Actual source code: test8.c

slepc-3.17.0 2022-03-31
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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[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
 12:   "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
 13:   "The command line options are:\n"
 14:   "  -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";

 16: #include <slepceps.h>
 17: #include <petscblaslapack.h>

 19: /*
 20:    User-defined routines
 21: */
 22: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y);
 23: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag);

 25: int main(int argc,char **argv)
 26: {
 27:   Mat            A;               /* operator matrix */
 28:   EPS            eps;             /* eigenproblem solver context */
 29:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
 30:   PetscMPIInt    size;
 31:   PetscInt       N,n=10,nev;

 33:   SlepcInitialize(&argc,&argv,(char*)0,help);
 34:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 37:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 38:   N = n*n;
 39:   PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,n);

 41:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 42:      Compute the operator matrix that defines the eigensystem, Ax=kx
 43:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 45:   MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
 46:   MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_Laplacian2D);
 47:   MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)(void))MatMult_Laplacian2D);
 48:   MatShellSetOperation(A,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Laplacian2D);

 50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51:                 Create the eigensolver and set various options
 52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 54:   /*
 55:      Create eigensolver context
 56:   */
 57:   EPSCreate(PETSC_COMM_WORLD,&eps);

 59:   /*
 60:      Set operators. In this case, it is a standard eigenvalue problem
 61:   */
 62:   EPSSetOperators(eps,A,NULL);
 63:   EPSSetProblemType(eps,EPS_HEP);
 64:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

 66:   /*
 67:      Set solver parameters at runtime
 68:   */
 69:   EPSSetFromOptions(eps);

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:                       Solve the eigensystem
 73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 75:   EPSSolve(eps);
 76:   EPSGetDimensions(eps,&nev,NULL,NULL);
 77:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

 79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 80:                     Display solution and clean up
 81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 83:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
 84:   EPSDestroy(&eps);
 85:   MatDestroy(&A);
 86:   SlepcFinalize();
 87:   return 0;
 88: }

 90: /*
 91:     Compute the matrix vector multiplication y<---T*x where T is a nx by nx
 92:     tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
 93:     DU on the superdiagonal.
 94:  */
 95: static void tv(int nx,const PetscScalar *x,PetscScalar *y)
 96: {
 97:   PetscScalar dd,dl,du;
 98:   int         j;

100:   dd  = 4.0;
101:   dl  = -1.0;
102:   du  = -1.0;

104:   y[0] =  dd*x[0] + du*x[1];
105:   for (j=1;j<nx-1;j++)
106:     y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
107:   y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
108: }

110: /*
111:     Matrix-vector product subroutine for the 2D Laplacian.

113:     The matrix used is the 2 dimensional discrete Laplacian on unit square with
114:     zero Dirichlet boundary condition.

116:     Computes y <-- A*x, where A is the block tridiagonal matrix

118:                  | T -I          |
119:                  |-I  T -I       |
120:              A = |   -I  T       |
121:                  |        ...  -I|
122:                  |           -I T|

124:     The subroutine TV is called to compute y<--T*x.
125:  */
126: PetscErrorCode MatMult_Laplacian2D(Mat A,Vec x,Vec y)
127: {
128:   void              *ctx;
129:   int               nx,lo,i,j;
130:   const PetscScalar *px;
131:   PetscScalar       *py;

134:   MatShellGetContext(A,&ctx);
135:   nx = *(int*)ctx;
136:   VecGetArrayRead(x,&px);
137:   VecGetArray(y,&py);

139:   tv(nx,&px[0],&py[0]);
140:   for (i=0;i<nx;i++) py[i] -= px[nx+i];

142:   for (j=2;j<nx;j++) {
143:     lo = (j-1)*nx;
144:     tv(nx,&px[lo],&py[lo]);
145:     for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i] + px[lo+nx+i];
146:   }

148:   lo = (nx-1)*nx;
149:   tv(nx,&px[lo],&py[lo]);
150:   for (i=0;i<nx;i++) py[lo+i] -= px[lo-nx+i];

152:   VecRestoreArrayRead(x,&px);
153:   VecRestoreArray(y,&py);
154:   PetscFunctionReturn(0);
155: }

157: PetscErrorCode MatGetDiagonal_Laplacian2D(Mat A,Vec diag)
158: {
160:   VecSet(diag,4.0);
161:   PetscFunctionReturn(0);
162: }

164: /*TEST

166:    testset:
167:       args: -n 20 -eps_nev 4 -eps_ncv 11 -eps_max_it 40000
168:       requires: !single
169:       output_file: output/test8_1.out
170:       test:
171:          suffix: 1
172:          args: -eps_type {{power subspace arnoldi}}
173:       test:
174:          suffix: 1_lanczos
175:          args: -eps_type lanczos -eps_lanczos_reorthog local
176:       test:
177:          suffix: 1_lapack
178:          args: -eps_type lapack
179:          timeoutfactor: 2
180:       test:
181:          suffix: 1_elemental
182:          args: -eps_type elemental
183:          requires: elemental
184:       test:
185:          suffix: 1_krylovschur_vecs
186:          args: -bv_type vecs -bv_orthog_refine always -eps_ncv 10
187:       test:
188:          suffix: 1_jd
189:          args: -eps_type jd -eps_jd_blocksize 3
190:       test:
191:          suffix: 1_gd
192:          args: -eps_type gd -eps_gd_blocksize 3 -eps_tol 1e-8
193:       test:
194:          suffix: 1_gd2
195:          args: -eps_type gd -eps_gd_double_expansion
196:       test:
197:          suffix: 1_primme
198:          args: -eps_type primme -eps_conv_abs
199:          requires: primme

201:    testset:
202:       args: -eps_nev 4 -eps_smallest_real -eps_max_it 600
203:       output_file: output/test8_2.out
204:       test:
205:          suffix: 2
206:          args: -eps_type {{rqcg lobpcg}}
207:       test:
208:          suffix: 2_lanczos
209:          args: -eps_type lanczos -eps_lanczos_reorthog local
210:       test:
211:          suffix: 2_arpack
212:          args: -eps_type arpack -eps_ncv 6
213:          requires: arpack !single
214:       test:
215:          suffix: 2_primme
216:          args: -eps_type primme -eps_conv_abs -eps_primme_method lobpcg_orthobasisw -eps_ncv 24
217:          requires: primme

219:    testset:
220:       args: -eps_nev 12 -eps_mpd 9 -eps_smallest_real -eps_max_it 1000
221:       output_file: output/test8_3.out
222:       test:
223:          suffix: 3_rqcg
224:          args: -eps_type rqcg
225:       test:
226:          suffix: 3_lanczos
227:          args: -eps_type lanczos -eps_lanczos_reorthog local
228:       test:
229:          suffix: 3_lobpcg
230:          args: -eps_type lobpcg -eps_lobpcg_blocksize 3 -eps_lobpcg_locking 0 -st_ksp_type preonly -st_pc_type jacobi
231:          requires: !__float128
232:       test:
233:          suffix: 3_lobpcg_quad
234:          args: -eps_type lobpcg -eps_lobpcg_blocksize 3 -eps_lobpcg_locking 0 -st_ksp_type preonly -st_pc_type jacobi -eps_tol 1e-25
235:          requires: __float128
236: TEST*/