Date: 2022-03-04T17:37:41+00:00

Actual source code: matnull.c

      2: /*
      3:     Routines to project vectors out of null spaces.
      4: */

      6: #include <petsc/private/matimpl.h>

      8: PetscClassId MAT_NULLSPACE_CLASSID;

     10: /*@C
     11:    MatNullSpaceSetFunction - set a function that removes a null space from a vector
     12:    out of null spaces.

     14:    Logically Collective on MatNullSpace

     16:    Input Parameters:
     17: +  sp - the null space object
     18: .  rem - the function that removes the null space
     19: -  ctx - context for the remove function

     21:    Level: advanced

     23: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), MatSetNullSpace(), MatNullSpace, MatNullSpaceCreate()
     24: @*/
     25: PetscErrorCode  MatNullSpaceSetFunction(MatNullSpace sp, PetscErrorCode (*rem)(MatNullSpace,Vec,void*),void *ctx)
     26: {
     29:   sp->remove = rem;
     30:   sp->rmctx  = ctx;
     31:   return(0);
     32: }

     34: /*@C
     35:    MatNullSpaceGetVecs - get vectors defining the null space

     37:    Not Collective

     39:    Input Parameter:
     40: .  sp - null space object

     42:    Output Parameters:
     43: +  has_cnst - PETSC_TRUE if the null space contains the constant vector, otherwise PETSC_FALSE
     44: .  n - number of vectors (excluding constant vector) in null space
     45: -  vecs - orthonormal vectors that span the null space (excluding the constant vector)

     47:    Level: developer

     49:    Notes:
     50:       These vectors and the array are owned by the MatNullSpace and should not be destroyed or freeded by the caller

     52: .seealso: MatNullSpaceCreate(), MatGetNullSpace(), MatGetNearNullSpace()
     53: @*/
     54: PetscErrorCode MatNullSpaceGetVecs(MatNullSpace sp,PetscBool *has_const,PetscInt *n,const Vec **vecs)
     55: {

     59:   if (has_const) *has_const = sp->has_cnst;
     60:   if (n) *n = sp->n;
     61:   if (vecs) *vecs = sp->vecs;
     62:   return(0);
     63: }

     65: /*@
     66:    MatNullSpaceCreateRigidBody - create rigid body modes from coordinates

     68:    Collective on Vec

     70:    Input Parameter:
     71: .  coords - block of coordinates of each node, must have block size set

     73:    Output Parameter:
     74: .  sp - the null space

     76:    Level: advanced

     78:    Notes:
     79:      If you are solving an elasticity problem you should likely use this, in conjunction with MatSetNearNullspace(), to provide information that
     80:      the PCGAMG preconditioner can use to construct a much more efficient preconditioner.

     82:      If you are solving an elasticity problem with pure Neumann boundary conditions you can use this in conjunction with MatSetNullspace() to
     83:      provide this information to the linear solver so it can handle the null space appropriately in the linear solution.

     85: .seealso: MatNullSpaceCreate(), MatSetNearNullspace(), MatSetNullspace()
     86: @*/
     87: PetscErrorCode MatNullSpaceCreateRigidBody(Vec coords,MatNullSpace *sp)
     88: {
     89:   PetscErrorCode    ierr;
     90:   const PetscScalar *x;
     91:   PetscScalar       *v[6],dots[5];
     92:   Vec               vec[6];
     93:   PetscInt          n,N,dim,nmodes,i,j;
     94:   PetscReal         sN;

     97:   VecGetBlockSize(coords,&dim);
     98:   VecGetLocalSize(coords,&n);
     99:   VecGetSize(coords,&N);
    100:   n   /= dim;
    101:   N   /= dim;
    102:   sN = 1./PetscSqrtReal((PetscReal)N);
    103:   switch (dim) {
    104:   case 1:
    105:     MatNullSpaceCreate(PetscObjectComm((PetscObject)coords),PETSC_TRUE,0,NULL,sp);
    106:     break;
    107:   case 2:
    108:   case 3:
    109:     nmodes = (dim == 2) ? 3 : 6;
    110:     VecCreate(PetscObjectComm((PetscObject)coords),&vec[0]);
    111:     VecSetSizes(vec[0],dim*n,dim*N);
    112:     VecSetBlockSize(vec[0],dim);
    113:     VecSetUp(vec[0]);
    114:     for (i=1; i<nmodes; i++) {VecDuplicate(vec[0],&vec[i]);}
    115:     for (i=0; i<nmodes; i++) {VecGetArray(vec[i],&v[i]);}
    116:     VecGetArrayRead(coords,&x);
    117:     for (i=0; i<n; i++) {
    118:       if (dim == 2) {
    119:         v[0][i*2+0] = sN;
    120:         v[0][i*2+1] = 0.;
    121:         v[1][i*2+0] = 0.;
    122:         v[1][i*2+1] = sN;
    123:         /* Rotations */
    124:         v[2][i*2+0] = -x[i*2+1];
    125:         v[2][i*2+1] = x[i*2+0];
    126:       } else {
    127:         v[0][i*3+0] = sN;
    128:         v[0][i*3+1] = 0.;
    129:         v[0][i*3+2] = 0.;
    130:         v[1][i*3+0] = 0.;
    131:         v[1][i*3+1] = sN;
    132:         v[1][i*3+2] = 0.;
    133:         v[2][i*3+0] = 0.;
    134:         v[2][i*3+1] = 0.;
    135:         v[2][i*3+2] = sN;

