Actual source code: snesnoise.c

      2: #include <petsc/private/snesimpl.h>

      4: PETSC_INTERN PetscErrorCode SNESDiffParameterCreate_More(SNES,Vec,void**);
      5: PETSC_INTERN PetscErrorCode SNESDiffParameterCompute_More(SNES,void*,Vec,Vec,PetscReal*,PetscReal*);
      6: PETSC_INTERN PetscErrorCode SNESDiffParameterDestroy_More(void*);

      8: /* Data used by Jorge's diff parameter computation method */
      9: typedef struct {
     10:   Vec      *workv;           /* work vectors */
     11:   FILE     *fp;              /* output file */
     12:   PetscInt function_count;   /* count of function evaluations for diff param estimation */
     13:   double   fnoise_min;       /* minimim allowable noise */
     14:   double   hopt_min;         /* minimum allowable hopt */
     15:   double   h_first_try;      /* first try for h used in diff parameter estimate */
     16:   PetscInt fnoise_resets;    /* number of times we've reset the noise estimate */
     17:   PetscInt hopt_resets;      /* number of times we've reset the hopt estimate */
     18: } DIFFPAR_MORE;

     21: PETSC_INTERN PetscErrorCode SNESDefaultMatrixFreeSetParameters2(Mat,double,double,double);
     22: PETSC_INTERN PetscErrorCode SNESUnSetMatrixFreeParameter(SNES snes);
     23: PETSC_INTERN PetscErrorCode SNESNoise_dnest_(PetscInt*,PetscScalar*,PetscScalar*,PetscScalar*,PetscScalar*,PetscScalar*,PetscInt*,PetscScalar*);

     25: static PetscErrorCode JacMatMultCompare(SNES,Vec,Vec,double);

     27: PetscErrorCode SNESDiffParameterCreate_More(SNES snes,Vec x,void **outneP)
     28: {
     29:   DIFFPAR_MORE   *neP;
     30:   Vec            w;
     31:   PetscRandom    rctx;  /* random number generator context */
     33:   PetscBool      flg;
     34:   char           noise_file[PETSC_MAX_PATH_LEN];

     37:   PetscNewLog(snes,&neP);

     39:   neP->function_count = 0;
     40:   neP->fnoise_min     = 1.0e-20;
     41:   neP->hopt_min       = 1.0e-8;
     42:   neP->h_first_try    = 1.0e-3;
     43:   neP->fnoise_resets  = 0;
     44:   neP->hopt_resets    = 0;

     46:   /* Create work vectors */
     47:   VecDuplicateVecs(x,3,&neP->workv);
     48:   w    = neP->workv[0];

     50:   /* Set components of vector w to random numbers */
     51:   PetscRandomCreate(PetscObjectComm((PetscObject)snes),&rctx);
     52:   PetscRandomSetFromOptions(rctx);
     53:   VecSetRandom(w,rctx);
     54:   PetscRandomDestroy(&rctx);

     56:   /* Open output file */
     57:   PetscOptionsGetString(((PetscObject)snes)->options,((PetscObject)snes)->prefix,"-snes_mf_noise_file",noise_file,sizeof(noise_file),&flg);
     58:   if (flg) neP->fp = fopen(noise_file,"w");
     59:   else     neP->fp = fopen("noise.out","w");
     60:   if (!neP->fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_OPEN,"Cannot open file");
     61:   PetscInfo(snes,"Creating Jorge's differencing parameter context\n");

     63:   *outneP = neP;
     64:   return(0);
     65: }

     67: PetscErrorCode SNESDiffParameterDestroy_More(void *nePv)
     68: {
     69:   DIFFPAR_MORE   *neP = (DIFFPAR_MORE*)nePv;
     71:   int            err;

     74:   /* Destroy work vectors and close output file */
     75:   VecDestroyVecs(3,&neP->workv);
     76:   err  = fclose(neP->fp);
     77:   if (err) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SYS,"fclose() failed on file");
     78:   PetscFree(neP);
     79:   return(0);
     80: }

