Actual source code: matnull.c
petsc-3.9.4 2018-09-11
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: If you are solving an elasticity problems you should likely use this, in conjunction with ee MatSetNearNullspace(), to provide information that
81: the PCGAMG preconditioner can use to construct a much more efficient preconditioner.
83: If you are solving an elasticity problem with pure Neumann boundary conditions you can use this in conjunction with MatSetNullspace() to
84: provide this information to the linear solver so it can handle the null space appropriately in the linear solution.
87: .seealso: MatNullSpaceCreate(), MatSetNearNullspace(), MatSetNullspace()
88: @*/
89: PetscErrorCode MatNullSpaceCreateRigidBody(Vec coords,MatNullSpace *sp)
90: {
91: PetscErrorCode ierr;
92: const PetscScalar *x;
93: PetscScalar *v[6],dots[5];
94: Vec vec[6];
95: PetscInt n,N,dim,nmodes,i,j;
96: PetscReal sN;
99: VecGetBlockSize(coords,&dim);
100: VecGetLocalSize(coords,&n);
101: VecGetSize(coords,&N);
102: n /= dim;
103: N /= dim;
104: sN = 1./PetscSqrtReal((PetscReal)N);
105: switch (dim) {
106: case 1:
107: MatNullSpaceCreate(PetscObjectComm((PetscObject)coords),PETSC_TRUE,0,NULL,sp);
108: break;
109: case 2:
110: case 3:
111: nmodes = (dim == 2) ? 3 : 6;
112: VecCreate(PetscObjectComm((PetscObject)coords),&vec[0]);
113: VecSetSizes(vec[0],dim*n,dim*N);
114: VecSetBlockSize(vec[0],dim);
115: VecSetUp(vec[0]);
116: for (i=1; i<nmodes; i++) {VecDuplicate(vec[0],&vec[i]);}
117: for (i=0; i<nmodes; i++) {VecGetArray(vec[i],&v[i]);}
118: VecGetArrayRead(coords,&x);
119: for (i=0; i<n; i++) {
120: if (dim == 2) {
121: v[0][i*2+0] = sN;
122: v[0][i*2+1] = 0.;
123: v[1][i*2+0] = 0.;
124: v[1][i*2+1] = sN;
125: /* Rotations */
126: v[2][i*2+0] = -x[i*2+1];
127: v[2][i*2+1] = x[i*2+0];
128: } else {
129: v[0][i*3+0] = sN;
130: v[0][i*3+1] = 0.;
131: v[0][i*3+2] = 0.;
132: v[1][i*3+0] = 0.;
133: v[1][i*3+1] = sN;
134: v[1][i*3+2] = 0.;
135: v[2][i*3+0] = 0.;
136: v[2][i*3+1] = 0.;
137: v[2][i*3+2] = sN;
139: v[3][i*3+0] = x[i*3+1];
140: v[3][i*3+1] = -x[i*3+0];
141: v[3][i*3+2] = 0.;
142: v[4][i*3+0] = 0.;
143: v[4][i*3+1] = -x[i*3+2];
144: v[4][i*3+2] = x[i*3+1];
145: v[5][i*3+0] = x[i*3+2];
146: v[5][i*3+1] = 0.;
147: v[5][i*3+2] = -x[i*3+0];
148: }
149: }
150: for (i=0; i<nmodes; i++) {VecRestoreArray(vec[i],&v[i]);}
151: VecRestoreArrayRead(coords,&x);
152: for (i=dim; i<nmodes; i++) {
153: /* Orthonormalize vec[i] against vec[0:i-1] */
154: VecMDot(vec[i],i,vec,dots);
155: for (j=0; j<i; j++) dots[j] *= -1.;
156: VecMAXPY(vec[i],i,dots,vec);
157: VecNormalize(vec[i],NULL);
158: }
159: MatNullSpaceCreate(PetscObjectComm((PetscObject)coords),PETSC_FALSE,nmodes,vec,sp);
160: for (i=0; i<nmodes; i++) {VecDestroy(&vec[i]);}
161: }
162: return(0);
163: }
165: /*@C
166: MatNullSpaceView - Visualizes a null space object.
168: Collective on MatNullSpace
170: Input Parameters:
171: + matnull - the null space
172: - viewer - visualization context
174: Level: advanced
176: Fortran Note:
177: This routine is not supported in Fortran.
