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: + comm - the communicator to share the monitor
23: . host - the X display to open, or `NULL` for the local machine
24: . label - the title to put in the title bar
25: . x - the horizontal screen coordinates of the upper left coordinate of the window
26: . y - the vertical coordinates of the upper left coordinate of the window
27: . m - the screen width in pixels
28: . n - the screen height in pixels
29: - howoften - if positive then determines the frequency of the plotting, if -1 then only at the final time
31: Output Parameter:
32: . ctx - the context
34: Options Database Key:
35: . -ts_monitor_sp_eig - plot egienvalues of linearized right hand side
37: Level: intermediate
39: Notes:
40: Use `TSMonitorSPEigCtxDestroy()` to destroy the context
42: Currently only works if the Jacobian is provided explicitly.
44: Currently only works for ODEs u_t - F(t,u) = 0; that is with no mass matrix.
46: .seealso: [](ch_ts), `TSMonitorSPEigTimeStep()`, `TSMonitorSet()`, `TSMonitorLGSolution()`, `TSMonitorLGError()`
47: @*/
48: PetscErrorCode TSMonitorSPEigCtxCreate(MPI_Comm comm, const char host[], const char label[], int x, int y, int m, int n, PetscInt howoften, TSMonitorSPEigCtx *ctx)
49: {
50: PetscDraw win;
51: PC pc;
53: PetscFunctionBegin;
54: PetscCall(PetscNew(ctx));
55: PetscCall(PetscRandomCreate(comm, &(*ctx)->rand));
56: PetscCall(PetscRandomSetFromOptions((*ctx)->rand));
57: PetscCall(PetscDrawCreate(comm, host, label, x, y, m, n, &win));
58: PetscCall(PetscDrawSetFromOptions(win));
59: PetscCall(PetscDrawSPCreate(win, 1, &(*ctx)->drawsp));
60: PetscCall(KSPCreate(comm, &(*ctx)->ksp));
61: PetscCall(KSPSetOptionsPrefix((*ctx)->ksp, "ts_monitor_sp_eig_")); /* this is wrong, used use also prefix from the TS */
62: PetscCall(KSPSetType((*ctx)->ksp, KSPGMRES));
63: PetscCall(KSPGMRESSetRestart((*ctx)->ksp, 200));
64: PetscCall(KSPSetTolerances((*ctx)->ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, 200));
65: PetscCall(KSPSetComputeSingularValues((*ctx)->ksp, PETSC_TRUE));
66: PetscCall(KSPSetFromOptions((*ctx)->ksp));
67: PetscCall(KSPGetPC((*ctx)->ksp, &pc));
68: PetscCall(PCSetType(pc, PCNONE));
70: (*ctx)->howoften = howoften;
71: (*ctx)->computeexplicitly = PETSC_FALSE;
73: PetscCall(PetscOptionsGetBool(NULL, NULL, "-ts_monitor_sp_eig_explicitly", &(*ctx)->computeexplicitly, NULL));
75: (*ctx)->comm = comm;
76: (*ctx)->xmin = -2.1;
77: (*ctx)->xmax = 1.1;
78: (*ctx)->ymin = -1.1;
79: (*ctx)->ymax = 1.1;
80: PetscFunctionReturn(PETSC_SUCCESS);
81: }
83: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr, PetscReal xi, PetscBool *flg)
84: {
85: PetscReal yr, yi;
87: PetscFunctionBegin;
88: PetscCall(TSComputeLinearStability(ts, xr, xi, &yr, &yi));
89: if ((yr * yr + yi * yi) <= 1.0) *flg = PETSC_TRUE;
90: else *flg = PETSC_FALSE;
91: PetscFunctionReturn(PETSC_SUCCESS);
92: }
94: PetscErrorCode TSMonitorSPEig(TS ts, PetscInt step, PetscReal ptime, Vec v, void *monctx)
95: {
96: TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx)monctx;
97: KSP ksp = ctx->ksp;
98: PetscInt n, N, nits, neig, i, its = 200;
99: PetscReal *r, *c, time_step_save;
100: PetscDrawSP drawsp = ctx->drawsp;
101: Mat A, B;
102: Vec xdot;
103: SNES snes;
105: PetscFunctionBegin;
106: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* -1 indicates interpolated solution */
107: if (!step) PetscFunctionReturn(PETSC_SUCCESS);
108: if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
109: PetscCall(VecDuplicate(v, &xdot));
110: PetscCall(TSGetSNES(ts, &snes));
111: PetscCall(SNESGetJacobian(snes, &A, &B, NULL, NULL));
112: PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &B));
113: /*
114: This doesn't work because methods keep and use internal information about the shift so it
115: seems we would need code for each method to trick the correct Jacobian in being computed.