    137:         v[3][i*3+0] = x[i*3+1];
    138:         v[3][i*3+1] = -x[i*3+0];
    139:         v[3][i*3+2] = 0.;
    140:         v[4][i*3+0] = 0.;
    141:         v[4][i*3+1] = -x[i*3+2];
    142:         v[4][i*3+2] = x[i*3+1];
    143:         v[5][i*3+0] = x[i*3+2];
    144:         v[5][i*3+1] = 0.;
    145:         v[5][i*3+2] = -x[i*3+0];
    146:       }
    147:     }
    148:     for (i=0; i<nmodes; i++) {VecRestoreArray(vec[i],&v[i]);}
    149:     VecRestoreArrayRead(coords,&x);
    150:     for (i=dim; i<nmodes; i++) {
    151:       /* Orthonormalize vec[i] against vec[0:i-1] */
    152:       VecMDot(vec[i],i,vec,dots);
    153:       for (j=0; j<i; j++) dots[j] *= -1.;
    154:       VecMAXPY(vec[i],i,dots,vec);
    155:       VecNormalize(vec[i],NULL);
    156:     }
    157:     MatNullSpaceCreate(PetscObjectComm((PetscObject)coords),PETSC_FALSE,nmodes,vec,sp);
    158:     for (i=0; i<nmodes; i++) {VecDestroy(&vec[i]);}
    159:   }
    160:   return(0);
    161: }

    163: /*@C
    164:    MatNullSpaceView - Visualizes a null space object.

    166:    Collective on MatNullSpace

    168:    Input Parameters:
    169: +  matnull - the null space
    170: -  viewer - visualization context

    172:    Level: advanced

    174:    Fortran Note:
    175:    This routine is not supported in Fortran.

    177: .seealso: MatNullSpaceCreate(), PetscViewerASCIIOpen()
    178: @*/
    179: PetscErrorCode MatNullSpaceView(MatNullSpace sp,PetscViewer viewer)
    180: {
    182:   PetscBool      iascii;

    186:   if (!viewer) {
    187:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
    188:   }

    192:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    193:   if (iascii) {
    194:     PetscViewerFormat format;
    195:     PetscInt          i;
    196:     PetscViewerGetFormat(viewer,&format);
    197:     PetscObjectPrintClassNamePrefixType((PetscObject)sp,viewer);
    198:     PetscViewerASCIIPushTab(viewer);
    199:     PetscViewerASCIIPrintf(viewer,"Contains %D vector%s%s\n",sp->n,sp->n==1 ? "" : "s",sp->has_cnst ? " and the constant" : "");
    200:     if (sp->remove) {PetscViewerASCIIPrintf(viewer,"Has user-provided removal function\n");}
    201:     if (!(format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) {
    202:       for (i=0; i<sp->n; i++) {
    203:         VecView(sp->vecs[i],viewer);
    204:       }
    205:     }
    206:     PetscViewerASCIIPopTab(viewer);
    207:   }
    208:   return(0);
    209: }

    211: /*@C
    212:    MatNullSpaceCreate - Creates a data structure used to project vectors
    213:    out of null spaces.

    215:    Collective

    217:    Input Parameters:
    218: +  comm - the MPI communicator associated with the object
    219: .  has_cnst - PETSC_TRUE if the null space contains the constant vector; otherwise PETSC_FALSE
    220: .  n - number of vectors (excluding constant vector) in null space
    221: -  vecs - the vectors that span the null space (excluding the constant vector);
    222:           these vectors must be orthonormal. These vectors are NOT copied, so do not change them
    223:           after this call. You should free the array that you pass in and destroy the vectors (this will reduce the reference count
    224:           for them by one).

    226:    Output Parameter:
    227: .  SP - the null space context

    229:    Level: advanced

    231:    Notes:
    232:     See MatNullSpaceSetFunction() as an alternative way of providing the null space information instead of setting vecs.

