Actual source code: ex3.c

      2: static char help[] ="Solves a simple time-dependent linear PDE (the heat equation).\n\
      3: Input parameters include:\n\
      4:   -m <points>, where <points> = number of grid points\n\
      5:   -time_dependent_rhs : Treat the problem as having a time-dependent right-hand side\n\
      6:   -use_ifunc          : Use IFunction/IJacobian interface\n\
      7:   -debug              : Activate debugging printouts\n\
      8:   -nox                : Deactivate x-window graphics\n\n";

     10: /*
     11:    Concepts: TS^time-dependent linear problems
     12:    Concepts: TS^heat equation
     13:    Concepts: TS^diffusion equation
     14:    Processors: 1
     15: */

     17: /* ------------------------------------------------------------------------

     19:    This program solves the one-dimensional heat equation (also called the
     20:    diffusion equation),
     21:        u_t = u_xx,
     22:    on the domain 0 <= x <= 1, with the boundary conditions
     23:        u(t,0) = 0, u(t,1) = 0,
     24:    and the initial condition
     25:        u(0,x) = sin(6*pi*x) + 3*sin(2*pi*x).
     26:    This is a linear, second-order, parabolic equation.

     28:    We discretize the right-hand side using finite differences with
     29:    uniform grid spacing h:
     30:        u_xx = (u_{i+1} - 2u_{i} + u_{i-1})/(h^2)
     31:    We then demonstrate time evolution using the various TS methods by
     32:    running the program via
     33:        ex3 -ts_type <timestepping solver>

     35:    We compare the approximate solution with the exact solution, given by
     36:        u_exact(x,t) = exp(-36*pi*pi*t) * sin(6*pi*x) +
     37:                       3*exp(-4*pi*pi*t) * sin(2*pi*x)

     39:    Notes:
     40:    This code demonstrates the TS solver interface to two variants of
     41:    linear problems, u_t = f(u,t), namely
     42:      - time-dependent f:   f(u,t) is a function of t
     43:      - time-independent f: f(u,t) is simply f(u)

     45:     The parallel version of this code is ts/tutorials/ex4.c

     47:   ------------------------------------------------------------------------- */

     49: /*
     50:    Include "petscts.h" so that we can use TS solvers.  Note that this file
     51:    automatically includes:
     52:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
     53:      petscmat.h  - matrices
     54:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
     55:      petscviewer.h - viewers               petscpc.h   - preconditioners
     56:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
     57: */

     59: #include <petscts.h>
     60: #include <petscdraw.h>

     62: /*
     63:    User-defined application context - contains data needed by the
     64:    application-provided call-back routines.
     65: */
     66: typedef struct {
     67:   Vec         solution;          /* global exact solution vector */
     68:   PetscInt    m;                 /* total number of grid points */
     69:   PetscReal   h;                 /* mesh width h = 1/(m-1) */
     70:   PetscBool   debug;             /* flag (1 indicates activation of debugging printouts) */
     71:   PetscViewer viewer1,viewer2;   /* viewers for the solution and error */
     72:   PetscReal   norm_2,norm_max;   /* error norms */
     73:   Mat         A;                 /* RHS mat, used with IFunction interface */
     74:   PetscReal   oshift;            /* old shift applied, prevent to recompute the IJacobian */
     75: } AppCtx;

     77: /*
     78:    User-defined routines
     79: */
     80: extern PetscErrorCode InitialConditions(Vec,AppCtx*);
     81: extern PetscErrorCode RHSMatrixHeat(TS,PetscReal,Vec,Mat,Mat,void*);
     82: extern PetscErrorCode IFunctionHeat(TS,PetscReal,Vec,Vec,Vec,void*);
     83: extern PetscErrorCode IJacobianHeat(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
     84: extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*);
     85: extern PetscErrorCode ExactSolution(PetscReal,Vec,AppCtx*);

     87: int main(int argc,char **argv)
     88: {
     89:   AppCtx         appctx;                 /* user-defined application context */
     90:   TS             ts;                     /* timestepping context */
     91:   Mat            A;                      /* matrix data structure */
     92:   Vec            u;                      /* approximate solution vector */
     93:   PetscReal      time_total_max = 100.0; /* default max total time */
     94:   PetscInt       time_steps_max = 100;   /* default max timesteps */
     95:   PetscDraw      draw;                   /* drawing context */
     97:   PetscInt       steps,m;
     98:   PetscMPIInt    size;
     99:   PetscReal      dt;
    100:   PetscBool      flg,flg_string;

