Actual source code: tseig.c

  1: #include <petsc/private/tsimpl.h>
  2: #include <petscdraw.h>

  4: struct _n_TSMonitorSPEigCtx {
  5:   PetscDrawSP drawsp;
  6:   KSP         ksp;
  7:   PetscInt    howoften; /* when > 0 uses step % howoften, when negative only final solution plotted */
  8:   PetscBool   computeexplicitly;
  9:   MPI_Comm    comm;
 10:   PetscRandom rand;
 11:   PetscReal   xmin, xmax, ymin, ymax;
 12: };

 14: /*@C
 15:   TSMonitorSPEigCtxCreate - Creates a context for use with `TS` to monitor the eigenvalues of the linearized operator

 17:   Collective

 19:   Input Parameters:
 20: + comm     - the communicator to share the monitor
 21: . host     - the X display to open, or `NULL` for the local machine
 22: . label    - the title to put in the title bar
 23: . x        - the horizontal screen coordinates of the upper left coordinate of the window
 24: . y        - the vertical coordinates of the upper left coordinate of the window
 25: . m        - the screen width in pixels
 26: . n        - the screen height in pixels
 27: - howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time

 29:   Output Parameter:
 30: . ctx - the context

 32:   Options Database Key:
 33: . -ts_monitor_sp_eig - plot egienvalues of linearized right-hand side

 35:   Level: intermediate

 37:   Notes:
 38:   Use `TSMonitorSPEigCtxDestroy()` to destroy the context

 40:   Currently only works if the Jacobian is provided explicitly.

 42:   Currently only works for ODEs u_t - F(t,u) = 0; that is with no mass matrix.

 44: .seealso: [](ch_ts), `TSMonitorSPEigTimeStep()`, `TSMonitorSet()`, `TSMonitorLGSolution()`, `TSMonitorLGError()`
 45: @*/
 46: PetscErrorCode TSMonitorSPEigCtxCreate(MPI_Comm comm, const char host[], const char label[], int x, int y, int m, int n, PetscInt howoften, TSMonitorSPEigCtx *ctx)
 47: {
 48:   PetscDraw win;
 49:   PC        pc;

 51:   PetscFunctionBegin;
 52:   PetscCall(PetscNew(ctx));
 53:   PetscCall(PetscRandomCreate(comm, &(*ctx)->rand));
 54:   PetscCall(PetscRandomSetFromOptions((*ctx)->rand));
 55:   PetscCall(PetscDrawCreate(comm, host, label, x, y, m, n, &win));
 56:   PetscCall(PetscDrawSetFromOptions(win));
 57:   PetscCall(PetscDrawSPCreate(win, 1, &(*ctx)->drawsp));
 58:   PetscCall(KSPCreate(comm, &(*ctx)->ksp));
 59:   PetscCall(KSPSetOptionsPrefix((*ctx)->ksp, "ts_monitor_sp_eig_")); /* this is wrong, used use also prefix from the TS */
 60:   PetscCall(KSPSetType((*ctx)->ksp, KSPGMRES));
 61:   PetscCall(KSPGMRESSetRestart((*ctx)->ksp, 200));
 62:   PetscCall(KSPSetTolerances((*ctx)->ksp, 1.e-10, PETSC_CURRENT, PETSC_CURRENT, 200));
 63:   PetscCall(KSPSetComputeSingularValues((*ctx)->ksp, PETSC_TRUE));
 64:   PetscCall(KSPSetFromOptions((*ctx)->ksp));
 65:   PetscCall(KSPGetPC((*ctx)->ksp, &pc));
 66:   PetscCall(PCSetType(pc, PCNONE));

 68:   (*ctx)->howoften          = howoften;
 69:   (*ctx)->computeexplicitly = PETSC_FALSE;

 71:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-ts_monitor_sp_eig_explicitly", &(*ctx)->computeexplicitly, NULL));

