Actual source code: snesmfj2.c
2: #include <petsc/private/snesimpl.h>
3: /* matimpl.h is needed only for logging of matrix operation */
4: #include <petsc/private/matimpl.h>
6: PETSC_INTERN PetscErrorCode SNESUnSetMatrixFreeParameter(SNES);
8: PETSC_INTERN PetscErrorCode SNESDiffParameterCreate_More(SNES, Vec, void **);
9: PETSC_INTERN PetscErrorCode SNESDiffParameterCompute_More(SNES, void *, Vec, Vec, PetscReal *, PetscReal *);
10: PETSC_INTERN PetscErrorCode SNESDiffParameterDestroy_More(void *);
12: typedef struct { /* default context for matrix-free SNES */
13: SNES snes; /* SNES context */
14: Vec w; /* work vector */
15: MatNullSpace sp; /* null space context */
16: PetscReal error_rel; /* square root of relative error in computing function */
17: PetscReal umin; /* minimum allowable u'a value relative to |u|_1 */
18: PetscBool jorge; /* flag indicating use of Jorge's method for determining the differencing parameter */
19: PetscReal h; /* differencing parameter */
20: PetscBool need_h; /* flag indicating whether we must compute h */
21: PetscBool need_err; /* flag indicating whether we must currently compute error_rel */
22: PetscBool compute_err; /* flag indicating whether we must ever compute error_rel */
23: PetscInt compute_err_iter; /* last iter where we've computer error_rel */
24: PetscInt compute_err_freq; /* frequency of computing error_rel */
25: void *data; /* implementation-specific data */
26: } MFCtx_Private;
28: PetscErrorCode SNESMatrixFreeDestroy2_Private(Mat mat)
29: {
30: MFCtx_Private *ctx;
32: PetscFunctionBegin;
33: PetscCall(MatShellGetContext(mat, &ctx));
34: PetscCall(VecDestroy(&ctx->w));
35: PetscCall(MatNullSpaceDestroy(&ctx->sp));
36: if (ctx->jorge || ctx->compute_err) PetscCall(SNESDiffParameterDestroy_More(ctx->data));
37: PetscCall(PetscFree(ctx));
38: PetscFunctionReturn(PETSC_SUCCESS);
39: }
41: /*
42: SNESMatrixFreeView2_Private - Views matrix-free parameters.
43: */
44: PetscErrorCode SNESMatrixFreeView2_Private(Mat J, PetscViewer viewer)
45: {
46: MFCtx_Private *ctx;
47: PetscBool iascii;
49: PetscFunctionBegin;
50: PetscCall(MatShellGetContext(J, &ctx));
51: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
52: if (iascii) {
53: PetscCall(PetscViewerASCIIPrintf(viewer, " SNES matrix-free approximation:\n"));
54: if (ctx->jorge) PetscCall(PetscViewerASCIIPrintf(viewer, " using Jorge's method of determining differencing parameter\n"));
55: PetscCall(PetscViewerASCIIPrintf(viewer, " err=%g (relative error in function evaluation)\n", (double)ctx->error_rel));
56: PetscCall(PetscViewerASCIIPrintf(viewer, " umin=%g (minimum iterate parameter)\n", (double)ctx->umin));
57: if (ctx->compute_err) PetscCall(PetscViewerASCIIPrintf(viewer, " freq_err=%" PetscInt_FMT " (frequency for computing err)\n", ctx->compute_err_freq));
58: }
59: PetscFunctionReturn(PETSC_SUCCESS);
60: }
62: /*
63: SNESMatrixFreeMult2_Private - Default matrix-free form for Jacobian-vector
64: product, y = F'(u)*a:
65: y = (F(u + ha) - F(u)) /h,
66: where F = nonlinear function, as set by SNESSetFunction()
67: u = current iterate
68: h = difference interval
69: */
70: PetscErrorCode SNESMatrixFreeMult2_Private(Mat mat, Vec a, Vec y)
