Real SlepcEigenSolver<T>::get_relative_error(unsigned int i) { int ierr=0; PetscReal error; ierr = EPSComputeRelativeError(_eps, i, &error); LIBMESH_CHKERRABORT(ierr); return error; }
Real SlepcEigenSolver<T>::get_relative_error(unsigned int i) { int ierr=0; PetscReal error; ierr = EPSComputeRelativeError(_eps, i, &error); CHKERRABORT(libMesh::COMM_WORLD,ierr); return error; }
Real SlepcEigenSolver<T>::get_relative_error(unsigned int i) { PetscErrorCode ierr=0; PetscReal error; #if SLEPC_VERSION_LESS_THAN(3,6,0) ierr = EPSComputeRelativeError(_eps, i, &error); #else ierr = EPSComputeError(_eps, i, EPS_ERROR_RELATIVE, &error); #endif LIBMESH_CHKERR(ierr); return error; }
int main(int argc,char **args) { Mat A; PetscInt i; PetscErrorCode ierr; char file[PETSC_MAX_PATH_LEN]; PetscLogDouble numberOfFlops, tsolve1, tsolve2; EPS eps; /* eigenproblem solver context */ const EPSType type; PetscReal error,tol,re,im; PetscScalar kr,ki; Vec xr=0,xi=0; PetscInt nev,maxit,its,nconv; EPSWhich which; EPSProblemType problemType; PetscMPIInt rank; PetscMPIInt numberOfProcessors; PetscBool flg; PetscBool isComplex; PetscViewer fd; SlepcInitialize(&argc,&args,(char*)0,help); ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr); ierr = MPI_Comm_size(PETSC_COMM_WORLD,&numberOfProcessors);CHKERRQ(ierr); ierr = PetscOptionsGetString(PETSC_NULL,"-fin",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr); if (!flg) { SETERRQ(PETSC_COMM_WORLD,1,"Must indicate matrix file with the -fin option"); } /* Read file */ ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr); // Create matrix ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); // Load matrix from file ierr = MatLoad(A,fd);CHKERRQ(ierr); // Destroy viewer ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr); // Assemble matrix ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); //ierr = PetscPrintf(PETSC_COMM_SELF,"Reading matrix completes.\n");CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create the eigensolver and set various options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Create eigensolver context */ ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr); /* Set operators. In this case, it is a standard eigenvalue problem */ ierr = EPSSetOperators(eps,A,PETSC_NULL);CHKERRQ(ierr); //ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr); /* Set solver parameters at runtime */ ierr = EPSSetFromOptions(eps);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve the eigensystem - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscTime(tsolve1); ierr = EPSSolve(eps);CHKERRQ(ierr); PetscTime(tsolve2); /* Optional: Get some information from the solver and display it */ ierr = EPSGetProblemType(eps, &problemType);CHKERRQ(ierr); ierr = EPSGetWhichEigenpairs(eps, &which);CHKERRQ(ierr); ierr = EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); ierr = EPSGetType(eps,&type);CHKERRQ(ierr); ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr); ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr); ierr = EPSGetIterationNumber(eps,&its);CHKERRQ(ierr); ierr = PetscGetFlops(&numberOfFlops);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) isComplex = 1; #else isComplex = 0; #endif //Print output: ierr = PetscPrintf(PETSC_COMM_WORLD,"%D\t %D\t %D\t %D\t %D\t %.4G\t %s\t %D\t %D\t %F\t %2.1e\t",isComplex, numberOfProcessors, problemType, which, nev, tol, type, nconv, its, numberOfFlops, (tsolve2-tsolve1));CHKERRQ(ierr); if (nconv>0) { for (i=0;i<nconv;i++) { /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and ki (imaginary part) */ ierr = EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);CHKERRQ(ierr); /* Compute the relative error associated to each eigenpair */ ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im!=0.0) { // ierr = PetscPrintf(PETSC_COMM_WORLD," %9F%+9F j %12G\n",re,im,error);CHKERRQ(ierr); } else { // ierr = PetscPrintf(PETSC_COMM_WORLD," %12F %12G\n",re,error);CHKERRQ(ierr); } ierr = PetscPrintf(PETSC_COMM_WORLD,"%12G\t", error);CHKERRQ(ierr); } } ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr); //Destructors ierr = MatDestroy(&A);CHKERRQ(ierr); //ierr = PetscFinalize(); ierr = SlepcFinalize();CHKERRQ(ierr); return 0; }
