Actual source code: matnull.c
petsc-3.13.6 2020-09-29
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      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 Arguments:
     40: .  sp - null space object

     42:    Output Arguments:
     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 Argument:
     71: .  coords - block of coordinates of each node, must have block size set

     73:    Output Argument:
     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.

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

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

    138:         v[3][i*3+0] = x[i*3+1];
    139:         v[3][i*3+1] = -x[i*3+0];
    140:         v[3][i*3+2] = 0.;
    141:         v[4][i*3+0] = 0.;
    142:         v[4][i*3+1] = -x[i*3+2];
    143:         v[4][i*3+2] = x[i*3+1];
    144:         v[5][i*3+0] = x[i*3+2];
    145:         v[5][i*3+1] = 0.;
    146:         v[5][i*3+2] = -x[i*3+0];
    147:       }
    148:     }
    149:     for (i=0; i<nmodes; i++) {VecRestoreArray(vec[i],&v[i]);}
    150:     VecRestoreArrayRead(coords,&x);
    151:     for (i=dim; i<nmodes; i++) {
    152:       /* Orthonormalize vec[i] against vec[0:i-1] */
    153:       VecMDot(vec[i],i,vec,dots);
    154:       for (j=0; j<i; j++) dots[j] *= -1.;
    155:       VecMAXPY(vec[i],i,dots,vec);
    156:       VecNormalize(vec[i],NULL);
    157:     }
    158:     MatNullSpaceCreate(PetscObjectComm((PetscObject)coords),PETSC_FALSE,nmodes,vec,sp);
    159:     for (i=0; i<nmodes; i++) {VecDestroy(&vec[i]);}
    160:   }
    161:   return(0);
    162: }

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

    167:    Collective on MatNullSpace

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

    173:    Level: advanced

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

    178: .seealso: MatNullSpaceCreate(), PetscViewerASCIIOpen()
    179: @*/
    180: PetscErrorCode MatNullSpaceView(MatNullSpace sp,PetscViewer viewer)
    181: {
    183:   PetscBool      iascii;

    187:   if (!viewer) {
    188:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
    189:   }

    193:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    194:   if (iascii) {
    195:     PetscViewerFormat format;
    196:     PetscInt          i;
    197:     PetscViewerGetFormat(viewer,&format);
    198:     PetscObjectPrintClassNamePrefixType((PetscObject)sp,viewer);
    199:     PetscViewerASCIIPushTab(viewer);
    200:     PetscViewerASCIIPrintf(viewer,"Contains %D vector%s%s\n",sp->n,sp->n==1 ? "" : "s",sp->has_cnst ? " and the constant" : "");
    201:     if (sp->remove) {PetscViewerASCIIPrintf(viewer,"Has user-provided removal function\n");}
    202:     if (!(format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) {
    203:       for (i=0; i<sp->n; i++) {
    204:         VecView(sp->vecs[i],viewer);
    205:       }
    206:     }
    207:     PetscViewerASCIIPopTab(viewer);
    208:   }
    209:   return(0);
    210: }

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

    216:    Collective

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

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

    230:    Level: advanced

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

    235:       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
    236:        need to pass in a function that eliminates the constant function into MatNullSpaceSetFunction().

    238:   Users manual sections:
    239: .   Section 4.19 Solving Singular Systems

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

    250:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
    254:   if (n) {
    255:     for (i=0; i<n; i++) {
    256:       /* prevent the user from changes values in the vector */
    257:       VecLockReadPush(vecs[i]);
    258:     }
    259:   }
    260: #if defined(PETSC_USE_DEBUG)
    261:   if (n) {
    262:     PetscScalar *dots;
    263:     for (i=0; i<n; i++) {
    264:       PetscReal norm;
    265:       VecNorm(vecs[i],NORM_2,&norm);
    266:       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);
    267:     }
    268:     if (has_cnst) {
    269:       for (i=0; i<n; i++) {
    270:         PetscScalar sum;
    271:         VecSum(vecs[i],&sum);
    272:         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));
    273:       }
    274:     }
    275:     PetscMalloc1(n-1,&dots);
    276:     for (i=0; i<n-1; i++) {
    277:       PetscInt j;
    278:       VecMDot(vecs[i],n-i-1,vecs+i+1,dots);
    279:       for (j=0;j<n-i-1;j++) {
    280:         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]));
    281:       }
    282:     }
    283:     PetscFree(dots);
    284:   }
    285: #endif

    287:   *SP = NULL;
    288:   MatInitializePackage();

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

    292:   sp->has_cnst = has_cnst;
    293:   sp->n        = n;
    294:   sp->vecs     = 0;
    295:   sp->alpha    = 0;
    296:   sp->remove   = 0;
    297:   sp->rmctx    = 0;

    299:   if (n) {
    300:     PetscMalloc1(n,&sp->vecs);
    301:     PetscMalloc1(n,&sp->alpha);
    302:     PetscLogObjectMemory((PetscObject)sp,n*(sizeof(Vec)+sizeof(PetscScalar)));
    303:     for (i=0; i<n; i++) {
    304:       PetscObjectReference((PetscObject)vecs[i]);
    305:       sp->vecs[i] = vecs[i];
    306:     }
    307:   }

    309:   *SP = sp;
    310:   return(0);
    311: }

    313: /*@
    314:    MatNullSpaceDestroy - Destroys a data structure used to project vectors
    315:    out of null spaces.