    234:       If has_cnst is PETSC_TRUE you do not need to pass a constant vector in as a fourth argument to this routine, nor do you
    235:        need to pass in a function that eliminates the constant function into MatNullSpaceSetFunction().

    237:   Users manual sections:
    238: .   sec_singular

    240: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), MatSetNullSpace(), MatNullSpace, MatNullSpaceSetFunction()
    241: @*/
    242: PetscErrorCode  MatNullSpaceCreate(MPI_Comm comm,PetscBool has_cnst,PetscInt n,const Vec vecs[],MatNullSpace *SP)
    243: {
    244:   MatNullSpace   sp;
    246:   PetscInt       i;

    249:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
    253:   if (n) {
    254:     for (i=0; i<n; i++) {
    255:       /* prevent the user from changes values in the vector */
    256:       VecLockReadPush(vecs[i]);
    257:     }
    258:   }
    259:   if (PetscUnlikelyDebug(n)) {
    260:     PetscScalar *dots;
    261:     for (i=0; i<n; i++) {
    262:       PetscReal norm;
    263:       VecNorm(vecs[i],NORM_2,&norm);
    264:       if (PetscAbsReal(norm - 1) > PETSC_SQRT_MACHINE_EPSILON) SETERRQ2(PetscObjectComm((PetscObject)vecs[i]),PETSC_ERR_ARG_WRONG,"Vector %D must have 2-norm of 1.0, it is %g",i,(double)norm);
    265:     }
    266:     if (has_cnst) {
    267:       for (i=0; i<n; i++) {
    268:         PetscScalar sum;
    269:         VecSum(vecs[i],&sum);
    270:         if (PetscAbsScalar(sum) > PETSC_SQRT_MACHINE_EPSILON) SETERRQ2(PetscObjectComm((PetscObject)vecs[i]),PETSC_ERR_ARG_WRONG,"Vector %D must be orthogonal to constant vector, inner product is %g",i,(double)PetscAbsScalar(sum));
    271:       }
    272:     }
    273:     PetscMalloc1(n-1,&dots);
    274:     for (i=0; i<n-1; i++) {
    275:       PetscInt j;
    276:       VecMDot(vecs[i],n-i-1,vecs+i+1,dots);
    277:       for (j=0;j<n-i-1;j++) {
    278:         if (PetscAbsScalar(dots[j]) > PETSC_SQRT_MACHINE_EPSILON) SETERRQ3(PetscObjectComm((PetscObject)vecs[i]),PETSC_ERR_ARG_WRONG,"Vector %D must be orthogonal to vector %D, inner product is %g",i,i+j+1,(double)PetscAbsScalar(dots[j]));
    279:       }
    280:     }
    281:     PetscFree(dots);
    282:   }

    284:   *SP = NULL;
    285:   MatInitializePackage();

    287:   PetscHeaderCreate(sp,MAT_NULLSPACE_CLASSID,"MatNullSpace","Null space","Mat",comm,MatNullSpaceDestroy,MatNullSpaceView);

    289:   sp->has_cnst = has_cnst;
    290:   sp->n        = n;
    291:   sp->vecs     = NULL;
    292:   sp->alpha    = NULL;
    293:   sp->remove   = NULL;
    294:   sp->rmctx    = NULL;

    296:   if (n) {
    297:     PetscMalloc1(n,&sp->vecs);
    298:     PetscMalloc1(n,&sp->alpha);
    299:     PetscLogObjectMemory((PetscObject)sp,n*(sizeof(Vec)+sizeof(PetscScalar)));
    300:     for (i=0; i<n; i++) {
    301:       PetscObjectReference((PetscObject)vecs[i]);
    302:       sp->vecs[i] = vecs[i];
    303:     }
    304:   }

    306:   *SP = sp;
    307:   return(0);
    308: }

    310: /*@
    311:    MatNullSpaceDestroy - Destroys a data structure used to project vectors
    312:    out of null spaces.

    314:    Collective on MatNullSpace

    316:    Input Parameter:
    317: .  sp - the null space context to be destroyed

    319:    Level: advanced

    321: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
    322: @*/
    323: PetscErrorCode  MatNullSpaceDestroy(MatNullSpace *sp)
    324: {
    326:   PetscInt       i;

    329:   if (!*sp) return(0);
    331:   if (--((PetscObject)(*sp))->refct > 0) {*sp = NULL; return(0);}

    333:   for (i=0; i < (*sp)->n; i++) {
    334:     VecLockReadPop((*sp)->vecs[i]);
    335:   }

    337:   VecDestroyVecs((*sp)->n,&(*sp)->vecs);
    338:   PetscFree((*sp)->alpha);
    339:   PetscHeaderDestroy(sp);
    340:   return(0);
    341: }

    343: /*@C
    344:    MatNullSpaceRemove - Removes all the components of a null space from a vector.

