Date: 2015-10-02T22:12:17+00:00

Actual source code: fdmatrix.c
petsc-3.6.2 2015-10-02
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      2: /*
      3:    This is where the abstract matrix operations are defined that are
      4:   used for finite difference computations of Jacobians using coloring.
      5: */

      7: #include <petsc/private/matimpl.h>        /*I "petscmat.h" I*/
      8: #include <petsc/private/isimpl.h>

     12: PetscErrorCode  MatFDColoringSetF(MatFDColoring fd,Vec F)
     13: {

     17:   if (F) {
     18:     VecCopy(F,fd->w1);
     19:     fd->fset = PETSC_TRUE;
     20:   } else {
     21:     fd->fset = PETSC_FALSE;
     22:   }
     23:   return(0);
     24: }

     26: #include <petscdraw.h>
     29: static PetscErrorCode MatFDColoringView_Draw_Zoom(PetscDraw draw,void *Aa)
     30: {
     31:   MatFDColoring  fd = (MatFDColoring)Aa;
     33:   PetscInt       i,j,nz,row;
     34:   PetscReal      x,y;
     35:   MatEntry       *Jentry=fd->matentry;

     38:   /* loop over colors  */
     39:   nz = 0;
     40:   for (i=0; i<fd->ncolors; i++) {
     41:     for (j=0; j<fd->nrows[i]; j++) {
     42:       row = Jentry[nz].row;
     43:       y   = fd->M - row - fd->rstart;
     44:       x   = (PetscReal)Jentry[nz++].col;
     45:       PetscDrawRectangle(draw,x,y,x+1,y+1,i+1,i+1,i+1,i+1);
     46:     }
     47:   }
     48:   return(0);
     49: }

     53: static PetscErrorCode MatFDColoringView_Draw(MatFDColoring fd,PetscViewer viewer)
     54: {
     56:   PetscBool      isnull;
     57:   PetscDraw      draw;
     58:   PetscReal      xr,yr,xl,yl,h,w;

     61:   PetscViewerDrawGetDraw(viewer,0,&draw);
     62:   PetscDrawIsNull(draw,&isnull); if (isnull) return(0);

     64:   PetscObjectCompose((PetscObject)fd,"Zoomviewer",(PetscObject)viewer);

     66:   xr   = fd->N; yr  = fd->M; h = yr/10.0; w = xr/10.0;
     67:   xr  += w;     yr += h;    xl = -w;     yl = -h;
     68:   PetscDrawSetCoordinates(draw,xl,yl,xr,yr);
     69:   PetscDrawZoom(draw,MatFDColoringView_Draw_Zoom,fd);
     70:   PetscObjectCompose((PetscObject)fd,"Zoomviewer",NULL);
     71:   return(0);
     72: }

     76: /*@C
     77:    MatFDColoringView - Views a finite difference coloring context.

     79:    Collective on MatFDColoring

     81:    Input  Parameters:
     82: +  c - the coloring context
     83: -  viewer - visualization context

     85:    Level: intermediate

     87:    Notes:
     88:    The available visualization contexts include
     89: +     PETSC_VIEWER_STDOUT_SELF - standard output (default)
     90: .     PETSC_VIEWER_STDOUT_WORLD - synchronized standard
     91:         output where only the first processor opens
     92:         the file.  All other processors send their
     93:         data to the first processor to print.
     94: -     PETSC_VIEWER_DRAW_WORLD - graphical display of nonzero structure

     96:    Notes:
     97:      Since PETSc uses only a small number of basic colors (currently 33), if the coloring
     98:    involves more than 33 then some seemingly identical colors are displayed making it look
     99:    like an illegal coloring. This is just a graphical artifact.

