Date: 2015-10-02T22:26:53+00:00

Actual source code: tseig.c
petsc-3.6.2 2015-10-02
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      2: #include <petsc/private/tsimpl.h>        /*I "petscts.h"  I*/
      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: };

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

     22:    Collective on TS

     24:    Input Parameters:
     25: +  host - the X display to open, or null for the local machine
     26: .  label - the title to put in the title bar
     27: .  x, y - the screen coordinates of the upper left coordinate of the window
     28: .  m, n - the screen width and 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:    Notes:
     38:    Use TSMonitorSPEigCtxDestroy() to destroy.

     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:    Level: intermediate

     46: .keywords: TS, monitor, line graph, residual, seealso

     48: .seealso: TSMonitorSPEigTimeStep(), TSMonitorSet(), TSMonitorLGSolution(), TSMonitorLGError()

     50: @*/
     51: PetscErrorCode  TSMonitorSPEigCtxCreate(MPI_Comm comm,const char host[],const char label[],int x,int y,int m,int n,PetscInt howoften,TSMonitorSPEigCtx *ctx)
     52: {
     53:   PetscDraw      win;
     55:   PC             pc;

     58:   PetscNew(ctx);
     59:   PetscRandomCreate(comm,&(*ctx)->rand);
     60:   PetscRandomSetFromOptions((*ctx)->rand);
     61:   PetscDrawCreate(comm,host,label,x,y,m,n,&win);
     62:   PetscDrawSetFromOptions(win);
     63:   PetscDrawSPCreate(win,1,&(*ctx)->drawsp);
     64:   KSPCreate(comm,&(*ctx)->ksp);
     65:   KSPSetOptionsPrefix((*ctx)->ksp,"ts_monitor_sp_eig_"); /* this is wrong, used use also prefix from the TS */
     66:   KSPSetType((*ctx)->ksp,KSPGMRES);
     67:   KSPGMRESSetRestart((*ctx)->ksp,200);
     68:   KSPSetTolerances((*ctx)->ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,200);
     69:   KSPSetComputeSingularValues((*ctx)->ksp,PETSC_TRUE);
     70:   KSPSetFromOptions((*ctx)->ksp);
     71:   KSPGetPC((*ctx)->ksp,&pc);
     72:   PCSetType(pc,PCNONE);

     74:   (*ctx)->howoften          = howoften;
     75:   (*ctx)->computeexplicitly = PETSC_FALSE;

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

     79:   (*ctx)->comm = comm;
     80:   (*ctx)->xmin = -2.1;
     81:   (*ctx)->xmax = 1.1;
     82:   (*ctx)->ymin = -1.1;
     83:   (*ctx)->ymax = 1.1;
     84:   return(0);
     85: }

     89: static PetscErrorCode TSLinearStabilityIndicator(TS ts, PetscReal xr,PetscReal xi,PetscBool *flg)
     90: {
     92:   PetscReal      yr,yi;

     95:   TSComputeLinearStability(ts,xr,xi,&yr,&yi);
     96:   if ((yr*yr + yi*yi) <= 1.0) *flg = PETSC_TRUE;
     97:   else *flg = PETSC_FALSE;
     98:   return(0);
     99: }

    103: PetscErrorCode TSMonitorSPEig(TS ts,PetscInt step,PetscReal ptime,Vec v,void *monctx)
    104: {
    105:   TSMonitorSPEigCtx ctx = (TSMonitorSPEigCtx) monctx;
    106:   PetscErrorCode    ierr;
    107:   KSP               ksp = ctx->ksp;
    108:   PetscInt          n,N,nits,neig,i,its = 200;
    109:   PetscReal         *r,*c,time_step_save;
    110:   PetscDrawSP       drawsp = ctx->drawsp;
    111:   Mat               A,B;
    112:   Vec               xdot;
    113:   SNES              snes;

    116:   if (!step) return(0);
    117:   if (((ctx->howoften > 0) && (!(step % ctx->howoften))) || ((ctx->howoften == -1) && ts->reason)) {
    118:     VecDuplicate(v,&xdot);
    119:     TSGetSNES(ts,&snes);
    120:     SNESGetJacobian(snes,&A,&B,NULL,NULL);
    121:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&B);
    122:     /*
    123:        This doesn't work because methods keep and use internal information about the shift so it
    124:        seems we would need code for each method to trick the correct Jacobian in being computed.
    125:      */
    126:     time_step_save = ts->time_step;
    127:     ts->time_step  = PETSC_MAX_REAL;