 73:   (*ctx)->comm = comm;
 74:   (*ctx)->xmin = -2.1;
 75:   (*ctx)->xmax = 1.1;
 76:   (*ctx)->ymin = -1.1;
 77:   (*ctx)->ymax = 1.1;
 78:   PetscFunctionReturn(PETSC_SUCCESS);
 79: }

 81: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr, PetscReal xi, PetscBool *flg)
 82: {
 83:   PetscReal yr, yi;

 85:   PetscFunctionBegin;
 86:   PetscCall(TSComputeLinearStability(ts, xr, xi, &yr, &yi));
 87:   if ((yr * yr + yi * yi) <= 1.0) *flg = PETSC_TRUE;
 88:   else *flg = PETSC_FALSE;
 89:   PetscFunctionReturn(PETSC_SUCCESS);
 90: }

 92: /*@C
 93:   TSMonitorSPEig - Monitors the eigenvalues of the linearized right-hand-side operator on a scatter plot at each time step

 95:   Collective

 97:   Input Parameters:
 98: + ts     - the `TS` context
 99: . step   - the current time-step number (a negative value indicates an interpolated solution and is ignored)
100: . ptime  - the current time
101: . v      - the current solution
102: - monctx - the `TSMonitorSPEigCtx` context, created with `TSMonitorSPEigCtxCreate()`

104:   Options Database Key:
105: . -ts_monitor_sp_eig - plot eigenvalues of linearized right-hand side

107:   Level: intermediate

109:   Notes:
110:   This is not called directly by users; pass this function to `TSMonitorSet()` along with the context created by `TSMonitorSPEigCtxCreate()` and `TSMonitorSPEigCtxDestroy()`.

112:   Currently only works when the Jacobian is provided explicitly and the ODE has no mass matrix.

114: .seealso: [](ch_ts), `TS`, `TSMonitorSet()`, `TSMonitorSPEigCtxCreate()`, `TSMonitorSPEigCtxDestroy()`
115: @*/
116: PetscErrorCode TSMonitorSPEig(TS ts, PetscInt step, PetscReal ptime, Vec v, void *monctx)
117: {
118:   TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx)monctx;
119:   KSP               ksp = ctx->ksp;
120:   PetscInt          n, N, nits, neig, i, its = 200;
121:   PetscReal        *r, *c, time_step_save;
122:   PetscDrawSP       drawsp = ctx->drawsp;
123:   Mat               A, B;
124:   Vec               xdot;
125:   SNES              snes;

127:   PetscFunctionBegin;
128:   if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* -1 indicates interpolated solution */
129:   if (!step) PetscFunctionReturn(PETSC_SUCCESS);
130:   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
131:     PetscCall(VecDuplicate(v, &xdot));
132:     PetscCall(TSGetSNES(ts, &snes));
133:     PetscCall(SNESGetJacobian(snes, &A, &B, NULL, NULL));
134:     PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &B));
135:     /*
136:        This doesn't work because methods keep and use internal information about the shift so it
137:        seems we would need code for each method to trick the correct Jacobian in being computed.
138:      */
139:     time_step_save = ts->time_step;
140:     ts->time_step  = PETSC_MAX_REAL;

142:     PetscCall(SNESComputeJacobian(snes, v, A, B));

144:     ts->time_step = time_step_save;

146:     PetscCall(KSPSetOperators(ksp, B, B));
147:     PetscCall(VecGetSize(v, &n));
148:     if (n < 200) its = n;
149:     PetscCall(KSPSetTolerances(ksp, 1.e-10, PETSC_CURRENT, PETSC_CURRENT, its));
150:     PetscCall(VecSetRandom(xdot, ctx->rand));
151:     PetscCall(KSPSolve(ksp, xdot, xdot));
152:     PetscCall(VecDestroy(&xdot));
153:     PetscCall(KSPGetIterationNumber(ksp, &nits));
154:     N = nits + 2;

