Esempio n. 1
0
/*
   BVOrthogonalizeCGS1 - Compute |v'| (estimated), |v| and one step of CGS with
   only one global synchronization
*/
PetscErrorCode BVOrthogonalizeCGS1(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *onorm,PetscReal *norm)
{
  PetscErrorCode ierr;
  PetscInt       i;
  PetscReal      sum,nrm,beta;
  Vec            w=v;

  PetscFunctionBegin;
  /* h = W^* v ; alpha = (v, v) */
  bv->k = j;
  if (onorm || norm) {
    if (!v) {
      bv->k++;
      ierr = BVGetColumn(bv,j,&w);CHKERRQ(ierr);
    }
    ierr = BVDotVec(bv,w,H);CHKERRQ(ierr);
    if (!v) {
      ierr = BVRestoreColumn(bv,j,&w);CHKERRQ(ierr);
      bv->k--;
      beta = PetscSqrtReal(PetscRealPart(H[bv->nc+j]));
    } else {
      ierr = BVNormVec(bv,w,NORM_2,&beta);CHKERRQ(ierr);
    }
  } else {
    if (!v) { ierr = BVDotColumn(bv,j,H);CHKERRQ(ierr); }
    else { ierr = BVDotVec(bv,w,H);CHKERRQ(ierr); }
  }

  /* q = v - V h */
  if (bv->indef) {
    for (i=0;i<bv->nc+j;i++) H[i] /= bv->omega[i];  /* apply inverse of signature */
  }
  if (!v) { ierr = BVMultColumn(bv,-1.0,1.0,j,H);CHKERRQ(ierr); }
  else { ierr = BVMultVec(bv,-1.0,1.0,w,H);CHKERRQ(ierr); }
  if (bv->indef) {
    for (i=0;i<bv->nc+j;i++) H[i] *= bv->omega[i];  /* revert signature */
  }

  /* compute |v| */
  if (onorm) *onorm = beta;

  if (bv->indef) {
    if (!v) { ierr = BVNormColumn(bv,j,NORM_2,&nrm);CHKERRQ(ierr); }
    else { ierr = BVNormVec(bv,w,NORM_2,&nrm);CHKERRQ(ierr); }
    if (norm) *norm = nrm;
    bv->omega[bv->nc+j] = (nrm<0.0)? -1.0: 1.0;
  } else if (norm) {
    /* estimate |v'| from |v| */
    sum = 0.0;
    for (i=0;i<bv->nc+j;i++) sum += PetscRealPart(H[i]*PetscConj(H[i]));
    *norm = beta*beta-sum;
    if (*norm <= 0.0) {
      if (!v) { ierr = BVNormColumn(bv,j,NORM_2,norm);CHKERRQ(ierr); }
      else { ierr = BVNormVec(bv,w,NORM_2,norm);CHKERRQ(ierr); }
    } else *norm = PetscSqrtReal(*norm);
  }
  PetscFunctionReturn(0);
}
Esempio n. 2
0
static PetscErrorCode SVDOneSideTRLanczosMGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n)
{
  PetscErrorCode ierr;
  PetscReal      a,b;
  PetscScalar    gamma;
  PetscInt       i,k=nconv+l;
  Vec            ui,ui1,vi;

  PetscFunctionBegin;
  ierr = BVGetColumn(V,k,&vi);CHKERRQ(ierr);
  ierr = BVGetColumn(U,k,&ui);CHKERRQ(ierr);
  ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
  ierr = BVRestoreColumn(V,k,&vi);CHKERRQ(ierr);
  ierr = BVRestoreColumn(U,k,&ui);CHKERRQ(ierr);
  if (l>0) {
    ierr = BVMultColumn(U,-1.0,1.0,k,&gamma);CHKERRQ(ierr);
    beta[nconv] = PetscRealPart(gamma);
  }
  ierr = BVNormColumn(U,k,NORM_2,&a);CHKERRQ(ierr);
  ierr = BVScaleColumn(U,k,1.0/a);CHKERRQ(ierr);
  alpha[k] = a;

  for (i=k+1;i<n;i++) {
    ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
    ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = BVOrthogonalizeColumn(V,i,NULL,&b,NULL);CHKERRQ(ierr);
    ierr = BVScaleColumn(V,i,1.0/b);CHKERRQ(ierr);
    beta[i-1] = b;

    ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVGetColumn(U,i,&ui);CHKERRQ(ierr);
    ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
    ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = VecAXPY(ui,-b,ui1);CHKERRQ(ierr);
    ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = BVRestoreColumn(U,i,&ui);CHKERRQ(ierr);
    ierr = BVNormColumn(U,i,NORM_2,&a);CHKERRQ(ierr);
    ierr = BVScaleColumn(U,i,1.0/a);CHKERRQ(ierr);
    alpha[i] = a;
  }

  ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
  ierr = BVGetColumn(U,n-1,&ui1);CHKERRQ(ierr);
  ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
  ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
  ierr = BVRestoreColumn(U,n-1,&ui1);CHKERRQ(ierr);
  ierr = BVOrthogonalizeColumn(V,n,NULL,&b,NULL);CHKERRQ(ierr);
  beta[n-1] = b;
  PetscFunctionReturn(0);
}
Esempio n. 3
0
/*
  BVOrthogonalizeCGS - Orthogonalize with classical Gram-Schmidt
*/
static PetscErrorCode BVOrthogonalizeCGS(BV bv,PetscInt j,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
{
  PetscErrorCode ierr;
  PetscReal      onrm,nrm;
  PetscInt       i,k,l;

  PetscFunctionBegin;
  if (v) k = bv->k;
  else k = j;
  switch (bv->orthog_ref) {

  case BV_ORTHOG_REFINE_IFNEEDED:
    ierr = BVOrthogonalizeCGS1(bv,k,v,bv->h,&onrm,&nrm);CHKERRQ(ierr);
    /* ||q|| < eta ||h|| */
    l = 1;
    while (l<3 && nrm && nrm < bv->orthog_eta*onrm) {
      l++;
      ierr = BVOrthogonalizeCGS1(bv,k,v,bv->c,&onrm,&nrm);CHKERRQ(ierr);
      for (i=0;i<bv->nc+k;i++) bv->h[i] += bv->c[i];
    }
    if (norm) *norm = nrm;
    if (lindep) {
      if (nrm < bv->orthog_eta*onrm) *lindep = PETSC_TRUE;
      else *lindep = PETSC_FALSE;
    }
    break;

  case BV_ORTHOG_REFINE_NEVER:
    ierr = BVOrthogonalizeCGS1(bv,k,v,bv->h,NULL,NULL);CHKERRQ(ierr);
    /* compute |v| */
    if (norm || lindep) {
      if (v) { ierr = BVNormVec(bv,v,NORM_2,&nrm);CHKERRQ(ierr); }
      else { ierr = BVNormColumn(bv,k,NORM_2,&nrm);CHKERRQ(ierr); }
    }
    if (norm) *norm = nrm;
    /* linear dependence check: just test for exactly zero norm */
    if (lindep) *lindep = nrm? PETSC_FALSE: PETSC_TRUE;
    break;

  case BV_ORTHOG_REFINE_ALWAYS:
    ierr = BVOrthogonalizeCGS1(bv,k,v,bv->h,NULL,NULL);CHKERRQ(ierr);
    if (lindep) {
      ierr = BVOrthogonalizeCGS1(bv,k,v,bv->c,&onrm,&nrm);CHKERRQ(ierr);
      if (norm) *norm = nrm;
      if (nrm==0.0 || nrm < bv->orthog_eta*onrm) *lindep = PETSC_TRUE;
      else *lindep = PETSC_FALSE;
    } else {
      ierr = BVOrthogonalizeCGS1(bv,k,v,bv->c,NULL,norm);CHKERRQ(ierr);
    }
    for (i=0;i<bv->nc+k;i++) bv->h[i] += bv->c[i];
    break;
  }
  PetscFunctionReturn(0);
}
Esempio n. 4
0
/*
  Custom CGS orthogonalization, preprocess after first orthogonalization
*/
static PetscErrorCode SVDOrthogonalizeCGS(BV V,PetscInt i,PetscScalar* h,PetscReal a,BVOrthogRefineType refine,PetscReal eta,PetscReal *norm)
{
  PetscErrorCode ierr;
  PetscReal      sum,onorm;
  PetscScalar    dot;
  PetscInt       j;

