Exemplo n.º 1
0
static PetscErrorCode PCApplySymmetricRight_ILU(PC pc,Vec x,Vec y)
{
  PetscErrorCode ierr;
  PC_ILU         *icc = (PC_ILU*)pc->data;

  PetscFunctionBegin;
  ierr = MatBackwardSolve(((PC_Factor*)icc)->fact,x,y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Exemplo n.º 2
0
int main(int argc,char **args)
{
  PetscMPIInt    size;
  PetscErrorCode ierr;
  Vec            x,y,b,s1,s2;
  Mat            A;                    /* linear system matrix */
  Mat            sA,sB,sC;             /* symmetric part of the matrices */
  PetscInt       n,mbs=16,bs=1,nz=3,prob=1,i,j,k1,k2,col[3],lf,block, row,Ii,J,n1,inc;
  PetscReal      norm1,norm2,rnorm,tol=PETSC_SMALL;
  PetscScalar    neg_one = -1.0,four=4.0,value[3];
  IS             perm, iscol;
  PetscRandom    rdm;
  PetscBool      doIcc=PETSC_TRUE,equal;
  MatInfo        minfo1,minfo2;
  MatFactorInfo  factinfo;
  MatType        type;

  PetscInitialize(&argc,&args,(char*)0,help);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
  ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);

  n    = mbs*bs;
  ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatSeqBAIJSetPreallocation(A,bs,nz,NULL);CHKERRQ(ierr);

  ierr = MatCreate(PETSC_COMM_SELF,&sA);CHKERRQ(ierr);
  ierr = MatSetSizes(sA,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetType(sA,MATSEQSBAIJ);CHKERRQ(ierr);
  ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
  ierr = MatGetType(sA,&type);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)sA,MATSEQSBAIJ,&doIcc);CHKERRQ(ierr);
  ierr = MatSeqSBAIJSetPreallocation(sA,bs,nz,NULL);CHKERRQ(ierr);
  ierr = MatSetOption(sA,MAT_IGNORE_LOWER_TRIANGULAR,PETSC_TRUE);CHKERRQ(ierr);

  /* Test MatGetOwnershipRange() */
  ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
  if (i-Ii || j-J) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
  }

  /* Assemble matrix */
  if (bs == 1) {
    ierr = PetscOptionsGetInt(NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
    if (prob == 1) { /* tridiagonal matrix */
      value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
      for (i=1; i<n-1; i++) {
        col[0] = i-1; col[1] = i; col[2] = i+1;
        ierr   = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
        ierr   = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      }
      i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;

      value[0]= 0.1; value[1]=-1; value[2]=2;

      ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);

      i        = 0;
      col[0]   = n-1;   col[1] = 1;      col[2] = 0;
      value[0] = 0.1; value[1] = -1.0; value[2] = 2;

      ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);

    } else if (prob ==2) { /* matrix for the five point stencil */
      n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
      if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
      for (i=0; i<n1; i++) {
        for (j=0; j<n1; j++) {
          Ii = j + n1*i;
          if (i>0) {
            J    = Ii - n1;
            ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
            ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
          }
          if (i<n1-1) {
            J    = Ii + n1;
            ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
            ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
          }
          if (j>0) {
            J    = Ii - 1;
            ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
            ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
          }
          if (j<n1-1) {
            J    = Ii + 1;
            ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
            ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
          }
          ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
          ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
        }
      }
    }

  } else { /* bs > 1 */
    for (block=0; block<n/bs; block++) {
      /* diagonal blocks */
      value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
      for (i=1+block*bs; i<bs-1+block*bs; i++) {
        col[0] = i-1; col[1] = i; col[2] = i+1;
        ierr   = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
        ierr   = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      }
      i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;

      value[0]=-1.0; value[1]=4.0;

      ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);

      i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;

      value[0]=4.0; value[1] = -1.0;

      ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
    /* off-diagonal blocks */
    value[0]=-1.0;
    for (i=0; i<(n/bs-1)*bs; i++) {
      col[0]=i+bs;

      ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);

      col[0]=i; row=i+bs;

      ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* Test MatGetInfo() of A and sA */
  ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
  ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
  /*
  printf("A matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
  printf("sA matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
  */
  i  = (int) (minfo1.nz_used - minfo2.nz_used);
  j  = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
  k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
  k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
  if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error (compare A and sA): MatGetInfo()\n");CHKERRQ(ierr);
  }

  /* Test MatDuplicate() */
  ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
  ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);CHKERRQ(ierr);
  ierr = MatEqual(sA,sB,&equal);CHKERRQ(ierr);
  if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDuplicate()");

  /* Test MatNorm() */
  ierr  = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
  ierr  = MatNorm(sB,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
  rnorm = PetscAbsReal(norm1-norm2)/norm2;
  if (rnorm > tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
  }
  ierr  = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
  ierr  = MatNorm(sB,NORM_INFINITY,&norm2);CHKERRQ(ierr);
  rnorm = PetscAbsReal(norm1-norm2)/norm2;
  if (rnorm > tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
  }
  ierr  = MatNorm(A,NORM_1,&norm1);CHKERRQ(ierr);
  ierr  = MatNorm(sB,NORM_1,&norm2);CHKERRQ(ierr);
  rnorm = PetscAbsReal(norm1-norm2)/norm2;
  if (rnorm > tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
  }

  /* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
  ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
  ierr = MatGetInfo(sB,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
  /*
  printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
  printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
  */
  i  = (int) (minfo1.nz_used - minfo2.nz_used);
  j  = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
  k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
  k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
  if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error(compare A and sB): MatGetInfo()\n");CHKERRQ(ierr);
  }

  ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
  ierr = MatGetSize(sB,&i,&j);CHKERRQ(ierr);
  if (i-Ii || j-J) {
    PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
  }

  ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
  ierr = MatGetBlockSize(sB, &i);CHKERRQ(ierr);
  if (i-Ii) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
  }

  ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
  ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
  ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
  ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);

  /* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
#if !defined(PETSC_USE_COMPLEX)
  /* Scaling matrix with complex numbers results non-spd matrix,
     causing crash of MatForwardSolve() and MatBackwardSolve() */
  ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
  ierr = MatDiagonalScale(sB,x,x);CHKERRQ(ierr);
  ierr = MatMultEqual(A,sB,10,&equal);CHKERRQ(ierr);
  if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");

  ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
  ierr = MatGetDiagonal(sB,s2);CHKERRQ(ierr);
  ierr = VecAXPY(s2,neg_one,s1);CHKERRQ(ierr);
  ierr = VecNorm(s2,NORM_1,&norm1);CHKERRQ(ierr);
  if (norm1>tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal(), ||s1-s2||=%G\n",norm1);CHKERRQ(ierr);
  }

  {
    PetscScalar alpha=0.1;
    ierr = MatScale(A,alpha);CHKERRQ(ierr);
    ierr = MatScale(sB,alpha);CHKERRQ(ierr);
  }
#endif

  /* Test MatGetRowMaxAbs() */
  ierr   = MatGetRowMaxAbs(A,s1,NULL);CHKERRQ(ierr);
  ierr   = MatGetRowMaxAbs(sB,s2,NULL);CHKERRQ(ierr);
  ierr   = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
  ierr   = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
  norm1 -= norm2;
  if (norm1<-tol || norm1>tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetRowMaxAbs() \n");CHKERRQ(ierr);
  }

  /* Test MatMult() */
  for (i=0; i<40; i++) {
    ierr   = VecSetRandom(x,rdm);CHKERRQ(ierr);
    ierr   = MatMult(A,x,s1);CHKERRQ(ierr);
    ierr   = MatMult(sB,x,s2);CHKERRQ(ierr);
    ierr   = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
    ierr   = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
    norm1 -= norm2;
    if (norm1<-tol || norm1>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
    }
  }

