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 on TS
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: Notes:
35: Use TSMonitorSPEigCtxDestroy() to destroy.
37: Currently only works if the Jacobian is provided explicitly.
39: Currently only works for ODEs u_t - F(t,u) = 0; that is with no mass matrix.
41: Level: intermediate
43: .seealso: `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: PetscNew(ctx);
52: PetscRandomCreate(comm, &(*ctx)->rand);
53: PetscRandomSetFromOptions((*ctx)->rand);
54: PetscDrawCreate(comm, host, label, x, y, m, n, &win);
55: PetscDrawSetFromOptions(win);
56: PetscDrawSPCreate(win, 1, &(*ctx)->drawsp);
57: KSPCreate(comm, &(*ctx)->ksp);
58: KSPSetOptionsPrefix((*ctx)->ksp, "ts_monitor_sp_eig_"); /* this is wrong, used use also prefix from the TS */
59: KSPSetType((*ctx)->ksp, KSPGMRES);
60: KSPGMRESSetRestart((*ctx)->ksp, 200);
61: KSPSetTolerances((*ctx)->ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, 200);
62: KSPSetComputeSingularValues((*ctx)->ksp, PETSC_TRUE);
63: KSPSetFromOptions((*ctx)->ksp);
64: KSPGetPC((*ctx)->ksp, &pc);
65: PCSetType(pc, PCNONE);
67: (*ctx)->howoften = howoften;
68: (*ctx)->computeexplicitly = PETSC_FALSE;
70: 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: return 0;
78: }
80: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr, PetscReal xi, PetscBool *flg)
81: {
82: PetscReal yr, yi;
84: TSComputeLinearStability(ts, xr, xi, &yr, &yi);
85: if ((yr * yr + yi * yi) <= 1.0) *flg = PETSC_TRUE;
86: else *flg = PETSC_FALSE;
87: return 0;
88: }
90: PetscErrorCode TSMonitorSPEig(TS ts, PetscInt step, PetscReal ptime, Vec v, void *monctx)
91: {
92: TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx)monctx;
93: KSP ksp = ctx->ksp;
94: PetscInt n, N, nits, neig, i, its = 200;
95: PetscReal *r, *c, time_step_save;
96: PetscDrawSP drawsp = ctx->drawsp;
97: Mat A, B;
98: Vec xdot;
99: SNES snes;
101: if (step < 0) return 0; /* -1 indicates interpolated solution */
102: if (!step) return 0;
103: if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
104: VecDuplicate(v, &xdot);
105: TSGetSNES(ts, &snes);
106: SNESGetJacobian(snes, &A, &B, NULL, NULL);
107: MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &B);
108: /*
109: This doesn't work because methods keep and use internal information about the shift so it
110: seems we would need code for each method to trick the correct Jacobian in being computed.
111: */
112: time_step_save = ts->time_step;
113: ts->time_step = PETSC_MAX_REAL;
115: SNESComputeJacobian(snes, v, A, B);
117: ts->time_step = time_step_save;
119: KSPSetOperators(ksp, B, B);
120: VecGetSize(v, &n);
121: if (n < 200) its = n;
122: KSPSetTolerances(ksp, 1.e-10, PETSC_DEFAULT, PETSC_DEFAULT, its);
123: VecSetRandom(xdot, ctx->rand);
124: KSPSolve(ksp, xdot, xdot);
125: VecDestroy(&xdot);
126: KSPGetIterationNumber(ksp, &nits);
127: N = nits + 2;
129: if (nits) {
130: PetscDraw draw;
131: PetscReal pause;
132: PetscDrawAxis axis;
133: PetscReal xmin, xmax, ymin, ymax;
135: PetscDrawSPReset(drawsp);
136: PetscDrawSPSetLimits(drawsp, ctx->xmin, ctx->xmax, ctx->ymin, ctx->ymax);
137: PetscMalloc2(PetscMax(n, N), &r, PetscMax(n, N), &c);
138: if (ctx->computeexplicitly) {
139: KSPComputeEigenvaluesExplicitly(ksp, n, r, c);
140: neig = n;
141: } else {
142: KSPComputeEigenvalues(ksp, N, r, c, &neig);
143: }
144: /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
145: for (i = 0; i < neig; i++) r[i] = -r[i];
146: for (i = 0; i < neig; i++) {
147: if (ts->ops->linearstability) {
148: PetscReal fr, fi;
149: TSComputeLinearStability(ts, r[i], c[i], &fr, &fi);
150: if ((fr * fr + fi * fi) > 1.0) 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));
151: }
152: PetscDrawSPAddPoint(drawsp, r + i, c + i);
153: }
154: PetscFree2(r, c);
155: PetscDrawSPGetDraw(drawsp, &draw);
156: PetscDrawGetPause(draw, &pause);
157: PetscDrawSetPause(draw, 0.0);
158: PetscDrawSPDraw(drawsp, PETSC_TRUE);
159: PetscDrawSetPause(draw, pause);
160: if (ts->ops->linearstability) {
161: PetscDrawSPGetAxis(drawsp, &axis);
162: PetscDrawAxisGetLimits(axis, &xmin, &xmax, &ymin, &ymax);
163: PetscDrawIndicatorFunction(draw, xmin, xmax, ymin, ymax, PETSC_DRAW_CYAN, (PetscErrorCode(*)(void *, PetscReal, PetscReal, PetscBool *))TSLinearStabilityIndicator, ts);
164: PetscDrawSPDraw(drawsp, PETSC_FALSE);
165: }
166: PetscDrawSPSave(drawsp);
167: }
168: MatDestroy(&B);
169: }
170: return 0;
171: }
173: /*@C
174: TSMonitorSPEigCtxDestroy - Destroys a scatter plot context that was created with TSMonitorSPEigCtxCreate().
176: Collective on TSMonitorSPEigCtx
178: Input Parameter:
179: . ctx - the monitor context
181: Level: intermediate
183: .seealso: `TSMonitorSPEigCtxCreate()`, `TSMonitorSet()`, `TSMonitorSPEig();`
184: @*/
185: PetscErrorCode TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
186: {
187: PetscDraw draw;
189: PetscDrawSPGetDraw((*ctx)->drawsp, &draw);
190: PetscDrawDestroy(&draw);
191: PetscDrawSPDestroy(&(*ctx)->drawsp);
192: KSPDestroy(&(*ctx)->ksp);
193: PetscRandomDestroy(&(*ctx)->rand);
194: PetscFree(*ctx);
195: return 0;
196: }