  PetscFunctionBegin;
  switch (refine) {
  case BV_ORTHOG_REFINE_NEVER:
    ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
    break;
  case BV_ORTHOG_REFINE_ALWAYS:
    ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
    ierr = BVDotColumn(V,i,h);CHKERRQ(ierr);
    ierr = BVMultColumn(V,-1.0,1.0,i,h);CHKERRQ(ierr);
    ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
    break;
  case BV_ORTHOG_REFINE_IFNEEDED:
    dot = h[i];
    onorm = PetscSqrtReal(PetscRealPart(dot)) / a;
    sum = 0.0;
    for (j=0;j<i;j++) {
      sum += PetscRealPart(h[j] * PetscConj(h[j]));
    }
    *norm = PetscRealPart(dot)/(a*a) - sum;
    if (*norm>0.0) *norm = PetscSqrtReal(*norm);
    else {
      ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
    }
    if (*norm < eta*onorm) {
      ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
      ierr = BVDotColumn(V,i,h);CHKERRQ(ierr);
      ierr = BVMultColumn(V,-1.0,1.0,i,h);CHKERRQ(ierr);
      ierr = BVNormColumn(V,i,NORM_2,norm);CHKERRQ(ierr);
    }
    break;
  }
  PetscFunctionReturn(0);
}
Esempio n. 5
0
int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  Vec            t,v;
  Mat            Q,M;
  BV             X,Y;
  PetscInt       i,j,n=10,kx=6,lx=3,ky=5,ly=2;
  PetscScalar    *q,*z;
  PetscReal      nrm;
  PetscViewer    view;
  PetscBool      verbose,trans;

  SlepcInitialize(&argc,&argv,(char*)0,help);
  ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-kx",&kx,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-lx",&lx,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-ky",&ky,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-ly",&ly,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"First BV with %D active columns (%D leading columns) of dimension %D.\n",kx,lx,n);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Second BV with %D active columns (%D leading columns) of dimension %D.\n",ky,ly,n);CHKERRQ(ierr);

  /* Create template vector */
  ierr = VecCreate(PETSC_COMM_WORLD,&t);CHKERRQ(ierr);
  ierr = VecSetSizes(t,PETSC_DECIDE,n);CHKERRQ(ierr);
  ierr = VecSetFromOptions(t);CHKERRQ(ierr);

  /* Create BV object X */
  ierr = BVCreate(PETSC_COMM_WORLD,&X);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)X,"X");CHKERRQ(ierr);
  ierr = BVSetSizesFromVec(X,t,kx+2);CHKERRQ(ierr);  /* two extra columns to test active columns */
  ierr = BVSetFromOptions(X);CHKERRQ(ierr);
  ierr = BVSetActiveColumns(X,lx,kx);CHKERRQ(ierr);

  /* Set up viewer */
  ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
  }

  /* Fill X entries */
  for (j=0;j<kx+2;j++) {
    ierr = BVGetColumn(X,j,&v);CHKERRQ(ierr);
    ierr = VecZeroEntries(v);CHKERRQ(ierr);
    for (i=0;i<4;i++) {
      if (i+j<n) {
        ierr = VecSetValue(v,i+j,(PetscScalar)(3*i+j-2),INSERT_VALUES);CHKERRQ(ierr);
      }
    }
    ierr = VecAssemblyBegin(v);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(v);CHKERRQ(ierr);
    ierr = BVRestoreColumn(X,j,&v);CHKERRQ(ierr);
  }
  if (verbose) {
    ierr = BVView(X,view);CHKERRQ(ierr);
  }

  /* Create BV object Y */
  ierr = BVCreate(PETSC_COMM_WORLD,&Y);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)Y,"Y");CHKERRQ(ierr);
  ierr = BVSetSizesFromVec(Y,t,ky+1);CHKERRQ(ierr);
  ierr = BVSetFromOptions(Y);CHKERRQ(ierr);
  ierr = BVSetActiveColumns(Y,ly,ky);CHKERRQ(ierr);

  /* Fill Y entries */
  for (j=0;j<ky+1;j++) {
    ierr = BVGetColumn(Y,j,&v);CHKERRQ(ierr);
    ierr = VecSet(v,(PetscScalar)(j+1)/4.0);CHKERRQ(ierr);
    ierr = BVRestoreColumn(Y,j,&v);CHKERRQ(ierr);
  }
  if (verbose) {
    ierr = BVView(Y,view);CHKERRQ(ierr);
  }

  /* Create Mat */
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,kx,ky,NULL,&Q);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)Q,"Q");CHKERRQ(ierr);
  ierr = MatDenseGetArray(Q,&q);CHKERRQ(ierr);
  for (i=0;i<kx;i++)
    for (j=0;j<ky;j++)
      q[i+j*kx] = (i<j)? 2.0: -0.5;
  ierr = MatDenseRestoreArray(Q,&q);CHKERRQ(ierr);
  if (verbose) {
    ierr = MatView(Q,NULL);CHKERRQ(ierr);
  }

  /* Test BVMult */
  ierr = BVMult(Y,2.0,1.0,X,Q);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVMult - - - - - - - - -\n");CHKERRQ(ierr);
    ierr = BVView(Y,view);CHKERRQ(ierr);
  }