    102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    103:      Initialize program and set problem parameters
    104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    106:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
    107:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
    108:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!");

    110:   m    = 60;
    111:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
    112:   PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug);
    113:   flg_string = PETSC_FALSE;
    114:   PetscOptionsGetBool(NULL,NULL,"-test_string_viewer",&flg_string,NULL);

    116:   appctx.m        = m;
    117:   appctx.h        = 1.0/(m-1.0);
    118:   appctx.norm_2   = 0.0;
    119:   appctx.norm_max = 0.0;

    121:   PetscPrintf(PETSC_COMM_SELF,"Solving a linear TS problem on 1 processor\n");

    123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    124:      Create vector data structures
    125:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    127:   /*
    128:      Create vector data structures for approximate and exact solutions
    129:   */
    130:   VecCreateSeq(PETSC_COMM_SELF,m,&u);
    131:   VecDuplicate(u,&appctx.solution);

    133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    134:      Set up displays to show graphs of the solution and error
    135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    137:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,"",80,380,400,160,&appctx.viewer1);
    138:   PetscViewerDrawGetDraw(appctx.viewer1,0,&draw);
    139:   PetscDrawSetDoubleBuffer(draw);
    140:   PetscViewerDrawOpen(PETSC_COMM_SELF,0,"",80,0,400,160,&appctx.viewer2);
    141:   PetscViewerDrawGetDraw(appctx.viewer2,0,&draw);
    142:   PetscDrawSetDoubleBuffer(draw);

    144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    145:      Create timestepping solver context
    146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    148:   TSCreate(PETSC_COMM_SELF,&ts);
    149:   TSSetProblemType(ts,TS_LINEAR);

    151:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    152:      Set optional user-defined monitoring routine
    153:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    155:   if (!flg_string) {
    156:     TSMonitorSet(ts,Monitor,&appctx,NULL);
    157:   }

    159:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    161:      Create matrix data structure; set matrix evaluation routine.
    162:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    164:   MatCreate(PETSC_COMM_SELF,&A);
    165:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m,m);
    166:   MatSetFromOptions(A);
    167:   MatSetUp(A);

    169:   flg  = PETSC_FALSE;
    170:   PetscOptionsGetBool(NULL,NULL,"-use_ifunc",&flg,NULL);
    171:   if (!flg) {
    172:     appctx.A = NULL;
    173:     PetscOptionsGetBool(NULL,NULL,"-time_dependent_rhs",&flg,NULL);
    174:     if (flg) {
    175:       /*
    176:          For linear problems with a time-dependent f(u,t) in the equation
    177:          u_t = f(u,t), the user provides the discretized right-hand-side
    178:          as a time-dependent matrix.
    179:       */
    180:       TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
    181:       TSSetRHSJacobian(ts,A,A,RHSMatrixHeat,&appctx);
    182:     } else {
    183:       /*
    184:          For linear problems with a time-independent f(u) in the equation
    185:          u_t = f(u), the user provides the discretized right-hand-side
    186:          as a matrix only once, and then sets the special Jacobian evaluation
    187:          routine TSComputeRHSJacobianConstant() which will NOT recompute the Jacobian.
    188:       */
    189:       RHSMatrixHeat(ts,0.0,u,A,A,&appctx);
    190:       TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
    191:       TSSetRHSJacobian(ts,A,A,TSComputeRHSJacobianConstant,&appctx);
    192:     }
    193:   } else {
    194:     Mat J;

    196:     RHSMatrixHeat(ts,0.0,u,A,A,&appctx);
    197:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&J);
    198:     TSSetIFunction(ts,NULL,IFunctionHeat,&appctx);
    199:     TSSetIJacobian(ts,J,J,IJacobianHeat,&appctx);
    200:     MatDestroy(&J);

    202:     PetscObjectReference((PetscObject)A);
    203:     appctx.A = A;
    204:     appctx.oshift = PETSC_MIN_REAL;
    205:   }
    206:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    207:      Set solution vector and initial timestep
    208:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    210:   dt   = appctx.h*appctx.h/2.0;
    211:   TSSetTimeStep(ts,dt);

    213:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    214:      Customize timestepping solver:
    215:        - Set the solution method to be the Backward Euler method.
    216:        - Set timestepping duration info
    217:      Then set runtime options, which can override these defaults.
    218:      For example,
    219:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
    220:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
    221:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    223:   TSSetMaxSteps(ts,time_steps_max);
    224:   TSSetMaxTime(ts,time_total_max);
    225:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    226:   TSSetFromOptions(ts);