  /* MatMultAdd() */
  for (i=0; i<40; i++) {
    ierr   = VecSetRandom(x,rdm);CHKERRQ(ierr);
    ierr   = VecSetRandom(y,rdm);CHKERRQ(ierr);
    ierr   = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
    ierr   = MatMultAdd(sB,x,y,s2);CHKERRQ(ierr);
    ierr   = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
    ierr   = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
    norm1 -= norm2;
    if (norm1<-tol || norm1>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(),  norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
    }
  }

  /* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
  ierr  = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iscol);CHKERRQ(ierr);
  ierr  = ISDestroy(&iscol);CHKERRQ(ierr);
  norm1 = tol;
  inc   = bs;

  /* initialize factinfo */
  ierr = PetscMemzero(&factinfo,sizeof(MatFactorInfo));CHKERRQ(ierr);

  for (lf=-1; lf<10; lf += inc) {
    if (lf==-1) {  /* Cholesky factor of sB (duplicate sA) */
      factinfo.fill = 5.0;

      ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
      ierr = MatCholeskyFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
    } else if (!doIcc) break;
    else {       /* incomplete Cholesky factor */
      factinfo.fill   = 5.0;
      factinfo.levels = lf;

      ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
      ierr = MatICCFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
    }
    ierr = MatCholeskyFactorNumeric(sC,sB,&factinfo);CHKERRQ(ierr);
    /* MatView(sC, PETSC_VIEWER_DRAW_WORLD); */

    /* test MatGetDiagonal on numeric factor */
    /*
    if (lf == -1) {
      ierr = MatGetDiagonal(sC,s1);CHKERRQ(ierr);
      printf(" in ex74.c, diag: \n");
      ierr = VecView(s1,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
    }
    */

    ierr = MatMult(sB,x,b);CHKERRQ(ierr);

    /* test MatForwardSolve() and MatBackwardSolve() */
    if (lf == -1) {
      ierr = MatForwardSolve(sC,b,s1);CHKERRQ(ierr);
      ierr = MatBackwardSolve(sC,s1,s2);CHKERRQ(ierr);
      ierr = VecAXPY(s2,neg_one,x);CHKERRQ(ierr);
      ierr = VecNorm(s2,NORM_2,&norm2);CHKERRQ(ierr);
      if (10*norm1 < norm2) {
        ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G, bs=%d\n",norm2,bs);CHKERRQ(ierr);
      }
    }

    /* test MatSolve() */
    ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
    ierr = MatDestroy(&sC);CHKERRQ(ierr);
    /* Check the error */
    ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
    ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
    /* printf("lf: %d, error: %G\n", lf,norm2); */
    if (10*norm1 < norm2 && lf-inc != -1) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"lf=%D, %D, Norm of error=%G, %G\n",lf-inc,lf,norm1,norm2);CHKERRQ(ierr);
    }
    norm1 = norm2;
    if (norm2 < tol && lf != -1) break;
  }

  ierr = ISDestroy(&perm);CHKERRQ(ierr);

  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = MatDestroy(&sB);CHKERRQ(ierr);
  ierr = MatDestroy(&sA);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&y);CHKERRQ(ierr);
  ierr = VecDestroy(&s1);CHKERRQ(ierr);
  ierr = VecDestroy(&s2);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);

  ierr = PetscFinalize();
  return 0;
}
Exemplo n.º 3
0
int main(int argc,char **args)
{
  Mat            A,B,Fact;
  Vec            xx,s1,s2,yy;
  PetscErrorCode ierr;
  PetscInt       m=45,rows[2],cols[2],bs=1,i,row,col,*idx,M;
  PetscScalar    rval,vals1[4],vals2[4];
  PetscRandom    rdm;
  IS             is1,is2;
  PetscReal      s1norm,s2norm,rnorm,tol = 1.e-4;
  PetscBool      flg;
  MatFactorInfo  info;