    101: .seealso: MatFDColoringCreate()

    103: .keywords: Mat, finite differences, coloring, view
    104: @*/
    105: PetscErrorCode  MatFDColoringView(MatFDColoring c,PetscViewer viewer)
    106: {
    107:   PetscErrorCode    ierr;
    108:   PetscInt          i,j;
    109:   PetscBool         isdraw,iascii;
    110:   PetscViewerFormat format;

    114:   if (!viewer) {
    115:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)c),&viewer);
    116:   }

    120:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);
    121:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    122:   if (isdraw) {
    123:     MatFDColoringView_Draw(c,viewer);
    124:   } else if (iascii) {
    125:     PetscObjectPrintClassNamePrefixType((PetscObject)c,viewer);
    126:     PetscViewerASCIIPrintf(viewer,"  Error tolerance=%g\n",(double)c->error_rel);
    127:     PetscViewerASCIIPrintf(viewer,"  Umin=%g\n",(double)c->umin);
    128:     PetscViewerASCIIPrintf(viewer,"  Number of colors=%D\n",c->ncolors);

    130:     PetscViewerGetFormat(viewer,&format);
    131:     if (format != PETSC_VIEWER_ASCII_INFO) {
    132:       PetscInt row,col,nz;
    133:       nz = 0;
    134:       for (i=0; i<c->ncolors; i++) {
    135:         PetscViewerASCIIPrintf(viewer,"  Information for color %D\n",i);
    136:         PetscViewerASCIIPrintf(viewer,"    Number of columns %D\n",c->ncolumns[i]);
    137:         for (j=0; j<c->ncolumns[i]; j++) {
    138:           PetscViewerASCIIPrintf(viewer,"      %D\n",c->columns[i][j]);
    139:         }
    140:         PetscViewerASCIIPrintf(viewer,"    Number of rows %D\n",c->nrows[i]);
    141:         for (j=0; j<c->nrows[i]; j++) {
    142:           row  = c->matentry[nz].row;
    143:           col  = c->matentry[nz++].col;
    144:           PetscViewerASCIIPrintf(viewer,"      %D %D \n",row,col);
    145:         }
    146:       }
    147:     }
    148:     PetscViewerFlush(viewer);
    149:   }
    150:   return(0);
    151: }

    155: /*@
    156:    MatFDColoringSetParameters - Sets the parameters for the sparse approximation of
    157:    a Jacobian matrix using finite differences.

    159:    Logically Collective on MatFDColoring

    161:    The Jacobian is estimated with the differencing approximation
    162: .vb
    163:        F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
    164:        h = error_rel*u[i]                 if  abs(u[i]) > umin
    165:          = +/- error_rel*umin             otherwise, with +/- determined by the sign of u[i]
    166:        dx_{i} = (0, ... 1, .... 0)
    167: .ve

    169:    Input Parameters:
    170: +  coloring - the coloring context
    171: .  error_rel - relative error
    172: -  umin - minimum allowable u-value magnitude

    174:    Level: advanced

    176: .keywords: Mat, finite differences, coloring, set, parameters

    178: .seealso: MatFDColoringCreate(), MatFDColoringSetFromOptions()

    180: @*/
    181: PetscErrorCode MatFDColoringSetParameters(MatFDColoring matfd,PetscReal error,PetscReal umin)
    182: {
    187:   if (error != PETSC_DEFAULT) matfd->error_rel = error;
    188:   if (umin != PETSC_DEFAULT)  matfd->umin      = umin;
    189:   return(0);
    190: }

    194: /*@
    195:    MatFDColoringSetBlockSize - Sets block size for efficient inserting entries of Jacobian matrix.

    197:    Logically Collective on MatFDColoring

    199:    Input Parameters:
    200: +  coloring - the coloring context
    201: .  brows - number of rows in the block
    202: -  bcols - number of columns in the block

    204:    Level: intermediate

    206: .keywords: Mat, coloring

    208: .seealso: MatFDColoringCreate(), MatFDColoringSetFromOptions()

    210: @*/
    211: PetscErrorCode MatFDColoringSetBlockSize(MatFDColoring matfd,PetscInt brows,PetscInt bcols)
    212: {
    217:   if (brows != PETSC_DEFAULT) matfd->brows = brows;
    218:   if (bcols != PETSC_DEFAULT) matfd->bcols = bcols;
    219:   return(0);
    220: }

    224: /*@
    225:    MatFDColoringSetUp - Sets up the internal data structures of matrix coloring context for the later use.

