Actual source code: ex16.c

slepc-3.7.3 2016-09-29
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */

 22: static char help[] = "Simple quadratic eigenvalue problem.\n\n"
 23:   "The command line options are:\n"
 24:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 25:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

 27: #include <slepcpep.h>

 31: int main(int argc,char **argv)
 32: {
 33:   Mat            M,C,K,A[3];      /* problem matrices */
 34:   PEP            pep;             /* polynomial eigenproblem solver context */
 35:   PEPType        type;
 36:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nconv;
 37:   PetscBool      flag,terse;
 38:   PetscReal      error,re,im;
 39:   PetscScalar    kr,ki;
 40:   Vec            xr,xi;

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

 45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 46:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
 47:   if (!flag) m=n;
 48:   N = n*m;
 49:   PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%D (%Dx%D grid)\n\n",N,n,m);

 51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 52:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
 53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 55:   /* K is the 2-D Laplacian */
 56:   MatCreate(PETSC_COMM_WORLD,&K);
 57:   MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N);
 58:   MatSetFromOptions(K);
 59:   MatSetUp(K);
 60:   MatGetOwnershipRange(K,&Istart,&Iend);
 61:   for (II=Istart;II<Iend;II++) {
 62:     i = II/n; j = II-i*n;
 63:     if (i>0) { MatSetValue(K,II,II-n,-1.0,INSERT_VALUES); }
 64:     if (i<m-1) { MatSetValue(K,II,II+n,-1.0,INSERT_VALUES); }
 65:     if (j>0) { MatSetValue(K,II,II-1,-1.0,INSERT_VALUES); }
 66:     if (j<n-1) { MatSetValue(K,II,II+1,-1.0,INSERT_VALUES); }
 67:     MatSetValue(K,II,II,4.0,INSERT_VALUES);
 68:   }
 69:   MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
 70:   MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);

 72:   /* C is the 1-D Laplacian on horizontal lines */
 73:   MatCreate(PETSC_COMM_WORLD,&C);
 74:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);
 75:   MatSetFromOptions(C);
 76:   MatSetUp(C);
 77:   MatGetOwnershipRange(C,&Istart,&Iend);
 78:   for (II=Istart;II<Iend;II++) {
 79:     i = II/n; j = II-i*n;
 80:     if (j>0) { MatSetValue(C,II,II-1,-1.0,INSERT_VALUES); }
 81:     if (j<n-1) { MatSetValue(C,II,II+1,-1.0,INSERT_VALUES); }
 82:     MatSetValue(C,II,II,2.0,INSERT_VALUES);
 83:   }
 84:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
 85:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

 87:   /* M is a diagonal matrix */
 88:   MatCreate(PETSC_COMM_WORLD,&M);
 89:   MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N);
 90:   MatSetFromOptions(M);
 91:   MatSetUp(M);
 92:   MatGetOwnershipRange(M,&Istart,&Iend);
 93:   for (II=Istart;II<Iend;II++) {
 94:     MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES);
 95:   }
 96:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
 97:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

 99:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
100:                 Create the eigensolver and set various options
101:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

103:   /*
104:      Create eigensolver context
105:   */
106:   PEPCreate(PETSC_COMM_WORLD,&pep);

108:   /*
109:      Set matrices and problem type
110:   */
111:   A[0] = K; A[1] = C; A[2] = M;
112:   PEPSetOperators(pep,3,A);
113:   PEPSetProblemType(pep,PEP_HERMITIAN);

115:   /*
116:      Set solver parameters at runtime
117:   */
118:   PEPSetFromOptions(pep);

120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121:                       Solve the eigensystem
122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

124:   PEPSolve(pep);

126:   /*
127:      Optional: Get some information from the solver and display it
128:   */
129:   PEPGetType(pep,&type);
130:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
131:   PEPGetDimensions(pep,&nev,NULL,NULL);
132:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:                     Display solution and clean up
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

138:   /* show detailed info unless -terse option is given by user */
139:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
140:   if (terse) {
141:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
142:   } else {
143:     PEPGetConverged(pep,&nconv);
144:     if (nconv>0) {
145:       MatCreateVecs(M,&xr,&xi);
146:       /* display eigenvalues and relative errors */
147:       PetscPrintf(PETSC_COMM_WORLD,
148:            "\n           k          ||P(k)x||/||kx||\n"
149:            "   ----------------- ------------------\n");
150:       for (i=0;i<nconv;i++) {
151:         /* get converged eigenpairs */
152:         PEPGetEigenpair(pep,i,&kr,&ki,xr,xi);
153:         /* compute the relative error associated to each eigenpair */
154:         PEPComputeError(pep,i,PEP_ERROR_RELATIVE,&error);
155: #if defined(PETSC_USE_COMPLEX)
156:         re = PetscRealPart(kr);
157:         im = PetscImaginaryPart(kr);
158: #else
159:         re = kr;
160:         im = ki;
161: #endif
162:         if (im!=0.0) {
163:           PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi   %12g\n",(double)re,(double)im,(double)error);
164:         } else {
165:           PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);
166:         }
167:       }
168:       PetscPrintf(PETSC_COMM_WORLD,"\n");
169:       VecDestroy(&xr);
170:       VecDestroy(&xi);
171:     }
172:   }
173:   PEPDestroy(&pep);
174:   MatDestroy(&M);
175:   MatDestroy(&C);
176:   MatDestroy(&K);
177:   SlepcFinalize();
178:   return ierr;
179: }