  PetscInitialize(&argc,&args,(char*)0,help);

  /* Test MatSetValues() and MatGetValues() */
  ierr = PetscOptionsGetInt(NULL,"-mat_block_size",&bs,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-mat_size",&m,NULL);CHKERRQ(ierr);
  M    = m*bs;
  ierr = MatCreateSeqBAIJ(PETSC_COMM_SELF,bs,M,M,1,NULL,&A);CHKERRQ(ierr);
  ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
  ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,M,M,15,NULL,&B);CHKERRQ(ierr);
  ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
  ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
  ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
  ierr = VecCreateSeq(PETSC_COMM_SELF,M,&xx);CHKERRQ(ierr);
  ierr = VecDuplicate(xx,&s1);CHKERRQ(ierr);
  ierr = VecDuplicate(xx,&s2);CHKERRQ(ierr);
  ierr = VecDuplicate(xx,&yy);CHKERRQ(ierr);

  /* For each row add atleast 15 elements */
  for (row=0; row<M; row++) {
    for (i=0; i<25*bs; i++) {
      ierr = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
      col  = (PetscInt)(PetscRealPart(rval)*M);
      ierr = MatSetValues(A,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues(B,1,&row,1,&col,&rval,INSERT_VALUES);CHKERRQ(ierr);
    }
  }

  /* Now set blocks of values */
  for (i=0; i<20*bs; i++) {
    ierr     = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    cols[0]  = (PetscInt)(PetscRealPart(rval)*M);
    vals1[0] = rval;
    ierr     = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    cols[1]  = (PetscInt)(PetscRealPart(rval)*M);
    vals1[1] = rval;
    ierr     = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    rows[0]  = (PetscInt)(PetscRealPart(rval)*M);
    vals1[2] = rval;
    ierr     = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    rows[1]  = (PetscInt)(PetscRealPart(rval)*M);
    vals1[3] = rval;
    ierr     = MatSetValues(A,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
    ierr     = MatSetValues(B,2,rows,2,cols,vals1,INSERT_VALUES);CHKERRQ(ierr);
  }

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* Test MatNorm() */
  ierr  = MatNorm(A,NORM_FROBENIUS,&s1norm);CHKERRQ(ierr);
  ierr  = MatNorm(B,NORM_FROBENIUS,&s2norm);CHKERRQ(ierr);
  rnorm = PetscAbsReal(s2norm-s1norm)/s2norm;
  if (rnorm>tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
  }
  ierr  = MatNorm(A,NORM_INFINITY,&s1norm);CHKERRQ(ierr);
  ierr  = MatNorm(B,NORM_INFINITY,&s2norm);CHKERRQ(ierr);
  rnorm = PetscAbsReal(s2norm-s1norm)/s2norm;
  if (rnorm>tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
  }
  ierr  = MatNorm(A,NORM_1,&s1norm);CHKERRQ(ierr);
  ierr  = MatNorm(B,NORM_1,&s2norm);CHKERRQ(ierr);
  rnorm = PetscAbsReal(s2norm-s1norm)/s2norm;
  if (rnorm>tol) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_NORM_1()- NormA=%16.14e NormB=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
  }

  /* MatShift() */
  rval = 10*s1norm;
  ierr = MatShift(A,rval);CHKERRQ(ierr);
  ierr = MatShift(B,rval);CHKERRQ(ierr);

  /* Test MatTranspose() */
  ierr = MatTranspose(A,MAT_REUSE_MATRIX,&A);CHKERRQ(ierr);
  ierr = MatTranspose(B,MAT_REUSE_MATRIX,&B);CHKERRQ(ierr);

