Actual source code: matnull.c

petsc-3.7.0 2016-04-25
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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(), MatSetNullSpace(), 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;
 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: }

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: }

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

220:    Collective on MPI_Comm

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

231:    Output Parameter:
232: .  SP - the null space context

234:    Level: advanced

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

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

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

244: .keywords: PC, null space, create

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

255:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
259: #if defined(PETSC_USE_DEBUG)
260:   if (n) {
261:     PetscScalar *dots;
262:     for (i=0; i<n; i++) {
263:       PetscReal norm;
264:       VecNorm(vecs[i],NORM_2,&norm);
265:       if (PetscAbsReal(norm - 1.0) > 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);
266:     }
267:     if (has_cnst) {
268:       for (i=0; i<n; i++) {
269:         PetscScalar sum;
270:         VecSum(vecs[i],&sum);
271:         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));
272:       }
273:     }
274:     PetscMalloc1(n-1,&dots);
275:     for (i=0; i<n-1; i++) {
276:       PetscInt j;
277:       VecMDot(vecs[i],n-i-1,vecs+i+1,dots);
278:       for (j=0;j<n-i-1;j++) {
279:         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]));
280:       }
281:     }
282:     PetscFree(dots);
283:   }
284: #endif

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

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

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

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

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

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

318:    Collective on MatNullSpace

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

323:    Level: advanced

325: .keywords: PC, null space, destroy

327: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
328: @*/
329: PetscErrorCode  MatNullSpaceDestroy(MatNullSpace *sp)
330: {

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

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

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
353: -  vec - the vector from which the null space is to be removed

355:    Level: advanced

357: .keywords: PC, null space, remove

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


371:   if (sp->has_cnst) {
372:     VecGetSize(vec,&N);
373:     if (N > 0) {
374:       VecSum(vec,&sum);
375:       sum  = sum/((PetscScalar)(-1.0*N));
376:       VecShift(vec,sum);
377:     }
378:   }

380:   if (sp->n) {
381:     VecMDot(vec,sp->n,sp->vecs,sp->alpha);
382:     for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
383:     VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
384:   }

386:   if (sp->remove) {
387:     (*sp->remove)(sp,vec,sp->rmctx);
388:   }
389:   return(0);
390: }

394: /*@
395:    MatNullSpaceTest  - Tests if the claimed null space is really a
396:      null space of a matrix

398:    Collective on MatNullSpace

400:    Input Parameters:
401: +  sp - the null space context
402: -  mat - the matrix

404:    Output Parameters:
405: .  isNull - PETSC_TRUE if the nullspace is valid for this matrix

407:    Level: advanced

409: .keywords: PC, null space, remove

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

426:   n    = sp->n;
427:   PetscOptionsGetBool(((PetscObject)sp)->options,NULL,"-mat_null_space_test_view",&flg1,NULL);
428:   PetscOptionsGetBool(((PetscObject)sp)->options,NULL,"-mat_null_space_test_view_draw",&flg2,NULL);

430:   if (n) {
431:     VecDuplicate(sp->vecs[0],&l);
432:   } else {
433:     MatCreateVecs(mat,&l,NULL);
434:   }

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

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

475:   if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
476:   VecDestroy(&l);
477:   if (isNull) *isNull = consistent;
478:   return(0);
479: }