Actual source code: ex19.c

slepc-3.18.0 2022-10-01
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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 for the 3-D Laplacian built with the DM interface.\n\n"
 12: "Use -seed <k> to modify the random initial vector.\n"
 13: "Use -da_grid_x <nx> etc. to change the problem size.\n\n";

 15: #include <slepceps.h>
 16: #include <petscdmda.h>
 17: #include <petsctime.h>

 19: PetscErrorCode GetExactEigenvalues(PetscInt M,PetscInt N,PetscInt P,PetscInt nconv,PetscReal *exact)
 20: {
 21:   PetscInt       n,i,j,k,l;
 22:   PetscReal      *evals,ax,ay,az,sx,sy,sz;

 25:   ax = PETSC_PI/2/(M+1);
 26:   ay = PETSC_PI/2/(N+1);
 27:   az = PETSC_PI/2/(P+1);
 28:   n = PetscCeilReal(PetscPowReal((PetscReal)nconv,0.33333)+1);
 29:   PetscMalloc1(n*n*n,&evals);
 30:   l = 0;
 31:   for (i=1;i<=n;i++) {
 32:     sx = PetscSinReal(ax*i);
 33:     for (j=1;j<=n;j++) {
 34:       sy = PetscSinReal(ay*j);
 35:       for (k=1;k<=n;k++) {
 36:         sz = PetscSinReal(az*k);
 37:         evals[l++] = 4.0*(sx*sx+sy*sy+sz*sz);
 38:       }
 39:     }
 40:   }
 41:   PetscSortReal(n*n*n,evals);
 42:   for (i=0;i<nconv;i++) exact[i] = evals[i];
 43:   PetscFree(evals);
 44:   return 0;
 45: }

 47: PetscErrorCode FillMatrix(DM da,Mat A)
 48: {
 49:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,idx;
 50:   PetscScalar    v[7];
 51:   MatStencil     row,col[7];

 54:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
 55:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

 57:   for (k=zs;k<zs+zm;k++) {
 58:     for (j=ys;j<ys+ym;j++) {
 59:       for (i=xs;i<xs+xm;i++) {
 60:         row.i=i; row.j=j; row.k=k;
 61:         col[0].i=row.i; col[0].j=row.j; col[0].k=row.k;
 62:         v[0]=6.0;
 63:         idx=1;
 64:         if (k>0) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j; col[idx].k=k-1; idx++; }
 65:         if (j>0) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j-1; col[idx].k=k; idx++; }
 66:         if (i>0) { v[idx]=-1.0; col[idx].i=i-1; col[idx].j=j; col[idx].k=k; idx++; }
 67:         if (i<mx-1) { v[idx]=-1.0; col[idx].i=i+1; col[idx].j=j; col[idx].k=k; idx++; }
 68:         if (j<my-1) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j+1; col[idx].k=k; idx++; }
 69:         if (k<mz-1) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j; col[idx].k=k+1; idx++; }
 70:         MatSetValuesStencil(A,1,&row,idx,col,v,INSERT_VALUES);
 71:       }
 72:     }
 73:   }
 74:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 75:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 76:   return 0;
 77: }

 79: int main(int argc,char **argv)
 80: {
 81:   Mat            A;               /* operator matrix */
 82:   EPS            eps;             /* eigenproblem solver context */
 83:   EPSType        type;
 84:   DM             da;
 85:   Vec            v0;
 86:   PetscReal      error,tol,re,im,*exact;
 87:   PetscScalar    kr,ki;
 88:   PetscInt       M,N,P,m,n,p,nev,maxit,i,its,nconv,seed;
 89:   PetscLogDouble t1,t2,t3;
 90:   PetscBool      flg,terse;
 91:   PetscRandom    rctx;

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

 96:   PetscPrintf(PETSC_COMM_WORLD,"\n3-D Laplacian Eigenproblem\n\n");

 98:   /* show detailed info unless -terse option is given by user */
 99:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:      Compute the operator matrix that defines the eigensystem, Ax=kx
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

105:   PetscCall(DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,
106:                       DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,10,10,10,
107:                       PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,
108:                       1,1,NULL,NULL,NULL,&da));
109:   DMSetFromOptions(da);
110:   DMSetUp(da);

112:   /* print DM information */
113:   DMDAGetInfo(da,NULL,&M,&N,&P,&m,&n,&p,NULL,NULL,NULL,NULL,NULL,NULL);
114:   PetscPrintf(PETSC_COMM_WORLD," Grid partitioning: %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",m,n,p);

116:   /* create and fill the matrix */
117:   DMCreateMatrix(da,&A);
118:   FillMatrix(da,A);

