `Tao` context
185: . X   - compute Hessian at this point
186: - ctx - ignored

188:   Output Parameters:
189: + H - Hessian matrix of type `MATMFFD`
190: - B - should be `NULL` or equal to `H`

192:   Level: advanced

194:   Note:
195:   This can be passed to `TaoSetHessian()` to use `MATMFFD` for approximate Hessian-vector products.  The matrix `H` can originate from
196:   `MatCreateMFFD()` or from `TaoTermCreateHessianMFFD()`.

198: .seealso: `Tao`, `MATMFFD`, `MatCreateMFFD()`, `TaoTermCreateHessianMFFD()`
199: @*/
200: PetscErrorCode TaoDefaultComputeHessianMFFD(Tao tao, Vec X, Mat H, Mat B, PetscCtx ctx)
201: {
202:   PetscInt  n, N;
203:   PetscBool assembled;

205:   PetscFunctionBegin;
206:   PetscCheck(!B || B == H, PetscObjectComm((PetscObject)tao), PETSC_ERR_SUP, "Preconditioning Hessian matrix");
207:   PetscCall(MatAssembled(H, &assembled));
208:   if (!assembled) {
209:     PetscCall(VecGetSize(X, &N));
210:     PetscCall(VecGetLocalSize(X, &n));
211:     PetscCall(MatSetSizes(H, n, n, N, N));
212:     PetscCall(MatSetType(H, MATMFFD));
213:     PetscCall(MatSetUp(H));
214:     PetscCall(MatMFFDSetFunction(H, (PetscErrorCode (*)(void *, Vec, Vec))TaoComputeGradient, tao));
215:   }
216:   PetscCall(MatMFFDSetBase(H, X, NULL));
217:   PetscCall(MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY));
218:   PetscCall(MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY));
219:   PetscFunctionReturn(PETSC_SUCCESS);
220: }