/*
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/*
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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SLEPc - Scalable Library for Eigenvalue Problem Computations
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SLEPc - Scalable Library for Eigenvalue Problem Computations
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Copyright (c) 2002-2009, Universidad Politecnica de Valencia, Spain
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Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
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This file is part of SLEPc.
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This file is part of SLEPc.
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SLEPc is free software: you can redistribute it and/or modify it under the
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SLEPc is free software: you can redistribute it and/or modify it under the
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terms of version 3 of the GNU Lesser General Public License as published by
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terms of version 3 of the GNU Lesser General Public License as published by
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the Free Software Foundation.
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the Free Software Foundation.
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SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
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SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
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FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
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more details.
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more details.
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You should have received a copy of the GNU Lesser General Public License
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You should have received a copy of the GNU Lesser General Public License
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along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
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along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
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*/
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*/
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static char help[] = "Standard symmetric eigenproblem corresponding to the Laplacian operator in 2 dimensions.\n\n"
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static char help[] = "Standard symmetric eigenproblem corresponding to the Laplacian operator in 2 dimensions.\n\n"
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"The command line options are:\n"
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"The command line options are:\n"
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" -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
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" -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
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" -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";
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" -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";
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#include "slepceps.h"
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#include "slepceps.h"
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#undef __FUNCT__
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#undef __FUNCT__
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#define __FUNCT__ "main"
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#define __FUNCT__ "main"
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int main( int argc, char **argv )
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int main( int argc, char **argv )
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{
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{
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Mat A; /* operator matrix */
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Mat A; /* operator matrix */
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EPS eps; /* eigenproblem solver context */
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EPS eps; /* eigenproblem solver context */
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const EPSType type;
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const EPSType type;
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PetscReal error, tol, re, im;
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PetscReal error, tol, re, im;
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PetscScalar kr, ki;
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PetscScalar kr, ki;
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PetscErrorCode ierr;
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PetscErrorCode ierr;
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PetscInt N, n=10, m, Istart, Iend, II, nev, maxit, i, j, its, nconv;
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PetscInt N, n=10, m, Istart, Iend, II, nev, maxit, i, j, its, nconv;
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PetscTruth flag;
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PetscTruth flag;
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SlepcInitialize(&argc,&argv,(char*)0,help);
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SlepcInitialize(&argc,&argv,(char*)0,help);
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ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
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ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
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ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);CHKERRQ(ierr);
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ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,&flag);CHKERRQ(ierr);
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if( flag==PETSC_FALSE ) m=n;
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if( flag==PETSC_FALSE ) m=n;
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N = n*m;
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N = n*m;
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ierr = PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem, N=%d (%dx%d grid)\n\n",N,n,m);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem, N=%d (%dx%d grid)\n\n",N,n,m);CHKERRQ(ierr);
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Compute the operator matrix that defines the eigensystem, Ax=kx
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Compute the operator matrix that defines the eigensystem, Ax=kx
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
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ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
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ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
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ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
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ierr = MatSetFromOptions(A);CHKERRQ(ierr);
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ierr = MatSetFromOptions(A);CHKERRQ(ierr);
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ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
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ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
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for( II=Istart; II<Iend; II++ ) {
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for( II=Istart; II<Iend; II++ ) {
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i = II/n; j = II-i*n;
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i = II/n; j = II-i*n;
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if(i>0) { ierr = MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(i>0) { ierr = MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(i<m-1) { ierr = MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(i<m-1) { ierr = MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(j>0) { ierr = MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(j>0) { ierr = MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(j<n-1) { ierr = MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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if(j<n-1) { ierr = MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
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ierr = MatSetValue(A,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr);
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ierr = MatSetValue(A,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr);
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}
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}
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ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
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ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
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ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
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ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Create the eigensolver and set various options
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Create the eigensolver and set various options
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/*
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/*
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Create eigensolver context
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Create eigensolver context
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*/
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*/
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ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);
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ierr = EPSCreate(PETSC_COMM_WORLD,&eps);CHKERRQ(ierr);
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/*
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/*
