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
17: Optional functions:
18: -------------------
19: MatMFFDView_ - prints information about the parameters being used.
20: This is called when SNESView() or -snes_view is used.
22: MatMFFDSetFromOptions_ - checks the options database for options that
23: apply to this method.
25: MatMFFDDestroy_ - frees any space allocated by the routines above
27: */
29: /*
30: This include file defines the data structure MatMFFD that
31: includes information about the computation of h. It is shared by
32: all implementations that people provide
33: */
34: #include <petsc/private/matimpl.h>
35: #include <../src/mat/impls/mffd/mffdimpl.h> /*I "petscmat.h" I*/
37: /*
38: The method has one parameter that is used to
39: "cutoff" very small values. This is stored in a data structure
40: that is only visible to this file. If your method has no parameters
41: it can omit this, if it has several simply reorganize the data structure.
42: The data structure is "hung-off" the MatMFFD data structure in
43: the void *hctx; field.
44: */
45: typedef struct {
46: PetscReal umin; /* minimum allowable u'a value relative to |u|_1 */
47: } MatMFFD_DS;
51: /*
52: MatMFFDCompute_DS - Standard PETSc code for computing the
53: differencing paramter (h) for use with matrix-free finite differences.
55: Input Parameters:
56: + ctx - the matrix free context
57: . U - the location at which you want the Jacobian
58: - a - the direction you want the derivative
61: Output Parameter:
62: . h - the scale computed
64: */
65: static PetscErrorCode MatMFFDCompute_DS(MatMFFD ctx,Vec U,Vec a,PetscScalar *h,PetscBool *zeroa) 66: {
67: MatMFFD_DS *hctx = (MatMFFD_DS*)ctx->hctx;
68: PetscReal nrm,sum,umin = hctx->umin;
69: PetscScalar dot;
73: if (!(ctx->count % ctx->recomputeperiod)) {
74: /*
75: This algorithm requires 2 norms and 1 inner product. Rather than
76: use directly the VecNorm() and VecDot() routines (and thus have
77: three separate collective operations, we use the VecxxxBegin/End() routines
78: */
79: VecDotBegin(U,a,&dot);
80: VecNormBegin(a,NORM_1,&sum);
81: VecNormBegin(a,NORM_2,&nrm);
82: VecDotEnd(U,a,&dot);
83: VecNormEnd(a,NORM_1,&sum);
84: VecNormEnd(a,NORM_2,&nrm);
86: if (nrm == 0.0) {
87: *zeroa = PETSC_TRUE;
88: return(0);
89: }
90: *zeroa = PETSC_FALSE;
92: /*
93: Safeguard for step sizes that are "too small"
94: */
95: if (PetscAbsScalar(dot) < umin*sum && PetscRealPart(dot) >= 0.0) dot = umin*sum;
96: else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin*sum) dot = -umin*sum;
97: *h = ctx->error_rel*dot/(nrm*nrm);
98: } else {
99: *h = ctx->currenth;
100: }
101: if (*h != *h) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Differencing parameter is not a number sum = %g dot = %g norm = %g",(double)sum,(double)PetscRealPart(dot),(double)nrm);
102: ctx->count++;
103: return(0);
104: }
108: /*
109: MatMFFDView_DS - Prints information about this particular
110: method for computing h. Note that this does not print the general
111: information about the matrix-free method, as such info is printed
112: by the calling routine.
114: Input Parameters:
115: + ctx - the matrix free context
116: - viewer - the PETSc viewer
117: */
118: static PetscErrorCode MatMFFDView_DS(MatMFFD ctx,PetscViewer viewer)119: {
120: MatMFFD_DS *hctx = (MatMFFD_DS*)ctx->hctx;
122: PetscBool iascii;
125: /*
126: Currently this only handles the ascii file viewers, others
127: could be added, but for this type of object other viewers
128: make less sense
129: */
130: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
131: if (iascii) {
132: PetscViewerASCIIPrintf(viewer," umin=%g (minimum iterate parameter)\n",(double)hctx->umin);
133: }
134: return(0);
135: }
139: /*
140: MatMFFDSetFromOptions_DS - Looks in the options database for
141: any options appropriate for this method.