  /* Now do MatGetValues()  */
  for (i=0; i<30; i++) {
    ierr    = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    cols[0] = (PetscInt)(PetscRealPart(rval)*M);
    ierr    = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    cols[1] = (PetscInt)(PetscRealPart(rval)*M);
    ierr    = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    rows[0] = (PetscInt)(PetscRealPart(rval)*M);
    ierr    = PetscRandomGetValue(rdm,&rval);CHKERRQ(ierr);
    rows[1] = (PetscInt)(PetscRealPart(rval)*M);
    ierr    = MatGetValues(A,2,rows,2,cols,vals1);CHKERRQ(ierr);
    ierr    = MatGetValues(B,2,rows,2,cols,vals2);CHKERRQ(ierr);
    ierr    = PetscMemcmp(vals1,vals2,4*sizeof(PetscScalar),&flg);CHKERRQ(ierr);
    if (!flg) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetValues bs = %D\n",bs);CHKERRQ(ierr);
    }
  }

  /* Test MatMult(), MatMultAdd() */
  for (i=0; i<40; i++) {
    ierr  = VecSetRandom(xx,rdm);CHKERRQ(ierr);
    ierr  = VecSet(s2,0.0);CHKERRQ(ierr);
    ierr  = MatMult(A,xx,s1);CHKERRQ(ierr);
    ierr  = MatMultAdd(A,xx,s2,s2);CHKERRQ(ierr);
    ierr  = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
    ierr  = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
    rnorm = s2norm-s1norm;
    if (rnorm<-tol || rnorm>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"MatMult not equal to MatMultAdd Norm1=%e Norm2=%e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
    }
  }

  /* Test MatMult() */
  ierr = MatMultEqual(A,B,10,&flg);CHKERRQ(ierr);
  if (!flg) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult()\n");CHKERRQ(ierr);
  }

  /* Test MatMultAdd() */
  ierr = MatMultAddEqual(A,B,10,&flg);CHKERRQ(ierr);
  if (!flg) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultAdd()\n");CHKERRQ(ierr);
  }

  /* Test MatMultTranspose() */
  ierr = MatMultTransposeEqual(A,B,10,&flg);CHKERRQ(ierr);
  if (!flg) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTranspose()\n");CHKERRQ(ierr);
  }

  /* Test MatMultTransposeAdd() */
  ierr = MatMultTransposeAddEqual(A,B,10,&flg);CHKERRQ(ierr);
  if (!flg) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMultTransposeAdd()\n");CHKERRQ(ierr);
  }

  /* Do LUFactor() on both the matrices */
  ierr = PetscMalloc1(M,&idx);CHKERRQ(ierr);
  for (i=0; i<M; i++) idx[i] = i;
  ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,PETSC_COPY_VALUES,&is1);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PETSC_COMM_SELF,M,idx,PETSC_COPY_VALUES,&is2);CHKERRQ(ierr);
  ierr = PetscFree(idx);CHKERRQ(ierr);
  ierr = ISSetPermutation(is1);CHKERRQ(ierr);
  ierr = ISSetPermutation(is2);CHKERRQ(ierr);

  ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);

  info.fill          = 2.0;
  info.dtcol         = 0.0;
  info.zeropivot     = 1.e-14;
  info.pivotinblocks = 1.0;

  if (bs < 4) {
    ierr = MatGetFactor(A,"petsc",MAT_FACTOR_LU,&Fact);CHKERRQ(ierr);
    ierr = MatLUFactorSymbolic(Fact,A,is1,is2,&info);CHKERRQ(ierr);
    ierr = MatLUFactorNumeric(Fact,A,&info);CHKERRQ(ierr);
    ierr = VecSetRandom(yy,rdm);CHKERRQ(ierr);
    ierr = MatForwardSolve(Fact,yy,xx);CHKERRQ(ierr);
    ierr = MatBackwardSolve(Fact,xx,s1);CHKERRQ(ierr);
    ierr = MatDestroy(&Fact);CHKERRQ(ierr);
    ierr = VecScale(s1,-1.0);CHKERRQ(ierr);
    ierr = MatMultAdd(A,s1,yy,yy);CHKERRQ(ierr);
    ierr = VecNorm(yy,NORM_2,&rnorm);CHKERRQ(ierr);
    if (rnorm<-tol || rnorm>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatForwardSolve/MatBackwardSolve - Norm1=%16.14e bs = %D\n",rnorm,bs);CHKERRQ(ierr);
    }
  }