     82: PetscErrorCode SNESDiffParameterCompute_More(SNES snes,void *nePv,Vec x,Vec p,double *fnoise,double *hopt)
     83: {
     84:   DIFFPAR_MORE   *neP = (DIFFPAR_MORE*)nePv;
     85:   Vec            w, xp, fvec;    /* work vectors to use in computing h */
     86:   double         zero = 0.0, hl, hu, h, fnoise_s, fder2_s;
     87:   PetscScalar    alpha;
     88:   PetscScalar    fval[7], tab[7][7], eps[7], f = -1;
     89:   double         rerrf = -1., fder2;
     91:   PetscInt       iter, k, i, j,  info;
     92:   PetscInt       nf = 7;         /* number of function evaluations */
     93:   PetscInt       fcount;
     94:   MPI_Comm       comm;
     95:   FILE           *fp;
     96:   PetscBool      noise_test = PETSC_FALSE;

     99:   PetscObjectGetComm((PetscObject)snes,&comm);
    100:   /* Call to SNESSetUp() just to set data structures in SNES context */
    101:   if (!snes->setupcalled) {SNESSetUp(snes);}

    103:   w    = neP->workv[0];
    104:   xp   = neP->workv[1];
    105:   fvec = neP->workv[2];
    106:   fp   = neP->fp;

    108:   /* Initialize parameters */
    109:   hl       = zero;
    110:   hu       = zero;
    111:   h        = neP->h_first_try;
    112:   fnoise_s = zero;
    113:   fder2_s  = zero;
    114:   fcount   = neP->function_count;

    116:   /* We have 5 tries to attempt to compute a good hopt value */
    117:   SNESGetIterationNumber(snes,&i);
    118:   PetscFPrintf(comm,fp,"\n ------- SNES iteration %D ---------\n",i);
    119:   for (iter=0; iter<5; iter++) {
    120:     neP->h_first_try = h;

    122:     /* Compute the nf function values needed to estimate the noise from
    123:        the difference table */
    124:     for (k=0; k<nf; k++) {
    125:       alpha = h * (k+1 - (nf+1)/2);
    126:       VecWAXPY(xp,alpha,p,x);
    127:       SNESComputeFunction(snes,xp,fvec);
    128:       neP->function_count++;
    129:       VecDot(fvec,w,&fval[k]);
    130:     }
    131:     f = fval[(nf+1)/2 - 1];

    133:     /* Construct the difference table */
    134:     for (i=0; i<nf; i++) tab[i][0] = fval[i];

    136:     for (j=0; j<nf-1; j++) {
    137:       for (i=0; i<nf-j-1; i++) {
    138:         tab[i][j+1] = tab[i+1][j] - tab[i][j];
    139:       }
    140:     }

    142:     /* Print the difference table */
    143:     PetscFPrintf(comm,fp,"Difference Table: iter = %D\n",iter);
    144:     for (i=0; i<nf; i++) {
    145:       for (j=0; j<nf-i; j++) {
    146:         PetscFPrintf(comm,fp," %10.2e ",tab[i][j]);
    147:       }
    148:       PetscFPrintf(comm,fp,"\n");
    149:     }

    151:     /* Call the noise estimator */
    152:     SNESNoise_dnest_(&nf,fval,&h,fnoise,&fder2,hopt,&info,eps);