  /* Test BVMultVec */
  ierr = BVGetColumn(Y,0,&v);CHKERRQ(ierr);
  ierr = PetscMalloc1(kx-lx,&z);CHKERRQ(ierr);
  z[0] = 2.0;
  for (i=1;i<kx-lx;i++) z[i] = -0.5*z[i-1];
  ierr = BVMultVec(X,-1.0,1.0,v,z);CHKERRQ(ierr);
  ierr = PetscFree(z);CHKERRQ(ierr);
  ierr = BVRestoreColumn(Y,0,&v);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVMultVec - - - - - - -\n");CHKERRQ(ierr);
    ierr = BVView(Y,view);CHKERRQ(ierr);
  }

  /* Test BVDot */
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,ky,kx,NULL,&M);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)M,"M");CHKERRQ(ierr);
  ierr = BVDot(X,Y,M);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVDot - - - - - - - - -\n");CHKERRQ(ierr);
    ierr = MatView(M,NULL);CHKERRQ(ierr);
  }

  /* Test BVDotVec */
  ierr = BVGetColumn(Y,0,&v);CHKERRQ(ierr);
  ierr = PetscMalloc1(kx-lx,&z);CHKERRQ(ierr);
  ierr = BVDotVec(X,v,z);CHKERRQ(ierr);
  ierr = BVRestoreColumn(Y,0,&v);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVDotVec - - - - - - -\n");CHKERRQ(ierr);
    ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,kx-lx,z,&v);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject)v,"z");CHKERRQ(ierr);
    ierr = VecView(v,view);CHKERRQ(ierr);
    ierr = VecDestroy(&v);CHKERRQ(ierr);
  }
  ierr = PetscFree(z);CHKERRQ(ierr);

  /* Test BVMultInPlace and BVScale */
  ierr = PetscOptionsHasName(NULL,"-trans",&trans);CHKERRQ(ierr);
  if (trans) {
    Mat Qt;
    ierr = MatTranspose(Q,MAT_INITIAL_MATRIX,&Qt);CHKERRQ(ierr);
    ierr = BVMultInPlaceTranspose(X,Qt,lx+1,ky);CHKERRQ(ierr);
    ierr = MatDestroy(&Qt);CHKERRQ(ierr);
  } else {
    ierr = BVMultInPlace(X,Q,lx+1,ky);CHKERRQ(ierr);
  }
  ierr = BVScale(X,2.0);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"After BVMultInPlace - - - - -\n");CHKERRQ(ierr);
    ierr = BVView(X,view);CHKERRQ(ierr);
  }

  /* Test BVNorm */
  ierr = BVNormColumn(X,lx,NORM_2,&nrm);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"2-Norm or X[%D] = %g\n",lx,(double)nrm);CHKERRQ(ierr);
  ierr = BVNorm(X,NORM_FROBENIUS,&nrm);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Frobenius Norm or X = %g\n",(double)nrm);CHKERRQ(ierr);

  ierr = BVDestroy(&X);CHKERRQ(ierr);
  ierr = BVDestroy(&Y);CHKERRQ(ierr);
  ierr = MatDestroy(&Q);CHKERRQ(ierr);
  ierr = MatDestroy(&M);CHKERRQ(ierr);
  ierr = VecDestroy(&t);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return 0;
}
Esempio n. 6
0
int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  Vec            t,v;
  Mat            B,M;
  BV             X;
  PetscInt       i,j,n=10,k=5,Istart,Iend,col[3];
  PetscScalar    value[3],alpha;
  PetscReal      nrm;
  PetscViewer    view;
  PetscBool      verbose,FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

  SlepcInitialize(&argc,&argv,(char*)0,help);
  ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-k",&k,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"Test BV with non-standard inner product (n=%D, k=%D).\n",n,k);CHKERRQ(ierr);

  /* Create inner product matrix */
  ierr = MatCreate(PETSC_COMM_WORLD,&B);CHKERRQ(ierr);
  ierr = MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetFromOptions(B);CHKERRQ(ierr);
  ierr = MatSetUp(B);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)B,"B");CHKERRQ(ierr);

  ierr = MatGetOwnershipRange(B,&Istart,&Iend);CHKERRQ(ierr);
  if (Istart==0) FirstBlock=PETSC_TRUE;
  if (Iend==n) LastBlock=PETSC_TRUE;
  value[0]=-1.0; value[1]=2.0; value[2]=-1.0;
  for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
    col[0]=i-1; col[1]=i; col[2]=i+1;
    ierr = MatSetValues(B,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
  }
  if (LastBlock) {
    i=n-1; col[0]=n-2; col[1]=n-1;
    ierr = MatSetValues(B,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
  }
  if (FirstBlock) {
    i=0; col[0]=0; col[1]=1; value[0]=2.0; value[1]=-1.0;
    ierr = MatSetValues(B,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatGetVecs(B,&t,NULL);CHKERRQ(ierr);

