Actual source code: matnull.c
petsc-3.13.6 2020-09-29
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: }