    228:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    229:      Solve the problem
    230:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    232:   /*
    233:      Evaluate initial conditions
    234:   */
    235:   InitialConditions(u,&appctx);

    237:   /*
    238:      Run the timestepping solver
    239:   */
    240:   TSSolve(ts,u);
    241:   TSGetStepNumber(ts,&steps);

    243:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    244:      View timestepping solver info
    245:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    247:   PetscPrintf(PETSC_COMM_SELF,"avg. error (2 norm) = %g, avg. error (max norm) = %g\n",(double)(appctx.norm_2/steps),(double)(appctx.norm_max/steps));
    248:   if (!flg_string) {
    249:     TSView(ts,PETSC_VIEWER_STDOUT_SELF);
    250:   } else {
    251:     PetscViewer stringviewer;
    252:     char        string[512];
    253:     const char  *outstring;

    255:     PetscViewerStringOpen(PETSC_COMM_WORLD,string,sizeof(string),&stringviewer);
    256:     TSView(ts,stringviewer);
    257:     PetscViewerStringGetStringRead(stringviewer,&outstring,NULL);
    258:     if ((char*)outstring != (char*)string) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"String returned from viewer does not equal original string");
    259:     PetscPrintf(PETSC_COMM_WORLD,"Output from string viewer:%s\n",outstring);
    260:     PetscViewerDestroy(&stringviewer);
    261:   }

    263:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    264:      Free work space.  All PETSc objects should be destroyed when they
    265:      are no longer needed.
    266:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    268:   TSDestroy(&ts);
    269:   MatDestroy(&A);
    270:   VecDestroy(&u);
    271:   PetscViewerDestroy(&appctx.viewer1);
    272:   PetscViewerDestroy(&appctx.viewer2);
    273:   VecDestroy(&appctx.solution);
    274:   MatDestroy(&appctx.A);

    276:   /*
    277:      Always call PetscFinalize() before exiting a program.  This routine
    278:        - finalizes the PETSc libraries as well as MPI
    279:        - provides summary and diagnostic information if certain runtime
    280:          options are chosen (e.g., -log_view).
    281:   */
    282:   PetscFinalize();
    283:   return ierr;
    284: }
    285: /* --------------------------------------------------------------------- */
    286: /*
    287:    InitialConditions - Computes the solution at the initial time.

    289:    Input Parameter:
    290:    u - uninitialized solution vector (global)
    291:    appctx - user-defined application context

    293:    Output Parameter:
    294:    u - vector with solution at initial time (global)
    295: */
    296: PetscErrorCode InitialConditions(Vec u,AppCtx *appctx)
    297: {
    298:   PetscScalar    *u_localptr,h = appctx->h;
    300:   PetscInt       i;

    302:   /*
    303:     Get a pointer to vector data.
    304:     - For default PETSc vectors, VecGetArray() returns a pointer to
    305:       the data array.  Otherwise, the routine is implementation dependent.
    306:     - You MUST call VecRestoreArray() when you no longer need access to
    307:       the array.
    308:     - Note that the Fortran interface to VecGetArray() differs from the
    309:       C version.  See the users manual for details.
    310:   */
    311:   VecGetArrayWrite(u,&u_localptr);

    313:   /*
    314:      We initialize the solution array by simply writing the solution
    315:      directly into the array locations.  Alternatively, we could use
    316:      VecSetValues() or VecSetValuesLocal().
    317:   */
    318:   for (i=0; i<appctx->m; i++) u_localptr[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

    320:   /*
    321:      Restore vector
    322:   */
    323:   VecRestoreArrayWrite(u,&u_localptr);

    325:   /*
    326:      Print debugging information if desired
    327:   */
    328:   if (appctx->debug) {
    329:     PetscPrintf(PETSC_COMM_WORLD,"Initial guess vector\n");
    330:     VecView(u,PETSC_VIEWER_STDOUT_SELF);
    331:   }

    333:   return 0;
    334: }
    335: /* --------------------------------------------------------------------- */
    336: /*
    337:    ExactSolution - Computes the exact solution at a given time.