116: */
117: time_step_save = ts->time_step;
118: ts->time_step = PETSC_MAX_REAL;
120: PetscCall(SNESComputeJacobian(snes, v, A, B));
122: ts->time_step = time_step_save;
124: PetscCall(KSPSetOperators(ksp, B, B));
125: PetscCall(VecGetSize(v, &n));
126: if (n < 200) its = n;
127: PetscCall(KSPSetTolerances(ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, its));
128: PetscCall(VecSetRandom(xdot, ctx->rand));
129: PetscCall(KSPSolve(ksp, xdot, xdot));
130: PetscCall(VecDestroy(&xdot));
131: PetscCall(KSPGetIterationNumber(ksp, &nits));
132: N = nits + 2;
134: if (nits) {
135: PetscDraw draw;
136: PetscReal pause;
137: PetscDrawAxis axis;
138: PetscReal xmin, xmax, ymin, ymax;
140: PetscCall(PetscDrawSPReset(drawsp));
141: PetscCall(PetscDrawSPSetLimits(drawsp, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax));
142: PetscCall(PetscMalloc2(PetscMax(n, N), &r, PetscMax(n, N), &c));
143: if (ctx->computeexplicitly) {
144: PetscCall(KSPComputeEigenvaluesExplicitly(ksp, n, r, c));
145: neig = n;
146: } else {
147: PetscCall(KSPComputeEigenvalues(ksp, N, r, c, &neig));
148: }
149: /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
150: for (i = 0; i < neig; i++) r[i] = -r[i];
151: for (i = 0; i < neig; i++) {
152: if (ts->ops->linearstability) {
153: PetscReal fr, fi;
154: PetscCall(TSComputeLinearStability(ts, r[i], c[i], &fr, &fi));
155: 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)));
156: }
157: PetscCall(PetscDrawSPAddPoint(drawsp, r + i, c + i));
158: }
159: PetscCall(PetscFree2(r, c));
160: PetscCall(PetscDrawSPGetDraw(drawsp, &draw));
161: PetscCall(PetscDrawGetPause(draw, &pause));
162: PetscCall(PetscDrawSetPause(draw, 0.0));
163: PetscCall(PetscDrawSPDraw(drawsp, PETSC_TRUE));
164: PetscCall(PetscDrawSetPause(draw, pause));
165: if (ts->ops->linearstability) {
166: PetscCall(PetscDrawSPGetAxis(drawsp, &axis));
167: PetscCall(PetscDrawAxisGetLimits(axis, &xmin, &xmax, &ymin, &ymax));
168: PetscCall(PetscDrawIndicatorFunction(draw, xmin, xmax, ymin, ymax, PETSC_DRAW_CYAN, (PetscErrorCode(*)(void *, PetscReal, PetscReal, PetscBool *))TSLinearStabilityIndicator, ts));
169: PetscCall(PetscDrawSPDraw(drawsp, PETSC_FALSE));
170: }
171: PetscCall(PetscDrawSPSave(drawsp));
172: }
173: PetscCall(MatDestroy(&B));
174: }
175: PetscFunctionReturn(PETSC_SUCCESS);
176: }
178: /*@C
179: TSMonitorSPEigCtxDestroy - Destroys a scatter plot context that was created with `TSMonitorSPEigCtxCreate()`.
181: Collective
183: Input Parameter:
184: . ctx - the monitor context
186: Level: intermediate
188: Note:
189: Should be passed to `TSMonitorSet()` along with `TSMonitorSPEig()` an the context created with `TSMonitorSPEigCtxCreate()`
191: .seealso: [](ch_ts), `TSMonitorSPEigCtxCreate()`, `TSMonitorSet()`, `TSMonitorSPEig();`
192: @*/
193: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
194: {
195: PetscDraw draw;
197: PetscFunctionBegin;
198: PetscCall(PetscDrawSPGetDraw((*ctx)->drawsp, &draw));
199: PetscCall(PetscDrawDestroy(&draw));
200: PetscCall(PetscDrawSPDestroy(&(*ctx)->drawsp));
201: PetscCall(KSPDestroy(&(*ctx)->ksp));
202: PetscCall(PetscRandomDestroy(&(*ctx)->rand));
203: PetscCall(PetscFree(*ctx));
204: PetscFunctionReturn(PETSC_SUCCESS);
205: }