    227:    Collective on Mat

    229:    Input Parameters:
    230: +  mat - the matrix containing the nonzero structure of the Jacobian
    231: .  iscoloring - the coloring of the matrix; usually obtained with MatGetColoring() or DMCreateColoring()
    232: -  color - the matrix coloring context

    234:    Level: beginner

    236: .keywords: MatFDColoring, setup

    238: .seealso: MatFDColoringCreate(), MatFDColoringDestroy()
    239: @*/
    240: PetscErrorCode MatFDColoringSetUp(Mat mat,ISColoring iscoloring,MatFDColoring color)
    241: {

    247:   if (color->setupcalled) return(0);

    249:   PetscLogEventBegin(MAT_FDColoringSetUp,mat,0,0,0);
    250:   if (mat->ops->fdcoloringsetup) {
    251:     (*mat->ops->fdcoloringsetup)(mat,iscoloring,color);
    252:   } else SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Code not yet written for matrix type %s",((PetscObject)mat)->type_name);

    254:   color->setupcalled = PETSC_TRUE;
    255:    PetscLogEventEnd(MAT_FDColoringSetUp,mat,0,0,0);
    256:   return(0);
    257: }

    261: /*@C
    262:    MatFDColoringGetFunction - Gets the function to use for computing the Jacobian.

    264:    Not Collective

    266:    Input Parameters:
    267: .  coloring - the coloring context

    269:    Output Parameters:
    270: +  f - the function
    271: -  fctx - the optional user-defined function context

    273:    Level: intermediate

    275: .keywords: Mat, Jacobian, finite differences, set, function

    277: .seealso: MatFDColoringCreate(), MatFDColoringSetFunction(), MatFDColoringSetFromOptions()

    279: @*/
    280: PetscErrorCode  MatFDColoringGetFunction(MatFDColoring matfd,PetscErrorCode (**f)(void),void **fctx)
    281: {
    284:   if (f) *f = matfd->f;
    285:   if (fctx) *fctx = matfd->fctx;
    286:   return(0);
    287: }

    291: /*@C
    292:    MatFDColoringSetFunction - Sets the function to use for computing the Jacobian.

    294:    Logically Collective on MatFDColoring

    296:    Input Parameters:
    297: +  coloring - the coloring context
    298: .  f - the function
    299: -  fctx - the optional user-defined function context

    301:    Calling sequence of (*f) function:
    302:     For SNES:    PetscErrorCode (*f)(SNES,Vec,Vec,void*)
    303:     If not using SNES: PetscErrorCode (*f)(void *dummy,Vec,Vec,void*) and dummy is ignored

    305:    Level: advanced

    307:    Notes: This function is usually used automatically by SNES (when one uses SNESSetJacobian() with the argument
    308:      SNESComputeJacobianDefaultColor()) and only needs to be used by someone computing a matrix via coloring directly by
    309:      calling MatFDColoringApply()

    311:    Fortran Notes:
    312:     In Fortran you must call MatFDColoringSetFunction() for a coloring object to
    313:   be used without SNES or within the SNES solvers.

    315: .keywords: Mat, Jacobian, finite differences, set, function

    317: .seealso: MatFDColoringCreate(), MatFDColoringGetFunction(), MatFDColoringSetFromOptions()

    319: @*/
    320: PetscErrorCode  MatFDColoringSetFunction(MatFDColoring matfd,PetscErrorCode (*f)(void),void *fctx)
    321: {
    324:   matfd->f    = f;
    325:   matfd->fctx = fctx;
    326:   return(0);
    327: }

    331: /*@
    332:    MatFDColoringSetFromOptions - Sets coloring finite difference parameters from
    333:    the options database.