  ierr = MatLUFactor(B,is1,is2,&info);CHKERRQ(ierr);
  ierr = MatLUFactor(A,is1,is2,&info);CHKERRQ(ierr);

  /* Test MatSolveAdd() */
  for (i=0; i<10; i++) {
    ierr  = VecSetRandom(xx,rdm);CHKERRQ(ierr);
    ierr  = VecSetRandom(yy,rdm);CHKERRQ(ierr);
    ierr  = MatSolveAdd(B,xx,yy,s2);CHKERRQ(ierr);
    ierr  = MatSolveAdd(A,xx,yy,s1);CHKERRQ(ierr);
    ierr  = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
    ierr  = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
    rnorm = s2norm-s1norm;
    if (rnorm<-tol || rnorm>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
    }
  }

  /* Test MatSolveAdd() when x = A'b +x */
  for (i=0; i<10; i++) {
    ierr  = VecSetRandom(xx,rdm);CHKERRQ(ierr);
    ierr  = VecSetRandom(s1,rdm);CHKERRQ(ierr);
    ierr  = VecCopy(s2,s1);CHKERRQ(ierr);
    ierr  = MatSolveAdd(B,xx,s2,s2);CHKERRQ(ierr);
    ierr  = MatSolveAdd(A,xx,s1,s1);CHKERRQ(ierr);
    ierr  = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
    ierr  = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
    rnorm = s2norm-s1norm;
    if (rnorm<-tol || rnorm>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveAdd(same) - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
    }
  }

  /* Test MatSolve() */
  for (i=0; i<10; i++) {
    ierr  = VecSetRandom(xx,rdm);CHKERRQ(ierr);
    ierr  = MatSolve(B,xx,s2);CHKERRQ(ierr);
    ierr  = MatSolve(A,xx,s1);CHKERRQ(ierr);
    ierr  = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
    ierr  = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
    rnorm = s2norm-s1norm;
    if (rnorm<-tol || rnorm>tol) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolve - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
    }
  }

  /* Test MatSolveTranspose() */
  if (bs < 8) {
    for (i=0; i<10; i++) {
      ierr  = VecSetRandom(xx,rdm);CHKERRQ(ierr);
      ierr  = MatSolveTranspose(B,xx,s2);CHKERRQ(ierr);
      ierr  = MatSolveTranspose(A,xx,s1);CHKERRQ(ierr);
      ierr  = VecNorm(s1,NORM_2,&s1norm);CHKERRQ(ierr);
      ierr  = VecNorm(s2,NORM_2,&s2norm);CHKERRQ(ierr);
      rnorm = s2norm-s1norm;
      if (rnorm<-tol || rnorm>tol) {
        ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatSolveTranspose - Norm1=%16.14e Norm2=%16.14e bs = %D\n",s1norm,s2norm,bs);CHKERRQ(ierr);
      }
    }
  }

  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = MatDestroy(&B);CHKERRQ(ierr);
  ierr = VecDestroy(&xx);CHKERRQ(ierr);
  ierr = VecDestroy(&s1);CHKERRQ(ierr);
  ierr = VecDestroy(&s2);CHKERRQ(ierr);
  ierr = VecDestroy(&yy);CHKERRQ(ierr);
  ierr = ISDestroy(&is1);CHKERRQ(ierr);
  ierr = ISDestroy(&is2);CHKERRQ(ierr);
  ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return 0;
}