Actual source code: mffddef.c
2: /*
3: Implements the DS PETSc approach for computing the h
4: parameter used with the finite difference based matrix-free
5: Jacobian-vector products.
7: To make your own: clone this file and modify for your needs.
9: Mandatory functions:
10: -------------------
11: MatMFFDCompute_ - for a given point and direction computes h
13: MatCreateMFFD _ - fills in the MatMFFD data structure
14: for this particular implementation
16: Optional functions:
17: -------------------
18: MatMFFDView_ - prints information about the parameters being used.
19: This is called when SNESView() or -snes_view is used.
21: MatMFFDSetFromOptions_ - checks the options database for options that
22: apply to this method.
24: MatMFFDDestroy_ - frees any space allocated by the routines above
26: */
28: /*
29: This include file defines the data structure MatMFFD that
30: includes information about the computation of h. It is shared by
31: all implementations that people provide
32: */
33: #include <petsc/private/matimpl.h>
34: #include <../src/mat/impls/mffd/mffdimpl.h>
36: /*
37: The method has one parameter that is used to
38: "cutoff" very small values. This is stored in a data structure
39: that is only visible to this file. If your method has no parameters
40: it can omit this, if it has several simply reorganize the data structure.
41: The data structure is "hung-off" the MatMFFD data structure in
42: the void *hctx; field.
43: */
44: typedef struct {
45: PetscReal umin; /* minimum allowable u'a value relative to |u|_1 */
46: } MatMFFD_DS;
48: /*
49: MatMFFDCompute_DS - Standard PETSc code for computing the
50: differencing parameter (h) for use with matrix-free finite differences.
52: Input Parameters:
53: + ctx - the matrix free context
54: . U - the location at which you want the Jacobian
55: - a - the direction you want the derivative
57: Output Parameter:
58: . h - the scale computed
60: */
61: static PetscErrorCode MatMFFDCompute_DS(MatMFFD ctx, Vec U, Vec a, PetscScalar *h, PetscBool *zeroa)
62: {
63: MatMFFD_DS *hctx = (MatMFFD_DS *)ctx->hctx;
64: PetscReal nrm, sum, umin = hctx->umin;
65: PetscScalar dot;
67: if (!(ctx->count % ctx->recomputeperiod)) {
68: /*
69: This algorithm requires 2 norms and 1 inner product. Rather than
70: use directly the VecNorm() and VecDot() routines (and thus have
71: three separate collective operations, we use the VecxxxBegin/End() routines
72: */
73: VecDotBegin(U, a, &dot);
74: VecNormBegin(a, NORM_1, &sum);
75: VecNormBegin(a, NORM_2, &nrm);
76: VecDotEnd(U, a, &dot);
77: VecNormEnd(a, NORM_1, &sum);
78: VecNormEnd(a, NORM_2, &nrm);
80: if (nrm == 0.0) {
81: *zeroa = PETSC_TRUE;
82: return 0;
83: }
84: *zeroa = PETSC_FALSE;
86: /*
87: Safeguard for step sizes that are "too small"
88: */
89: if (PetscAbsScalar(dot) < umin * sum && PetscRealPart(dot) >= 0.0) dot = umin * sum;
90: else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin * sum) dot = -umin * sum;
91: *h = ctx->error_rel * dot / (nrm * nrm);
93: } else {
94: *h = ctx->currenth;
95: }
96: ctx->count++;
97: return 0;
98: }
100: /*
101: MatMFFDView_DS - Prints information about this particular
102: method for computing h. Note that this does not print the general
103: information about the matrix-free method, as such info is printed
104: by the calling routine.
106: Input Parameters:
107: + ctx - the matrix free context
108: - viewer - the PETSc viewer
109: */
110: static PetscErrorCode MatMFFDView_DS(MatMFFD ctx, PetscViewer viewer)
111: {
112: MatMFFD_DS *hctx = (MatMFFD_DS *)ctx->hctx;
113: PetscBool iascii;
115: /*
116: Currently this only handles the ascii file viewers, others
117: could be added, but for this type of object other viewers
118: make less sense
119: */
120: PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii);
121: if (iascii) PetscViewerASCIIPrintf(viewer, " umin=%g (minimum iterate parameter)\n", (double)hctx->umin);
122: return 0;
123: }
125: /*
126: MatMFFDSetFromOptions_DS - Looks in the options database for
127: any options appropriate for this method.
