PetscErrorCode NEPSetUp_NArnoldi(NEP nep) { PetscErrorCode ierr; PetscBool istrivial; PetscFunctionBegin; if (nep->ncv) { /* ncv set */ if (nep->ncv<nep->nev) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must be at least nev"); } else if (nep->mpd) { /* mpd set */ nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd); } else { /* neither set: defaults depend on nev being small or large */ if (nep->nev<500) nep->ncv = PetscMin(nep->n,PetscMax(2*nep->nev,nep->nev+15)); else { nep->mpd = 500; nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd); } } if (!nep->mpd) nep->mpd = nep->ncv; if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd"); if (!nep->max_it) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv); if (!nep->max_funcs) nep->max_funcs = nep->max_it; if (!nep->split) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NARNOLDI only available for split operator"); ierr = RGIsTrivial(nep->rg,&istrivial);CHKERRQ(ierr); if (!istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver does not support region filtering"); ierr = NEPAllocateSolution(nep,0);CHKERRQ(ierr); ierr = NEPSetWorkVecs(nep,3);CHKERRQ(ierr); /* set-up DS and transfer split operator functions */ ierr = DSSetType(nep->ds,DSNEP);CHKERRQ(ierr); ierr = DSSetFN(nep->ds,nep->nt,nep->f);CHKERRQ(ierr); ierr = DSAllocate(nep->ds,nep->ncv);CHKERRQ(ierr); PetscFunctionReturn(0); }
PetscErrorCode EPSSetUp_Arnoldi(EPS eps) { PetscErrorCode ierr; PetscFunctionBegin; ierr = EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);CHKERRQ(ierr); if (eps->ncv>eps->nev+eps->mpd) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must not be larger than nev+mpd"); if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv); if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); } if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which"); if (!eps->extraction) { ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr); } if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver"); ierr = EPSAllocateSolution(eps,1);CHKERRQ(ierr); ierr = EPS_SetInnerProduct(eps);CHKERRQ(ierr); ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr); if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) { ierr = DSSetRefined(eps->ds,PETSC_TRUE);CHKERRQ(ierr); } ierr = DSSetExtraRow(eps->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr); /* dispatch solve method */ if (eps->isgeneralized && eps->ishermitian && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method does not work for indefinite problems"); eps->ops->solve = EPSSolve_Arnoldi; PetscFunctionReturn(0); }
int main(int argc,char **argv) { PetscErrorCode ierr; DS ds; PetscScalar *A; PetscInt i,j,n=10,ld; PetscViewer viewer; PetscBool verbose; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Compute symmetric matrix exponential - dimension %D.\n",n);CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr); /* Create DS object */ ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr); ierr = DSSetType(ds,DSHEP);CHKERRQ(ierr); ierr = DSSetFromOptions(ds);CHKERRQ(ierr); ld = n+2; /* test leading dimension larger than n */ ierr = DSAllocate(ds,ld);CHKERRQ(ierr); ierr = DSSetDimensions(ds,n,0,0,0);CHKERRQ(ierr); /* Set up viewer */ ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr); ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr); if (verbose) { ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr); } /* Fill with a symmetric Toeplitz matrix */ ierr = DSGetArray(ds,DS_MAT_A,&A);CHKERRQ(ierr); for (i=0;i<n;i++) A[i+i*ld]=2.0; for (j=1;j<3;j++) { for (i=0;i<n-j;i++) { A[i+(i+j)*ld]=1.0; A[(i+j)+i*ld]=1.0; } } ierr = DSRestoreArray(ds,DS_MAT_A,&A);CHKERRQ(ierr); ierr = DSSetState(ds,DS_STATE_RAW);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Compute matrix exponential */ ierr = DSComputeFunction(ds,SLEPC_FUNCTION_EXP);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n");CHKERRQ(ierr); ierr = DSViewMat(ds,viewer,DS_MAT_F);CHKERRQ(ierr); } ierr = DSDestroy(&ds);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }
PetscErrorCode EPSSetUp_Lanczos(EPS eps) { EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data; BVOrthogRefineType refine; PetscReal eta; PetscErrorCode ierr; PetscFunctionBegin; ierr = EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);CHKERRQ(ierr); if (eps->ncv>eps->nev+eps->mpd) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must not be larger than nev+mpd"); if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv); if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); } switch (eps->which) { case EPS_LARGEST_IMAGINARY: case EPS_SMALLEST_IMAGINARY: case EPS_TARGET_IMAGINARY: SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which"); default: ; /* default case to remove warning */ } if (!eps->extraction) { ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr); } else if (eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type"); if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver"); ierr = EPSAllocateSolution(eps,1);CHKERRQ(ierr); ierr = EPS_SetInnerProduct(eps);CHKERRQ(ierr); if (lanczos->reorthog != EPS_LANCZOS_REORTHOG_FULL) { ierr = BVGetOrthogonalization(eps->V,NULL,&refine,&eta);CHKERRQ(ierr); ierr = BVSetOrthogonalization(eps->V,BV_ORTHOG_MGS,refine,eta);CHKERRQ(ierr); ierr = PetscInfo(eps,"Switching to MGS orthogonalization\n");CHKERRQ(ierr); } if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_SELECTIVE) { ierr = BVDuplicate(eps->V,&lanczos->AV);CHKERRQ(ierr); } ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr); ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr); if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) { ierr = EPSSetWorkVecs(eps,1);CHKERRQ(ierr); } /* dispatch solve method */ if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method is only available for Hermitian problems"); if (eps->isgeneralized && eps->ishermitian && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method does not work for indefinite problems"); eps->ops->solve = EPSSolve_Lanczos; PetscFunctionReturn(0); }
PetscErrorCode SVDSetUp_TRLanczos(SVD svd) { PetscErrorCode ierr; PetscInt N; PetscFunctionBegin; ierr = SVDMatGetSize(svd,NULL,&N);CHKERRQ(ierr); ierr = SVDSetDimensions_Default(svd);CHKERRQ(ierr); if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(PetscObjectComm((PetscObject)svd),1,"The value of ncv must not be larger than nev+mpd"); if (!svd->max_it) svd->max_it = PetscMax(N/svd->ncv,100); svd->leftbasis = PETSC_TRUE; ierr = SVDAllocateSolution(svd,1);CHKERRQ(ierr); ierr = DSSetType(svd->ds,DSSVD);CHKERRQ(ierr); ierr = DSSetCompact(svd->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSAllocate(svd->ds,svd->ncv);CHKERRQ(ierr); PetscFunctionReturn(0); }