  /* Create BV object X */
  ierr = BVCreate(PETSC_COMM_WORLD,&X);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)X,"X");CHKERRQ(ierr);
  ierr = BVSetSizesFromVec(X,t,k);CHKERRQ(ierr);
  ierr = BVSetFromOptions(X);CHKERRQ(ierr);
  ierr = BVSetMatrix(X,B,PETSC_FALSE);CHKERRQ(ierr);

  /* Set up viewer */
  ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&view);CHKERRQ(ierr);
  if (verbose) {
    ierr = PetscViewerPushFormat(view,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
  }

  /* Fill X entries */
  for (j=0;j<k;j++) {
    ierr = BVGetColumn(X,j,&v);CHKERRQ(ierr);
    ierr = VecZeroEntries(v);CHKERRQ(ierr);
    for (i=0;i<4;i++) {
      if (i+j<n) {
        ierr = VecSetValue(v,i+j,(PetscScalar)(3*i+j-2),INSERT_VALUES);CHKERRQ(ierr);
      }
    }
    ierr = VecAssemblyBegin(v);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(v);CHKERRQ(ierr);
    ierr = BVRestoreColumn(X,j,&v);CHKERRQ(ierr);
  }
  if (verbose) {
    ierr = MatView(B,view);CHKERRQ(ierr);
    ierr = BVView(X,view);CHKERRQ(ierr);
  }

  /* Test BVNormColumn */
  ierr = BVNormColumn(X,0,NORM_2,&nrm);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"B-Norm or X[0] = %g\n",(double)nrm);CHKERRQ(ierr);

  /* Test BVOrthogonalizeColumn */
  for (j=0;j<k;j++) {
    ierr = BVOrthogonalizeColumn(X,j,NULL,&nrm,NULL);CHKERRQ(ierr);
    alpha = 1.0/nrm;
    ierr = BVScaleColumn(X,j,alpha);CHKERRQ(ierr);
  }
  if (verbose) {
    ierr = BVView(X,view);CHKERRQ(ierr);
  }

  /* Check orthogonality */
  ierr = MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&M);CHKERRQ(ierr);
  ierr = BVDot(X,X,M);CHKERRQ(ierr);
  ierr = MatShift(M,-1.0);CHKERRQ(ierr);
  ierr = MatNorm(M,NORM_1,&nrm);CHKERRQ(ierr);
  if (nrm<100*PETSC_MACHINE_EPSILON) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality < 100*eps\n");CHKERRQ(ierr);
  } else {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)nrm);CHKERRQ(ierr);
  }

  ierr = BVDestroy(&X);CHKERRQ(ierr);
  ierr = MatDestroy(&M);CHKERRQ(ierr);
  ierr = MatDestroy(&B);CHKERRQ(ierr);
  ierr = VecDestroy(&t);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return 0;
}
Esempio n. 7
0
PetscErrorCode NEPSolve_NArnoldi(NEP nep)
{
  PetscErrorCode     ierr;
  Mat                T=nep->function,Tsigma;
  Vec                f,r=nep->work[0],x=nep->work[1],w=nep->work[2];
  PetscScalar        *X,lambda;
  PetscReal          beta,resnorm=0.0,nrm;
  PetscInt           n;
  PetscBool          breakdown;
  KSPConvergedReason kspreason;

  PetscFunctionBegin;
  /* get initial space and shift */
  ierr = NEPGetDefaultShift(nep,&lambda);CHKERRQ(ierr);
  if (!nep->nini) {
    ierr = BVSetRandomColumn(nep->V,0,nep->rand);CHKERRQ(ierr);
    ierr = BVNormColumn(nep->V,0,NORM_2,&nrm);CHKERRQ(ierr);
    ierr = BVScaleColumn(nep->V,0,1.0/nrm);CHKERRQ(ierr);
    n = 1;
  } else n = nep->nini;

  /* build projected matrices for initial space */
  ierr = DSSetDimensions(nep->ds,n,0,0,0);CHKERRQ(ierr);
  ierr = NEPProjectOperator(nep,0,n);CHKERRQ(ierr);