    339:    Input Parameters:
    340:    t - current time
    341:    solution - vector in which exact solution will be computed
    342:    appctx - user-defined application context

    344:    Output Parameter:
    345:    solution - vector with the newly computed exact solution
    346: */
    347: PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
    348: {
    349:   PetscScalar    *s_localptr,h = appctx->h,ex1,ex2,sc1,sc2,tc = t;
    351:   PetscInt       i;

    353:   /*
    354:      Get a pointer to vector data.
    355:   */
    356:   VecGetArrayWrite(solution,&s_localptr);

    358:   /*
    359:      Simply write the solution directly into the array locations.
    360:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
    361:   */
    362:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*tc);
    363:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*tc);
    364:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
    365:   for (i=0; i<appctx->m; i++) s_localptr[i] = PetscSinScalar(sc1*(PetscReal)i)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i)*ex2;

    367:   /*
    368:      Restore vector
    369:   */
    370:   VecRestoreArrayWrite(solution,&s_localptr);
    371:   return 0;
    372: }
    373: /* --------------------------------------------------------------------- */
    374: /*
    375:    Monitor - User-provided routine to monitor the solution computed at
    376:    each timestep.  This example plots the solution and computes the
    377:    error in two different norms.

    379:    This example also demonstrates changing the timestep via TSSetTimeStep().

    381:    Input Parameters:
    382:    ts     - the timestep context
    383:    step   - the count of the current step (with 0 meaning the
    384:              initial condition)
    385:    time   - the current time
    386:    u      - the solution at this timestep
    387:    ctx    - the user-provided context for this monitoring routine.
    388:             In this case we use the application context which contains
    389:             information about the problem size, workspace and the exact
    390:             solution.
    391: */
    392: PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
    393: {
    394:   AppCtx         *appctx = (AppCtx*) ctx;   /* user-defined application context */
    396:   PetscReal      norm_2,norm_max,dt,dttol;

    398:   /*
    399:      View a graph of the current iterate
    400:   */
    401:   VecView(u,appctx->viewer2);

    403:   /*
    404:      Compute the exact solution
    405:   */
    406:   ExactSolution(time,appctx->solution,appctx);

    408:   /*
    409:      Print debugging information if desired
    410:   */
    411:   if (appctx->debug) {
    412:     PetscPrintf(PETSC_COMM_SELF,"Computed solution vector\n");
    413:     VecView(u,PETSC_VIEWER_STDOUT_SELF);
    414:     PetscPrintf(PETSC_COMM_SELF,"Exact solution vector\n");
    415:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);
    416:   }

    418:   /*
    419:      Compute the 2-norm and max-norm of the error
    420:   */
    421:   VecAXPY(appctx->solution,-1.0,u);
    422:   VecNorm(appctx->solution,NORM_2,&norm_2);
    423:   norm_2 = PetscSqrtReal(appctx->h)*norm_2;
    424:   VecNorm(appctx->solution,NORM_MAX,&norm_max);

    426:   TSGetTimeStep(ts,&dt);
    427:   PetscPrintf(PETSC_COMM_WORLD,"Timestep %3D: step size = %g, time = %g, 2-norm error = %g, max norm error = %g\n",step,(double)dt,(double)time,(double)norm_2,(double)norm_max);

    429:   appctx->norm_2   += norm_2;
    430:   appctx->norm_max += norm_max;

    432:   dttol = .0001;
    433:   PetscOptionsGetReal(NULL,NULL,"-dttol",&dttol,NULL);
    434:   if (dt < dttol) {
    435:     dt  *= .999;
    436:     TSSetTimeStep(ts,dt);
    437:   }

    439:   /*
    440:      View a graph of the error
    441:   */
    442:   VecView(appctx->solution,appctx->viewer1);

    444:   /*
    445:      Print debugging information if desired
    446:   */
    447:   if (appctx->debug) {
    448:     PetscPrintf(PETSC_COMM_SELF,"Error vector\n");
    449:     VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);
    450:   }

    452:   return 0;
    453: }
    454: /* --------------------------------------------------------------------- */
    455: /*
    456:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
    457:    matrix for the heat equation.

