Actual source code: matnull.c
petsc-3.6.4 2016-04-12
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) viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)sp));
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: }
214: /*@
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: See MatNullSpaceSetFunction() as an alternative way of providing the null space information instead of setting vecs.
236: 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
237: need to pass in a function that eliminates the constant function into MatNullSpaceSetFunction().
239: Users manual sections:
240: . Section 4.19 Solving Singular Systems
242: .keywords: PC, null space, create
244: .seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), MatSetNullSpace(), MatNullSpace, MatNullSpaceSetFunction()
245: @*/
246: PetscErrorCode MatNullSpaceCreate(MPI_Comm comm,PetscBool has_cnst,PetscInt n,const Vec vecs[],MatNullSpace *SP)
247: {
248: MatNullSpace sp;
250: PetscInt i;
253: if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
258: *SP = NULL;
259: MatInitializePackage();
261: PetscHeaderCreate(sp,MAT_NULLSPACE_CLASSID,"MatNullSpace","Null space","Mat",comm,MatNullSpaceDestroy,MatNullSpaceView);
263: sp->has_cnst = has_cnst;
264: sp->n = n;
265: sp->vecs = 0;
266: sp->alpha = 0;
267: sp->remove = 0;
268: sp->rmctx = 0;
270: if (n) {
271: PetscMalloc1(n,&sp->vecs);
272: PetscMalloc1(n,&sp->alpha);
273: PetscLogObjectMemory((PetscObject)sp,n*(sizeof(Vec)+sizeof(PetscScalar)));
274: for (i=0; i<n; i++) {
275: PetscObjectReference((PetscObject)vecs[i]);
276: sp->vecs[i] = vecs[i];
277: }
278: }
280: *SP = sp;
281: return(0);
282: }
286: /*@
287: MatNullSpaceDestroy - Destroys a data structure used to project vectors
288: out of null spaces.
290: Collective on MatNullSpace
292: Input Parameter:
293: . sp - the null space context to be destroyed
295: Level: advanced
297: .keywords: PC, null space, destroy
299: .seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
300: @*/
301: PetscErrorCode MatNullSpaceDestroy(MatNullSpace *sp)
302: {
306: if (!*sp) return(0);
308: if (--((PetscObject)(*sp))->refct > 0) {*sp = 0; return(0);}
310: VecDestroyVecs((*sp)->n,&(*sp)->vecs);
311: PetscFree((*sp)->alpha);
312: PetscHeaderDestroy(sp);
313: return(0);
314: }
318: /*@C
319: MatNullSpaceRemove - Removes all the components of a null space from a vector.
321: Collective on MatNullSpace
323: Input Parameters:
324: + sp - the null space context
325: - vec - the vector from which the null space is to be removed
327: Level: advanced
329: .keywords: PC, null space, remove
331: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
332: @*/
333: PetscErrorCode MatNullSpaceRemove(MatNullSpace sp,Vec vec)
334: {
335: PetscScalar sum;
336: PetscInt i,N;
343: if (sp->has_cnst) {
344: VecGetSize(vec,&N);
345: if (N > 0) {
346: VecSum(vec,&sum);
347: sum = sum/((PetscScalar)(-1.0*N));
348: VecShift(vec,sum);
349: }
350: }
352: if (sp->n) {
353: VecMDot(vec,sp->n,sp->vecs,sp->alpha);
354: for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
355: VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);
356: }
358: if (sp->remove) {
359: (*sp->remove)(sp,vec,sp->rmctx);
360: }
361: return(0);
362: }
366: /*@
367: MatNullSpaceTest - Tests if the claimed null space is really a
368: null space of a matrix
370: Collective on MatNullSpace
372: Input Parameters:
373: + sp - the null space context
374: - mat - the matrix
376: Output Parameters:
377: . isNull - PETSC_TRUE if the nullspace is valid for this matrix
379: Level: advanced
381: .keywords: PC, null space, remove
383: .seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
384: @*/
385: PetscErrorCode MatNullSpaceTest(MatNullSpace sp,Mat mat,PetscBool *isNull)
386: {
387: PetscScalar sum;
388: PetscReal nrm;
389: PetscInt j,n,N;
391: Vec l,r;
392: PetscBool flg1 = PETSC_FALSE,flg2 = PETSC_FALSE,consistent = PETSC_TRUE;
393: PetscViewer viewer;
398: n = sp->n;
399: PetscOptionsGetBool(NULL,"-mat_null_space_test_view",&flg1,NULL);
400: PetscOptionsGetBool(NULL,"-mat_null_space_test_view_draw",&flg2,NULL);
402: if (n) {
403: VecDuplicate(sp->vecs[0],&l);
404: } else {
405: MatCreateVecs(mat,&l,NULL);
406: }
408: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)sp),&viewer);
409: if (sp->has_cnst) {
410: VecDuplicate(l,&r);
411: VecGetSize(l,&N);
412: sum = 1.0/N;
413: VecSet(l,sum);
414: MatMult(mat,l,r);
415: VecNorm(r,NORM_2,&nrm);
416: if (nrm >= 1.e-7) consistent = PETSC_FALSE;
417: if (flg1) {
418: if (consistent) {
419: PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are likely null vector");
420: } else {
421: PetscPrintf(PetscObjectComm((PetscObject)sp),"Constants are unlikely null vector ");
422: }
423: PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * 1/N || = %g\n",(double)nrm);
424: }
425: if (!consistent && flg1) {VecView(r,viewer);}
426: if (!consistent && flg2) {VecView(r,viewer);}
427: VecDestroy(&r);
428: }
430: for (j=0; j<n; j++) {
431: (*mat->ops->mult)(mat,sp->vecs[j],l);
432: VecNorm(l,NORM_2,&nrm);
433: if (nrm >= 1.e-7) consistent = PETSC_FALSE;
434: if (flg1) {
435: if (consistent) {
436: PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D is likely null vector",j);
437: } else {
438: PetscPrintf(PetscObjectComm((PetscObject)sp),"Null vector %D unlikely null vector ",j);
439: consistent = PETSC_FALSE;
440: }
441: PetscPrintf(PetscObjectComm((PetscObject)sp),"|| A * v[%D] || = %g\n",j,(double)nrm);
442: }
443: if (!consistent && flg1) {VecView(l,viewer);}
444: if (!consistent && flg2) {VecView(l,viewer);}
445: }
447: if (sp->remove) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
448: VecDestroy(&l);
449: if (isNull) *isNull = consistent;
450: return(0);
451: }