Actual source code: matnull.c
petsc-3.10.5 2019-03-28
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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: .keywords: PC, null space, create

     25: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), MatSetNullSpace(), MatNullSpace, MatNullSpaceCreate()
     26: @*/
     27: PetscErrorCode  MatNullSpaceSetFunction(MatNullSpace sp, PetscErrorCode (*rem)(MatNullSpace,Vec,void*),void *ctx)
     28: {
     31:   sp->remove = rem;
     32:   sp->rmctx  = ctx;
     33:   return(0);
     34: }

     36: /*@C
     37:    MatNullSpaceGetVecs - get vectors defining the null space

     39:    Not Collective

     41:    Input Arguments:
     42: .  sp - null space object

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

     49:    Level: developer

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

     54: .seealso: MatNullSpaceCreate(), MatGetNullSpace(), MatGetNearNullSpace()
     55: @*/
     56: PetscErrorCode MatNullSpaceGetVecs(MatNullSpace sp,PetscBool *has_const,PetscInt *n,const Vec **vecs)
     57: {

     61:   if (has_const) *has_const = sp->has_cnst;
     62:   if (n) *n = sp->n;
     63:   if (vecs) *vecs = sp->vecs;
     64:   return(0);
     65: }

     67: /*@
     68:    MatNullSpaceCreateRigidBody - create rigid body modes from coordinates

     70:    Collective on Vec

     72:    Input Argument:
     73: .  coords - block of coordinates of each node, must have block size set

     75:    Output Argument:
     76: .  sp - the null space

     78:    Level: advanced

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

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

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

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

    140:         v[3][i*3+0] = x[i*3+1];
    141:         v[3][i*3+1] = -x[i*3+0];
    142:         v[3][i*3+2] = 0.;
    143:         v[4][i*3+0] = 0.;
    144:         v[4][i*3+1] = -x[i*3+2];
    145:         v[4][i*3+2] = x[i*3+1];
    146:         v[5][i*3+0] = x[i*3+2];
    147:         v[5][i*3+1] = 0.;
    148:         v[5][i*3+2] = -x[i*3+0];
    149:       }
    150:     }
    151:     for (i=0; i<nmodes; i++) {VecRestoreArray(vec[i],&v[i]);}
    152:     VecRestoreArrayRead(coords,&x);
    153:     for (i=dim; i<nmodes; i++) {
    154:       /* Orthonormalize vec[i] against vec[0:i-1] */
    155:       VecMDot(vec[i],i,vec,dots);
    156:       for (j=0; j<i; j++) dots[j] *= -1.;
    157:       VecMAXPY(vec[i],i,dots,vec);
    158:       VecNormalize(vec[i],NULL);
    159:     }
    160:     MatNullSpaceCreate(PetscObjectComm((PetscObject)coords),PETSC_FALSE,nmodes,vec,sp);
    161:     for (i=0; i<nmodes; i++) {VecDestroy(&vec[i]);}
    162:   }
    163:   return(0);
    164: }

    166: /*@C
    167:    MatNullSpaceView - Visualizes a null space object.

    169:    Collective on MatNullSpace

    171:    Input Parameters:
    172: +  matnull - the null space
    173: -  viewer - visualization context

    175:    Level: advanced

    177:    Fortran Note:
    178:    This routine is not supported in Fortran.

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

    189:   if (!viewer) {
    190:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
    191:   }

    195:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    196:   if (iascii) {
    197:     PetscViewerFormat format;
    198:     PetscInt          i;
    199:     PetscViewerGetFormat(viewer,&format);
    200:     PetscObjectPrintClassNamePrefixType((PetscObject)sp,viewer);
    201:     PetscViewerASCIIPushTab(viewer);
    202:     PetscViewerASCIIPrintf(viewer,"Contains %D vector%s%s\n",sp->n,sp->n==1 ? "" : "s",sp->has_cnst ? " and the constant" : "");
    203:     if (sp->remove) {PetscViewerASCIIPrintf(viewer,"Has user-provided removal function\n");}
    204:     if (!(format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) {
    205:       for (i=0; i<sp->n; i++) {
    206:         VecView(sp->vecs[i],viewer);
    207:       }
    208:     }
    209:     PetscViewerASCIIPopTab(viewer);
    210:   }
    211:   return(0);
    212: }

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

    218:    Collective on MPI_Comm

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

    229:    Output Parameter:
    230: .  SP - the null space context

    232:    Level: advanced

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

    237:       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
    238:        need to pass in a function that eliminates the constant function into MatNullSpaceSetFunction().