120:   /* create random initial vector */
121:   seed = 1;
122:   PetscOptionsGetInt(NULL,NULL,"-seed",&seed,NULL);
124:   MatCreateVecs(A,&v0,NULL);
125:   PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
126:   PetscRandomSetFromOptions(rctx);
127:   for (i=0;i<seed;i++) {   /* simulate different seeds in the random generator */
128:     VecSetRandom(v0,rctx);
129:   }

131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
132:                 Create the eigensolver and set various options
133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

135:   /*
136:      Create eigensolver context
137:   */
138:   EPSCreate(PETSC_COMM_WORLD,&eps);

140:   /*
141:      Set operators. In this case, it is a standard eigenvalue problem
142:   */
143:   EPSSetOperators(eps,A,NULL);
144:   EPSSetProblemType(eps,EPS_HEP);

146:   /*
147:      Set specific solver options
148:   */
149:   EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
150:   EPSSetTolerances(eps,1e-8,PETSC_DEFAULT);
151:   EPSSetInitialSpace(eps,1,&v0);

153:   /*
154:      Set solver parameters at runtime
155:   */
156:   EPSSetFromOptions(eps);

158:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
159:                       Solve the eigensystem
160:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

162:   PetscTime(&t1);
163:   EPSSetUp(eps);
164:   PetscTime(&t2);
165:   EPSSolve(eps);
166:   PetscTime(&t3);
167:   if (!terse) {
168:     EPSGetIterationNumber(eps,&its);
169:     PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its);

171:     /*
172:        Optional: Get some information from the solver and display it
173:     */
174:     EPSGetType(eps,&type);
175:     PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
176:     EPSGetDimensions(eps,&nev,NULL,NULL);
177:     PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
178:     EPSGetTolerances(eps,&tol,&maxit);
179:     PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit);
180:   }

182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183:                     Display solution and clean up
184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

186:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
187:   else {
188:     /*
189:        Get number of converged approximate eigenpairs
190:     */
191:     EPSGetConverged(eps,&nconv);
192:     PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %" PetscInt_FMT "\n\n",nconv);

194:     if (nconv>0) {
195:       PetscMalloc1(nconv,&exact);
196:       GetExactEigenvalues(M,N,P,nconv,exact);
197:       /*
198:          Display eigenvalues and relative errors
199:       */
200:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,
201:            "           k          ||Ax-kx||/||kx||   Eigenvalue Error \n"
202:            "   ----------------- ------------------ ------------------\n"));

204:       for (i=0;i<nconv;i++) {
205:         /*
206:           Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
207:           ki (imaginary part)
208:         */
209:         EPSGetEigenpair(eps,i,&kr,&ki,NULL,NULL);
210:         /*
211:            Compute the relative error associated to each eigenpair
212:         */
213:         EPSComputeError(eps,i,EPS_ERROR_RELATIVE,&error);

215: #if defined(PETSC_USE_COMPLEX)
216:         re = PetscRealPart(kr);
217:         im = PetscImaginaryPart(kr);
218: #else
219:         re = kr;
220:         im = ki;
221: #endif
223:         PetscPrintf(PETSC_COMM_WORLD,"   %12g       %12g        %12g\n",(double)re,(double)error,(double)PetscAbsReal(re-exact[i]));
224:       }
225:       PetscFree(exact);
226:       PetscPrintf(PETSC_COMM_WORLD,"\n");
227:     }
228:   }

230:   /*
231:      Show computing times
232:   */
233:   PetscOptionsHasName(NULL,NULL,"-showtimes",&flg);
234:   if (flg) PetscPrintf(PETSC_COMM_WORLD," Elapsed time: %g (setup), %g (solve)\n",(double)(t2-t1),(double)(t3-t2));

236:   /*
237:      Free work space
238:   */
239:   EPSDestroy(&eps);
240:   MatDestroy(&A);
241:   VecDestroy(&v0);
242:   PetscRandomDestroy(&rctx);
243:   DMDestroy(&da);
244:   SlepcFinalize();
245:   return 0;
246: }

248: /*TEST

250:    testset:
251:       args: -eps_nev 8 -terse
252:       requires: double
253:       output_file: output/ex19_1.out
254:       test:
255:          suffix: 1_krylovschur
256:          args: -eps_type krylovschur -eps_ncv 64
257:       test:
258:          suffix: 1_lobpcg
259:          args: -eps_type lobpcg -eps_tol 1e-7
260:       test:
261:          suffix: 1_blopex
262:          args: -eps_type blopex -eps_tol 1e-7 -eps_blopex_blocksize 4
263:          requires: blopex

265: TEST*/