    317:    Collective on MatNullSpace

    319:    Input Parameter:
    320: .  sp - the null space context to be destroyed

    322:    Level: advanced

    324: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
    325: @*/
    326: PetscErrorCode  MatNullSpaceDestroy(MatNullSpace *sp)
    327: {
    329:   PetscInt       i;

    332:   if (!*sp) return(0);
    334:   if (--((PetscObject)(*sp))->refct > 0) {*sp = 0; return(0);}

    336:   for (i=0; i < (*sp)->n; i++) {
    337:     VecLockReadPop((*sp)->vecs[i]);
    338:   }

    340:   VecDestroyVecs((*sp)->n,&(*sp)->vecs);
    341:   PetscFree((*sp)->alpha);
    342:   PetscHeaderDestroy(sp);
    343:   return(0);
    344: }

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

    349:    Collective on MatNullSpace

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

    355:    Level: advanced

    357: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
    358: @*/
    359: PetscErrorCode  MatNullSpaceRemove(MatNullSpace sp,Vec vec)
    360: {
    361:   PetscScalar    sum;
    362:   PetscInt       i,N;

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

    370:   if (sp->has_cnst) {
    371:     VecGetSize(vec,&N);
    372:     if (N > 0) {
    373:       VecSum(vec,&sum);
    374:       sum  = sum/((PetscScalar)(-1.0*N));
    375:       VecShift(vec,sum);
    376:     }
    377:   }

    379:   if (sp->n) {
    380:     VecMDot(vec,sp->n,sp->vecs,sp->alpha);
    381:     for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
    382:     VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
    383:   }

    385:   if (sp->remove) {
    386:     (*sp->remove)(sp,vec,sp->rmctx);
    387:   }
    388:   return(0);
    389: }

    391: /*@
    392:    MatNullSpaceTest  - Tests if the claimed null space is really a
    393:      null space of a matrix

    395:    Collective on MatNullSpace

    397:    Input Parameters:
    398: +  sp - the null space context
    399: -  mat - the matrix

    401:    Output Parameters:
    402: .  isNull - PETSC_TRUE if the nullspace is valid for this matrix

    404:    Level: advanced

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

    421:   n    = sp->n;
    422:   PetscOptionsGetBool(((PetscObject)sp)->options,((PetscObject)mat)->prefix,"-mat_null_space_test_view",&flg1,NULL);
    423:   PetscOptionsGetBool(((PetscObject)sp)->options,((PetscObject)mat)->prefix,"-mat_null_space_test_view_draw",&flg2,NULL);

    425:   if (n) {
    426:     VecDuplicate(sp->vecs[0],&l);
    427:   } else {
    428:     MatCreateVecs(mat,&l,NULL);
    429:   }

    431:   PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
    432:   if (sp->has_cnst) {
    433:     VecDuplicate(l,&r);
    434:     VecGetSize(l,&N);
    435:     sum  = 1.0/N;
    436:     VecSet(l,sum);
    437:     MatMult(mat,l,r);
    438:     VecNorm(r,NORM_2,&nrm);
    439:     if (nrm >= tol) consistent = PETSC_FALSE;
    440:     if (flg1) {
    441:       if (consistent) {
    442:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are likely null vector");
    443:       } else {
    444:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are unlikely null vector ");
    445:       }
    446:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * 1/N || = %g\n",(double)nrm);
    447:     }
    448:     if (!consistent && flg1) {VecView(r,viewer);}
    449:     if (!consistent && flg2) {VecView(r,viewer);}
    450:     VecDestroy(&r);
    451:   }

    453:   for (j=0; j<n; j++) {
    454:     (*mat->ops->mult)(mat,sp->vecs[j],l);
    455:     VecNorm(l,NORM_2,&nrm);
    456:     if (nrm >= tol) consistent = PETSC_FALSE;
    457:     if (flg1) {
    458:       if (consistent) {
    459:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D is likely null vector",j);
    460:       } else {
    461:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D unlikely null vector ",j);
    462:         consistent = PETSC_FALSE;
    463:       }
    464:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * v[%D] || = %g\n",j,(double)nrm);
    465:     }
    466:     if (!consistent && flg1) {VecView(l,viewer);}
    467:     if (!consistent && flg2) {VecView(l,viewer);}
    468:   }

    470:   if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
    471:   VecDestroy(&l);
    472:   if (isNull) *isNull = consistent;
    473:   return(0);
    474: }