mat/interface/matnull.c

#define PETSCMAT_DLL

/*
    Routines to project vectors out of null spaces.
*/

#include "include/private/matimpl.h"      /*I "petscmat.h" I*/
#include "petscsys.h"

PetscCookie PETSCMAT_DLLEXPORT MAT_NULLSPACE_COOKIE;

#undef __FUNCT__
#define __FUNCT__ "MatNullSpaceSetFunction"
/*@C
   MatNullSpaceSetFunction - set a function that removes a null space from a vector
   out of null spaces.

   Collective on MatNullSpace

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

   Level: advanced

.keywords: PC, null space, create

.seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), KSPSetNullSpace(), MatNullSpace, MatNullSpaceCreate()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatNullSpaceSetFunction(MatNullSpace sp, PetscErrorCode (*rem)(Vec,void*),void *ctx)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp,MAT_NULLSPACE_COOKIE,1);
  sp->remove = rem;
  sp->rmctx  = ctx;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatNullSpaceCreate"
/*@
   MatNullSpaceCreate - Creates a data structure used to project vectors
   out of null spaces.

   Collective on MPI_Comm

   Input Parameters:
+  comm - the MPI communicator associated with the object
.  has_cnst - PETSC_TRUE if the null space contains the constant vector; otherwise PETSC_FALSE
.  n - number of vectors (excluding constant vector) in null space
-  vecs - the vectors that span the null space (excluding the constant vector);
          these vectors must be orthonormal. These vectors are NOT copied, so do not change them
          after this call. You should free the array that you pass in.

   Output Parameter:
.  SP - the null space context

   Level: advanced

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

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

  Users manual sections:
.   sec_singular

.keywords: PC, null space, create

.seealso: MatNullSpaceDestroy(), MatNullSpaceRemove(), KSPSetNullSpace(), MatNullSpace, MatNullSpaceSetFunction()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatNullSpaceCreate(MPI_Comm comm,PetscTruth has_cnst,PetscInt n,const Vec vecs[],MatNullSpace *SP)
{
  MatNullSpace   sp;
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  if (n < 0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Number of vectors (given %D) cannot be negative",n);
  if (n) PetscValidPointer(vecs,4);
  for (i=0; i<n; i++) PetscValidHeaderSpecific(vecs[i],VEC_COOKIE,4);
  PetscValidPointer(SP,5);

  *SP = PETSC_NULL;
#ifndef PETSC_USE_DYNAMIC_LIBRARIES
  ierr = MatInitializePackage(PETSC_NULL);CHKERRQ(ierr);
#endif

  ierr = PetscHeaderCreate(sp,_p_MatNullSpace,int,MAT_NULLSPACE_COOKIE,0,"MatNullSpace",comm,MatNullSpaceDestroy,0);CHKERRQ(ierr);

  sp->has_cnst = has_cnst;
  sp->n        = n;
  sp->vecs     = 0;
  sp->alpha    = 0;
  sp->vec      = 0;
  sp->remove   = 0;
  sp->rmctx    = 0;

  if (n) {
    ierr = PetscMalloc(n*sizeof(Vec),&sp->vecs);CHKERRQ(ierr);
    ierr = PetscMalloc(n*sizeof(PetscScalar),&sp->alpha);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory(sp,n*(sizeof(Vec)+sizeof(PetscScalar)));CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      ierr = PetscObjectReference((PetscObject)vecs[i]);CHKERRQ(ierr);
      sp->vecs[i] = vecs[i];
    }
  }

  *SP          = sp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatNullSpaceDestroy"
/*@
   MatNullSpaceDestroy - Destroys a data structure used to project vectors
   out of null spaces.

   Collective on MatNullSpace

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

   Level: advanced

.keywords: PC, null space, destroy

.seealso: MatNullSpaceCreate(), MatNullSpaceRemove(), MatNullSpaceSetFunction()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatNullSpaceDestroy(MatNullSpace sp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp,MAT_NULLSPACE_COOKIE,1);
  if (--((PetscObject)sp)->refct > 0) PetscFunctionReturn(0);

  if (sp->vec)  { ierr = VecDestroy(sp->vec);CHKERRQ(ierr); }
  if (sp->vecs) { ierr = VecDestroyVecs(sp->vecs,sp->n);CHKERRQ(ierr); }
  ierr = PetscFree(sp->alpha);CHKERRQ(ierr);
  ierr = PetscHeaderDestroy(sp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatNullSpaceRemove"
/*@C
   MatNullSpaceRemove - Removes all the components of a null space from a vector.

   Collective on MatNullSpace

   Input Parameters:
+  sp - the null space context
.  vec - the vector from which the null space is to be removed
-  out - if this is requested (not PETSC_NULL) then this is a vector with the null space removed otherwise
         the removal is done in-place (in vec)

   Note: The user is not responsible for the vector returned and should not destroy it.

