Actual source code: dmlocalts.c
1: #include <petsc/private/dmimpl.h>
2: #include <petsc/private/tsimpl.h>
4: typedef struct {
5: PetscErrorCode (*boundarylocal)(DM, PetscReal, Vec, Vec, void *);
6: PetscErrorCode (*ifunctionlocal)(DM, PetscReal, Vec, Vec, Vec, void *);
7: PetscErrorCode (*ijacobianlocal)(DM, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *);
8: PetscErrorCode (*rhsfunctionlocal)(DM, PetscReal, Vec, Vec, void *);
9: void *boundarylocalctx;
10: void *ifunctionlocalctx;
11: void *ijacobianlocalctx;
12: void *rhsfunctionlocalctx;
13: Vec lumpedmassinv;
14: Mat mass;
15: KSP kspmass;
16: } DMTS_Local;
18: static PetscErrorCode DMTSDestroy_DMLocal(DMTS tdm)
19: {
20: PetscFunctionBegin;
21: PetscCall(PetscFree(tdm->data));
22: PetscFunctionReturn(PETSC_SUCCESS);
23: }
25: static PetscErrorCode DMTSDuplicate_DMLocal(DMTS oldtdm, DMTS tdm)
26: {
27: PetscFunctionBegin;
28: PetscCall(PetscNew((DMTS_Local **)&tdm->data));
29: if (oldtdm->data) PetscCall(PetscMemcpy(tdm->data, oldtdm->data, sizeof(DMTS_Local)));
30: PetscFunctionReturn(PETSC_SUCCESS);
31: }
33: static PetscErrorCode DMLocalTSGetContext(DM dm, DMTS tdm, DMTS_Local **dmlocalts)
34: {
35: PetscFunctionBegin;
36: *dmlocalts = NULL;
37: if (!tdm->data) {
38: PetscCall(PetscNew((DMTS_Local **)&tdm->data));
40: tdm->ops->destroy = DMTSDestroy_DMLocal;
41: tdm->ops->duplicate = DMTSDuplicate_DMLocal;
42: }
43: *dmlocalts = (DMTS_Local *)tdm->data;
44: PetscFunctionReturn(PETSC_SUCCESS);
45: }
47: static PetscErrorCode TSComputeIFunction_DMLocal(TS ts, PetscReal time, Vec X, Vec X_t, Vec F, void *ctx)
48: {
49: DM dm;
50: Vec locX, locX_t, locF;
51: DMTS_Local *dmlocalts = (DMTS_Local *)ctx;
53: PetscFunctionBegin;
58: PetscCall(TSGetDM(ts, &dm));
59: PetscCall(DMGetLocalVector(dm, &locX));
60: PetscCall(DMGetLocalVector(dm, &locX_t));
61: PetscCall(DMGetLocalVector(dm, &locF));
62: PetscCall(VecZeroEntries(locX));
63: PetscCall(VecZeroEntries(locX_t));
64: if (dmlocalts->boundarylocal) PetscCall((*dmlocalts->boundarylocal)(dm, time, locX, locX_t, dmlocalts->boundarylocalctx));
65: PetscCall(DMGlobalToLocalBegin(dm, X, INSERT_VALUES, locX));
66: PetscCall(DMGlobalToLocalEnd(dm, X, INSERT_VALUES, locX));
67: PetscCall(DMGlobalToLocalBegin(dm, X_t, INSERT_VALUES, locX_t));
68: PetscCall(DMGlobalToLocalEnd(dm, X_t, INSERT_VALUES, locX_t));
69: PetscCall(VecZeroEntries(locF));
70: CHKMEMQ;
71: PetscCall((*dmlocalts->ifunctionlocal)(dm, time, locX, locX_t, locF, dmlocalts->ifunctionlocalctx));
72: CHKMEMQ;
73: PetscCall(VecZeroEntries(F));
74: PetscCall(DMLocalToGlobalBegin(dm, locF, ADD_VALUES, F));
75: PetscCall(DMLocalToGlobalEnd(dm, locF, ADD_VALUES, F));
76: PetscCall(DMRestoreLocalVector(dm, &locX));
77: PetscCall(DMRestoreLocalVector(dm, &locX_t));
78: PetscCall(DMRestoreLocalVector(dm, &locF));
79: PetscFunctionReturn(PETSC_SUCCESS);
80: }
82: static PetscErrorCode TSComputeRHSFunction_DMLocal(TS ts, PetscReal time, Vec X, Vec F, void *ctx)
83: {
84: DM dm;
85: Vec locX, locF;
86: DMTS_Local *dmlocalts = (DMTS_Local *)ctx;
88: PetscFunctionBegin;