156:     if (nits) {
157:       PetscDraw     draw;
158:       PetscReal     pause;
159:       PetscDrawAxis axis;
160:       PetscReal     xmin, xmax, ymin, ymax;

162:       PetscCall(PetscDrawSPReset(drawsp));
163:       PetscCall(PetscDrawSPSetLimits(drawsp, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax));
164:       PetscCall(PetscMalloc2(PetscMax(n, N), &r, PetscMax(n, N), &c));
165:       if (ctx->computeexplicitly) {
166:         PetscCall(KSPComputeEigenvaluesExplicitly(ksp, n, r, c));
167:         neig = n;
168:       } else {
169:         PetscCall(KSPComputeEigenvalues(ksp, N, r, c, &neig));
170:       }
171:       /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
172:       for (i = 0; i < neig; i++) r[i] = -r[i];
173:       for (i = 0; i < neig; i++) {
174:         if (ts->ops->linearstability) {
175:           PetscReal fr, fi;
176:           PetscCall(TSComputeLinearStability(ts, r[i], c[i], &fr, &fi));
177:           if ((fr * fr + fi * fi) > 1.0) PetscCall(PetscPrintf(ctx->comm, "Linearized Eigenvalue %g + %g i linear stability function %g norm indicates unstable scheme\n", (double)r[i], (double)c[i], (double)(fr * fr + fi * fi)));
178:         }
179:         PetscCall(PetscDrawSPAddPoint(drawsp, r + i, c + i));
180:       }
181:       PetscCall(PetscFree2(r, c));
182:       PetscCall(PetscDrawSPGetDraw(drawsp, &draw));
183:       PetscCall(PetscDrawGetPause(draw, &pause));
184:       PetscCall(PetscDrawSetPause(draw, 0.0));
185:       PetscCall(PetscDrawSPDraw(drawsp, PETSC_TRUE));
186:       PetscCall(PetscDrawSetPause(draw, pause));
187:       if (ts->ops->linearstability) {
188:         PetscCall(PetscDrawSPGetAxis(drawsp, &axis));
189:         PetscCall(PetscDrawAxisGetLimits(axis, &xmin, &xmax, &ymin, &ymax));
190:         PetscCall(PetscDrawIndicatorFunction(draw, xmin, xmax, ymin, ymax, PETSC_DRAW_CYAN, (PetscErrorCode (*)(void *, PetscReal, PetscReal, PetscBool *))TSLinearStabilityIndicator, ts));
191:         PetscCall(PetscDrawSPDraw(drawsp, PETSC_FALSE));
192:       }
193:       PetscCall(PetscDrawSPSave(drawsp));
194:     }
195:     PetscCall(MatDestroy(&B));
196:   }
197:   PetscFunctionReturn(PETSC_SUCCESS);
198: }

200: /*@C
201:   TSMonitorSPEigCtxDestroy - Destroys a scatter plot context that was created with `TSMonitorSPEigCtxCreate()`.

203:   Collective

205:   Input Parameter:
206: . ctx - the monitor context

208:   Level: intermediate

210:   Note:
211:   Should be passed to `TSMonitorSet()` along with `TSMonitorSPEig()` an the context created with `TSMonitorSPEigCtxCreate()`

213: .seealso: [](ch_ts), `TSMonitorSPEigCtxCreate()`, `TSMonitorSet()`, `TSMonitorSPEig()`
214: @*/
215: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
216: {
217:   PetscDraw draw;

219:   PetscFunctionBegin;
220:   PetscCall(PetscDrawSPGetDraw((*ctx)->drawsp, &draw));
221:   PetscCall(PetscDrawDestroy(&draw));
222:   PetscCall(PetscDrawSPDestroy(&(*ctx)->drawsp));
223:   PetscCall(KSPDestroy(&(*ctx)->ksp));
224:   PetscCall(PetscRandomDestroy(&(*ctx)->rand));
225:   PetscCall(PetscFree(*ctx));
226:   PetscFunctionReturn(PETSC_SUCCESS);
227: }