    154:     /* Output statements */
    155:     rerrf = *fnoise/PetscAbsScalar(f);
    156:     if (info == 1) {PetscFPrintf(comm,fp,"%s\n","Noise detected");}
    157:     if (info == 2) {PetscFPrintf(comm,fp,"%s\n","Noise not detected; h is too small");}
    158:     if (info == 3) {PetscFPrintf(comm,fp,"%s\n","Noise not detected; h is too large");}
    159:     if (info == 4) {PetscFPrintf(comm,fp,"%s\n","Noise detected, but unreliable hopt");}
    160:     PetscFPrintf(comm,fp,"Approximate epsfcn %g  %g  %g  %g  %g  %g\n",(double)eps[0],(double)eps[1],(double)eps[2],(double)eps[3],(double)eps[4],(double)eps[5]);
    161:     PetscFPrintf(comm,fp,"h = %g, fnoise = %g, fder2 = %g, rerrf = %g, hopt = %g\n\n",(double)h, (double)*fnoise, (double)fder2, (double)rerrf, (double)*hopt);

    163:     /* Save fnoise and fder2. */
    164:     if (*fnoise) fnoise_s = *fnoise;
    165:     if (fder2) fder2_s = fder2;

    167:     /* Check for noise detection. */
    168:     if (fnoise_s && fder2_s) {
    169:       *fnoise = fnoise_s;
    170:       fder2   = fder2_s;
    171:       *hopt   = 1.68*sqrt(*fnoise/PetscAbsScalar(fder2));
    172:       goto theend;
    173:     } else {

    175:       /* Update hl and hu, and determine new h */
    176:       if (info == 2 || info == 4) {
    177:         hl = h;
    178:         if (hu == zero) h = 100*h;
    179:         else            h = PetscMin(100*h,0.1*hu);
    180:       } else if (info == 3) {
    181:         hu = h;
    182:         h  = PetscMax(1.0e-3,sqrt(hl/hu))*hu;
    183:       }
    184:     }
    185:   }
    186: theend:

    188:   if (*fnoise < neP->fnoise_min) {
    189:     PetscFPrintf(comm,fp,"Resetting fnoise: fnoise1 = %g, fnoise_min = %g\n",(double)*fnoise,(double)neP->fnoise_min);
    190:     *fnoise = neP->fnoise_min;
    191:     neP->fnoise_resets++;
    192:   }
    193:   if (*hopt < neP->hopt_min) {
    194:     PetscFPrintf(comm,fp,"Resetting hopt: hopt1 = %g, hopt_min = %g\n",(double)*hopt,(double)neP->hopt_min);
    195:     *hopt = neP->hopt_min;
    196:     neP->hopt_resets++;
    197:   }

    199:   PetscFPrintf(comm,fp,"Errors in derivative:\n");
    200:   PetscFPrintf(comm,fp,"f = %g, fnoise = %g, fder2 = %g, hopt = %g\n",(double)f,(double)*fnoise,(double)fder2,(double)*hopt);

    202:   /* For now, compute h **each** MV Mult!! */
    203:   /*
    204:   PetscOptionsHasName(NULL,"-matrix_free_jorge_each_mvp",&flg);
    205:   if (!flg) {
    206:     Mat mat;
    207:     SNESGetJacobian(snes,&mat,NULL,NULL);
    208:     SNESDefaultMatrixFreeSetParameters2(mat,PETSC_DEFAULT,PETSC_DEFAULT,*hopt);
    209:   }
    210:   */
    211:   fcount = neP->function_count - fcount;
    212:   PetscInfo5(snes,"fct_now = %D, fct_cum = %D, rerrf=%g, sqrt(noise)=%g, h_more=%g\n",fcount,neP->function_count,(double)rerrf,(double)PetscSqrtReal(*fnoise),(double)*hopt);

    214:   PetscOptionsGetBool(NULL,NULL,"-noise_test",&noise_test,NULL);
    215:   if (noise_test) {
    216:     JacMatMultCompare(snes,x,p,*hopt);
    217:   }
    218:   return(0);
    219: }