92: PetscCall(TSGetDM(ts, &dm));
93: PetscCall(DMGetLocalVector(dm, &locX));
94: PetscCall(DMGetLocalVector(dm, &locF));
95: PetscCall(VecZeroEntries(locX));
96: if (dmlocalts->boundarylocal) PetscCall((*dmlocalts->boundarylocal)(dm, time, locX, NULL, dmlocalts->boundarylocalctx));
97: PetscCall(DMGlobalToLocalBegin(dm, X, INSERT_VALUES, locX));
98: PetscCall(DMGlobalToLocalEnd(dm, X, INSERT_VALUES, locX));
99: PetscCall(VecZeroEntries(locF));
100: CHKMEMQ;
101: PetscCall((*dmlocalts->rhsfunctionlocal)(dm, time, locX, locF, dmlocalts->rhsfunctionlocalctx));
102: CHKMEMQ;
103: PetscCall(VecZeroEntries(F));
104: PetscCall(DMLocalToGlobalBegin(dm, locF, ADD_VALUES, F));
105: PetscCall(DMLocalToGlobalEnd(dm, locF, ADD_VALUES, F));
106: if (dmlocalts->lumpedmassinv) {
107: PetscCall(VecPointwiseMult(F, dmlocalts->lumpedmassinv, F));
108: } else if (dmlocalts->kspmass) {
109: Vec tmp;
111: PetscCall(DMGetGlobalVector(dm, &tmp));
112: PetscCall(KSPSolve(dmlocalts->kspmass, F, tmp));
113: PetscCall(VecCopy(tmp, F));
114: PetscCall(DMRestoreGlobalVector(dm, &tmp));
115: }
116: PetscCall(DMRestoreLocalVector(dm, &locX));
117: PetscCall(DMRestoreLocalVector(dm, &locF));
118: PetscFunctionReturn(PETSC_SUCCESS);
119: }
121: static PetscErrorCode TSComputeIJacobian_DMLocal(TS ts, PetscReal time, Vec X, Vec X_t, PetscReal a, Mat A, Mat B, void *ctx)
122: {
123: DM dm;
124: Vec locX, locX_t;
125: DMTS_Local *dmlocalts = (DMTS_Local *)ctx;
127: PetscFunctionBegin;
128: PetscCall(TSGetDM(ts, &dm));
129: if (dmlocalts->ijacobianlocal) {
130: PetscCall(DMGetLocalVector(dm, &locX));
131: PetscCall(DMGetLocalVector(dm, &locX_t));
132: PetscCall(VecZeroEntries(locX));
133: PetscCall(VecZeroEntries(locX_t));
134: if (dmlocalts->boundarylocal) PetscCall((*dmlocalts->boundarylocal)(dm, time, locX, locX_t, dmlocalts->boundarylocalctx));
135: PetscCall(DMGlobalToLocalBegin(dm, X, INSERT_VALUES, locX));
136: PetscCall(DMGlobalToLocalEnd(dm, X, INSERT_VALUES, locX));
137: PetscCall(DMGlobalToLocalBegin(dm, X_t, INSERT_VALUES, locX_t));
138: PetscCall(DMGlobalToLocalEnd(dm, X_t, INSERT_VALUES, locX_t));
139: CHKMEMQ;
140: PetscCall((*dmlocalts->ijacobianlocal)(dm, time, locX, locX_t, a, A, B, dmlocalts->ijacobianlocalctx));
141: CHKMEMQ;
142: PetscCall(DMRestoreLocalVector(dm, &locX));
143: PetscCall(DMRestoreLocalVector(dm, &locX_t));
144: } else {
145: MatFDColoring fdcoloring;
146: PetscCall(PetscObjectQuery((PetscObject)dm, "DMDASNES_FDCOLORING", (PetscObject *)&fdcoloring));
147: if (!fdcoloring) {
148: ISColoring coloring;
150: PetscCall(DMCreateColoring(dm, dm->coloringtype, &coloring));
151: PetscCall(MatFDColoringCreate(B, coloring, &fdcoloring));
152: PetscCall(ISColoringDestroy(&coloring));
153: switch (dm->coloringtype) {
154: case IS_COLORING_GLOBAL:
155: PetscCall(MatFDColoringSetFunction(fdcoloring, (PetscErrorCode(*)(void))TSComputeIFunction_DMLocal, dmlocalts));
156: break;
157: default:
158: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "No support for coloring type '%s'", ISColoringTypes[dm->coloringtype]);
159: }