    335:    Collective on MatFDColoring

    337:    The Jacobian, F'(u), is estimated with the differencing approximation
    338: .vb
    339:        F'(u)_{:,i} = [F(u+h*dx_{i}) - F(u)]/h where
    340:        h = error_rel*u[i]                 if  abs(u[i]) > umin
    341:          = +/- error_rel*umin             otherwise, with +/- determined by the sign of u[i]
    342:        dx_{i} = (0, ... 1, .... 0)
    343: .ve

    345:    Input Parameter:
    346: .  coloring - the coloring context

    348:    Options Database Keys:
    349: +  -mat_fd_coloring_err <err> - Sets <err> (square root of relative error in the function)
    350: .  -mat_fd_coloring_umin <umin> - Sets umin, the minimum allowable u-value magnitude
    351: .  -mat_fd_type - "wp" or "ds" (see MATMFFD_WP or MATMFFD_DS)
    352: .  -mat_fd_coloring_view - Activates basic viewing
    353: .  -mat_fd_coloring_view ::ascii_info - Activates viewing info
    354: -  -mat_fd_coloring_view draw - Activates drawing

    356:     Level: intermediate

    358: .keywords: Mat, finite differences, parameters

    360: .seealso: MatFDColoringCreate(), MatFDColoringView(), MatFDColoringSetParameters()

    362: @*/
    363: PetscErrorCode  MatFDColoringSetFromOptions(MatFDColoring matfd)
    364: {
    366:   PetscBool      flg;
    367:   char           value[3];

    372:   PetscObjectOptionsBegin((PetscObject)matfd);
    373:   PetscOptionsReal("-mat_fd_coloring_err","Square root of relative error in function","MatFDColoringSetParameters",matfd->error_rel,&matfd->error_rel,0);
    374:   PetscOptionsReal("-mat_fd_coloring_umin","Minimum allowable u magnitude","MatFDColoringSetParameters",matfd->umin,&matfd->umin,0);
    375:   PetscOptionsString("-mat_fd_type","Algorithm to compute h, wp or ds","MatFDColoringCreate",matfd->htype,value,3,&flg);
    376:   if (flg) {
    377:     if (value[0] == 'w' && value[1] == 'p') matfd->htype = "wp";
    378:     else if (value[0] == 'd' && value[1] == 's') matfd->htype = "ds";
    379:     else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Unknown finite differencing type %s",value);
    380:   }
    381:   PetscOptionsInt("-mat_fd_coloring_brows","Number of block rows","MatFDColoringSetBlockSize",matfd->brows,&matfd->brows,NULL);
    382:   PetscOptionsInt("-mat_fd_coloring_bcols","Number of block columns","MatFDColoringSetBlockSize",matfd->bcols,&matfd->bcols,&flg);
    383:   if (flg && matfd->bcols > matfd->ncolors) {
    384:     /* input bcols cannot be > matfd->ncolors, thus set it as ncolors */
    385:     matfd->bcols = matfd->ncolors;
    386:   }

    388:   /* process any options handlers added with PetscObjectAddOptionsHandler() */
    389:   PetscObjectProcessOptionsHandlers((PetscObject)matfd);
    390:   PetscOptionsEnd();
    391:   return(0);
    392: }

    396: PetscErrorCode MatFDColoringViewFromOptions(MatFDColoring fd,const char prefix[],const char optionname[])
    397: {
    398:   PetscErrorCode    ierr;
    399:   PetscBool         flg;
    400:   PetscViewer       viewer;
    401:   PetscViewerFormat format;

    404:   if (prefix) {
    405:     PetscOptionsGetViewer(PetscObjectComm((PetscObject)fd),prefix,optionname,&viewer,&format,&flg);
    406:   } else {
    407:     PetscOptionsGetViewer(PetscObjectComm((PetscObject)fd),((PetscObject)fd)->prefix,optionname,&viewer,&format,&flg);
    408:   }
    409:   if (flg) {
    410:     PetscViewerPushFormat(viewer,format);
    411:     MatFDColoringView(fd,viewer);
    412:     PetscViewerPopFormat(viewer);
    413:     PetscViewerDestroy(&viewer);
    414:   }
    415:   return(0);
    416: }

    420: /*@
    421:    MatFDColoringCreate - Creates a matrix coloring context for finite difference
    422:    computation of Jacobians.

