Actual source code: ex16.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[] = "Simple quadratic eigenvalue problem.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

 16: #include <slepcpep.h>

 18: int main(int argc,char **argv)
 19: {
 20:   Mat            M,C,K,A[3];      /* problem matrices */
 21:   PEP            pep;             /* polynomial eigenproblem solver context */
 22:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nconv;
 23:   PetscBool      flag,terse;
 24:   PetscReal      error,re,im;
 25:   PetscScalar    kr,ki;
 26:   Vec            xr,xi;
 27:   BV             V;
 28:   PetscRandom    rand;

 30:   SlepcInitialize(&argc,&argv,(char*)0,help);

 32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
 34:   if (!flag) m=n;
 35:   N = n*m;
 36:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m);

 38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 39:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
 40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 42:   /* K is the 2-D Laplacian */
 43:   MatCreate(PETSC_COMM_WORLD,&K);
 44:   MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N);
 45:   MatSetFromOptions(K);
 46:   MatSetUp(K);
 47:   MatGetOwnershipRange(K,&Istart,&Iend);
 48:   for (II=Istart;II<Iend;II++) {
 49:     i = II/n; j = II-i*n;
 50:     if (i>0) MatSetValue(K,II,II-n,-1.0,INSERT_VALUES);
 51:     if (i<m-1) MatSetValue(K,II,II+n,-1.0,INSERT_VALUES);
 52:     if (j>0) MatSetValue(K,II,II-1,-1.0,INSERT_VALUES);
 53:     if (j<n-1) MatSetValue(K,II,II+1,-1.0,INSERT_VALUES);
 54:     MatSetValue(K,II,II,4.0,INSERT_VALUES);
 55:   }
 56:   MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
 57:   MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);

 59:   /* C is the 1-D Laplacian on horizontal lines */
 60:   MatCreate(PETSC_COMM_WORLD,&C);
 61:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 62:   MatSetFromOptions(C);
 63:   MatSetUp(C);
 64:   MatGetOwnershipRange(C,&Istart,&Iend);
 65:   for (II=Istart;II<Iend;II++) {
 66:     i = II/n; j = II-i*n;
 67:     if (j>0) MatSetValue(C,II,II-1,-1.0,INSERT_VALUES);
 68:     if (j<n-1) MatSetValue(C,II,II+1,-1.0,INSERT_VALUES);
 69:     MatSetValue(C,II,II,2.0,INSERT_VALUES);
 70:   }
 71:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 72:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 74:   /* M is a diagonal matrix */
 75:   MatCreate(PETSC_COMM_WORLD,&M);
 76:   MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N);
 77:   MatSetFromOptions(M);
 78:   MatSetUp(M);
 79:   MatGetOwnershipRange(M,&Istart,&Iend);
 80:   for (II=Istart;II<Iend;II++) MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES);
 81:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
 82:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

 84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 85:                 Create the eigensolver and set various options
 86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 88:   /*
 89:      Create eigensolver context
 90:   */
 91:   PEPCreate(PETSC_COMM_WORLD,&pep);

 93:   /*
 94:      Set matrices and problem type
 95:   */
 96:   A[0] = K; A[1] = C; A[2] = M;
 97:   PEPSetOperators(pep,3,A);
 98:   PEPSetProblemType(pep,PEP_HERMITIAN);

100:   /*
101:      In complex scalars, use a real initial vector since in this example
102:      the matrices are all real, then all vectors generated by the solver
103:      will have a zero imaginary part. This is not really necessary.
104:   */
105:   PEPGetBV(pep,&V);
106:   BVGetRandomContext(V,&rand);
107:   PetscRandomSetInterval(rand,-1,1);

109:   /*
110:      Set solver parameters at runtime
111:   */
112:   PEPSetFromOptions(pep);

114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115:                       Solve the eigensystem
116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

118:   PEPSolve(pep);

120:   /*
121:      Optional: Get some information from the solver and display it
122:   */
123:   PEPGetDimensions(pep,&nev,NULL,NULL);
124:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127:                     Display solution and clean up
128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

130:   /* show detailed info unless -terse option is given by user */
131:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
132:   if (terse) PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
133:   else {
134:     PEPGetConverged(pep,&nconv);
135:     if (nconv>0) {
136:       MatCreateVecs(M,&xr,&xi);
137:       /* display eigenvalues and relative errors */
138:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,
139:            "\n           k          ||P(k)x||/||kx||\n"
140:            "   ----------------- ------------------\n"));
141:       for (i=0;i<nconv;i++) {
142:         /* get converged eigenpairs */
143:         PEPGetEigenpair(pep,i,&kr,&ki,xr,xi);
144:         /* compute the relative error associated to each eigenpair */
145:         PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error);
146: #if defined(PETSC_USE_COMPLEX)
147:         re = PetscRealPart(kr);
148:         im = PetscImaginaryPart(kr);
149: #else
150:         re = kr;
151:         im = ki;
152: #endif
153:         if (im!=0.0) PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi   %12g\n",(double)re,(double)im,(double)error);
154:         else PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);
155:       }
156:       PetscPrintf(PETSC_COMM_WORLD,"\n");
157:       VecDestroy(&xr);
158:       VecDestroy(&xi);
159:     }
160:   }
161:   PEPDestroy(&pep);
162:   MatDestroy(&M);
163:   MatDestroy(&C);
164:   MatDestroy(&K);
165:   SlepcFinalize();
166:   return 0;
167: }

169: /*TEST

171:    testset:
172:       args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
173:       output_file: output/ex16_1.out
174:       test:
175:          suffix: 1
176:          args: -pep_type {{toar qarnoldi}}
177:       test:
178:          suffix: 1_linear
179:          args: -pep_type linear -pep_linear_explicitmatrix
180:          requires: !single
181:       test:
182:          suffix: 1_linear_symm
183:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite -pep_scale scalar -pep_linear_bv_definite_tol 1e-12
184:          requires: !single
185:       test:
186:          suffix: 1_stoar
187:          args: -pep_type stoar -pep_scale scalar
188:          requires: double !cuda
189:       test:
190:          suffix: 1_stoar_t
191:          args: -pep_type stoar -pep_scale scalar -st_transform
192:          requires: double !cuda

194: TEST*/