160: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)fdcoloring, ((PetscObject)dm)->prefix));
161: PetscCall(MatFDColoringSetFromOptions(fdcoloring));
162: PetscCall(MatFDColoringSetUp(B, coloring, fdcoloring));
163: PetscCall(PetscObjectCompose((PetscObject)dm, "DMDASNES_FDCOLORING", (PetscObject)fdcoloring));
164: PetscCall(PetscObjectDereference((PetscObject)fdcoloring));
166: /* The following breaks an ugly reference counting loop that deserves a paragraph. MatFDColoringApply() will call
167: * VecDuplicate() with the state Vec and store inside the MatFDColoring. This Vec will duplicate the Vec, but the
168: * MatFDColoring is composed with the DM. We dereference the DM here so that the reference count will eventually
169: * drop to 0. Note the code in DMDestroy() that exits early for a negative reference count. That code path will be
170: * taken when the PetscObjectList for the Vec inside MatFDColoring is destroyed.
171: */
172: PetscCall(PetscObjectDereference((PetscObject)dm));
173: }
174: PetscCall(MatFDColoringApply(B, fdcoloring, X, ts));
175: }
176: /* This will be redundant if the user called both, but it's too common to forget. */
177: if (A != B) {
178: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
179: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
180: }
181: PetscFunctionReturn(PETSC_SUCCESS);
182: }
184: /*@C
185: DMTSSetBoundaryLocal - set the function for essential boundary data for a local implicit function evaluation.
186: It should set the essential boundary data for the local portion of the solution X, as well its time derivative X_t (if it is not NULL).
187: Vectors are initialized to zero before this function, so it is only needed for non homogeneous data.
189: Logically Collective
191: Input Parameters:
192: + dm - `DM` to associate callback with
193: . func - local function evaluation
194: - ctx - context for function evaluation
196: Level: intermediate
198: Note:
199: This function is somewhat optional: boundary data could potentially be inserted by a function passed to
200: `DMTSSetIFunctionLocal()`. The use case for this function is for discretizations with constraints (see
201: `DMGetDefaultConstraints()`): this function inserts boundary values before constraint interpolation.
203: .seealso: [](ch_ts), `DM`, `TS`, `DMTSSetIFunction()`, `DMTSSetIJacobianLocal()`
204: @*/
205: PetscErrorCode DMTSSetBoundaryLocal(DM dm, PetscErrorCode (*func)(DM, PetscReal, Vec, Vec, void *), void *ctx)
206: {
207: DMTS tdm;
208: DMTS_Local *dmlocalts;
210: PetscFunctionBegin;
212: PetscCall(DMGetDMTSWrite(dm, &tdm));
213: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
215: dmlocalts->boundarylocal = func;
216: dmlocalts->boundarylocalctx = ctx;
218: PetscFunctionReturn(PETSC_SUCCESS);
219: }
221: /*@C
222: DMTSGetIFunctionLocal - get the local implicit function evaluation function. This function is called with local vector
223: containing the local vector information PLUS ghost point information. It should compute a result for all local
224: elements and `DM` will automatically accumulate the overlapping values.
226: Logically Collective
228: Input Parameter:
229: . dm - `DM` to associate callback with
231: Output Parameters:
232: + func - local function evaluation
233: - ctx - context for function evaluation
235: Level: beginner
237: .seealso: [](ch_ts), `DM`, `DMTSSetIFunctionLocal()`, `DMTSSetIFunction()`, `DMTSSetIJacobianLocal()`
238: @*/
239: PetscErrorCode DMTSGetIFunctionLocal(DM dm, PetscErrorCode (**func)(DM, PetscReal, Vec, Vec, Vec, void *), void **ctx)
240: {
241: DMTS tdm;
242: DMTS_Local *dmlocalts;
243: PetscErrorCode ierr;
245: PetscFunctionBegin;
247: ierr = DMGetDMTS(dm, &tdm);
248: CHKERRQ(ierr);
249: ierr = DMLocalTSGetContext(dm, tdm, &dmlocalts);
250: CHKERRQ(ierr);
251: if (func) {
253: *func = dmlocalts->ifunctionlocal;
254: }
255: if (ctx) {
257: *ctx = dmlocalts->ifunctionlocalctx;
258: }
259: PetscFunctionReturn(PETSC_SUCCESS);
260: }
262: /*@C
263: DMTSSetIFunctionLocal - set a local implicit function evaluation function. This function is called with local vector
264: containing the local vector information PLUS ghost point information. It should compute a result for all local
265: elements and `DM` will automatically accumulate the overlapping values.
267: Logically Collective
269: Input Parameters:
270: + dm - `DM` to associate callback with
271: . func - local function evaluation
272: - ctx - context for function evaluation
274: Level: beginner
276: .seealso: [](ch_ts), `DM`, `DMTSGetIFunctionLocal()`, `DMTSSetIFunction()`, `DMTSSetIJacobianLocal()`
277: @*/
278: PetscErrorCode DMTSSetIFunctionLocal(DM dm, PetscErrorCode (*func)(DM, PetscReal, Vec, Vec, Vec, void *), void *ctx)
279: {
280: DMTS tdm;
281: DMTS_Local *dmlocalts;
283: PetscFunctionBegin;
285: PetscCall(DMGetDMTSWrite(dm, &tdm));
286: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
288: dmlocalts->ifunctionlocal = func;
289: dmlocalts->ifunctionlocalctx = ctx;
291: PetscCall(DMTSSetIFunction(dm, TSComputeIFunction_DMLocal, dmlocalts));
292: if (!tdm->ops->ijacobian) { /* Call us for the Jacobian too, can be overridden by the user. */
293: PetscCall(DMTSSetIJacobian(dm, TSComputeIJacobian_DMLocal, dmlocalts));
294: }
295: PetscFunctionReturn(PETSC_SUCCESS);
296: }
298: /*@C
299: DMTSGetIJacobianLocal - get a local Jacobian evaluation function
301: Logically Collective
303: Input Parameter:
304: . dm - `DM` to associate callback with
306: Output Parameters:
307: + func - local Jacobian evaluation
308: - ctx - optional context for local Jacobian evaluation
310: Level: beginner
312: .seealso: [](ch_ts), `DM`, `DMTSSetIJacobianLocal()`, `DMTSSetIFunctionLocal()`, `DMTSSetIJacobian()`, `DMTSSetIFunction()`
313: @*/
314: PetscErrorCode DMTSGetIJacobianLocal(DM dm, PetscErrorCode (**func)(DM, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *), void **ctx)
315: {
316: DMTS tdm;
317: DMTS_Local *dmlocalts;
318: PetscErrorCode ierr;
320: PetscFunctionBegin;
322: ierr = DMGetDMTS(dm, &tdm);
323: CHKERRQ(ierr);
324: ierr = DMLocalTSGetContext(dm, tdm, &dmlocalts);
325: CHKERRQ(ierr);
326: if (func) {
328: *func = dmlocalts->ijacobianlocal;
329: }
330: if (ctx) {
332: *ctx = dmlocalts->ijacobianlocalctx;
333: }
334: PetscFunctionReturn(PETSC_SUCCESS);
335: }
337: /*@C
338: DMTSSetIJacobianLocal - set a local Jacobian evaluation function
340: Logically Collective
342: Input Parameters:
343: + dm - `DM` to associate callback with