    240:   Users manual sections:
    241: .   Section 4.19 Solving Singular Systems

    243: .keywords: PC, null space, create

    245: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), MatSetNullSpace(), MatNullSpace, MatNullSpaceSetFunction()
    246: @*/
    247: PetscErrorCode  MatNullSpaceCreate(MPI_Comm comm,PetscBool has_cnst,PetscInt n,const Vec vecs[],MatNullSpace *SP)
    248: {
    249:   MatNullSpace   sp;
    251:   PetscInt       i;

    254:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
    258:   if (n) {
    259:     for (i=0; i<n; i++) {
    260:       /* prevent the user from changes values in the vector */
    261:       VecLockPush(vecs[i]);
    262:     }
    263:   }
    264: #if defined(PETSC_USE_DEBUG)
    265:   if (n) {
    266:     PetscScalar *dots;
    267:     for (i=0; i<n; i++) {
    268:       PetscReal norm;
    269:       VecNorm(vecs[i],NORM_2,&norm);
    270:       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);
    271:     }
    272:     if (has_cnst) {
    273:       for (i=0; i<n; i++) {
    274:         PetscScalar sum;
    275:         VecSum(vecs[i],&sum);
    276:         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));
    277:       }
    278:     }
    279:     PetscMalloc1(n-1,&dots);
    280:     for (i=0; i<n-1; i++) {
    281:       PetscInt j;
    282:       VecMDot(vecs[i],n-i-1,vecs+i+1,dots);
    283:       for (j=0;j<n-i-1;j++) {
    284:         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]));
    285:       }
    286:     }
    287:     PetscFree(dots);
    288:   }
    289: #endif

    291:   *SP = NULL;
    292:   MatInitializePackage();

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

    296:   sp->has_cnst = has_cnst;
    297:   sp->n        = n;
    298:   sp->vecs     = 0;
    299:   sp->alpha    = 0;
    300:   sp->remove   = 0;
    301:   sp->rmctx    = 0;

    303:   if (n) {
    304:     PetscMalloc1(n,&sp->vecs);
    305:     PetscMalloc1(n,&sp->alpha);
    306:     PetscLogObjectMemory((PetscObject)sp,n*(sizeof(Vec)+sizeof(PetscScalar)));
    307:     for (i=0; i<n; i++) {
    308:       PetscObjectReference((PetscObject)vecs[i]);
    309:       sp->vecs[i] = vecs[i];
    310:     }
    311:   }

    313:   *SP = sp;
    314:   return(0);
    315: }

    317: /*@
    318:    MatNullSpaceDestroy - Destroys a data structure used to project vectors
    319:    out of null spaces.

    321:    Collective on MatNullSpace

    323:    Input Parameter:
    324: .  sp - the null space context to be destroyed

    326:    Level: advanced

    328: .keywords: PC, null space, destroy

    330: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
    331: @*/
    332: PetscErrorCode  MatNullSpaceDestroy(MatNullSpace *sp)
    333: {
    335:   PetscInt       i;

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

    342:   for (i=0; i < (*sp)->n; i++) {
    343:     VecLockPop((*sp)->vecs[i]);
    344:   }

    346:   VecDestroyVecs((*sp)->n,&(*sp)->vecs);
    347:   PetscFree((*sp)->alpha);
    348:   PetscHeaderDestroy(sp);
    349:   return(0);
    350: }

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

    355:    Collective on MatNullSpace

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

    361:    Level: advanced

    363: .keywords: PC, null space, remove

    365: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
    366: @*/
    367: PetscErrorCode  MatNullSpaceRemove(MatNullSpace sp,Vec vec)
    368: {
    369:   PetscScalar    sum;
    370:   PetscInt       i,N;

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

    378:   if (sp->has_cnst) {
    379:     VecGetSize(vec,&N);
    380:     if (N > 0) {
    381:       VecSum(vec,&sum);
    382:       sum  = sum/((PetscScalar)(-1.0*N));
    383:       VecShift(vec,sum);
    384:     }
    385:   }

    387:   if (sp->n) {
    388:     VecMDot(vec,sp->n,sp->vecs,sp->alpha);
    389:     for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
    390:     VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
    391:   }

    393:   if (sp->remove) {
    394:     (*sp->remove)(sp,vec,sp->rmctx);
    395:   }
    396:   return(0);
    397: }

    399: /*@
    400:    MatNullSpaceTest  - Tests if the claimed null space is really a
    401:      null space of a matrix

    403:    Collective on MatNullSpace

    405:    Input Parameters:
    406: +  sp - the null space context
    407: -  mat - the matrix

    409:    Output Parameters:
    410: .  isNull - PETSC_TRUE if the nullspace is valid for this matrix

    412:    Level: advanced

    414: .keywords: PC, null space, remove

    416: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
    417: @*/
    418: PetscErrorCode  MatNullSpaceTest(MatNullSpace sp,Mat mat,PetscBool  *isNull)
    419: {
    420:   PetscScalar    sum;
    421:   PetscReal      nrm,tol = 10. * PETSC_SQRT_MACHINE_EPSILON;
    422:   PetscInt       j,n,N;
    424:   Vec            l,r;
    425:   PetscBool      flg1 = PETSC_FALSE,flg2 = PETSC_FALSE,consistent = PETSC_TRUE;
    426:   PetscViewer    viewer;

    431:   n    = sp->n;
    432:   PetscOptionsGetBool(((PetscObject)sp)->options,((PetscObject)mat)->prefix,"-mat_null_space_test_view",&flg1,NULL);
    433:   PetscOptionsGetBool(((PetscObject)sp)->options,((PetscObject)mat)->prefix,"-mat_null_space_test_view_draw",&flg2,NULL);

    435:   if (n) {
    436:     VecDuplicate(sp->vecs[0],&l);
    437:   } else {
    438:     MatCreateVecs(mat,&l,NULL);
    439:   }

    441:   PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
    442:   if (sp->has_cnst) {
    443:     VecDuplicate(l,&r);
    444:     VecGetSize(l,&N);
    445:     sum  = 1.0/N;
    446:     VecSet(l,sum);
    447:     MatMult(mat,l,r);
    448:     VecNorm(r,NORM_2,&nrm);
    449:     if (nrm >= tol) consistent = PETSC_FALSE;
    450:     if (flg1) {
    451:       if (consistent) {
    452:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are likely null vector");
    453:       } else {
    454:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are unlikely null vector ");
    455:       }
    456:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * 1/N || = %g\n",(double)nrm);
    457:     }
    458:     if (!consistent && flg1) {VecView(r,viewer);}
    459:     if (!consistent && flg2) {VecView(r,viewer);}
    460:     VecDestroy(&r);
    461:   }

    463:   for (j=0; j<n; j++) {
    464:     (*mat->ops->mult)(mat,sp->vecs[j],l);
    465:     VecNorm(l,NORM_2,&nrm);
    466:     if (nrm >= tol) consistent = PETSC_FALSE;
    467:     if (flg1) {
    468:       if (consistent) {
    469:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D is likely null vector",j);
    470:       } else {
    471:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D unlikely null vector ",j);
    472:         consistent = PETSC_FALSE;
    473:       }
    474:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * v[%D] || = %g\n",j,(double)nrm);
    475:     }
    476:     if (!consistent && flg1) {VecView(l,viewer);}
    477:     if (!consistent && flg2) {VecView(l,viewer);}
    478:   }

    480:   if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
    481:   VecDestroy(&l);
    482:   if (isNull) *isNull = consistent;
    483:   return(0);
    484: }