71: {
72: MFCtx_Private *ctx;
73: SNES snes;
74: PetscReal h, norm, sum, umin, noise;
75: PetscScalar hs, dot;
76: Vec w, U, F;
77: MPI_Comm comm;
78: PetscInt iter;
79: PetscErrorCode (*eval_fct)(SNES, Vec, Vec);
81: PetscFunctionBegin;
82: /* We log matrix-free matrix-vector products separately, so that we can
83: separate the performance monitoring from the cases that use conventional
84: storage. We may eventually modify event logging to associate events
85: with particular objects, hence alleviating the more general problem. */
86: PetscCall(PetscLogEventBegin(MATMFFD_Mult, a, y, 0, 0));
88: PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
89: PetscCall(MatShellGetContext(mat, &ctx));
90: snes = ctx->snes;
91: w = ctx->w;
92: umin = ctx->umin;
94: PetscCall(SNESGetSolution(snes, &U));
95: eval_fct = SNESComputeFunction;
96: PetscCall(SNESGetFunction(snes, &F, NULL, NULL));
98: /* Determine a "good" step size, h */
99: if (ctx->need_h) {
100: /* Use Jorge's method to compute h */
101: if (ctx->jorge) {
102: PetscCall(SNESDiffParameterCompute_More(snes, ctx->data, U, a, &noise, &h));
104: /* Use the Brown/Saad method to compute h */
105: } else {
106: /* Compute error if desired */
107: PetscCall(SNESGetIterationNumber(snes, &iter));
108: if ((ctx->need_err) || ((ctx->compute_err_freq) && (ctx->compute_err_iter != iter) && (!((iter - 1) % ctx->compute_err_freq)))) {
109: /* Use Jorge's method to compute noise */
110: PetscCall(SNESDiffParameterCompute_More(snes, ctx->data, U, a, &noise, &h));
112: ctx->error_rel = PetscSqrtReal(noise);
114: PetscCall(PetscInfo(snes, "Using Jorge's noise: noise=%g, sqrt(noise)=%g, h_more=%g\n", (double)noise, (double)ctx->error_rel, (double)h));
116: ctx->compute_err_iter = iter;
117: ctx->need_err = PETSC_FALSE;
118: }
120: PetscCall(VecDotBegin(U, a, &dot));
121: PetscCall(VecNormBegin(a, NORM_1, &sum));
122: PetscCall(VecNormBegin(a, NORM_2, &norm));
123: PetscCall(VecDotEnd(U, a, &dot));
124: PetscCall(VecNormEnd(a, NORM_1, &sum));
125: PetscCall(VecNormEnd(a, NORM_2, &norm));
127: /* Safeguard for step sizes too small */
128: if (sum == 0.0) {
129: dot = 1.0;
130: norm = 1.0;
131: } else if (PetscAbsScalar(dot) < umin * sum && PetscRealPart(dot) >= 0.0) dot = umin * sum;
132: else if (PetscAbsScalar(dot) < 0.0 && PetscRealPart(dot) > -umin * sum) dot = -umin * sum;
133: h = PetscRealPart(ctx->error_rel * dot / (norm * norm));
134: }
135: } else h = ctx->h;
137: if (!ctx->jorge || !ctx->need_h) PetscCall(PetscInfo(snes, "h = %g\n", (double)h));
139: /* Evaluate function at F(u + ha) */
140: hs = h;
141: PetscCall(VecWAXPY(w, hs, a, U));
142: PetscCall(eval_fct(snes, w, y));
143: PetscCall(VecAXPY(y, -1.0, F));
144: PetscCall(VecScale(y, 1.0 / hs));
145: if (mat->nullsp) PetscCall(MatNullSpaceRemove(mat->nullsp, y));
147: PetscCall(PetscLogEventEnd(MATMFFD_Mult, a, y, 0, 0));
148: PetscFunctionReturn(PETSC_SUCCESS);
149: }
151: /*@C
152: MatCreateSNESMFMore - Creates a matrix-free matrix
153: context for use with a `SNES` solver that uses the More method to compute an optimal h based on the noise of the function. This matrix can be used as
154: the Jacobian argument for the routine `SNESSetJacobian()`.