344: . func - local Jacobian evaluation
345: - ctx - optional context for local Jacobian evaluation
347: Level: beginner
349: .seealso: [](ch_ts), `DM`, `DMTSGetIJacobianLocal()`, `DMTSSetIFunctionLocal()`, `DMTSSetIJacobian()`, `DMTSSetIFunction()`
350: @*/
351: PetscErrorCode DMTSSetIJacobianLocal(DM dm, PetscErrorCode (*func)(DM, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *), void *ctx)
352: {
353: DMTS tdm;
354: DMTS_Local *dmlocalts;
356: PetscFunctionBegin;
358: PetscCall(DMGetDMTSWrite(dm, &tdm));
359: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
361: dmlocalts->ijacobianlocal = func;
362: dmlocalts->ijacobianlocalctx = ctx;
364: PetscCall(DMTSSetIJacobian(dm, TSComputeIJacobian_DMLocal, dmlocalts));
365: PetscFunctionReturn(PETSC_SUCCESS);
366: }
368: /*@C
369: DMTSGetRHSFunctionLocal - get a local rhs function evaluation function. This function is called with local vector
370: containing the local vector information PLUS ghost point information. It should compute a result for all local
371: elements and `DM` will automatically accumulate the overlapping values.
373: Logically Collective
375: Input Parameter:
376: . dm - `DM` to associate callback with
378: Output Parameters:
379: + func - local function evaluation
380: - ctx - context for function evaluation
382: Level: beginner
384: .seealso: [](ch_ts), `DM`, `DMTSSetRHSFunctionLocal()`, `DMTSSetRHSFunction()`, `DMTSSetIFunction()`, `DMTSSetIJacobianLocal()`
385: @*/
386: PetscErrorCode DMTSGetRHSFunctionLocal(DM dm, PetscErrorCode (**func)(DM, PetscReal, Vec, Vec, void *), void **ctx)
387: {
388: DMTS tdm;
389: DMTS_Local *dmlocalts;
390: PetscErrorCode ierr;
392: PetscFunctionBegin;
394: ierr = DMGetDMTS(dm, &tdm);
395: CHKERRQ(ierr);
396: ierr = DMLocalTSGetContext(dm, tdm, &dmlocalts);
397: CHKERRQ(ierr);
398: if (func) {
400: *func = dmlocalts->rhsfunctionlocal;
401: }
402: if (ctx) {
404: *ctx = dmlocalts->rhsfunctionlocalctx;
405: }
406: PetscFunctionReturn(PETSC_SUCCESS);
407: }
409: /*@C
410: DMTSSetRHSFunctionLocal - set a local rhs function evaluation function. This function is called with local vector
411: containing the local vector information PLUS ghost point information. It should compute a result for all local
412: elements and `DM` will automatically accumulate the overlapping values.
414: Logically Collective
416: Input Parameters:
417: + dm - `DM` to associate callback with
418: . func - local function evaluation
419: - ctx - context for function evaluation
421: Level: beginner
423: .seealso: [](ch_ts), `DM`, `DMTSGetRHSFunctionLocal()`, `DMTSSetRHSFunction()`, `DMTSSetIFunction()`, `DMTSSetIJacobianLocal()`
424: @*/
425: PetscErrorCode DMTSSetRHSFunctionLocal(DM dm, PetscErrorCode (*func)(DM, PetscReal, Vec, Vec, void *), void *ctx)
426: {
427: DMTS tdm;
428: DMTS_Local *dmlocalts;
430: PetscFunctionBegin;
432: PetscCall(DMGetDMTSWrite(dm, &tdm));
433: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
435: dmlocalts->rhsfunctionlocal = func;
436: dmlocalts->rhsfunctionlocalctx = ctx;
438: PetscCall(DMTSSetRHSFunction(dm, TSComputeRHSFunction_DMLocal, dmlocalts));
439: PetscFunctionReturn(PETSC_SUCCESS);
440: }
442: /*@C
443: DMTSCreateRHSMassMatrix - This creates the mass matrix associated with the given `DM`, and a solver to invert it, and stores them in the `DM` context.