int main(int argc,char **argv) { PetscErrorCode ierr; DS ds; SlepcSC sc; PetscScalar *A,*B,*wr,*wi; PetscReal re,im; PetscInt i,j,n=10,ld; PetscViewer viewer; PetscBool verbose; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GNHEP - dimension %D.\n",n);CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr); /* Create DS object */ ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr); ierr = DSSetType(ds,DSGNHEP);CHKERRQ(ierr); ierr = DSSetFromOptions(ds);CHKERRQ(ierr); ld = n+2; /* test leading dimension larger than n */ ierr = DSAllocate(ds,ld);CHKERRQ(ierr); ierr = DSSetDimensions(ds,n,0,0,0);CHKERRQ(ierr); /* Set up viewer */ ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr); ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr); if (verbose) { ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr); } /* Fill A with Grcar matrix */ ierr = DSGetArray(ds,DS_MAT_A,&A);CHKERRQ(ierr); ierr = PetscMemzero(A,sizeof(PetscScalar)*ld*n);CHKERRQ(ierr); for (i=1;i<n;i++) A[i+(i-1)*ld]=-1.0; for (j=0;j<4;j++) { for (i=0;i<n-j;i++) A[i+(i+j)*ld]=1.0; } ierr = DSRestoreArray(ds,DS_MAT_A,&A);CHKERRQ(ierr); /* Fill B with an identity matrix */ ierr = DSGetArray(ds,DS_MAT_B,&B);CHKERRQ(ierr); ierr = PetscMemzero(B,sizeof(PetscScalar)*ld*n);CHKERRQ(ierr); for (i=0;i<n;i++) B[i+i*ld]=1.0; ierr = DSRestoreArray(ds,DS_MAT_B,&B);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Solve */ ierr = PetscMalloc2(n,&wr,n,&wi);CHKERRQ(ierr); ierr = DSGetSlepcSC(ds,&sc);CHKERRQ(ierr); sc->comparison = SlepcCompareLargestMagnitude; sc->comparisonctx = NULL; sc->map = NULL; sc->mapobj = NULL; ierr = DSSolve(ds,wr,wi);CHKERRQ(ierr); ierr = DSSort(ds,wr,wi,NULL,NULL,NULL);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Print eigenvalues */ ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n",n);CHKERRQ(ierr); for (i=0;i<n;i++) { #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(wr[i]); im = PetscImaginaryPart(wr[i]); #else re = wr[i]; im = wi[i]; #endif if (PetscAbs(im)<1e-10) { ierr = PetscViewerASCIIPrintf(viewer," %.5f\n",(double)re);CHKERRQ(ierr); } else { ierr = PetscViewerASCIIPrintf(viewer," %.5f%+.5fi\n",(double)re,(double)im);CHKERRQ(ierr); } } ierr = PetscFree2(wr,wi);CHKERRQ(ierr); ierr = DSDestroy(&ds);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }
int main(int argc,char **argv) { PetscErrorCode ierr; DS ds; FN f1,f2,f3,funs[3]; PetscScalar *Id,*A,*B,*wr,*wi,coeffs[2]; PetscReal tau=0.001,h,a=20,xi,re,im; PetscInt i,n=10,ld,nev; PetscViewer viewer; PetscBool verbose; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr); ierr = PetscOptionsGetReal(NULL,"-tau",&tau,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type NEP - dimension %D, tau=%g.\n",n,(double)tau);CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr); /* Create DS object */ ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr); ierr = DSSetType(ds,DSNEP);CHKERRQ(ierr); ierr = DSSetFromOptions(ds);CHKERRQ(ierr); /* Set functions (prior to DSAllocate) */ ierr = FNCreate(PETSC_COMM_WORLD,&f1);CHKERRQ(ierr); ierr = FNSetType(f1,FNRATIONAL);CHKERRQ(ierr); coeffs[0] = -1.0; coeffs[1] = 0.0; ierr = FNSetParameters(f1,2,coeffs,0,NULL);CHKERRQ(ierr); ierr = FNCreate(PETSC_COMM_WORLD,&f2);CHKERRQ(ierr); ierr = FNSetType(f2,FNRATIONAL);CHKERRQ(ierr); coeffs[0] = 1.0; ierr = FNSetParameters(f2,1,coeffs,0,NULL);CHKERRQ(ierr); ierr = FNCreate(PETSC_COMM_WORLD,&f3);CHKERRQ(ierr); ierr = FNSetType(f3,FNEXP);CHKERRQ(ierr); coeffs[0] = -tau; ierr = FNSetParameters(f3,1,coeffs,0,NULL);CHKERRQ(ierr); funs[0] = f1; funs[1] = f2; funs[2] = f3; ierr = DSSetFN(ds,3,funs);CHKERRQ(ierr); /* Set dimensions */ ld = n+2; /* test leading