156: Input Parameters:
157: + snes - the `SNES` context
158: - x - vector where `SNES` solution is to be stored.
160: Output Parameter:
161: . J - the matrix-free matrix
163: Options Database Keys:
164: + -snes_mf_err <error_rel> - see `MatCreateSNESMF()`
165: . -snes_mf_umin <umin> - see `MatCreateSNESMF()`
166: . -snes_mf_compute_err - compute the square root or relative error in function
167: . -snes_mf_freq_err <freq> - set the frequency to recompute the parameters
168: - -snes_mf_jorge - use the method of Jorge More
170: Level: advanced
172: Notes:
173: This is an experimental approach, use `MatCreateSNESMF()`.
175: The matrix-free matrix context merely contains the function pointers
176: and work space for performing finite difference approximations of
177: Jacobian-vector products, J(u)*a, via
179: .vb
180: J(u)*a = [J(u+h*a) - J(u)]/h,
181: where by default
182: h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
183: = error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 otherwise
184: where
185: error_rel = square root of relative error in function evaluation
186: umin = minimum iterate parameter
187: Alternatively, the differencing parameter, h, can be set using
188: Jorge's nifty new strategy if one specifies the option
189: -snes_mf_jorge
190: .ve
192: The user can set these parameters via `MatMFFDSetFunctionError()`.
194: The user should call `MatDestroy()` when finished with the matrix-free
195: matrix context.
197: .seealso: `SNESCreateMF()`, `MatCreateMFFD()`, `MatDestroy()`, `MatMFFDSetFunctionError()`
198: @*/
199: PetscErrorCode MatCreateSNESMFMore(SNES snes, Vec x, Mat *J)
200: {
201: MPI_Comm comm;
202: MFCtx_Private *mfctx;
203: PetscInt n, nloc;
204: PetscBool flg;
205: char p[64];
207: PetscFunctionBegin;
208: PetscCall(PetscNew(&mfctx));
209: mfctx->sp = NULL;
210: mfctx->snes = snes;
211: mfctx->error_rel = PETSC_SQRT_MACHINE_EPSILON;
212: mfctx->umin = 1.e-6;
213: mfctx->h = 0.0;
214: mfctx->need_h = PETSC_TRUE;
215: mfctx->need_err = PETSC_FALSE;
216: mfctx->compute_err = PETSC_FALSE;
217: mfctx->compute_err_freq = 0;
218: mfctx->compute_err_iter = -1;
219: mfctx->compute_err = PETSC_FALSE;
220: mfctx->jorge = PETSC_FALSE;
222: PetscCall(PetscOptionsGetReal(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_err", &mfctx->error_rel, NULL));
223: PetscCall(PetscOptionsGetReal(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_umin", &mfctx->umin, NULL));
224: PetscCall(PetscOptionsGetBool(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_jorge", &mfctx->jorge, NULL));
225: PetscCall(PetscOptionsGetBool(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_compute_err", &mfctx->compute_err, NULL));
226: PetscCall(PetscOptionsGetInt(((PetscObject)snes)->options, ((PetscObject)snes)->prefix, "-snes_mf_freq_err", &mfctx->compute_err_freq, &flg));
227: if (flg) {
228: if (mfctx->compute_err_freq < 0) mfctx->compute_err_freq = 0;
229: mfctx->compute_err = PETSC_TRUE;
230: }
231: if (mfctx->compute_err) mfctx->need_err = PETSC_TRUE;
232: if (mfctx->jorge || mfctx->compute_err) {
233: PetscCall(SNESDiffParameterCreate_More(snes, x, &mfctx->data));
234: } else mfctx->data = NULL;
236: PetscCall(PetscOptionsHasHelp(((PetscObject)snes)->options, &flg));
237: PetscCall(PetscStrncpy(p, "-", sizeof(p)));
238: if (((PetscObject)snes)->prefix) PetscCall(PetscStrlcat(p, ((PetscObject)snes)->prefix, sizeof(p)));
239: if (flg) {
240: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " Matrix-free Options (via SNES):\n"));