    346:    Collective on MatNullSpace

    348:    Input Parameters:
    349: +  sp - the null space context (if this is NULL then no null space is removed)
    350: -  vec - the vector from which the null space is to be removed

    352:    Level: advanced

    354: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
    355: @*/
    356: PetscErrorCode  MatNullSpaceRemove(MatNullSpace sp,Vec vec)
    357: {
    358:   PetscScalar    sum;
    359:   PetscInt       i,N;

    363:   if (!sp) return(0);

    367:   if (sp->has_cnst) {
    368:     VecGetSize(vec,&N);
    369:     if (N > 0) {
    370:       VecSum(vec,&sum);
    371:       sum  = sum/((PetscScalar)(-1.0*N));
    372:       VecShift(vec,sum);
    373:     }
    374:   }

    376:   if (sp->n) {
    377:     VecMDot(vec,sp->n,sp->vecs,sp->alpha);
    378:     for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
    379:     VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
    380:   }

    382:   if (sp->remove) {
    383:     (*sp->remove)(sp,vec,sp->rmctx);
    384:   }
    385:   return(0);
    386: }

    388: /*@
    389:    MatNullSpaceTest  - Tests if the claimed null space is really a
    390:      null space of a matrix

    392:    Collective on MatNullSpace

    394:    Input Parameters:
    395: +  sp - the null space context
    396: -  mat - the matrix

    398:    Output Parameters:
    399: .  isNull - PETSC_TRUE if the nullspace is valid for this matrix

    401:    Level: advanced

    403: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
    404: @*/
    405: PetscErrorCode  MatNullSpaceTest(MatNullSpace sp,Mat mat,PetscBool  *isNull)
    406: {
    407:   PetscScalar    sum;
    408:   PetscReal      nrm,tol = 10. * PETSC_SQRT_MACHINE_EPSILON;
    409:   PetscInt       j,n,N;
    411:   Vec            l,r;
    412:   PetscBool      flg1 = PETSC_FALSE,flg2 = PETSC_FALSE,consistent = PETSC_TRUE;
    413:   PetscViewer    viewer;

    418:   n    = sp->n;
    419:   PetscOptionsGetBool(((PetscObject)sp)->options,((PetscObject)mat)->prefix,"-mat_null_space_test_view",&flg1,NULL);
    420:   PetscOptionsGetBool(((PetscObject)sp)->options,((PetscObject)mat)->prefix,"-mat_null_space_test_view_draw",&flg2,NULL);

    422:   if (n) {
    423:     VecDuplicate(sp->vecs[0],&l);
    424:   } else {
    425:     MatCreateVecs(mat,&l,NULL);
    426:   }

    428:   PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
    429:   if (sp->has_cnst) {
    430:     VecDuplicate(l,&r);
    431:     VecGetSize(l,&N);
    432:     sum  = 1.0/PetscSqrtReal(N);
    433:     VecSet(l,sum);
    434:     MatMult(mat,l,r);
    435:     VecNorm(r,NORM_2,&nrm);
    436:     if (nrm >= tol) consistent = PETSC_FALSE;
    437:     if (flg1) {
    438:       if (consistent) {
    439:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are likely null vector");
    440:       } else {
    441:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are unlikely null vector ");
    442:       }
    443:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * 1/N || = %g\n",(double)nrm);
    444:     }
    445:     if (!consistent && flg1) {VecView(r,viewer);}
    446:     if (!consistent && flg2) {VecView(r,viewer);}
    447:     VecDestroy(&r);
    448:   }

    450:   for (j=0; j<n; j++) {
    451:     (*mat->ops->mult)(mat,sp->vecs[j],l);
    452:     VecNorm(l,NORM_2,&nrm);
    453:     if (nrm >= tol) consistent = PETSC_FALSE;
    454:     if (flg1) {
    455:       if (consistent) {
    456:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D is likely null vector",j);
    457:       } else {
    458:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D unlikely null vector ",j);
    459:         consistent = PETSC_FALSE;
    460:       }
    461:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * v[%D] || = %g\n",j,(double)nrm);
    462:     }
    463:     if (!consistent && flg1) {VecView(l,viewer);}
    464:     if (!consistent && flg2) {VecView(l,viewer);}
    465:   }

    467:   if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
    468:   VecDestroy(&l);
    469:   if (isNull) *isNull = consistent;
    470:   return(0);
    471: }