129: Input Parameter:
130: . ctx - the matrix free context
132: */
133: static PetscErrorCode MatMFFDSetFromOptions_DS(MatMFFD ctx, PetscOptionItems *PetscOptionsObject)
134: {
135: MatMFFD_DS *hctx = (MatMFFD_DS *)ctx->hctx;
137: PetscOptionsHeadBegin(PetscOptionsObject, "Finite difference matrix free parameters");
138: PetscOptionsReal("-mat_mffd_umin", "umin", "MatMFFDDSSetUmin", hctx->umin, &hctx->umin, NULL);
139: PetscOptionsHeadEnd();
140: return 0;
141: }
143: /*
144: MatMFFDDestroy_DS - Frees the space allocated by
145: MatCreateMFFD_DS().
147: Input Parameter:
148: . ctx - the matrix free context
150: Note:
151: Does not free the ctx, that is handled by the calling routine
152: */
153: static PetscErrorCode MatMFFDDestroy_DS(MatMFFD ctx)
154: {
155: PetscFree(ctx->hctx);
156: return 0;
157: }
159: /*
160: The following two routines use the PetscObjectCompose() and PetscObjectQuery()
161: mechanism to allow the user to change the Umin parameter used in this method.
162: */
163: PetscErrorCode MatMFFDDSSetUmin_DS(Mat mat, PetscReal umin)
164: {
165: MatMFFD ctx = NULL;
166: MatMFFD_DS *hctx;
168: MatShellGetContext(mat, &ctx);
170: hctx = (MatMFFD_DS *)ctx->hctx;
171: hctx->umin = umin;
172: return 0;
173: }
175: /*@
176: MatMFFDDSSetUmin - Sets the "umin" parameter used by the
177: PETSc routine for computing the differencing parameter, h, which is used
178: for matrix-free Jacobian-vector products for a `MATMFFD` matrix.
180: Input Parameters:
181: + A - the `MATMFFD` matrix
182: - umin - the parameter
184: Level: advanced
186: Note:
187: See the manual page for `MatCreateSNESMF()` for a complete description of the
188: algorithm used to compute h.
190: .seealso: `MATMFFD`, `MatMFFDSetFunctionError()`, `MatCreateSNESMF()`
191: @*/
192: PetscErrorCode MatMFFDDSSetUmin(Mat A, PetscReal umin)
193: {
195: PetscTryMethod(A, "MatMFFDDSSetUmin_C", (Mat, PetscReal), (A, umin));
196: return 0;
197: }
199: /*MC
200: MATMFFD_DS - algorithm for compute the "h" used in the finite difference matrix-free matrix vector product, `MatMult()`.
202: Options Database Keys:
203: . -mat_mffd_umin <umin> - see `MatMFFDDSSetUmin()`
205: Level: intermediate
207: Notes:
208: Requires 2 norms and 1 inner product, but they are computed together
209: so only one parallel collective operation is needed. See `MATMFFD_WP` for a method
210: (with `KSPGMRES`) that requires NO collective operations.
212: Formula used:
213: F'(u)*a = [F(u+h*a) - F(u)]/h where
214: h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
215: = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 otherwise
216: where
217: error_rel = square root of relative error in function evaluation
218: umin = minimum iterate parameter
220: References:
221: . * - Dennis and Schnabel, "Numerical Methods for Unconstrained Optimization and Nonlinear Equations"
223: .seealso: `MATMFFD`, `MATMFFD_WP`, `MatCreateMFFD()`, `MatCreateSNESMF()`, `MATMFFD_WP`, `MatMFFDDSSetUmin()`
224: M*/
225: PETSC_EXTERN PetscErrorCode MatCreateMFFD_DS(MatMFFD ctx)
226: {
227: MatMFFD_DS *hctx;
229: /* allocate my own private data structure */
230: PetscNew(&hctx);
231: ctx->hctx = (void *)hctx;
232: /* set a default for my parameter */
233: hctx->umin = 1.e-6;
235: /* set the functions I am providing */
236: ctx->ops->compute = MatMFFDCompute_DS;
237: ctx->ops->destroy = MatMFFDDestroy_DS;
238: ctx->ops->view = MatMFFDView_DS;
239: ctx->ops->setfromoptions = MatMFFDSetFromOptions_DS;
241: PetscObjectComposeFunction((PetscObject)ctx->mat, "MatMFFDDSSetUmin_C", MatMFFDDSSetUmin_DS);
242: return 0;
243: }