Actual source code: ex1.c

slepc-3.17.2 2022-08-09
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  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:   SlepcInitialize(&argc,&argv,(char*)0,help);

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

 32:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 33:      Compute the operator matrix that defines the eigensystem, Ax=kx
 34:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

 76:   EPSSolve(eps);
 77:   /*
 78:      Optional: Get some information from the solver and display it
 79:   */
 80:   EPSGetIterationNumber(eps,&its);
 81:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its);
 82:   EPSGetType(eps,&type);
 83:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
 84:   EPSGetDimensions(eps,&nev,NULL,NULL);
 85:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
 86:   EPSGetTolerances(eps,&tol,&maxit);
 87:   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:   EPSGetConverged(eps,&nconv);
 96:   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:       EPSGetEigenpair(eps,i,&kr,&ki,xr,xi);
112:       /*
113:          Compute the relative error associated to each eigenpair
114:       */
115:       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) PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi %12g\n",(double)re,(double)im,(double)error);
125:       else PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);
126:     }
127:     PetscPrintf(PETSC_COMM_WORLD,"\n");
128:   }

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