    221: PetscErrorCode JacMatMultCompare(SNES snes,Vec x,Vec p,double hopt)
    222: {
    223:   Vec            yy1, yy2; /* work vectors */
    224:   PetscViewer    view2;    /* viewer */
    225:   Mat            J;        /* analytic Jacobian (set as preconditioner matrix) */
    226:   Mat            Jmf;      /* matrix-free Jacobian (set as true system matrix) */
    227:   double         h;        /* differencing parameter */
    228:   Vec            f;
    229:   PetscScalar    alpha;
    230:   PetscReal      yy1n,yy2n,enorm;
    232:   PetscInt       i;
    233:   PetscBool      printv = PETSC_FALSE;
    234:   char           filename[32];
    235:   MPI_Comm       comm;

    238:   PetscObjectGetComm((PetscObject)snes,&comm);
    239:   /* Compute function and analytic Jacobian at x */
    240:   SNESGetJacobian(snes,&Jmf,&J,NULL,NULL);
    241:   SNESComputeJacobian(snes,x,Jmf,J);
    242:   SNESGetFunction(snes,&f,NULL,NULL);
    243:   SNESComputeFunction(snes,x,f);

    245:   /* Duplicate work vectors */
    246:   VecDuplicate(x,&yy2);
    247:   VecDuplicate(x,&yy1);

    249:   /* Compute true matrix-vector product */
    250:   MatMult(J,p,yy1);
    251:   VecNorm(yy1,NORM_2,&yy1n);

    253:   /* View product vector if desired */
    254:   PetscOptionsGetBool(NULL,NULL,"-print_vecs",&printv,NULL);
    255:   if (printv) {
    256:     PetscViewerASCIIOpen(comm,"y1.out",&view2);
    257:     PetscViewerPushFormat(view2,PETSC_VIEWER_ASCII_COMMON);
    258:     VecView(yy1,view2);
    259:     PetscViewerPopFormat(view2);
    260:     PetscViewerDestroy(&view2);
    261:   }

    263:   /* Test Jacobian-vector product computation */
    264:   alpha = -1.0;
    265:   h     = 0.01 * hopt;
    266:   for (i=0; i<5; i++) {
    267:     /* Set differencing parameter for matrix-free multiplication */
    268:     SNESDefaultMatrixFreeSetParameters2(Jmf,PETSC_DEFAULT,PETSC_DEFAULT,h);

    270:     /* Compute matrix-vector product via differencing approximation */
    271:     MatMult(Jmf,p,yy2);
    272:     VecNorm(yy2,NORM_2,&yy2n);

    274:     /* View product vector if desired */
    275:     if (printv) {
    276:       sprintf(filename,"y2.%d.out",(int)i);
    277:       PetscViewerASCIIOpen(comm,filename,&view2);
    278:       PetscViewerPushFormat(view2,PETSC_VIEWER_ASCII_COMMON);
    279:       VecView(yy2,view2);
    280:       PetscViewerPopFormat(view2);
    281:       PetscViewerDestroy(&view2);
    282:     }

    284:     /* Compute relative error */
    285:     VecAXPY(yy2,alpha,yy1);
    286:     VecNorm(yy2,NORM_2,&enorm);
    287:     enorm = enorm/yy1n;
    288:     PetscFPrintf(comm,stdout,"h = %g: relative error = %g\n",(double)h,(double)enorm);
    289:     h    *= 10.0;
    290:   }
    291:   return(0);
    292: }

    294: static PetscInt lin_its_total = 0;

    296: PetscErrorCode SNESNoiseMonitor(SNES snes,PetscInt its,double fnorm,void *dummy)
    297: {
    299:   PetscInt       lin_its;

    302:   SNESGetLinearSolveIterations(snes,&lin_its);
    303:   lin_its_total += lin_its;
    304:   PetscPrintf(PetscObjectComm((PetscObject)snes), "iter = %D, SNES Function norm = %g, lin_its = %D, total_lin_its = %D\n",its,(double)fnorm,lin_its,lin_its_total);

    306:   SNESUnSetMatrixFreeParameter(snes);
    307:   return(0);
    308: }