179: .seealso: MatNullSpaceCreate(), PetscViewerASCIIOpen()
180: @*/
181: PetscErrorCode MatNullSpaceView(MatNullSpace sp,PetscViewer viewer)
182: {
184: PetscBool iascii;
188: if (!viewer) {
189: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
190: }
194: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
195: if (iascii) {
196: PetscViewerFormat format;
197: PetscInt i;
198: PetscViewerGetFormat(viewer,&format);
199: PetscObjectPrintClassNamePrefixType((PetscObject)sp,viewer);
200: PetscViewerASCIIPushTab(viewer);
201: PetscViewerASCIIPrintf(viewer,"Contains %D vector%s%s\n",sp->n,sp->n==1 ? "" : "s",sp->has_cnst ? " and the constant" : "");
202: if (sp->remove) {PetscViewerASCIIPrintf(viewer,"Has user-provided removal function\n");}
203: if (!(format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) {
204: for (i=0; i<sp->n; i++) {
205: VecView(sp->vecs[i],viewer);
206: }
207: }
208: PetscViewerASCIIPopTab(viewer);
209: }
210: return(0);
211: }
213: /*@C
214: MatNullSpaceCreate - Creates a data structure used to project vectors
215: out of null spaces.
217: Collective on MPI_Comm
219: Input Parameters:
220: + comm - the MPI communicator associated with the object
221: . has_cnst - PETSC_TRUE if the null space contains the constant vector; otherwise PETSC_FALSE
222: . n - number of vectors (excluding constant vector) in null space
223: - vecs - the vectors that span the null space (excluding the constant vector);
224: these vectors must be orthonormal. These vectors are NOT copied, so do not change them
225: after this call. You should free the array that you pass in and destroy the vectors (this will reduce the reference count
226: for them by one).
228: Output Parameter:
229: . SP - the null space context
231: Level: advanced
233: Notes: 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: .keywords: PC, null space, create
243: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), MatSetNullSpace(), MatNullSpace, MatNullSpaceSetFunction()
244: @*/
245: PetscErrorCode MatNullSpaceCreate(MPI_Comm comm,PetscBool has_cnst,PetscInt n,const Vec vecs[],MatNullSpace *SP)
246: {
247: MatNullSpace sp;
249: PetscInt i;
252: if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
256: if (n) {
257: for (i=0; i<n; i++) {
258: /* prevent the user from changes values in the vector */
259: VecLockPush(vecs[i]);
260: }
261: }
262: #if defined(PETSC_USE_DEBUG)
263: if (n) {
264: PetscScalar *dots;
265: for (i=0; i<n; i++) {
266: PetscReal norm;
267: VecNorm(vecs[i],NORM_2,&norm);
268: 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);
269: }
270: if (has_cnst) {
271: for (i=0; i<n; i++) {
272: PetscScalar sum;
273: VecSum(vecs[i],&sum);
274: 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));
275: }
276: }
277: PetscMalloc1(n-1,&dots);
278: for (i=0; i<n-1; i++) {
279: PetscInt j;
280: VecMDot(vecs[i],n-i-1,vecs+i+1,dots);
281: for (j=0;j<n-i-1;j++) {
282: 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]));
283: }
284: }
285: PetscFree(dots);
286: }
287: #endif
289: *SP = NULL;
290: MatInitializePackage();
292: PetscHeaderCreate(sp,MAT_NULLSPACE_CLASSID,"MatNullSpace","Null space","Mat",comm,MatNullSpaceDestroy,MatNullSpaceView);
294: sp->has_cnst = has_cnst;
295: sp->n = n;
296: sp->vecs = 0;
297: sp->alpha = 0;
298: sp->remove = 0;
299: sp->rmctx = 0;
301: if (n) {
302: PetscMalloc1(n,&sp->vecs);
303: PetscMalloc1(n,&sp->alpha);
304: PetscLogObjectMemory((PetscObject)sp,n*(sizeof(Vec)+sizeof(PetscScalar)));
305: for (i=0; i<n; i++) {
306: PetscObjectReference((PetscObject)vecs[i]);
307: sp->vecs[i] = vecs[i];
308: }
309: }
311: *SP = sp;
312: return(0);
313: }
315: /*@
316: MatNullSpaceDestroy - Destroys a data structure used to project vectors
317: out of null spaces.