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Set operators. In this case, it is a standard eigenvalue problem
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Set operators. In this case, it is a standard eigenvalue problem
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*/
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*/
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ierr = EPSSetOperators(eps,A,PETSC_NULL);CHKERRQ(ierr);
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ierr = EPSSetOperators(eps,A,PETSC_NULL);CHKERRQ(ierr);
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ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);
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ierr = EPSSetProblemType(eps,EPS_HEP);CHKERRQ(ierr);
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/*
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/*
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Set solver parameters at runtime
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Set solver parameters at runtime
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*/
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*/
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ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
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ierr = EPSSetFromOptions(eps);CHKERRQ(ierr);
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Solve the eigensystem
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Solve the eigensystem
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ierr = EPSSolve(eps);CHKERRQ(ierr);
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ierr = EPSSolve(eps);CHKERRQ(ierr);
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ierr = EPSGetIterationNumber(eps, &its);CHKERRQ(ierr);
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ierr = EPSGetIterationNumber(eps, &its);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);CHKERRQ(ierr);
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/*
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/*
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Optional: Get some information from the solver and display it
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Optional: Get some information from the solver and display it
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*/
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*/
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ierr = EPSGetType(eps,&type);CHKERRQ(ierr);
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ierr = EPSGetType(eps,&type);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);CHKERRQ(ierr);
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ierr = EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
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ierr = EPSGetDimensions(eps,&nev,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);CHKERRQ(ierr);
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ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr);
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ierr = EPSGetTolerances(eps,&tol,&maxit);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);CHKERRQ(ierr);
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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Display solution and clean up
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Display solution and clean up
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/*
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/*
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Get number of converged approximate eigenpairs
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Get number of converged approximate eigenpairs
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*/
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*/
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ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr);
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ierr = EPSGetConverged(eps,&nconv);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
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ierr = PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %d\n\n",nconv);
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CHKERRQ(ierr);
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CHKERRQ(ierr);
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if (nconv>0) {
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if (nconv>0) {
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/*
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/*
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Display eigenvalues and relative errors
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Display eigenvalues and relative errors
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*/
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*/
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ierr = PetscPrintf(PETSC_COMM_WORLD,
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ierr = PetscPrintf(PETSC_COMM_WORLD,
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" k ||Ax-kx||/||kx||\n"
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" k ||Ax-kx||/||kx||\n"
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" ----------------- ------------------\n" );CHKERRQ(ierr);
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" ----------------- ------------------\n" );CHKERRQ(ierr);
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for( i=0; i<nconv; i++ ) {
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for( i=0; i<nconv; i++ ) {
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/*
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/*
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Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
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Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
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ki (imaginary part)
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ki (imaginary part)
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*/
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*/
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ierr = EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
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ierr = EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
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/*
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/*
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Compute the relative error associated to each eigenpair
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Compute the relative error associated to each eigenpair
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*/
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*/
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ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr);
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ierr = EPSComputeRelativeError(eps,i,&error);CHKERRQ(ierr);
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#ifdef PETSC_USE_COMPLEX
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#ifdef PETSC_USE_COMPLEX
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re = PetscRealPart(kr);
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re = PetscRealPart(kr);
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im = PetscImaginaryPart(kr);
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im = PetscImaginaryPart(kr);
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#else
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#else
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re = kr;
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re = kr;
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im = ki;
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im = ki;
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#endif
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#endif
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if (im!=0.0) {
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if (im!=0.0) {
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ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12g\n",re,im,error);CHKERRQ(ierr);
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} else {
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} else {
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ierr = PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",re,error);CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD," %12f %12g\n",re,error);CHKERRQ(ierr);
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}
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}
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}
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}
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ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr);
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ierr = PetscPrintf(PETSC_COMM_WORLD,"\n" );CHKERRQ(ierr);
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}
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}
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/*
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/*
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Free work space
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Free work space
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*/
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*/
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ierr = EPSDestroy(eps);CHKERRQ(ierr);
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ierr = EPSDestroy(eps);CHKERRQ(ierr);
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ierr = MatDestroy(A);CHKERRQ(ierr);
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ierr = MatDestroy(A);CHKERRQ(ierr);
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ierr = SlepcFinalize();CHKERRQ(ierr);
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ierr = SlepcFinalize();CHKERRQ(ierr);
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return 0;
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return 0;
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}
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}
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