PETSC_EXTERN void PETSC_STDCALL epscomputerelativeerror_(EPS *eps,PetscInt *i,PetscReal *error, int *__ierr ){ *__ierr = EPSComputeRelativeError(*eps,*i,error); }
int SolarEigenvaluesSolver(Mat M, Vec epsCurrent, Vec epspmlQ, Mat D) { PetscErrorCode ierr; EPS eps; PetscInt nconv; Mat B; int nrow, ncol; ierr=MatGetSize(M,&nrow, &ncol); CHKERRQ(ierr); ierr=MatCreateAIJ(PETSC_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, nrow, ncol, 2, NULL, 2, NULL, &B); CHKERRQ(ierr); ierr=PetscObjectSetName((PetscObject)B, "epsmatrix"); CHKERRQ(ierr); if (D==PETSC_NULL) { // for purely real epsC, no absorption; ierr=MatDiagonalSet(B,epsCurrent,INSERT_VALUES); CHKERRQ(ierr); MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY); MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY); } else { Vec epsC; VecDuplicate(epsCurrent, &epsC); ierr = VecPointwiseMult(epsC, epsCurrent,epspmlQ); CHKERRQ(ierr); MatSetTwoDiagonals(B, epsC, D, 1.0); VecDestroy(&epsC); } PetscPrintf(PETSC_COMM_WORLD,"!!!---computing eigenvalues---!!! \n"); ierr=EPSCreate(PETSC_COMM_WORLD, &eps); CHKERRQ(ierr); ierr=EPSSetOperators(eps, M, B); CHKERRQ(ierr); //ierr=EPSSetProblemType(eps,EPS_PGNHEP);CHKERRQ(ierr); EPSSetFromOptions(eps); PetscLogDouble t1, t2, tpast; ierr = PetscTime(&t1);CHKERRQ(ierr); ierr=EPSSolve(eps); CHKERRQ(ierr); EPSGetConverged(eps, &nconv); CHKERRQ(ierr); { ierr = PetscTime(&t2);CHKERRQ(ierr); tpast = t2 - t1; int rank; MPI_Comm_rank(MPI_COMM_WORLD, &rank); if(rank==0) PetscPrintf(PETSC_COMM_SELF,"---The eigensolver time is %f s \n",tpast); } ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of converged eigenpairs: %d\n\n",nconv);CHKERRQ(ierr); double *krarray, *kiarray, *errorarray; krarray = (double *) malloc(sizeof(double)*nconv); kiarray = (double *) malloc(sizeof(double)*nconv); errorarray =(double *) malloc(sizeof(double)*nconv); int ni; for(ni=0; ni<nconv; ni++) { ierr=EPSGetEigenpair(eps,ni, krarray+ni,kiarray+ni,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); ierr = EPSComputeRelativeError(eps,ni,errorarray+ni);CHKERRQ(ierr); ierr=EPSComputeRelativeError(eps, ni, errorarray+ni ); } PetscPrintf(PETSC_COMM_WORLD, "Now print the eigenvalues: \n"); for(ni=0; ni<nconv; ni++) PetscPrintf(PETSC_COMM_WORLD," %g%+gi,", krarray[ni], kiarray[ni]); PetscPrintf(PETSC_COMM_WORLD, "\n\nNow print the normalized eigenvalues: \n"); for(ni=0; ni<nconv; ni++) PetscPrintf(PETSC_COMM_WORLD," %g%+gi,", sqrt(krarray[ni]+pow(omega,2))/(2*PI),kiarray[ni]); PetscPrintf(PETSC_COMM_WORLD, "\n\nstart printing erros"); for(ni=0; ni<nconv; ni++) PetscPrintf(PETSC_COMM_WORLD," %g,", errorarray[ni]); PetscPrintf(PETSC_COMM_WORLD,"\n\n Finish EPS Solving !!! \n\n"); /*-- destroy vectors and free space --*/ EPSDestroy(&eps); MatDestroy(&B); free(krarray); free(kiarray); free(errorarray); PetscFunctionReturn(0); }
int main( int argc, char **argv ) { Mat A; /* operator matrix */ Vec x; EPS eps; /* eigenproblem solver context */ const EPSType type; PetscReal error, tol, re, im; PetscScalar kr, ki; PetscErrorCode ierr; PetscInt N, n=10, m, i, j, II, Istart, Iend, nev, maxit, its, nconv; PetscScalar w; PetscBool flag; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr); ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);CHKERRQ(ierr); if(!flag) m=n; N = n*m; ierr = PetscPrintf(PETSC_COMM_WORLD,"\nFiedler vector of a 2-D regular mesh, N=%d (%dx%d grid)\n\n",N,n,m);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Compute the operator matrix that defines the eigensystem, Ax=kx In this example, A = L(G), where L is the Laplacian of graph G, i.e. Lii = degree of node i, Lij = -1 if edge (i,j) exists in G - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr); for( II=Istart; II<Iend; II++ ) { i = II/n; j = II-i*n; w = 0.0; if(i>0) { ierr = MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; } if(i<m-1) { ierr = MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; } if(j>0) { ierr = MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; } if(j<n-1) { ierr = MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); w=w+1.0; } ierr = MatSetValue(A,II,II,w,INSERT_VALUES);CHKERRQ(ierr); } ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create the eigensolver and set various options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Create eigensolver context */ ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr); /* Set operators. In this case, it is a standard eigenvalue problem */ ierr = EPSSetOperators(eps,A,PETSC_NULL);CHKERRQ(ierr); ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr); /* Select portion of spectrum */ ierr = EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);CHKERRQ(ierr); /* Set solver parameters at runtime */ ierr = EPSSetFromOptions(eps);CHKERRQ(ierr); /* Attach deflation space: in this case, the matrix has a constant nullspace, [1 1 ... 1]^T is the eigenvector of the zero eigenvalue */ ierr = MatGetVecs(A,&x,PETSC_NULL);CHKERRQ(ierr); ierr = VecSet(x,1.0);CHKERRQ(ierr); ierr = EPSSetDeflationSpace(eps,1,&x);CHKERRQ(ierr); ierr = VecDestroy(x); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve the eigensystem - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = EPSSolve(eps);CHKERRQ(ierr); ierr = EPSGetIterationNumber(eps, &its);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);CHKERRQ(ierr); /* Optional: Get some information from the solver and display it */ ierr = EPSGetType(eps,&type);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr); ierr = EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);CHKERRQ(ierr); ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Display solution and clean up - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Get number of converged approximate eigenpairs */ ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv); CHKERRQ(ierr); if (nconv>0) { /* Display eigenvalues and relative errors */ ierr = PetscPrintf(PETSC_COMM_WORLD, " k ||Ax-kx||/||kx||\n" " ----------------- ------------------\n" );CHKERRQ(ierr); for( i=0; i<nconv; i++ ) { /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and ki (imaginary part) */ ierr = EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr); /* Compute the relative error associated to each eigenpair */ ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr); #ifdef PETSC_USE_COMPLEX re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im!=0.0) { ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);CHKERRQ(ierr); } else { ierr = PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",re,error);CHKERRQ(ierr); } } ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr); } /* Free work space */ ierr = EPSDestroy(eps);CHKERRQ(ierr); ierr = MatDestroy(A);CHKERRQ(ierr); ierr = SlepcFinalize();CHKERRQ(ierr); return 0; }
bool eigenSolver::solve(int numEigenValues, std::string which) { if(!_A) return false; Mat A = _A->getMatrix(); Mat B = _B ? _B->getMatrix() : PETSC_NULL; PetscInt N, M; _try(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); _try(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); _try(MatGetSize(A, &N, &M)); PetscInt N2, M2; if (_B) { _try(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); _try(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); _try(MatGetSize(B, &N2, &M2)); } // generalized eigenvalue problem A x - \lambda B x = 0 EPS eps; _try(EPSCreate(PETSC_COMM_WORLD, &eps)); _try(EPSSetOperators(eps, A, B)); if(_hermitian) _try(EPSSetProblemType(eps, _B ? EPS_GHEP : EPS_HEP)); else _try(EPSSetProblemType(eps, _B ? EPS_GNHEP : EPS_NHEP)); // set some default options _try(EPSSetDimensions(eps, numEigenValues, PETSC_DECIDE, PETSC_DECIDE)); _try(EPSSetTolerances(eps, 