  /* prepare linear solver */
  ierr = NEPComputeFunction(nep,lambda,T,T);CHKERRQ(ierr);
  ierr = MatDuplicate(T,MAT_COPY_VALUES,&Tsigma);CHKERRQ(ierr);
  ierr = KSPSetOperators(nep->ksp,Tsigma,Tsigma);CHKERRQ(ierr);

  /* Restart loop */
  while (nep->reason == NEP_CONVERGED_ITERATING) {
    nep->its++;

    /* solve projected problem */
    ierr = DSSetDimensions(nep->ds,n,0,0,0);CHKERRQ(ierr);
    ierr = DSSetState(nep->ds,DS_STATE_RAW);CHKERRQ(ierr);
    ierr = DSSolve(nep->ds,nep->eigr,NULL);CHKERRQ(ierr);
    lambda = nep->eigr[0];

    /* compute Ritz vector, x = V*s */
    ierr = DSGetArray(nep->ds,DS_MAT_X,&X);CHKERRQ(ierr);
    ierr = BVSetActiveColumns(nep->V,0,n);CHKERRQ(ierr);
    ierr = BVMultVec(nep->V,1.0,0.0,x,X);CHKERRQ(ierr);
    ierr = DSRestoreArray(nep->ds,DS_MAT_X,&X);CHKERRQ(ierr);

    /* compute the residual, r = T(lambda)*x */
    ierr = NEPApplyFunction(nep,lambda,x,w,r,NULL,NULL);CHKERRQ(ierr);

    /* convergence test */
    ierr = VecNorm(r,NORM_2,&resnorm);CHKERRQ(ierr);
    nep->errest[nep->nconv] = resnorm;
    if (resnorm<=nep->rtol) {
      ierr = BVInsertVec(nep->V,nep->nconv,x);CHKERRQ(ierr);
      nep->nconv = nep->nconv + 1;
      nep->reason = NEP_CONVERGED_FNORM_RELATIVE;
    }
    ierr = NEPMonitor(nep,nep->its,nep->nconv,nep->eigr,nep->errest,1);CHKERRQ(ierr);

    if (nep->reason == NEP_CONVERGED_ITERATING) {

      /* continuation vector: f = T(sigma)\r */
      ierr = BVGetColumn(nep->V,n,&f);CHKERRQ(ierr);
      ierr = NEP_KSPSolve(nep,r,f);CHKERRQ(ierr);
      ierr = BVRestoreColumn(nep->V,n,&f);CHKERRQ(ierr);
      ierr = KSPGetConvergedReason(nep->ksp,&kspreason);CHKERRQ(ierr);
      if (kspreason<0) {
        ierr = PetscInfo1(nep,"iter=%D, linear solve failed, stopping solve\n",nep->its);CHKERRQ(ierr);
        nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
        break;
      }

      /* orthonormalize */
      ierr = BVOrthogonalizeColumn(nep->V,n,NULL,&beta,&breakdown);CHKERRQ(ierr);
      if (breakdown || beta==0.0) {
        ierr = PetscInfo1(nep,"iter=%D, orthogonalization failed, stopping solve\n",nep->its);CHKERRQ(ierr);
        nep->reason = NEP_DIVERGED_BREAKDOWN;
        break;
      }
      ierr = BVScaleColumn(nep->V,n,1.0/beta);CHKERRQ(ierr);

      /* update projected matrices */
      ierr = DSSetDimensions(nep->ds,n+1,0,0,0);CHKERRQ(ierr);
      ierr = NEPProjectOperator(nep,n,n+1);CHKERRQ(ierr);
      n++;
    }
    if (nep->its >= nep->max_it) nep->reason = NEP_DIVERGED_MAX_IT;
  }
  ierr = MatDestroy(&Tsigma);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Esempio n. 8
0
PetscErrorCode SVDSolve_TRLanczos(SVD svd)
{
  PetscErrorCode ierr;
  SVD_TRLANCZOS  *lanczos = (SVD_TRLANCZOS*)svd->data;
  PetscReal      *alpha,*beta,lastbeta,norm;
  PetscScalar    *Q,*swork=NULL,*w;
  PetscInt       i,k,l,nv,ld;
  Mat            U,VT;
  PetscBool      conv;
  BVOrthogType   orthog;

  PetscFunctionBegin;
  /* allocate working space */
  ierr = DSGetLeadingDimension(svd->ds,&ld);CHKERRQ(ierr);
  ierr = BVGetOrthogonalization(svd->V,&orthog,NULL,NULL);CHKERRQ(ierr);
  ierr = PetscMalloc1(ld,&w);CHKERRQ(ierr);
  if (lanczos->oneside && orthog == BV_ORTHOG_CGS) {
    ierr = PetscMalloc1(svd->ncv+1,&swork);CHKERRQ(ierr);
  }