    459:    Input Parameters:
    460:    ts - the TS context
    461:    t - current time
    462:    global_in - global input vector
    463:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    465:    Output Parameters:
    466:    AA - Jacobian matrix
    467:    BB - optionally different preconditioning matrix
    468:    str - flag indicating matrix structure

    470:    Notes:
    471:    Recall that MatSetValues() uses 0-based row and column numbers
    472:    in Fortran as well as in C.
    473: */
    474: PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec X,Mat AA,Mat BB,void *ctx)
    475: {
    476:   Mat            A       = AA;                /* Jacobian matrix */
    477:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
    478:   PetscInt       mstart  = 0;
    479:   PetscInt       mend    = appctx->m;
    481:   PetscInt       i,idx[3];
    482:   PetscScalar    v[3],stwo = -2./(appctx->h*appctx->h),sone = -.5*stwo;

    484:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    485:      Compute entries for the locally owned part of the matrix
    486:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    487:   /*
    488:      Set matrix rows corresponding to boundary data
    489:   */

    491:   mstart = 0;
    492:   v[0]   = 1.0;
    493:   MatSetValues(A,1,&mstart,1,&mstart,v,INSERT_VALUES);
    494:   mstart++;

    496:   mend--;
    497:   v[0] = 1.0;
    498:   MatSetValues(A,1,&mend,1,&mend,v,INSERT_VALUES);

    500:   /*
    501:      Set matrix rows corresponding to interior data.  We construct the
    502:      matrix one row at a time.
    503:   */
    504:   v[0] = sone; v[1] = stwo; v[2] = sone;
    505:   for (i=mstart; i<mend; i++) {
    506:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
    507:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
    508:   }

    510:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    511:      Complete the matrix assembly process and set some options
    512:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    513:   /*
    514:      Assemble matrix, using the 2-step process:
    515:        MatAssemblyBegin(), MatAssemblyEnd()
    516:      Computations can be done while messages are in transition
    517:      by placing code between these two statements.
    518:   */
    519:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    520:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    522:   /*
    523:      Set and option to indicate that we will never add a new nonzero location
    524:      to the matrix. If we do, it will generate an error.
    525:   */
    526:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    528:   return 0;
    529: }

    531: PetscErrorCode IFunctionHeat(TS ts,PetscReal t,Vec X,Vec Xdot,Vec r,void *ctx)
    532: {
    533:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */

    536:   MatMult(appctx->A,X,r);
    537:   VecAYPX(r,-1.0,Xdot);
    538:   return 0;
    539: }

    541: PetscErrorCode IJacobianHeat(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal s,Mat A,Mat B,void *ctx)
    542: {
    543:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */

    546:   if (appctx->oshift == s) return 0;
    547:   MatCopy(appctx->A,A,SAME_NONZERO_PATTERN);
    548:   MatScale(A,-1);
    549:   MatShift(A,s);
    550:   MatCopy(A,B,SAME_NONZERO_PATTERN);
    551:   appctx->oshift = s;
    552:   return 0;
    553: }

    555: /*TEST

    557:     test:
    558:       args: -nox -ts_type ssp -ts_dt 0.0005

    560:     test:
    561:       suffix: 2
    562:       args: -nox -ts_type ssp -ts_dt 0.0005 -time_dependent_rhs 1

    564:     test:
    565:       suffix: 3
    566:       args:  -nox -ts_type rosw -ts_max_steps 3 -ksp_converged_reason
    567:       filter: sed "s/ATOL/RTOL/g"
    568:       requires: !single

    570:     test:
    571:       suffix: 4
    572:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason
    573:       filter: sed "s/ATOL/RTOL/g"

    575:     test:
    576:       suffix: 5
    577:       args: -nox -ts_type beuler -ts_max_steps 3 -ksp_converged_reason -time_dependent_rhs
    578:       filter: sed "s/ATOL/RTOL/g"

    580:     test:
    581:       requires: !single
    582:       suffix: pod_guess
    583:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type pod -pc_type none -ksp_converged_reason

    585:     test:
    586:       requires: !single
    587:       suffix: pod_guess_Ainner
    588:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type pod -ksp_guess_pod_Ainner -pc_type none -ksp_converged_reason

    590:     test:
    591:       requires: !single
    592:       suffix: fischer_guess
    593:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -pc_type none -ksp_converged_reason

    595:     test:
    596:       requires: !single
    597:       suffix: fischer_guess_2
    598:       args: -nox -ts_type beuler -use_ifunc -ts_dt 0.0005 -ksp_guess_type fischer -ksp_guess_fischer_model 2,10 -pc_type none -ksp_converged_reason

    600:     test:
    601:       requires: !single
    602:       suffix: stringview
    603:       args: -nox -ts_type rosw -test_string_viewer

    605:     test:
    606:       requires: !single
    607:       suffix: stringview_euler
    608:       args: -nox -ts_type euler -test_string_viewer

    610: TEST*/