241: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " %ssnes_mf_err <err>: set sqrt of relative error in function (default %g)\n", p, (double)mfctx->error_rel));
242: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " %ssnes_mf_umin <umin>: see users manual (default %g)\n", p, (double)mfctx->umin));
243: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " %ssnes_mf_jorge: use Jorge More's method\n", p));
244: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " %ssnes_mf_compute_err: compute sqrt or relative error in function\n", p));
245: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " %ssnes_mf_freq_err <freq>: frequency to recompute this (default only once)\n", p));
246: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)snes), " %ssnes_mf_noise_file <file>: set file for printing noise info\n", p));
247: }
248: PetscCall(VecDuplicate(x, &mfctx->w));
249: PetscCall(PetscObjectGetComm((PetscObject)x, &comm));
250: PetscCall(VecGetSize(x, &n));
251: PetscCall(VecGetLocalSize(x, &nloc));
252: PetscCall(MatCreate(comm, J));
253: PetscCall(MatSetSizes(*J, nloc, n, n, n));
254: PetscCall(MatSetType(*J, MATSHELL));
255: PetscCall(MatShellSetContext(*J, mfctx));
256: PetscCall(MatShellSetOperation(*J, MATOP_MULT, (void (*)(void))SNESMatrixFreeMult2_Private));
257: PetscCall(MatShellSetOperation(*J, MATOP_DESTROY, (void (*)(void))SNESMatrixFreeDestroy2_Private));
258: PetscCall(MatShellSetOperation(*J, MATOP_VIEW, (void (*)(void))SNESMatrixFreeView2_Private));
259: PetscCall(MatSetUp(*J));
261: PetscFunctionReturn(PETSC_SUCCESS);
262: }
264: /*@C
265: MatSNESMFMoreSetParameters - Sets the parameters for the approximation of
266: matrix-vector products using finite differences, see `MatCreateSNESMFMore()`
268: Input Parameters:
269: + mat - the matrix
270: . error_rel - relative error (should be set to the square root of the relative error in the function evaluations)
271: . umin - minimum allowable u-value
272: - h - differencing parameter
274: Options Database Keys:
275: + -snes_mf_err <error_rel> - see `MatCreateSNESMF()`
276: . -snes_mf_umin <umin> - see `MatCreateSNESMF()`
277: . -snes_mf_compute_err - compute the square root or relative error in function
278: . -snes_mf_freq_err <freq> - set the frequency to recompute the parameters
279: - -snes_mf_jorge - use the method of Jorge More
281: Level: advanced
283: Note:
284: If the user sets the parameter h directly, then this value will be used
285: instead of the default computation as discussed in `MatCreateSNESMFMore()`
287: .seealso: `MatCreateSNESMF()`, `MatCreateSNESMFMore()`
288: @*/
289: PetscErrorCode MatSNESMFMoreSetParameters(Mat mat, PetscReal error, PetscReal umin, PetscReal h)
290: {
291: MFCtx_Private *ctx;
293: PetscFunctionBegin;
294: PetscCall(MatShellGetContext(mat, &ctx));
295: if (ctx) {
296: if (error != (PetscReal)PETSC_DEFAULT) ctx->error_rel = error;
297: if (umin != (PetscReal)PETSC_DEFAULT) ctx->umin = umin;
298: if (h != (PetscReal)PETSC_DEFAULT) {
299: ctx->h = h;
300: ctx->need_h = PETSC_FALSE;
301: }
302: }
303: PetscFunctionReturn(PETSC_SUCCESS);
304: }
306: PetscErrorCode SNESUnSetMatrixFreeParameter(SNES snes)
307: {
308: MFCtx_Private *ctx;
309: Mat mat;
311: PetscFunctionBegin;
312: PetscCall(SNESGetJacobian(snes, &mat, NULL, NULL, NULL));
313: PetscCall(MatShellGetContext(mat, &ctx));
314: if (ctx) ctx->need_h = PETSC_TRUE;
315: PetscFunctionReturn(PETSC_SUCCESS);
316: }