1.e-7, 20));//1.e-7 20 _try(EPSSetType(eps, EPSKRYLOVSCHUR)); //default //_try(EPSSetType(eps, EPSARNOLDI)); //_try(EPSSetType(eps, EPSARPACK)); //_try(EPSSetType(eps, EPSPOWER)); // override these options at runtime, petsc-style _try(EPSSetFromOptions(eps)); // force options specified directly as arguments if(numEigenValues) _try(EPSSetDimensions(eps, numEigenValues, PETSC_DECIDE, PETSC_DECIDE)); if(which == "smallest") _try(EPSSetWhichEigenpairs(eps, EPS_SMALLEST_MAGNITUDE)); else if(which == "smallestReal") _try(EPSSetWhichEigenpairs(eps, EPS_SMALLEST_REAL)); else if(which == "largest") _try(EPSSetWhichEigenpairs(eps, EPS_LARGEST_MAGNITUDE)); // print info #if (SLEPC_VERSION_RELEASE == 0 || (SLEPC_VERSION_MAJOR > 3 || (SLEPC_VERSION_MAJOR == 3 && SLEPC_VERSION_MINOR >= 4))) EPSType type; #else const EPSType type; #endif _try(EPSGetType(eps, &type)); Msg::Debug("SLEPc solution method: %s", type); PetscInt nev; _try(EPSGetDimensions(eps, &nev, PETSC_NULL, PETSC_NULL)); Msg::Debug("SLEPc number of requested eigenvalues: %d", nev); PetscReal tol; PetscInt maxit; _try(EPSGetTolerances(eps, &tol, &maxit)); Msg::Debug("SLEPc stopping condition: tol=%g, maxit=%d", tol, maxit); // solve Msg::Info("SLEPc solving..."); double t1 = Cpu(); _try(EPSSolve(eps)); // check convergence int its; _try(EPSGetIterationNumber(eps, &its)); EPSConvergedReason reason; _try(EPSGetConvergedReason(eps, &reason)); if(reason == EPS_CONVERGED_TOL){ double t2 = Cpu(); Msg::Debug("SLEPc converged in %d iterations (%g s)", its, t2-t1); } else if(reason == EPS_DIVERGED_ITS) Msg::Error("SLEPc diverged after %d iterations", its); else if(reason == EPS_DIVERGED_BREAKDOWN) Msg::Error("SLEPc generic breakdown in method"); #if (SLEPC_VERSION_MAJOR < 3 || (SLEPC_VERSION_MAJOR == 3 && SLEPC_VERSION_MINOR < 2)) else if(reason == EPS_DIVERGED_NONSYMMETRIC) Msg::Error("The operator is nonsymmetric"); #endif // get number of converged approximate eigenpairs PetscInt nconv; _try(EPSGetConverged(eps, &nconv)); Msg::Debug("SLEPc number of converged eigenpairs: %d", nconv); // ignore additional eigenvalues if we get more than what we asked if(nconv > nev) nconv = nev; if (nconv > 0) { Vec xr, xi; _try(MatGetVecs(A, PETSC_NULL, &xr)); _try(MatGetVecs(A, PETSC_NULL, &xi)); Msg::Debug(" Re[EigenValue] Im[EigenValue]" " Relative error"); for (int i = 0; i < nconv; i++){ PetscScalar kr, ki; _try(EPSGetEigenpair(eps, i, &kr, &ki, xr, xi)); PetscReal error; _try(EPSComputeRelativeError(eps, i, &error)); #if defined(PETSC_USE_COMPLEX) PetscReal re = PetscRealPart(kr); PetscReal im = PetscImaginaryPart(kr); #else PetscReal re = kr; PetscReal im = ki; #endif Msg::Debug("EIG %03d %s%.16e %s%.16e %3.6e", i, (re < 0) ? "" : " ", re, (im < 0) ? "" : " ", im, error); // store eigenvalues and eigenvectors _eigenValues.push_back(std::complex<double>(re, im)); PetscScalar *tmpr, *tmpi; _try(VecGetArray(xr, &tmpr)); _try(VecGetArray(xi, &tmpi)); std::vector<std::complex<double> > ev(N); for(int i = 0; i < N; i++){ #if defined(PETSC_USE_COMPLEX) ev[i] = tmpr[i]; #else ev[i] = std::complex<double>(tmpr[i], tmpi[i]); #endif } _eigenVectors.push_back(ev); } _try(VecDestroy(&xr)); _try(VecDestroy(&xi)); } _try(EPSDestroy(&eps)); if(reason == EPS_CONVERGED_TOL){ Msg::Debug("SLEPc done"); return true; } else{ Msg::Warning("SLEPc failed"); return false; } }
std::pair<unsigned int, unsigned int> SlepcEigenSolver<T>::_solve_generalized_helper (Mat mat_A, Mat mat_B, int nev, // number of requested eigenpairs int ncv, // number of basis vectors const double tol, // solver tolerance const unsigned int m_its) // maximum number of iterations { START_LOG("solve_generalized()", "SlepcEigenSolver"); int ierr=0; // converged eigen pairs and number of iterations int nconv=0; int its=0; #ifdef DEBUG // The relative error. PetscReal error, re, im; // Pointer to vectors of the real parts, imaginary parts. PetscScalar kr, ki; #endif // Set operators. ierr = EPSSetOperators (_eps, mat_A, mat_B); LIBMESH_CHKERRABORT(ierr); //set the problem type and the position of the spectrum set_slepc_problem_type(); set_slepc_position_of_spectrum(); // Set eigenvalues to be computed. #if SLEPC_VERSION_LESS_THAN(3,0,0) ierr = EPSSetDimensions (_eps, nev, ncv); #else ierr = EPSSetDimensions (_eps, nev, ncv, PETSC_DECIDE); #endif LIBMESH_CHKERRABORT(ierr); // Set the tolerance and maximum iterations. ierr = EPSSetTolerances (_eps, tol, m_its); LIBMESH_CHKERRABORT(ierr); // Set runtime options, e.g., // -eps_type <type>, -eps_nev <nev>, -eps_ncv <ncv> // Similar to PETSc, these options will override those specified // above as long as EPSSetFromOptions() is called _after_ any // other customization routines. ierr = EPSSetFromOptions (_eps); LIBMESH_CHKERRABORT(ierr); // Solve the eigenproblem. ierr = EPSSolve (_eps); LIBMESH_CHKERRABORT(ierr); // Get the number of iterations. ierr = EPSGetIterationNumber (_eps, &its); LIBMESH_CHKERRABORT(ierr); // Get number of converged eigenpairs. ierr = EPSGetConverged(_eps,&nconv); LIBMESH_CHKERRABORT(ierr); #ifdef DEBUG // ierr = PetscPrintf(this->comm().get(), // "\n Number of iterations: %d\n" // " Number of converged eigenpairs: %d\n\n", its, nconv); // Display eigenvalues and relative errors. ierr = PetscPrintf(this->comm().get(), " k ||Ax-kx||/|kx|\n" " ----------------- -----------------\n" ); LIBMESH_CHKERRABORT(ierr); for(int i=0; i<nconv; i++ ) { ierr = EPSGetEigenpair(_eps, i, &kr, &ki, PETSC_NULL, PETSC_NULL); LIBMESH_CHKERRABORT(ierr); ierr = EPSComputeRelativeError(_eps, i, &error); LIBMESH_CHKERRABORT(ierr); #ifdef LIBMESH_USE_COMPLEX_NUMBERS re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im != .0) { ierr = PetscPrintf(this->comm().get()," %9f%+9f i %12f\n", re, im, error); LIBMESH_CHKERRABORT(ierr); } else { ierr = PetscPrintf(this->comm().get()," %12f %12f\n", re, error); LIBMESH_CHKERRABORT(ierr); } } ierr = PetscPrintf(this->comm().get(),"\n" ); LIBMESH_CHKERRABORT(ierr); #endif // DEBUG STOP_LOG("solve_generalized()", "SlepcEigenSolver"); // return the number of converged eigenpairs // and the number of iterations return std::make_pair(nconv, its); }
/*@ EPSPrintSolution - Prints the computed eigenvalues. Collective on EPS Input Parameters: + eps - the eigensolver context - viewer - optional visualization context Options Database Key: . -eps_terse - print only minimal information Note: By default, this function prints a table with eigenvalues and associated relative errors. With -eps_terse only the eigenvalues are printed. Level: intermediate .seealso: PetscViewerASCIIOpen() @*/ PetscErrorCode EPSPrintSolution(EPS eps,PetscViewer viewer) { PetscBool terse,errok,isascii; PetscReal error,re,im; PetscScalar kr,ki; PetscInt i,j; PetscErrorCode ierr; PetscFunctionBegin; PetscValidHeaderSpecific(eps,EPS_CLASSID,1); if (!viewer) viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)eps)); PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2); PetscCheckSameComm(eps,1,viewer,2); EPSCheckSolved(eps,1); ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii); CHKERRQ(ierr); if (!isascii) PetscFunctionReturn(0); ierr = PetscOptionsHasName(NULL,"-eps_terse",&terse); CHKERRQ(ierr); if (terse) { if (eps->nconv<eps->nev) { ierr = PetscViewerASCIIPrintf(viewer," Problem: less than %D eigenvalues converged\n\n",eps->nev); CHKERRQ(ierr); } else { errok = PETSC_TRUE; for (i=0; i<eps->nev; i++) { ierr = EPSComputeRelativeError(eps,i,&error); CHKERRQ(ierr); errok = (errok && error<5.0*eps->tol)? PETSC_TRUE: PETSC_FALSE; } if (errok) { ierr = PetscViewerASCIIPrintf(viewer," All requested eigenvalues computed up to the required tolerance:"); CHKERRQ(ierr); for (i=0; i<=(eps->nev-1)/8; i++) { ierr = PetscViewerASCIIPrintf(viewer,"\n "); CHKERRQ(ierr); for (j=0; j<PetscMin(8,eps->nev-8*i); j++) { ierr = EPSGetEigenpair(eps,8*i+j,&kr,&ki,NULL,NULL); CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (PetscAbs(re)/PetscAbs(im)<PETSC_SMALL) re = 0.0; if (PetscAbs(im)/PetscAbs(re)<PETSC_SMALL) im = 0.0; if (im!