143: Input Parameter:
144: . ctx - the matrix free context
146: */
147: static PetscErrorCode MatMFFDSetFromOptions_DS(PetscOptions *PetscOptionsObject,MatMFFD ctx)148: {
150: MatMFFD_DS *hctx = (MatMFFD_DS*)ctx->hctx;
153: PetscOptionsHead(PetscOptionsObject,"Finite difference matrix free parameters");
154: PetscOptionsReal("-mat_mffd_umin","umin","MatMFFDDSSetUmin",hctx->umin,&hctx->umin,0);
155: PetscOptionsTail();
156: return(0);
157: }
161: /*
162: MatMFFDDestroy_DS - Frees the space allocated by
163: MatCreateMFFD_DS().
165: Input Parameter:
166: . ctx - the matrix free context
168: Notes:
169: Does not free the ctx, that is handled by the calling routine
170: */
171: static PetscErrorCode MatMFFDDestroy_DS(MatMFFD ctx)172: {
176: PetscFree(ctx->hctx);
177: return(0);
178: }
182: /*
183: The following two routines use the PetscObjectCompose() and PetscObjectQuery()
184: mechanism to allow the user to change the Umin parameter used in this method.
185: */
186: PetscErrorCode MatMFFDDSSetUmin_DS(Mat mat,PetscReal umin)187: {
188: MatMFFD ctx = (MatMFFD)mat->data;
189: MatMFFD_DS *hctx;
192: if (!ctx) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MatMFFDDSSetUmin() attached to non-shell matrix");
193: hctx = (MatMFFD_DS*)ctx->hctx;
194: hctx->umin = umin;
195: return(0);
196: }
200: /*@
201: MatMFFDDSSetUmin - Sets the "umin" parameter used by the
202: PETSc routine for computing the differencing parameter, h, which is used
203: for matrix-free Jacobian-vector products.
205: Input Parameters:
206: + A - the matrix created with MatCreateSNESMF()
207: - umin - the parameter
209: Level: advanced
211: Notes:
212: See the manual page for MatCreateSNESMF() for a complete description of the
213: algorithm used to compute h.
215: .seealso: MatMFFDSetFunctionError(), MatCreateSNESMF()
217: @*/
218: PetscErrorCodeMatMFFDDSSetUmin(Mat A,PetscReal umin)219: {
224: PetscTryMethod(A,"MatMFFDDSSetUmin_C",(Mat,PetscReal),(A,umin));
225: return(0);
226: }
228: /*MC
229: MATMFFD_DS - the code for compute the "h" used in the finite difference
230: matrix-free matrix vector product. This code
231: implements the strategy in Dennis and Schnabel, "Numerical Methods for Unconstrained
232: Optimization and Nonlinear Equations".
234: Options Database Keys:
235: . -mat_mffd_umin <umin> see MatMFFDDSSetUmin()
237: Level: intermediate
239: Notes: Requires 2 norms and 1 inner product, but they are computed together
240: so only one parallel collective operation is needed. See MATMFFD_WP for a method
241: (with GMRES) that requires NO collective operations.
243: Formula used:
244: F'(u)*a = [F(u+h*a) - F(u)]/h where
245: h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
246: = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 otherwise
247: where
248: error_rel = square root of relative error in function evaluation
249: umin = minimum iterate parameter
251: .seealso: MATMFFD, MatCreateMFFD(), MatCreateSNESMF(), MATMFFD_WP, MatMFFDDSSetUmin()
253: M*/
256: PETSC_EXTERN PetscErrorCode MatCreateMFFD_DS(MatMFFD ctx)257: {
258: MatMFFD_DS *hctx;
262: /* allocate my own private data structure */
263: PetscNewLog(ctx,&hctx);
264: ctx->hctx = (void*)hctx;
265: /* set a default for my parameter */
266: hctx->umin = 1.e-6;
268: /* set the functions I am providing */
269: ctx->ops->compute = MatMFFDCompute_DS;
270: ctx->ops->destroy = MatMFFDDestroy_DS;
271: ctx->ops->view = MatMFFDView_DS;
272: ctx->ops->setfromoptions = MatMFFDSetFromOptions_DS;
274: PetscObjectComposeFunction((PetscObject)ctx->mat,"MatMFFDDSSetUmin_C",MatMFFDDSSetUmin_DS);
275: return(0);
276: }