Actual source code: matnull.c

petsc-master 2014-12-26
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  2: /*
  3:     Routines to project vectors out of null spaces.
  4: */

  6: #include <petsc-private/matimpl.h>      /*I "petscmat.h" I*/

  8: PetscClassId MAT_NULLSPACE_CLASSID;

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

 16:    Logically Collective on MatNullSpace

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

 23:    Level: advanced

 25: .keywords: PC, null space, create

 27: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), KSPSetNullSpace(), MatNullSpace, MatNullSpaceCreate()
 28: @*/
 29: PetscErrorCode  MatNullSpaceSetFunction(MatNullSpace sp, PetscErrorCode (*rem)(MatNullSpace,Vec,void*),void *ctx)
 30: {
 33:   sp->remove = rem;
 34:   sp->rmctx  = ctx;
 35:   return(0);
 36: }

 40: /*@C
 41:    MatNullSpaceGetVecs - get vectors defining the null space

 43:    Not Collective

 45:    Input Arguments:
 46: .  sp - null space object

 48:    Output Arguments:
 49: +  has_cnst - PETSC_TRUE if the null space contains the constant vector, otherwise PETSC_FALSE
 50: .  n - number of vectors (excluding constant vector) in null space
 51: -  vecs - orthonormal vectors that span the null space (excluding the constant vector)

 53:    Level: developer

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

 58: .seealso: MatNullSpaceCreate(), MatGetNullSpace(), MatGetNearNullSpace()
 59: @*/
 60: PetscErrorCode MatNullSpaceGetVecs(MatNullSpace sp,PetscBool *has_const,PetscInt *n,const Vec **vecs)
 61: {

 65:   if (has_const) *has_const = sp->has_cnst;
 66:   if (n) *n = sp->n;
 67:   if (vecs) *vecs = sp->vecs;
 68:   return(0);
 69: }

 73: /*@
 74:    MatNullSpaceCreateRigidBody - create rigid body modes from coordinates

 76:    Collective on Vec

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

 81:    Output Argument:
 82: .  sp - the null space

 84:    Level: advanced

 86: .seealso: MatNullSpaceCreate()
 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;

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

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

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) viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)sp));

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

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

216:    Collective on MPI_Comm

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: 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: .   Section 4.18 Solving Singular Systems

240: .keywords: PC, null space, create

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

251:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);

256:   *SP = NULL;
257:   MatInitializePackage();

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

261:   sp->has_cnst = has_cnst;
262:   sp->n        = n;
263:   sp->vecs     = 0;
264:   sp->alpha    = 0;
265:   sp->remove   = 0;
266:   sp->rmctx    = 0;

268:   if (n) {
269:     PetscMalloc1(n,&sp->vecs);
270:     PetscMalloc1(n,&sp->alpha);
271:     PetscLogObjectMemory((PetscObject)sp,n*(sizeof(Vec)+sizeof(PetscScalar)));
272:     for (i=0; i<n; i++) {
273:       PetscObjectReference((PetscObject)vecs[i]);
274:       sp->vecs[i] = vecs[i];
275:     }
276:   }

278:   *SP = sp;
279:   return(0);
280: }

284: /*@
285:    MatNullSpaceDestroy - Destroys a data structure used to project vectors
286:    out of null spaces.

288:    Collective on MatNullSpace

290:    Input Parameter:
291: .  sp - the null space context to be destroyed

293:    Level: advanced

295: .keywords: PC, null space, destroy

297: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
298: @*/
299: PetscErrorCode  MatNullSpaceDestroy(MatNullSpace *sp)
300: {

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

308:   VecDestroyVecs((*sp)->n,&(*sp)->vecs);
309:   PetscFree((*sp)->alpha);
310:   PetscHeaderDestroy(sp);
311:   return(0);
312: }

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

319:    Collective on MatNullSpace

321:    Input Parameters:
322: +  sp - the null space context
323: -  vec - the vector from which the null space is to be removed

325:    Level: advanced

327: .keywords: PC, null space, remove

329: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
330: @*/
331: PetscErrorCode  MatNullSpaceRemove(MatNullSpace sp,Vec vec)
332: {
333:   PetscScalar    sum;
334:   PetscInt       i,N;


341:   if (sp->has_cnst) {
342:     VecGetSize(vec,&N);
343:     if (N > 0) {
344:       VecSum(vec,&sum);
345:       sum  = sum/((PetscScalar)(-1.0*N));
346:       VecShift(vec,sum);
347:     }
348:   }

350:   if (sp->n) {
351:     VecMDot(vec,sp->n,sp->vecs,sp->alpha);
352:     for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
353:     VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
354:   }

356:   if (sp->remove) {
357:     (*sp->remove)(sp,vec,sp->rmctx);
358:   }
359:   return(0);
360: }

364: /*@
365:    MatNullSpaceTest  - Tests if the claimed null space is really a
366:      null space of a matrix

368:    Collective on MatNullSpace

370:    Input Parameters:
371: +  sp - the null space context
372: -  mat - the matrix

374:    Output Parameters:
375: .  isNull - PETSC_TRUE if the nullspace is valid for this matrix

377:    Level: advanced

379: .keywords: PC, null space, remove

381: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
382: @*/
383: PetscErrorCode  MatNullSpaceTest(MatNullSpace sp,Mat mat,PetscBool  *isNull)
384: {
385:   PetscScalar    sum;
386:   PetscReal      nrm;
387:   PetscInt       j,n,N;
389:   Vec            l,r;
390:   PetscBool      flg1 = PETSC_FALSE,flg2 = PETSC_FALSE,consistent = PETSC_TRUE;
391:   PetscViewer    viewer;

396:   n    = sp->n;
397:   PetscOptionsGetBool(NULL,"-mat_null_space_test_view",&flg1,NULL);
398:   PetscOptionsGetBool(NULL,"-mat_null_space_test_view_draw",&flg2,NULL);

400:   if (n) {
401:     VecDuplicate(sp->vecs[0],&l);
402:   } else {
403:     MatCreateVecs(mat,&l,NULL);
404:   }

406:   PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
407:   if (sp->has_cnst) {
408:     VecDuplicate(l,&r);
409:     VecGetSize(l,&N);
410:     sum  = 1.0/N;
411:     VecSet(l,sum);
412:     MatMult(mat,l,r);
413:     VecNorm(r,NORM_2,&nrm);
414:     if (nrm >= 1.e-7) consistent = PETSC_FALSE;
415:     if (flg1) {
416:       if (consistent) {
417:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are likely null vector");
418:       } else {
419:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are unlikely null vector ");
420:       }
421:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * 1/N || = %g\n",(double)nrm);
422:     }
423:     if (!consistent && flg1) {VecView(r,viewer);}
424:     if (!consistent && flg2) {VecView(r,viewer);}
425:     VecDestroy(&r);
426:   }

428:   for (j=0; j<n; j++) {
429:     (*mat->ops->mult)(mat,sp->vecs[j],l);
430:     VecNorm(l,NORM_2,&nrm);
431:     if (nrm >= 1.e-7) consistent = PETSC_FALSE;
432:     if (flg1) {
433:       if (consistent) {
434:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D is likely null vector",j);
435:       } else {
436:         PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D unlikely null vector ",j);
437:         consistent = PETSC_FALSE;
438:       }
439:       PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * v[%D] || = %g\n",j,(double)nrm);
440:     }
441:     if (!consistent && flg1) {VecView(l,viewer);}
442:     if (!consistent && flg2) {VecView(l,viewer);}
443:   }

445:   if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
446:   VecDestroy(&l);
447:   if (isNull) *isNull = consistent;
448:   return(0);
449: }