=0.0) { ierr = PetscViewerASCIIPrintf(viewer,"%.5f%+.5fi",(double)re,(double)im); CHKERRQ(ierr); } else { ierr = PetscViewerASCIIPrintf(viewer,"%.5f",(double)re); CHKERRQ(ierr); } if (8*i+j+1<eps->nev) { ierr = PetscViewerASCIIPrintf(viewer,", "); CHKERRQ(ierr); } } } ierr = PetscViewerASCIIPrintf(viewer,"\n\n"); CHKERRQ(ierr); } else { ierr = PetscViewerASCIIPrintf(viewer," Problem: some of the first %D relative errors are higher than the tolerance\n\n",eps->nev); CHKERRQ(ierr); } } } else { ierr = PetscViewerASCIIPrintf(viewer," Number of converged approximate eigenpairs: %D\n\n",eps->nconv); CHKERRQ(ierr); if (eps->nconv>0) { ierr = PetscViewerASCIIPrintf(viewer, " k ||Ax-k%sx||/||kx||\n" " ----------------- ------------------\n",eps->isgeneralized?"B":""); CHKERRQ(ierr); for (i=0; i<eps->nconv; i++) { ierr = EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL); CHKERRQ(ierr); ierr = EPSComputeRelativeError(eps,i,&error); CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im!=0.0) { ierr = PetscViewerASCIIPrintf(viewer," % 9f%+9f i %12g\n",(double)re,(double)im,(double)error); CHKERRQ(ierr); } else { ierr = PetscViewerASCIIPrintf(viewer," % 12f %12g\n",(double)re,(double)error); CHKERRQ(ierr); } } ierr = PetscViewerASCIIPrintf(viewer,"\n"); CHKERRQ(ierr); } } PetscFunctionReturn(0); }
int eigen_solver(ndr_data_t *arg) { EPS eps; EPSType type; PetscReal error,tol,re,im; PetscScalar kr,ki; Vec xr,xi; PetscInt i,nev,maxit,its,nconv; PetscErrorCode ierr; ierr = MatGetVecs(arg->A,NULL,&xr);CHKERRQ(ierr); ierr = MatGetVecs(arg->A,NULL,&xi);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create the eigensolver and set various options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Create eigensolver context */ ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr); /* Set operators. In this case, it is a standard eigenvalue problem */ ierr = EPSSetOperators(eps,arg->A,NULL);CHKERRQ(ierr); ierr = EPSSetProblemType(eps,EPS_NHEP);CHKERRQ(ierr); /* Set solver parameters at runtime */ ierr = EPSSetFromOptions(eps);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve the eigensystem - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = EPSSolve(eps);CHKERRQ(ierr); /* Optional: Get some information from the solver and display it */ ierr = EPSGetIterationNumber(eps,&its);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);CHKERRQ(ierr); ierr = EPSGetType(eps,&type);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr); ierr = EPSGetDimensions(eps,&nev,NULL,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);CHKERRQ(ierr); ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Display solution and clean up - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Get number of converged approximate eigenpairs */ ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %D\n\n",nconv);CHKERRQ(ierr); if (nconv>0) { /* Display eigenvalues and relative errors */ ierr = PetscPrintf(PETSC_COMM_WORLD, " k ||Ax-kx||/||kx||\n" " ----------------- ------------------\n");CHKERRQ(ierr); for (i=0;i<nconv;i++) { /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and ki (imaginary part) */ ierr = EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);CHKERRQ(ierr); // VecView(xr,PETSC_VIEWER_STDOUT_WORLD); /* Compute the relative error associated to each eigenpair */ ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im!=0.0) { ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",(double)re,(double)im,(double)error);CHKERRQ(ierr); } else { ierr = PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error);CHKERRQ(ierr); } } ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr); } /* Free work space */ ierr = EPSDestroy(&eps);CHKERRQ(ierr); ierr = VecDestroy(&xr);CHKERRQ(ierr); ierr = VecDestroy(&xi);CHKERRQ(ierr); return 0; }
