Actual source code: tseig.c


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

  5: /* ------------------------------------------------------------------------*/
  6: struct _n_TSMonitorSPEigCtx {
  7:   PetscDrawSP drawsp;
  8:   KSP         ksp;
  9:   PetscInt    howoften; /* when > 0 uses step % howoften, when negative only final solution plotted */
 10:   PetscBool   computeexplicitly;
 11:   MPI_Comm    comm;
 12:   PetscRandom rand;
 13:   PetscReal   xmin, xmax, ymin, ymax;
 14: };

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

 19:    Collective

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

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

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

 34:    Level: intermediate

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

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

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

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

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

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

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

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

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

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

 91: PetscErrorCode TSMonitorSPEig(TS ts, PetscInt step, PetscReal ptime, Vec v, void *monctx)
 92: {
 93:   TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx)monctx;
 94:   KSP               ksp = ctx->ksp;
 95:   PetscInt          n, N, nits, neig, i, its = 200;
 96:   PetscReal        *r, *c, time_step_save;
 97:   PetscDrawSP       drawsp = ctx->drawsp;
 98:   Mat               A, B;
 99:   Vec               xdot;
100:   SNES              snes;

102:   PetscFunctionBegin;
103:   if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* -1 indicates interpolated solution */
104:   if (!step) PetscFunctionReturn(PETSC_SUCCESS);
105:   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
106:     PetscCall(VecDuplicate(v, &xdot));
107:     PetscCall(TSGetSNES(ts, &snes));
108:     PetscCall(SNESGetJacobian(snes, &A, &B, NULL, NULL));
109:     PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &B));
110:     /*
111:        This doesn't work because methods keep and use internal information about the shift so it
112:        seems we would need code for each method to trick the correct Jacobian in being computed.
113:      */
114:     time_step_save = ts->time_step;
115:     ts->time_step  = PETSC_MAX_REAL;

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

119:     ts->time_step = time_step_save;

121:     PetscCall(KSPSetOperators(ksp, B, B));
122:     PetscCall(VecGetSize(v, &n));
123:     if (n < 200) its = n;
124:     PetscCall(KSPSetTolerances(ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, its));
125:     PetscCall(VecSetRandom(xdot, ctx->rand));
126:     PetscCall(KSPSolve(ksp, xdot, xdot));
127:     PetscCall(VecDestroy(&xdot));
128:     PetscCall(KSPGetIterationNumber(ksp, &nits));
129:     N = nits + 2;

131:     if (nits) {
132:       PetscDraw     draw;
133:       PetscReal     pause;
134:       PetscDrawAxis axis;
135:       PetscReal     xmin, xmax, ymin, ymax;

137:       PetscCall(PetscDrawSPReset(drawsp));
138:       PetscCall(PetscDrawSPSetLimits(drawsp, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax));
139:       PetscCall(PetscMalloc2(PetscMax(n, N), &r, PetscMax(n, N), &c));
140:       if (ctx->computeexplicitly) {
141:         PetscCall(KSPComputeEigenvaluesExplicitly(ksp, n, r, c));
142:         neig = n;
143:       } else {
144:         PetscCall(KSPComputeEigenvalues(ksp, N, r, c, &neig));
145:       }
146:       /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
147:       for (i = 0; i < neig; i++) r[i] = -r[i];
148:       for (i = 0; i < neig; i++) {
149:         if (ts->ops->linearstability) {
150:           PetscReal fr, fi;
151:           PetscCall(TSComputeLinearStability(ts, r[i], c[i], &fr, &fi));
152:           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)));
153:         }
154:         PetscCall(PetscDrawSPAddPoint(drawsp, r + i, c + i));
155:       }
156:       PetscCall(PetscFree2(r, c));
157:       PetscCall(PetscDrawSPGetDraw(drawsp, &draw));
158:       PetscCall(PetscDrawGetPause(draw, &pause));
159:       PetscCall(PetscDrawSetPause(draw, 0.0));
160:       PetscCall(PetscDrawSPDraw(drawsp, PETSC_TRUE));
161:       PetscCall(PetscDrawSetPause(draw, pause));
162:       if (ts->ops->linearstability) {
163:         PetscCall(PetscDrawSPGetAxis(drawsp, &axis));
164:         PetscCall(PetscDrawAxisGetLimits(axis, &xmin, &xmax, &ymin, &ymax));
165:         PetscCall(PetscDrawIndicatorFunction(draw, xmin, xmax, ymin, ymax, PETSC_DRAW_CYAN, (PetscErrorCode(*)(void *, PetscReal, PetscReal, PetscBool *))TSLinearStabilityIndicator, ts));
166:         PetscCall(PetscDrawSPDraw(drawsp, PETSC_FALSE));
167:       }
168:       PetscCall(PetscDrawSPSave(drawsp));
169:     }
170:     PetscCall(MatDestroy(&B));
171:   }
172:   PetscFunctionReturn(PETSC_SUCCESS);
173: }

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

178:    Collective

180:    Input Parameter:
181: .  ctx - the monitor context

183:    Level: intermediate

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

188: .seealso: [](chapter_ts), `TSMonitorSPEigCtxCreate()`, `TSMonitorSet()`, `TSMonitorSPEig();`
189: @*/
190: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
191: {
192:   PetscDraw draw;

194:   PetscFunctionBegin;
195:   PetscCall(PetscDrawSPGetDraw((*ctx)->drawsp, &draw));
196:   PetscCall(PetscDrawDestroy(&draw));
197:   PetscCall(PetscDrawSPDestroy(&(*ctx)->drawsp));
198:   PetscCall(KSPDestroy(&(*ctx)->ksp));
199:   PetscCall(PetscRandomDestroy(&(*ctx)->rand));
200:   PetscCall(PetscFree(*ctx));
201:   PetscFunctionReturn(PETSC_SUCCESS);
202: }