445: Collective
447: Input Parameter:
448: . dm - `DM` providing the mass matrix
450: Level: developer
452: Note:
453: The idea here is that an explicit system can be given a mass matrix, based on the `DM`, which is inverted on the RHS at each step.
455: .seealso: [](ch_ts), `DM`, `DMTSCreateRHSMassMatrixLumped()`, `DMTSDestroyRHSMassMatrix()`, `DMCreateMassMatrix()`, `DMTS`
456: @*/
457: PetscErrorCode DMTSCreateRHSMassMatrix(DM dm)
458: {
459: DMTS tdm;
460: DMTS_Local *dmlocalts;
461: const char *prefix;
463: PetscFunctionBegin;
465: PetscCall(DMGetDMTSWrite(dm, &tdm));
466: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
467: PetscCall(DMCreateMassMatrix(dm, dm, &dmlocalts->mass));
468: PetscCall(KSPCreate(PetscObjectComm((PetscObject)dm), &dmlocalts->kspmass));
469: PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix));
470: PetscCall(KSPSetOptionsPrefix(dmlocalts->kspmass, prefix));
471: PetscCall(KSPAppendOptionsPrefix(dmlocalts->kspmass, "mass_"));
472: PetscCall(KSPSetFromOptions(dmlocalts->kspmass));
473: PetscCall(KSPSetOperators(dmlocalts->kspmass, dmlocalts->mass, dmlocalts->mass));
474: PetscFunctionReturn(PETSC_SUCCESS);
475: }
477: /*@C
478: DMTSCreateRHSMassMatrixLumped - This creates the lumped mass matrix associated with the given `DM`, and a solver to invert it, and stores them in the `DM` context.
480: Collective
482: Input Parameter:
483: . dm - `DM` providing the mass matrix
485: Level: developer
487: Note:
488: The idea here is that an explicit system can be given a mass matrix, based on the `DM`, which is inverted on the RHS at each step.
489: Since the matrix is lumped, inversion is trivial.
491: .seealso: [](ch_ts), `DM`, `DMTSCreateRHSMassMatrix()`, `DMTSDestroyRHSMassMatrix()`, `DMCreateMassMatrix()`, `DMTS`
492: @*/
493: PetscErrorCode DMTSCreateRHSMassMatrixLumped(DM dm)
494: {
495: DMTS tdm;
496: DMTS_Local *dmlocalts;
498: PetscFunctionBegin;
500: PetscCall(DMGetDMTSWrite(dm, &tdm));
501: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
502: PetscCall(DMCreateMassMatrixLumped(dm, &dmlocalts->lumpedmassinv));
503: PetscCall(VecReciprocal(dmlocalts->lumpedmassinv));
504: PetscCall(VecViewFromOptions(dmlocalts->lumpedmassinv, NULL, "-lumped_mass_inv_view"));
505: PetscFunctionReturn(PETSC_SUCCESS);
506: }
508: /*@C
509: DMTSDestroyRHSMassMatrix - Destroys the mass matrix and solver stored in the `DM` context, if they exist.
511: Logically Collective
513: Input Parameter:
514: . dm - `DM` providing the mass matrix
516: Level: developer
518: .seealso: [](ch_ts), `DM`, `DMTSCreateRHSMassMatrixLumped()`, `DMCreateMassMatrix()`, `DMCreateMassMatrix()`, `DMTS`
519: @*/
520: PetscErrorCode DMTSDestroyRHSMassMatrix(DM dm)
521: {
522: DMTS tdm;
523: DMTS_Local *dmlocalts;
525: PetscFunctionBegin;
527: PetscCall(DMGetDMTSWrite(dm, &tdm));
528: PetscCall(DMLocalTSGetContext(dm, tdm, &dmlocalts));
529: PetscCall(VecDestroy(&dmlocalts->lumpedmassinv));
530: PetscCall(MatDestroy(&dmlocalts->mass));
531: PetscCall(KSPDestroy(&dmlocalts->kspmass));
532: PetscFunctionReturn(PETSC_SUCCESS);
533: }