   Level: advanced

.keywords: PC, null space, remove

.seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatNullSpaceRemove(MatNullSpace sp,Vec vec,Vec *out)
{
  PetscScalar    sum;
  PetscInt       i,N;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp,MAT_NULLSPACE_COOKIE,1);
  PetscValidHeaderSpecific(vec,VEC_COOKIE,2);

  if (out) {
    PetscValidPointer(out,3);
    if (!sp->vec) {
      ierr = VecDuplicate(vec,&sp->vec);CHKERRQ(ierr);
      ierr = PetscLogObjectParent(sp,sp->vec);CHKERRQ(ierr);
    }
    ierr = VecCopy(vec,sp->vec);CHKERRQ(ierr);
    vec = *out = sp->vec;
  }

  if (sp->has_cnst) {
    ierr = VecGetSize(vec,&N);CHKERRQ(ierr);
    if (N > 0) {
      ierr = VecSum(vec,&sum);CHKERRQ(ierr);
      sum  = sum/(-1.0*N);
      ierr = VecShift(vec,sum);CHKERRQ(ierr);
    }
  }

  if (sp->n) {
    ierr = VecMDot(vec,sp->n,sp->vecs,sp->alpha);CHKERRQ(ierr);
    for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
    ierr = VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);CHKERRQ(ierr);
  }

  if (sp->remove){
    ierr = (*sp->remove)(vec,sp->rmctx);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatNullSpaceTest"
/*@
   MatNullSpaceTest  - Tests if the claimed null space is really a
     null space of a matrix

   Collective on MatNullSpace

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

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

   Level: advanced

.keywords: PC, null space, remove

.seealso: MatNullSpaceCreate(), MatNullSpaceDestroy(), MatNullSpaceSetFunction()
@*/
PetscErrorCode PETSCMAT_DLLEXPORT MatNullSpaceTest(MatNullSpace sp,Mat mat,PetscTruth *isNull)
{
  PetscScalar    sum;
  PetscReal      nrm;
  PetscInt       j,n,N,m;
  PetscErrorCode ierr;
  Vec            l,r;
  PetscTruth     flg1,flg2,consistent = PETSC_TRUE;
  PetscViewer    viewer;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp,MAT_NULLSPACE_COOKIE,1);
  PetscValidHeaderSpecific(mat,MAT_COOKIE,2);
  n = sp->n;
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_null_space_test_view",&flg1);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(PETSC_NULL,"-mat_null_space_test_view_draw",&flg2);CHKERRQ(ierr);

  if (!sp->vec) {
    if (n) {
      ierr = VecDuplicate(sp->vecs[0],&sp->vec);CHKERRQ(ierr);
    } else {
      ierr = MatGetLocalSize(mat,&m,PETSC_NULL);CHKERRQ(ierr);
      ierr = VecCreateMPI(((PetscObject)sp)->comm,m,PETSC_DETERMINE,&sp->vec);CHKERRQ(ierr);
    }
  }
  l    = sp->vec;

  ierr = PetscViewerASCIIGetStdout(((PetscObject)sp)->comm,&viewer);CHKERRQ(ierr);
  if (sp->has_cnst) {
    ierr = VecDuplicate(l,&r);CHKERRQ(ierr);
    ierr = VecGetSize(l,&N);CHKERRQ(ierr);
    sum  = 1.0/N;
    ierr = VecSet(l,sum);CHKERRQ(ierr);
    ierr = MatMult(mat,l,r);CHKERRQ(ierr);
    ierr = VecNorm(r,NORM_2,&nrm);CHKERRQ(ierr);
    if (nrm < 1.e-7) {
      ierr = PetscPrintf(((PetscObject)sp)->comm,"Constants are likely null vector");CHKERRQ(ierr);
    } else {
      ierr = PetscPrintf(((PetscObject)sp)->comm,"Constants are unlikely null vector ");CHKERRQ(ierr);
      consistent = PETSC_FALSE;
    }
    ierr = PetscPrintf(((PetscObject)sp)->comm,"|| A * 1 || = %G\n",nrm);CHKERRQ(ierr);
    if (nrm > 1.e-7 && flg1) {ierr = VecView(r,viewer);CHKERRQ(ierr);}
    if (nrm > 1.e-7 && flg2) {ierr = VecView(r,viewer);CHKERRQ(ierr);}
    ierr = VecDestroy(r);CHKERRQ(ierr);
  }

  for (j=0; j<n; j++) {
    ierr = (*mat->ops->mult)(mat,sp->vecs[j],l);CHKERRQ(ierr);
    ierr = VecNorm(l,NORM_2,&nrm);CHKERRQ(ierr);
    if (nrm < 1.e-7) {
      ierr = PetscPrintf(((PetscObject)sp)->comm,"Null vector %D is likely null vector",j);CHKERRQ(ierr);
    } else {
      ierr = PetscPrintf(((PetscObject)sp)->comm,"Null vector %D unlikely null vector ",j);CHKERRQ(ierr);
      consistent = PETSC_FALSE;
    }
    ierr = PetscPrintf(((PetscObject)sp)->comm,"|| A * v[%D] || = %G\n",j,nrm);CHKERRQ(ierr);
    if (nrm > 1.e-7 && flg1) {ierr = VecView(l,viewer);CHKERRQ(ierr);}
    if (nrm > 1.e-7 && flg2) {ierr = VecView(l,viewer);CHKERRQ(ierr);}
  }

  if (sp->remove){
    SETERRQ(PETSC_ERR_SUP,"Cannot test a null space provided as a function with MatNullSpaceSetFunction()");
  }
  *isNull = consistent;
  PetscFunctionReturn(0);
}