    424:    Collective on Mat

    426:    Input Parameters:
    427: +  mat - the matrix containing the nonzero structure of the Jacobian
    428: -  iscoloring - the coloring of the matrix; usually obtained with MatColoringCreate() or DMCreateColoring()

    430:     Output Parameter:
    431: .   color - the new coloring context

    433:     Level: intermediate

    435: .seealso: MatFDColoringDestroy(),SNESComputeJacobianDefaultColor(), ISColoringCreate(),
    436:           MatFDColoringSetFunction(), MatFDColoringSetFromOptions(), MatFDColoringApply(),
    437:           MatFDColoringView(), MatFDColoringSetParameters(), MatColoringCreate(), DMCreateColoring()
    438: @*/
    439: PetscErrorCode  MatFDColoringCreate(Mat mat,ISColoring iscoloring,MatFDColoring *color)
    440: {
    441:   MatFDColoring  c;
    442:   MPI_Comm       comm;
    444:   PetscInt       M,N;

    448:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must be assembled by calls to MatAssemblyBegin/End();");
    449:   PetscLogEventBegin(MAT_FDColoringCreate,mat,0,0,0);
    450:   MatGetSize(mat,&M,&N);
    451:   if (M != N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Only for square matrices");
    452:   PetscObjectGetComm((PetscObject)mat,&comm);
    453:   PetscHeaderCreate(c,MAT_FDCOLORING_CLASSID,"MatFDColoring","Jacobian computation via finite differences with coloring","Mat",comm,MatFDColoringDestroy,MatFDColoringView);

    455:   c->ctype = iscoloring->ctype;

    457:   if (mat->ops->fdcoloringcreate) {
    458:     (*mat->ops->fdcoloringcreate)(mat,iscoloring,c);
    459:   } else SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Code not yet written for matrix type %s",((PetscObject)mat)->type_name);

    461:   MatCreateVecs(mat,NULL,&c->w1);
    462:   PetscLogObjectParent((PetscObject)c,(PetscObject)c->w1);
    463:   VecDuplicate(c->w1,&c->w2);
    464:   PetscLogObjectParent((PetscObject)c,(PetscObject)c->w2);

    466:   c->error_rel    = PETSC_SQRT_MACHINE_EPSILON;
    467:   c->umin         = 100.0*PETSC_SQRT_MACHINE_EPSILON;
    468:   c->currentcolor = -1;
    469:   c->htype        = "wp";
    470:   c->fset         = PETSC_FALSE;
    471:   c->setupcalled  = PETSC_FALSE;

    473:   *color = c;
    474:   PetscObjectCompose((PetscObject)mat,"SNESMatFDColoring",(PetscObject)c);
    475:   PetscLogEventEnd(MAT_FDColoringCreate,mat,0,0,0);
    476:   return(0);
    477: }

    481: /*@
    482:     MatFDColoringDestroy - Destroys a matrix coloring context that was created
    483:     via MatFDColoringCreate().

    485:     Collective on MatFDColoring

    487:     Input Parameter:
    488: .   c - coloring context

    490:     Level: intermediate

    492: .seealso: MatFDColoringCreate()
    493: @*/
    494: PetscErrorCode  MatFDColoringDestroy(MatFDColoring *c)
    495: {
    497:   PetscInt       i;
    498:   MatFDColoring  color = *c;

    501:   if (!*c) return(0);
    502:   if (--((PetscObject)color)->refct > 0) {*c = 0; return(0);}