    129:     SNESComputeJacobian(snes,v,A,B);

    131:     ts->time_step  = time_step_save;

    133:     KSPSetOperators(ksp,B,B);
    134:     VecGetSize(v,&n);
    135:     if (n < 200) its = n;
    136:     KSPSetTolerances(ksp,1.e-10,PETSC_DEFAULT,PETSC_DEFAULT,its);
    137:     VecSetRandom(xdot,ctx->rand);
    138:     KSPSolve(ksp,xdot,xdot);
    139:     VecDestroy(&xdot);
    140:     KSPGetIterationNumber(ksp,&nits);
    141:     N    = nits+2;

    143:     if (nits) {
    144:       PetscDraw     draw;
    145:       PetscReal     pause;
    146:       PetscDrawAxis axis;
    147:       PetscReal     xmin,xmax,ymin,ymax;

    149:       PetscDrawSPReset(drawsp);
    150:       PetscDrawSPSetLimits(drawsp,ctx->xmin,ctx->xmax,ctx->ymin,ctx->ymax);
    151:       PetscMalloc2(PetscMax(n,N),&r,PetscMax(n,N),&c);
    152:       if (ctx->computeexplicitly) {
    153:         KSPComputeEigenvaluesExplicitly(ksp,n,r,c);
    154:         neig = n;
    155:       } else {
    156:         KSPComputeEigenvalues(ksp,N,r,c,&neig);
    157:       }
    158:       /* We used the positive operator to be able to reuse KSPs that require positive definiteness, now flip the spectrum as is conventional for ODEs */
    159:       for (i=0; i<neig; i++) r[i] = -r[i];
    160:       for (i=0; i<neig; i++) {
    161:         if (ts->ops->linearstability) {
    162:           PetscReal fr,fi;
    163:           TSComputeLinearStability(ts,r[i],c[i],&fr,&fi);
    164:           if ((fr*fr + fi*fi) > 1.0) {
    165:             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));
    166:           }
    167:         }
    168:         PetscDrawSPAddPoint(drawsp,r+i,c+i);
    169:       }
    170:       PetscFree2(r,c);
    171:       PetscDrawSPGetDraw(drawsp,&draw);
    172:       PetscDrawGetPause(draw,&pause);
    173:       PetscDrawSetPause(draw,0.0);
    174:       PetscDrawSPDraw(drawsp,PETSC_TRUE);
    175:       PetscDrawSetPause(draw,pause);

    177:       if (ts->ops->linearstability) {
    178:         PetscDrawSPGetAxis(drawsp,&axis);
    179:         PetscDrawAxisGetLimits(axis,&xmin,&xmax,&ymin,&ymax);
    180:         PetscDrawIndicatorFunction(draw,xmin,xmax,ymin,ymax,PETSC_DRAW_CYAN,(PetscErrorCode (*)(void*,PetscReal,PetscReal,PetscBool*))TSLinearStabilityIndicator,ts);
    181:         PetscDrawSPDraw(drawsp,PETSC_FALSE);
    182:       }
    183:     }
    184:     MatDestroy(&B);
    185:   }
    186:   return(0);
    187: }

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

    194:    Collective on TSMonitorSPEigCtx

    196:    Input Parameter:
    197: .  ctx - the monitor context

    199:    Level: intermediate

    201: .keywords: TS, monitor, line graph, destroy

    203: .seealso: TSMonitorSPEigCtxCreate(),  TSMonitorSet(), TSMonitorSPEig();
    204: @*/
    205: PetscErrorCode  TSMonitorSPEigCtxDestroy(TSMonitorSPEigCtx *ctx)
    206: {
    207:   PetscDraw      draw;

    211:   PetscDrawSPGetDraw((*ctx)->drawsp,&draw);
    212:   PetscDrawDestroy(&draw);
    213:   PetscDrawSPDestroy(&(*ctx)->drawsp);
    214:   KSPDestroy(&(*ctx)->ksp);
    215:   PetscRandomDestroy(&(*ctx)->rand);
    216:   PetscFree(*ctx);
    217:   return(0);
    218: }