  /* normalize start vector */
  if (!svd->nini) {
    ierr = BVSetRandomColumn(svd->V,0,svd->rand);CHKERRQ(ierr);
    ierr = BVNormColumn(svd->V,0,NORM_2,&norm);CHKERRQ(ierr);
    ierr = BVScaleColumn(svd->V,0,1.0/norm);CHKERRQ(ierr);
  }

  l = 0;
  while (svd->reason == SVD_CONVERGED_ITERATING) {
    svd->its++;

    /* inner loop */
    nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
    ierr = BVSetActiveColumns(svd->V,svd->nconv,nv);CHKERRQ(ierr);
    ierr = BVSetActiveColumns(svd->U,svd->nconv,nv);CHKERRQ(ierr);
    ierr = DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
    beta = alpha + ld;
    if (lanczos->oneside) {
      if (orthog == BV_ORTHOG_MGS) {
        ierr = SVDOneSideTRLanczosMGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv);CHKERRQ(ierr);
      } else {
        ierr = SVDOneSideTRLanczosCGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv,swork);CHKERRQ(ierr);
      }
    } else {
      ierr = SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv+l,nv);CHKERRQ(ierr);
    }
    lastbeta = beta[nv-1];
    ierr = DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
    ierr = BVScaleColumn(svd->V,nv,1.0/lastbeta);CHKERRQ(ierr);

    /* compute SVD of general matrix */
    ierr = DSSetDimensions(svd->ds,nv,nv,svd->nconv,svd->nconv+l);CHKERRQ(ierr);
    if (l==0) {
      ierr = DSSetState(svd->ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
    } else {
      ierr = DSSetState(svd->ds,DS_STATE_RAW);CHKERRQ(ierr);
    }
    ierr = DSSolve(svd->ds,w,NULL);CHKERRQ(ierr);
    ierr = DSSort(svd->ds,w,NULL,NULL,NULL,NULL);CHKERRQ(ierr);

    /* compute error estimates */
    k = 0;
    conv = PETSC_TRUE;
    ierr = DSGetArray(svd->ds,DS_MAT_U,&Q);CHKERRQ(ierr);
    ierr = DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
    beta = alpha + ld;
    for (i=svd->nconv;i<nv;i++) {
      svd->sigma[i] = PetscRealPart(w[i]);
      beta[i] = PetscRealPart(Q[nv-1+i*ld])*lastbeta;
      svd->errest[i] = PetscAbsScalar(beta[i]);
      if (svd->sigma[i] > svd->tol) svd->errest[i] /= svd->sigma[i];
      if (conv) {
        if (svd->errest[i] < svd->tol) k++;
        else conv = PETSC_FALSE;
      }
    }
    ierr = DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);CHKERRQ(ierr);
    ierr = DSRestoreArray(svd->ds,DS_MAT_U,&Q);CHKERRQ(ierr);

    /* check convergence and update l */
    if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;
    if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;
    if (svd->reason != SVD_CONVERGED_ITERATING) l = 0;
    else l = PetscMax((nv-svd->nconv-k)/2,0);

    /* compute converged singular vectors and restart vectors */
    ierr = DSGetMat(svd->ds,DS_MAT_VT,&VT);CHKERRQ(ierr);
    ierr = BVMultInPlaceTranspose(svd->V,VT,svd->nconv,svd->nconv+k+l);CHKERRQ(ierr);
    ierr = MatDestroy(&VT);CHKERRQ(ierr);
    ierr = DSGetMat(svd->ds,DS_MAT_U,&U);CHKERRQ(ierr);
    ierr = BVMultInPlace(svd->U,U,svd->nconv,svd->nconv+k+l);CHKERRQ(ierr);
    ierr = MatDestroy(&U);CHKERRQ(ierr);

    /* copy the last vector to be the next initial vector */
    if (svd->reason == SVD_CONVERGED_ITERATING) {
      ierr = BVCopyColumn(svd->V,nv,svd->nconv+k+l);CHKERRQ(ierr);
    }

    svd->nconv += k;
    ierr = SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);CHKERRQ(ierr);
  }

  /* orthonormalize U columns in one side method */
  if (lanczos->oneside) {
    for (i=0;i<svd->nconv;i++) {
      ierr = BVOrthogonalizeColumn(svd->U,i,NULL,&norm,NULL);CHKERRQ(ierr);
      ierr = BVScaleColumn(svd->U,i,1.0/norm);CHKERRQ(ierr);
    }
  }