    504:   for (i=0; i<color->ncolors; i++) {
    505:     PetscFree(color->columns[i]);
    506:   }
    507:   PetscFree(color->ncolumns);
    508:   PetscFree(color->columns);
    509:   PetscFree(color->nrows);
    510:   if (color->htype[0] == 'w') {
    511:     PetscFree(color->matentry2);
    512:   } else {
    513:     PetscFree(color->matentry);
    514:   }
    515:   PetscFree(color->dy);
    516:   if (color->vscale) {VecDestroy(&color->vscale);}
    517:   VecDestroy(&color->w1);
    518:   VecDestroy(&color->w2);
    519:   VecDestroy(&color->w3);
    520:   PetscHeaderDestroy(c);
    521:   return(0);
    522: }

    526: /*@C
    527:     MatFDColoringGetPerturbedColumns - Returns the indices of the columns that
    528:       that are currently being perturbed.

    530:     Not Collective

    532:     Input Parameters:
    533: .   coloring - coloring context created with MatFDColoringCreate()

    535:     Output Parameters:
    536: +   n - the number of local columns being perturbed
    537: -   cols - the column indices, in global numbering

    539:    Level: intermediate

    541: .seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView(), MatFDColoringApply()

    543: .keywords: coloring, Jacobian, finite differences
    544: @*/
    545: PetscErrorCode  MatFDColoringGetPerturbedColumns(MatFDColoring coloring,PetscInt *n,PetscInt *cols[])
    546: {
    548:   if (coloring->currentcolor >= 0) {
    549:     *n    = coloring->ncolumns[coloring->currentcolor];
    550:     *cols = coloring->columns[coloring->currentcolor];
    551:   } else {
    552:     *n = 0;
    553:   }
    554:   return(0);
    555: }

    559: /*@
    560:     MatFDColoringApply - Given a matrix for which a MatFDColoring context
    561:     has been created, computes the Jacobian for a function via finite differences.

    563:     Collective on MatFDColoring

    565:     Input Parameters:
    566: +   mat - location to store Jacobian
    567: .   coloring - coloring context created with MatFDColoringCreate()
    568: .   x1 - location at which Jacobian is to be computed
    569: -   sctx - context required by function, if this is being used with the SNES solver then it is SNES object, otherwise it is null

    571:     Options Database Keys:
    572: +    -mat_fd_type - "wp" or "ds"  (see MATMFFD_WP or MATMFFD_DS)
    573: .    -mat_fd_coloring_view - Activates basic viewing or coloring
    574: .    -mat_fd_coloring_view draw - Activates drawing of coloring
    575: -    -mat_fd_coloring_view ::ascii_info - Activates viewing of coloring info

    577:     Level: intermediate

    579: .seealso: MatFDColoringCreate(), MatFDColoringDestroy(), MatFDColoringView(), MatFDColoringSetFunction()

    581: .keywords: coloring, Jacobian, finite differences
    582: @*/
    583: PetscErrorCode  MatFDColoringApply(Mat J,MatFDColoring coloring,Vec x1,void *sctx)
    584: {
    586:   PetscBool      flg = PETSC_FALSE;

    592:   if (!coloring->f) SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_WRONGSTATE,"Must call MatFDColoringSetFunction()");
    593:   if (!J->ops->fdcoloringapply) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)J)->type_name);
    594:   if (!coloring->setupcalled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call MatFDColoringSetUp()");

    596:   MatSetUnfactored(J);
    597:   PetscOptionsGetBool(NULL,"-mat_fd_coloring_dont_rezero",&flg,NULL);
    598:   if (flg) {
    599:     PetscInfo(coloring,"Not calling MatZeroEntries()\n");
    600:   } else {
    601:     PetscBool assembled;
    602:     MatAssembled(J,&assembled);
    603:     if (assembled) {
    604:       MatZeroEntries(J);
    605:     }
    606:   }

    608:   PetscLogEventBegin(MAT_FDColoringApply,coloring,J,x1,0);
    609:   (*J->ops->fdcoloringapply)(J,coloring,x1,sctx);
    610:   PetscLogEventEnd(MAT_FDColoringApply,coloring,J,x1,0);
    611:   return(0);
    612: }