319: Collective on MatNullSpace
321: Input Parameter:
322: . sp - the null space context to be destroyed
324: Level: advanced
326: .keywords: PC, null space, destroy
328: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
329: @*/
330: PetscErrorCode MatNullSpaceDestroy(MatNullSpace *sp)
331: {
333: PetscInt i;
336: if (!*sp) return(0);
338: if (--((PetscObject)(*sp))->refct > 0) {*sp = 0; return(0);}
340: for (i=0; i < (*sp)->n; i++) {
341: VecLockPop((*sp)->vecs[i]);
342: }
344: VecDestroyVecs((*sp)->n,&(*sp)->vecs);
345: PetscFree((*sp)->alpha);
346: PetscHeaderDestroy(sp);
347: return(0);
348: }
350: /*@C
351: MatNullSpaceRemove - Removes all the components of a null space from a vector.
353: Collective on MatNullSpace
355: Input Parameters:
356: + sp - the null space context (if this is NULL then no null space is removed)
357: - vec - the vector from which the null space is to be removed
359: Level: advanced
361: .keywords: PC, null space, remove
363: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
364: @*/
365: PetscErrorCode MatNullSpaceRemove(MatNullSpace sp,Vec vec)
366: {
367: PetscScalar sum;
368: PetscInt i,N;
372: if (!sp) return(0);
376: if (sp->has_cnst) {
377: VecGetSize(vec,&N);
378: if (N > 0) {
379: VecSum(vec,&sum);
380: sum = sum/((PetscScalar)(-1.0*N));
381: VecShift(vec,sum);
382: }
383: }
385: if (sp->n) {
386: VecMDot(vec,sp->n,sp->vecs,sp->alpha);
387: for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
388: VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
389: }
391: if (sp->remove) {
392: (*sp->remove)(sp,vec,sp->rmctx);
393: }
394: return(0);
395: }
397: /*@
398: MatNullSpaceTest - Tests if the claimed null space is really a
399: null space of a matrix
401: Collective on MatNullSpace
403: Input Parameters:
404: + sp - the null space context
405: - mat - the matrix
407: Output Parameters:
408: . isNull - PETSC_TRUE if the nullspace is valid for this matrix
410: Level: advanced
412: .keywords: PC, null space, remove
414: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
415: @*/
416: PetscErrorCode MatNullSpaceTest(MatNullSpace sp,Mat mat,PetscBool *isNull)
417: {
418: PetscScalar sum;
419: PetscReal nrm,tol = 10. * PETSC_SQRT_MACHINE_EPSILON;
420: PetscInt j,n,N;
422: Vec l,r;
423: PetscBool flg1 = PETSC_FALSE,flg2 = PETSC_FALSE,consistent = PETSC_TRUE;
424: PetscViewer viewer;
429: n = sp->n;
430: PetscOptionsGetBool(((PetscObject)sp)->options,NULL,"-mat_null_space_test_view",&flg1,NULL);
431: PetscOptionsGetBool(((PetscObject)sp)->options,NULL,"-mat_null_space_test_view_draw",&flg2,NULL);
433: if (n) {
434: VecDuplicate(sp->vecs[0],&l);
435: } else {
436: MatCreateVecs(mat,&l,NULL);
437: }
439: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
440: if (sp->has_cnst) {
441: VecDuplicate(l,&r);
442: VecGetSize(l,&N);
443: sum = 1.0/N;
444: VecSet(l,sum);
445: MatMult(mat,l,r);
446: VecNorm(r,NORM_2,&nrm);
447: if (nrm >= tol) consistent = PETSC_FALSE;
448: if (flg1) {
449: if (consistent) {
450: PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are likely null vector");
451: } else {
452: PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are unlikely null vector ");
453: }
454: PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * 1/N || = %g\n",(double)nrm);
455: }
456: if (!consistent && flg1) {VecView(r,viewer);}
457: if (!consistent && flg2) {VecView(r,viewer);}
458: VecDestroy(&r);
459: }
461: for (j=0; j<n; j++) {
462: (*mat->ops->mult)(mat,sp->vecs[j],l);
463: VecNorm(l,NORM_2,&nrm);
464: if (nrm >= tol) consistent = PETSC_FALSE;
465: if (flg1) {
466: if (consistent) {
467: PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D is likely null vector",j);
468: } else {
469: PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D unlikely null vector ",j);
470: consistent = PETSC_FALSE;
471: }
472: PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * v[%D] || = %g\n",j,(double)nrm);
473: }
474: if (!consistent && flg1) {VecView(l,viewer);}
475: if (!consistent && flg2) {VecView(l,viewer);}
476: }
478: if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
479: VecDestroy(&l);
480: if (isNull) *isNull = consistent;
481: return(0);
482: }