  /* free working space */
  ierr = PetscFree(w);CHKERRQ(ierr);
  if (swork) { ierr = PetscFree(swork);CHKERRQ(ierr); }
  PetscFunctionReturn(0);
}
Esempio n. 9
0
static PetscErrorCode SVDOneSideTRLanczosCGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
{
  PetscErrorCode     ierr;
  PetscReal          a,b,eta;
  PetscScalar        gamma;
  PetscInt           i,j,k=nconv+l;
  Vec                ui,ui1,vi;
  BVOrthogRefineType refine;

  PetscFunctionBegin;
  ierr = BVGetColumn(V,k,&vi);CHKERRQ(ierr);
  ierr = BVGetColumn(U,k,&ui);CHKERRQ(ierr);
  ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
  ierr = BVRestoreColumn(V,k,&vi);CHKERRQ(ierr);
  ierr = BVRestoreColumn(U,k,&ui);CHKERRQ(ierr);
  if (l>0) {
    ierr = BVMultColumn(U,-1.0,1.0,k,&gamma);CHKERRQ(ierr);
    beta[nconv] = PetscRealPart(gamma);
  }
  ierr = BVGetOrthogonalization(V,NULL,&refine,&eta);CHKERRQ(ierr);

  for (i=k+1;i<n;i++) {
    ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
    ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = BVNormColumn(U,i-1,NORM_2,&a);CHKERRQ(ierr);
    if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
      ierr = BVSetActiveColumns(V,0,i+1);CHKERRQ(ierr);
      ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
      ierr = BVDotVec(V,vi,work);CHKERRQ(ierr);
      ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
      ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
    } else {
      ierr = BVSetActiveColumns(V,0,i);CHKERRQ(ierr);
      ierr = BVDotColumn(V,i,work);CHKERRQ(ierr);
    }

    ierr = BVScaleColumn(U,i-1,1.0/a);CHKERRQ(ierr);
    for (j=0;j<i;j++) work[j] = work[j] / a;
    ierr = BVMultColumn(V,-1.0,1.0/a,i,work);CHKERRQ(ierr);
    ierr = SVDOrthogonalizeCGS(V,i,work,a,refine,eta,&b);CHKERRQ(ierr);
    ierr = BVScaleColumn(V,i,1.0/b);CHKERRQ(ierr);

    ierr = BVGetColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVGetColumn(U,i,&ui);CHKERRQ(ierr);
    ierr = BVGetColumn(U,i-1,&ui1);CHKERRQ(ierr);
    ierr = SVDMatMult(svd,PETSC_FALSE,vi,ui);CHKERRQ(ierr);
    ierr = VecAXPY(ui,-b,ui1);CHKERRQ(ierr);
    ierr = BVRestoreColumn(V,i,&vi);CHKERRQ(ierr);
    ierr = BVRestoreColumn(U,i,&ui);CHKERRQ(ierr);
    ierr = BVRestoreColumn(U,i-1,&ui1);CHKERRQ(ierr);

    alpha[i-1] = a;
    beta[i-1] = b;
  }

  ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
  ierr = BVGetColumn(U,n-1,&ui1);CHKERRQ(ierr);
  ierr = SVDMatMult(svd,PETSC_TRUE,ui1,vi);CHKERRQ(ierr);
  ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
  ierr = BVRestoreColumn(U,n-1,&ui1);CHKERRQ(ierr);

  ierr = BVNormColumn(svd->U,n-1,NORM_2,&a);CHKERRQ(ierr);
  if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
    ierr = BVSetActiveColumns(V,0,n+1);CHKERRQ(ierr);
    ierr = BVGetColumn(V,n,&vi);CHKERRQ(ierr);
    ierr = BVDotVec(V,vi,work);CHKERRQ(ierr);
    ierr = BVRestoreColumn(V,n,&vi);CHKERRQ(ierr);
  } else {
    ierr = BVSetActiveColumns(V,0,n);CHKERRQ(ierr);
    ierr = BVDotColumn(V,n,work);CHKERRQ(ierr);
  }

  ierr = BVScaleColumn(U,n-1,1.0/a);CHKERRQ(ierr);
  for (j=0;j<n;j++) work[j] = work[j] / a;
  ierr = BVMultColumn(V,-1.0,1.0/a,n,work);CHKERRQ(ierr);
  ierr = SVDOrthogonalizeCGS(V,n,work,a,refine,eta,&b);CHKERRQ(ierr);
  ierr = BVSetActiveColumns(V,nconv,n);CHKERRQ(ierr);
  alpha[n-1] = a;
  beta[n-1] = b;
  PetscFunctionReturn(0);
}