dimension larger than n */ ierr = DSAllocate(ds,ld);CHKERRQ(ierr); ierr = DSSetDimensions(ds,n,0,0,0);CHKERRQ(ierr); /* Set up viewer */ ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr); ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr); if (verbose) { ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr); } /* Fill matrices */ ierr = DSGetArray(ds,DS_MAT_E0,&Id);CHKERRQ(ierr); for (i=0;i<n;i++) Id[i+i*ld]=1.0; ierr = DSRestoreArray(ds,DS_MAT_E0,&Id);CHKERRQ(ierr); h = PETSC_PI/(PetscReal)(n+1); ierr = DSGetArray(ds,DS_MAT_E1,&A);CHKERRQ(ierr); for (i=0;i<n;i++) A[i+i*ld]=-2.0/(h*h)+a; for (i=1;i<n;i++) { A[i+(i-1)*ld]=1.0/(h*h); A[(i-1)+i*ld]=1.0/(h*h); } ierr = DSRestoreArray(ds,DS_MAT_E1,&A);CHKERRQ(ierr); ierr = DSGetArray(ds,DS_MAT_E2,&B);CHKERRQ(ierr); for (i=0;i<n;i++) { xi = (i+1)*h; B[i+i*ld] = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI)); } ierr = DSRestoreArray(ds,DS_MAT_E2,&B);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Solve */ ierr = PetscMalloc2(n,&wr,n,&wi);CHKERRQ(ierr); ierr = DSSolve(ds,wr,wi);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Print first eigenvalue */ ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalue =\n",n);CHKERRQ(ierr); nev = 1; for (i=0;i<nev;i++) { #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(wr[i]); im = PetscImaginaryPart(wr[i]); #else re = wr[i]; im = wi[i]; #endif if (PetscAbs(im)<1e-10) { ierr = PetscViewerASCIIPrintf(viewer," %.5f\n",(double)re);CHKERRQ(ierr); } else { ierr = PetscViewerASCIIPrintf(viewer," %.5f%+.5fi\n",(double)re,(double)im);CHKERRQ(ierr); } } ierr = PetscFree2(wr,wi);CHKERRQ(ierr); ierr = FNDestroy(&f1);CHKERRQ(ierr); ierr = FNDestroy(&f2);CHKERRQ(ierr); ierr = FNDestroy(&f3);CHKERRQ(ierr); ierr = DSDestroy(&ds);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }
PetscErrorCode EPSSetUp_LAPACK(EPS eps) { PetscErrorCode ierr,ierra,ierrb; PetscBool isshift,denseok=PETSC_FALSE; Mat A,B,OP,Adense,Bdense; PetscScalar shift,*Ap,*Bp; PetscInt i,ld,nmat; KSP ksp; PC pc; Vec v; PetscFunctionBegin; eps->ncv = eps->n; if (eps->mpd) { ierr = PetscInfo(eps,"Warning: parameter mpd ignored\n");CHKERRQ(ierr); } if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); } if (eps->balance!=EPS_BALANCE_NONE) { ierr = PetscInfo(eps,"Warning: balancing ignored\n");CHKERRQ(ierr); } if (eps->extraction) { ierr = PetscInfo(eps,"Warning: extraction type ignored\n");CHKERRQ(ierr); } ierr = EPSAllocateSolution(eps,0);CHKERRQ(ierr); /* attempt to get dense representations of A and B separately */ ierr = PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&isshift);CHKERRQ(ierr); if (isshift) { ierr = STGetNumMatrices(eps->st,&nmat);CHKERRQ(ierr); ierr = STGetOperators(eps->st,0,&A);CHKERRQ(ierr); if (nmat>1) { ierr = STGetOperators(eps->st,1,&B);CHKERRQ(ierr); } PetscPushErrorHandler(PetscIgnoreErrorHandler,NULL); ierra = SlepcMatConvertSeqDense(A,&Adense);CHKERRQ(ierr); if (eps->isgeneralized) { ierrb = SlepcMatConvertSeqDense(B,&Bdense);CHKERRQ(ierr); } else { ierrb = 0; } PetscPopErrorHandler(); denseok = (ierra == 0 && ierrb == 0)? PETSC_TRUE: PETSC_FALSE; } else Adense = NULL; /* setup DS */ if (denseok) { if (eps->isgeneralized) { if (eps->ishermitian) { if (eps->ispositive) { ierr = DSSetType(eps->ds,DSGHEP);CHKERRQ(ierr); } else { ierr = DSSetType(eps->ds,DSGNHEP);CHKERRQ(ierr); /* TODO: should be DSGHIEP */ } } else { ierr = DSSetType(eps->ds,DSGNHEP);CHKERRQ(ierr); } } else { if (eps->ishermitian) { ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr); } else { ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr); } } } else { ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr); } ierr = DSAllocate(eps->ds,eps->ncv);CHKERRQ(ierr); ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr); ierr = DSSetDimensions(eps->ds,eps->ncv,0,0,0);CHKERRQ(ierr); if (denseok) { ierr = STGetShift(eps->st,&shift);CHKERRQ(ierr); if (shift != 0.0) { ierr = MatShift(Adense,shift);CHKERRQ(ierr); } /* use dummy pc and ksp to avoid problems when B is not positive definite */ ierr = STGetKSP(eps->st,&ksp);CHKERRQ(ierr); ierr = KSPSetType(ksp,KSPPREONLY);CHKERRQ(ierr); ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr); ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr); } else { ierr = PetscInfo(eps,"Using slow explicit operator\n");CHKERRQ(ierr); ierr = STComputeExplicitOperator(eps->st,&OP);CHKERRQ(ierr); ierr = MatDestroy(&Adense);CHKERRQ(ierr); ierr = SlepcMatConvertSeqDense(OP,&Adense);CHKERRQ(ierr); } /* fill DS matrices */ ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,ld,NULL,&v);CHKERRQ(ierr); ierr = DSGetArray(eps->ds,DS_MAT_A,&Ap);CHKERRQ(ierr); for (i=0;i<ld;i++) { ierr = VecPlaceArray(v,Ap+i*ld);CHKERRQ(ierr); ierr = MatGetColumnVector(Adense,v,i);CHKERRQ(ierr); ierr = VecResetArray(v);CHKERRQ(ierr); } ierr = DSRestoreArray(eps->ds,DS_MAT_A,&Ap);CHKERRQ(ierr); if (denseok && eps->isgeneralized) { ierr = DSGetArray(eps->ds,DS_MAT_B,&Bp);CHKERRQ(ierr); for (i=0;i<ld;i++) { ierr = VecPlaceArray(v,Bp+i*ld);CHKERRQ(ierr); ierr = MatGetColumnVector(Bdense,v,i);CHKERRQ(ierr); ierr = VecResetArray(v);CHKERRQ(ierr); } ierr = DSRestoreArray(eps->ds,DS_MAT_B,&Bp);CHKERRQ(ierr); } ierr = VecDestroy(&v);CHKERRQ(ierr); ierr = MatDestroy(&Adense);CHKERRQ(ierr); if (!denseok) { ierr = MatDestroy(&OP);CHKERRQ(ierr); } if (denseok && eps->isgeneralized) { ierr = MatDestroy(&Bdense);CHKERRQ(ierr); } PetscFunctionReturn(0); }
int main(int argc,char **argv) { PetscErrorCode ierr; DS ds; SlepcSC sc; PetscReal *T,*s,re,im; PetscScalar *eigr,*eigi; PetscInt i,n=10,l=2,k=5,ld; PetscViewer viewer; PetscBool verbose; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type GHIEP with compact storage - dimension %D.\n",n);CHKERRQ(ierr); ierr = PetscOptionsGetInt(NULL,"-l",&l,NULL);CHKERRQ(ierr); ierr = PetscOptionsGetInt(NULL,"-k",&k,NULL);CHKERRQ(ierr); if (l>n || k>n || l>k) SETERRQ(PETSC_COMM_WORLD,1,"Wrong value of dimensions"); ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr); /* Create DS object */ ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr); ierr = DSSetType(ds,DSGHIEP);CHKERRQ(ierr); ierr = DSSetFromOptions(ds);CHKERRQ(ierr); ld = n+2; /* test leading dimension larger than n */ ierr = DSAllocate(ds,ld);CHKERRQ(ierr); ierr = DSSetDimensions(ds,n,0,l,k);CHKERRQ(ierr); ierr = DSSetCompact(ds,PETSC_TRUE);CHKERRQ(ierr); /* Set up viewer */ ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr); ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr); if (verbose) { ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr); } /* Fill arrow-tridiagonal matrix */ ierr = DSGetArrayReal(ds,DS_MAT_T,&T);CHKERRQ(ierr); ierr = DSGetArrayReal(ds,DS_MAT_D,&s);CHKERRQ(ierr); for (i=0;i<n;i++) T[i] = (PetscReal)(i+1); for (i=k;i<n-1;i++) T[i+ld] = 1.0; for (i=l;i<k;i++) T[i+2*ld] = 1.0; T[2*ld+l+1] = -7; T[ld+k+1] = -7; /* Signature matrix */ for (i=0;i<n;i++) s[i] = 1.0; s[l+1] = -1.0; s[k+1] = -1.0; ierr = DSRestoreArrayReal(ds,DS_MAT_T,&T);CHKERRQ(ierr); ierr = DSRestoreArrayReal(ds,DS_MAT_D,&s);CHKERRQ(ierr); if (l==0 && k==0) { ierr = DSSetState(ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr); } else { ierr = DSSetState(ds,DS_STATE_RAW);CHKERRQ(ierr); } if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Solve */ ierr = PetscCalloc2(n,&eigr,n,&eigi);CHKERRQ(ierr); ierr = DSGetSlepcSC(ds,&sc);CHKERRQ(ierr); sc->comparison = SlepcCompareLargestMagnitude; sc->comparisonctx = NULL; sc->map = NULL; sc->mapobj = NULL; ierr = DSSolve(ds,eigr,eigi);CHKERRQ(ierr); ierr = DSSort(ds,eigr,eigi,NULL,NULL,NULL);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Print eigenvalues */ ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n",n);CHKERRQ(ierr); for (i=0;i<n;i++) { #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(eigr[i]); im = PetscImaginaryPart(eigr[i]); #else re = eigr[i]; im = eigi[i]; #endif if (PetscAbs(im)<1e-10) { ierr = PetscViewerASCIIPrintf(viewer," %.5f\n",(double)re);CHKERRQ(ierr); } else { ierr = PetscViewerASCIIPrintf(viewer," %.5f%+.5fi\n",(double)re,(double)im);CHKERRQ(ierr); } } ierr = PetscFree2(eigr,eigi);CHKERRQ(ierr); ierr = DSDestroy(&ds);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }
PetscErrorCode EPSSetUp_KrylovSchur(EPS eps) { PetscErrorCode ierr; EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data; enum { EPS_KS_DEFAULT,EPS_KS_SYMM,EPS_KS_SLICE,EPS_KS_INDEF } variant; PetscFunctionBegin; /* spectrum slicing requires special treatment of default values */ if (eps->which==EPS_ALL) { ierr = EPSSetUp_KrylovSchur_Slice(eps);CHKERRQ(ierr); } else { ierr = EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);CHKERRQ(ierr); if (eps->ncv>eps->nev+eps->mpd) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must not be larger than nev+mpd"); if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv); if (!eps->which) { ierr = EPSSetWhichEigenpairs_Default(eps);CHKERRQ(ierr); } } if (eps->isgeneralized && eps->ishermitian && !eps->ispositive && eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not implemented for indefinite problems"); if (eps->ishermitian && eps->ispositive && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which"); if (!eps->extraction) { ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr); } else if (eps->extraction!=EPS_RITZ && eps->extraction!=EPS_HARMONIC) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type"); if (!ctx->keep) ctx->keep = 0.5; ierr = EPSAllocateSolution(eps,1);CHKERRQ(ierr); ierr = EPS_SetInnerProduct(eps);CHKERRQ(ierr); if (eps->arbitrary) { ierr = EPSSetWorkVecs(eps,2);CHKERRQ(ierr); } else if (eps->ishermitian && !eps->ispositive){ ierr = EPSSetWorkVecs(eps,1);CHKERRQ(ierr); } /* dispatch solve method */ if (eps->ishermitian) { if (eps->which==EPS_ALL) { if (eps->isgeneralized && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing not implemented for indefinite problems"); else variant = EPS_KS_SLICE; } else if (eps->isgeneralized && !eps->ispositive) { variant = EPS_KS_INDEF; } else { switch (eps->extraction) { case EPS_RITZ: variant = EPS_KS_SYMM; break; case EPS_HARMONIC: variant = EPS_KS_DEFAULT; break; default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type"); } } } else { switch (eps->extraction) { case EPS_RITZ: variant = EPS_KS_DEFAULT; break; case EPS_HARMONIC: variant = EPS_KS_DEFAULT; break; default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type"); } } switch (variant) { case EPS_KS_DEFAULT: eps->ops->solve = EPSSolve_KrylovSchur_Default; eps->ops->computevectors = EPSComputeVectors_Schur; ierr = DSSetType(eps->ds,DSNHEP);CHKERRQ(ierr); ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr); break; case EPS_KS_SYMM: eps->ops->solve = EPSSolve_KrylovSchur_Symm; eps->ops->computevectors = EPSComputeVectors_Hermitian; ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr); ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSSetExtraRow(eps->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr); break; case EPS_KS_SLICE: eps->ops->solve = EPSSolve_KrylovSchur_Slice; eps->ops->computevectors = NULL; ierr = DSSetType(eps->ds,DSHEP);CHKERRQ(ierr); ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSAllocate(eps->ds,ctx->ncv+1);CHKERRQ(ierr); break; case EPS_KS_INDEF: eps->ops->solve = EPSSolve_KrylovSchur_Indefinite; eps->ops->computevectors = EPSComputeVectors_Indefinite; ierr = DSSetType(eps->ds,DSGHIEP);CHKERRQ(ierr); ierr = DSSetCompact(eps->ds,PETSC_TRUE);CHKERRQ(ierr); ierr = DSAllocate(eps->ds,eps->ncv+1);CHKERRQ(ierr); break; default: SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error"); } PetscFunctionReturn(0); }
int main(int argc,char **argv) { PetscErrorCode ierr; DS ds; SlepcSC sc; PetscScalar *A,*eig; PetscInt i,j,n,ld,bs,maxbw=3,nblks=8; PetscViewer viewer; PetscBool verbose; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(NULL,"-maxbw",&maxbw,NULL);CHKERRQ(ierr); ierr = PetscOptionsGetInt(NULL,"-nblks",&nblks,NULL);CHKERRQ(ierr); n = maxbw*nblks; bs = maxbw; ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a block HEP Dense System - dimension %D (bandwidth=%D, blocks=%D).\n",n,maxbw,nblks);CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr); /* Create DS object */ ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr); ierr = DSSetType(ds,DSHEP);CHKERRQ(ierr); ierr = DSSetMethod(ds,3);CHKERRQ(ierr); /* Select block divide-and-conquer */ ierr = DSSetBlockSize(ds,bs);CHKERRQ(ierr); ierr = DSSetFromOptions(ds);CHKERRQ(ierr); ld = n; ierr = DSAllocate(ds,ld);CHKERRQ(ierr); ierr = DSSetDimensions(ds,n,0,0,0);CHKERRQ(ierr); /* Set up viewer */ ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr); ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr); if (verbose) { ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr); } /* Fill with a symmetric band Toeplitz matrix */ ierr = DSGetArray(ds,DS_MAT_A,&A);CHKERRQ(ierr); for (i=0;i<n;i++) A[i+i*ld]=2.0; for (j=1;j<=bs;j++) { for (i=0;i<n-j;i++) { A[i+(i+j)*ld]=1.0; A[(i+j)+i*ld]=1.0; } } ierr = DSRestoreArray(ds,DS_MAT_A,&A);CHKERRQ(ierr); ierr = DSSetState(ds,DS_STATE_RAW);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Solve */ ierr = PetscMalloc1(n,&eig);CHKERRQ(ierr); ierr = DSGetSlepcSC(ds,&sc);CHKERRQ(ierr); sc->comparison = SlepcCompareSmallestReal; sc->comparisonctx = NULL; sc->map = NULL; sc->mapobj = NULL; ierr = DSSolve(ds,eig,NULL);CHKERRQ(ierr); ierr = DSSort(ds,eig,NULL,NULL,NULL,NULL);CHKERRQ(ierr); if (verbose) { ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr); ierr = DSView(ds,viewer);CHKERRQ(ierr); } /* Print eigenvalues */ ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n",n);CHKERRQ(ierr); for (i=0;i<n;i++) { ierr = PetscViewerASCIIPrintf(viewer," %.5f\n",(double)PetscRealPart(eig[i]));CHKERRQ(ierr); } ierr = PetscFree(eig);CHKERRQ(ierr); ierr = DSDestroy(&ds);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }