1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Standard symmetric eigenproblem corresponding to the Laplacian operator in 1 dimension.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";

 15: #include <slepceps.h>

 17: int main(int argc,char **argv)
 18: {
 19:   Mat            A;           /* problem matrix */
 20:   EPS            eps;         /* eigenproblem solver context */
 21:   EPSType        type;
 22:   PetscReal      error,tol,re,im;
 23:   PetscScalar    kr,ki;
 24:   Vec            xr,xi;
 25:   PetscInt       n=30,i,Istart,Iend,nev,maxit,its,nconv;

 27:   PetscFunctionBeginUser;
 28:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

 30:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 31:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%" PetscInt_FMT "\n\n",n));

 33:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 34:      Compute the operator matrix that defines the eigensystem, Ax=kx
 35:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 37:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
 38:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
 39:   PetscCall(MatSetFromOptions(A));

 41:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
 42:   for (i=Istart;i<Iend;i++) {
 43:     if (i>0) PetscCall(MatSetValue(A,i,i-1,-1.0,INSERT_VALUES));
 44:     if (i<n-1) PetscCall(MatSetValue(A,i,i+1,-1.0,INSERT_VALUES));
 45:     PetscCall(MatSetValue(A,i,i,2.0,INSERT_VALUES));
 46:   }
 47:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
 48:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

 50:   PetscCall(MatCreateVecs(A,NULL,&xr));
 51:   PetscCall(MatCreateVecs(A,NULL,&xi));

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:                 Create the eigensolver and set various options
 55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 56:   /*
 57:      Create eigensolver context
 58:   */
 59:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

 61:   /*
 62:      Set operators. In this case, it is a standard eigenvalue problem
 63:   */
 64:   PetscCall(EPSSetOperators(eps,A,NULL));
 65:   PetscCall(EPSSetProblemType(eps,EPS_HEP));

 67:   /*
 68:      Set solver parameters at runtime
 69:   */
 70:   PetscCall(EPSSetFromOptions(eps));

 72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 73:                       Solve the eigensystem
 74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 76:   PetscCall(EPSSolve(eps));
 77:   /*
 78:      Optional: Get some information from the solver and display it
 79:   */
 80:   PetscCall(EPSGetIterationNumber(eps,&its));
 81:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
 82:   PetscCall(EPSGetType(eps,&type));
 83:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
 84:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
 85:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
 86:   PetscCall(EPSGetTolerances(eps,&tol,&maxit));
 87:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:                     Display solution and clean up
 91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 92:   /*
 93:      Get number of converged approximate eigenpairs
 94:   */
 95:   PetscCall(EPSGetConverged(eps,&nconv));
 96:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv));

 98:   if (nconv>0) {
 99:     /*
100:        Display eigenvalues and relative errors
101:     */
102:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,
103:          "           k          ||Ax-kx||/||kx||\n"
104:          "   ----------------- ------------------\n"));

106:     for (i=0;i<nconv;i++) {
107:       /*
108:         Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
109:         ki (imaginary part)
110:       */
111:       PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,xr,xi));
112:       /*
113:          Compute the relative error associated to each eigenpair
114:       */
115:       PetscCall(EPSComputeError(eps,i,EPS_ERROR_RELATIVE,&error));

117: #if defined(PETSC_USE_COMPLEX)
118:       re = PetscRealPart(kr);
119:       im = PetscImaginaryPart(kr);
120: #else
121:       re = kr;
122:       im = ki;
123: #endif
124:       if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error));
125:       else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error));
126:     }
127:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
128:   }

130:   /*
131:      Free work space
132:   */
133:   PetscCall(EPSDestroy(&eps));
134:   PetscCall(MatDestroy(&A));
135:   PetscCall(VecDestroy(&xr));
136:   PetscCall(VecDestroy(&xi));
137:   PetscCall(SlepcFinalize());
138:   return 0;
139: }