int main(int argc,char **argv) { Mat A; /* operator matrix */ EPS eps; /* eigenproblem solver context */ EPSType type; DM da; Vec v0; PetscReal error,tol,re,im,*exact; PetscScalar kr,ki; PetscInt M,N,P,m,n,p,nev,maxit,i,its,nconv,seed; PetscLogDouble t1,t2,t3; PetscBool flg; PetscRandom rctx; PetscErrorCode ierr; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscPrintf(PETSC_COMM_WORLD,"\n3-D Laplacian Eigenproblem\n\n");CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Compute the operator matrix that defines the eigensystem, Ax=kx - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-10,-10,-10, PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE, 1,1,NULL,NULL,NULL,&da);CHKERRQ(ierr); /* print DM information */ ierr = DMDAGetInfo(da,NULL,&M,&N,&P,&m,&n,&p,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Grid partitioning: %D %D %D\n",m,n,p);CHKERRQ(ierr); /* create and fill the matrix */ ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr); ierr = FillMatrix(da,A);CHKERRQ(ierr); /* create random initial vector */ seed = 1; ierr = PetscOptionsGetInt(NULL,"-seed",&seed,NULL);CHKERRQ(ierr); if (seed<0) SETERRQ(PETSC_COMM_WORLD,1,"Seed must be >=0"); ierr = MatGetVecs(A,&v0,NULL);CHKERRQ(ierr); ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr); ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr); for (i=0;i<seed;i++) { /* simulate different seeds in the random generator */ ierr = VecSetRandom(v0,rctx);CHKERRQ(ierr); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create the eigensolver and set various options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Create eigensolver context */ ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr); /* Set operators. In this case, it is a standard eigenvalue problem */ ierr = EPSSetOperators(eps,A,NULL);CHKERRQ(ierr); ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr); /* Set specific solver options */ ierr = EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);CHKERRQ(ierr); ierr = EPSSetTolerances(eps,1e-8,PETSC_DEFAULT);CHKERRQ(ierr); ierr = EPSSetInitialSpace(eps,1,&v0);CHKERRQ(ierr); /* Set solver parameters at runtime */ ierr = EPSSetFromOptions(eps);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve the eigensystem - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = PetscTime(&t1);CHKERRQ(ierr); ierr = EPSSetUp(eps);CHKERRQ(ierr); ierr = PetscTime(&t2);CHKERRQ(ierr); ierr = EPSSolve(eps);CHKERRQ(ierr); ierr = PetscTime(&t3);CHKERRQ(ierr); ierr = EPSGetIterationNumber(eps,&its);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);CHKERRQ(ierr); /* Optional: Get some information from the solver and display it */ ierr = EPSGetType(eps,&type);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr); ierr = EPSGetDimensions(eps,&nev,NULL,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);CHKERRQ(ierr); ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Display solution and clean up - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Get number of converged approximate eigenpairs */ ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %D\n\n",nconv);CHKERRQ(ierr); if (nconv>0) { ierr = PetscMalloc1(nconv,&exact);CHKERRQ(ierr); ierr = GetExactEigenvalues(M,N,P,nconv,exact);CHKERRQ(ierr); /* Display eigenvalues and relative errors */ ierr = PetscPrintf(PETSC_COMM_WORLD, " k ||Ax-kx||/||kx|| Eigenvalue Error \n" " ----------------- ------------------ ------------------\n");CHKERRQ(ierr); for (i=0;i<nconv;i++) { /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and ki (imaginary part) */ ierr = EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL);CHKERRQ(ierr); /* Compute the relative error associated to each eigenpair */ ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im!=0.0) SETERRQ(PETSC_COMM_WORLD,1,"Eigenvalue should be real"); else { ierr = PetscPrintf(PETSC_COMM_WORLD," %12g %12g %12g\n",(double)re,(double)error,(double)PetscAbsReal(re-exact[i]));CHKERRQ(ierr); } } ierr = PetscFree(exact);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr); } /* Show computing times */ ierr = PetscOptionsHasName(NULL,"-showtimes",&flg);CHKERRQ(ierr); if (flg) { ierr = PetscPrintf(PETSC_COMM_WORLD," Elapsed time: %g (setup), %g (solve)\n",(double)(t2-t1),(double)(t3-t2));CHKERRQ(ierr); } /* Free work space */ ierr = EPSDestroy(&eps);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr); ierr = VecDestroy(&v0);CHKERRQ(ierr); ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr); ierr = DMDestroy(&da);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }
int main(int argc,char **argv) { Mat A; /* problem matrix */ EPS eps; /* eigenproblem solver context */ EPSType type; PetscReal error,tol,re,im; PetscScalar kr,ki,value[3]; Vec xr,xi; PetscInt n=30,i,Istart,Iend,col[3],nev,maxit,its,nconv; PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE; PetscErrorCode ierr; SlepcInitialize(&argc,&argv,(char*)0,help); ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%D\n\n",n);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Compute the operator matrix that defines the eigensystem, Ax=kx - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); ierr = MatSetUp(A);CHKERRQ(ierr); ierr = MatGetOwnershipRange(A,&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(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr); } if (LastBlock) { i=n-1; col[0]=n-2; col[1]=n-1; ierr = MatSetValues(A,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(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr); } ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatGetVecs(A,NULL,&xr);CHKERRQ(ierr); ierr = MatGetVecs(A,NULL,&xi);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create the eigensolver and set various options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Create eigensolver context */ ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr); /* Set operators. In this case, it is a standard eigenvalue problem */ ierr = EPSSetOperators(eps,A,NULL);CHKERRQ(ierr); ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr); /* Set solver parameters at runtime */ ierr = EPSSetFromOptions(eps);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve the eigensystem - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = EPSSolve(eps);CHKERRQ(ierr); /* Optional: Get some information from the solver and display it */ ierr = EPSGetIterationNumber(eps,&its);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);CHKERRQ(ierr); ierr = EPSGetType(eps,&type);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr); ierr = EPSGetDimensions(eps,&nev,NULL,NULL);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);CHKERRQ(ierr); ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Display solution and clean up - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* Get number of converged approximate eigenpairs */ ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %D\n\n",nconv);CHKERRQ(ierr); if (nconv>0) { /* Display eigenvalues and relative errors */ ierr = PetscPrintf(PETSC_COMM_WORLD, " k ||Ax-kx||/||kx||\n" " ----------------- ------------------\n");CHKERRQ(ierr); for (i=0;i<nconv;i++) { /* Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and ki (imaginary part) */ ierr = EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);CHKERRQ(ierr); /* Compute the relative error associated to each eigenpair */ ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) re = PetscRealPart(kr); im = PetscImaginaryPart(kr); #else re = kr; im = ki; #endif if (im!=0.0) { ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",(double)re,(double)im,(double)error);CHKERRQ(ierr); } else { ierr = PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",(double)re,(double)error);CHKERRQ(ierr); } } ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr); } /* Free work space */ ierr = EPSDestroy(&eps);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr); ierr = VecDestroy(&xr);CHKERRQ(ierr); ierr = VecDestroy(&xi);CHKERRQ(ierr); ierr = SlepcFinalize(); return 0; }