Actual source code: test9.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[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid. "
 12:   "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n"
 13:   "This example illustrates how the user can set the initial vector.\n\n"
 14:   "The command line options are:\n"
 15:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

 17: #include <slepceps.h>

 19: /*
 20:    User-defined routines
 21: */
 22: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
 23: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);

 25: /*
 26:    Check if computed eigenvectors have unit norm
 27: */
 28: PetscErrorCode CheckNormalizedVectors(EPS eps)
 29: {
 30:   PetscInt       i,nconv;
 31:   Mat            A;
 32:   Vec            xr,xi;
 33:   PetscReal      error=0.0,normr;
 34: #if !defined(PETSC_USE_COMPLEX)
 35:   PetscReal      normi;
 36: #endif

 39:   EPSGetConverged(eps,&nconv);
 40:   if (nconv>0) {
 41:     EPSGetOperators(eps,&A,NULL);
 42:     MatCreateVecs(A,&xr,&xi);
 43:     for (i=0;i<nconv;i++) {
 44:       EPSGetEigenvector(eps,i,xr,xi);
 45: #if defined(PETSC_USE_COMPLEX)
 46:       VecNorm(xr,NORM_2,&normr);
 47:       error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
 48: #else
 49:       VecNormBegin(xr,NORM_2,&normr);
 50:       VecNormBegin(xi,NORM_2,&normi);
 51:       VecNormEnd(xr,NORM_2,&normr);
 52:       VecNormEnd(xi,NORM_2,&normi);
 53:       error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
 54: #endif
 55:     }
 56:     VecDestroy(&xr);
 57:     VecDestroy(&xi);
 58:     if (error>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
 59:   }
 60:   return 0;
 61: }

 63: int main(int argc,char **argv)
 64: {
 65:   Vec            v0;              /* initial vector */
 66:   Mat            A;               /* operator matrix */
 67:   EPS            eps;             /* eigenproblem solver context */
 68:   PetscReal      tol=0.5*PETSC_SMALL;
 69:   PetscInt       N,m=15,nev;
 70:   PetscScalar    origin=0.0;
 71:   PetscBool      flg,delay,skipnorm=PETSC_FALSE;

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

 76:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 77:   N = m*(m+1)/2;
 78:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m);
 79:   PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);

 81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 82:      Compute the operator matrix that defines the eigensystem, Ax=kx
 83:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 85:   MatCreate(PETSC_COMM_WORLD,&A);
 86:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 87:   MatSetFromOptions(A);
 88:   MatSetUp(A);
 89:   MatMarkovModel(m,A);

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:                 Create the eigensolver and set various options
 93:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 95:   /*
 96:      Create eigensolver context
 97:   */
 98:   EPSCreate(PETSC_COMM_WORLD,&eps);

100:   /*
101:      Set operators. In this case, it is a standard eigenvalue problem
102:   */
103:   EPSSetOperators(eps,A,NULL);
104:   EPSSetProblemType(eps,EPS_NHEP);
105:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

107:   /*
108:      Set the custom comparing routine in order to obtain the eigenvalues
109:      closest to the target on the right only
110:   */
111:   EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);

113:   /*
114:      Set solver parameters at runtime
115:   */
116:   EPSSetFromOptions(eps);
117:   PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg);
118:   if (flg) {
119:     EPSArnoldiGetDelayed(eps,&delay);
120:     if (delay) PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n");
121:   }

123:   /*
124:      Set the initial vector. This is optional, if not done the initial
125:      vector is set to random values
126:   */
127:   MatCreateVecs(A,&v0,NULL);
128:   VecSetValue(v0,0,-1.5,INSERT_VALUES);
129:   VecSetValue(v0,1,2.1,INSERT_VALUES);
130:   VecAssemblyBegin(v0);
131:   VecAssemblyEnd(v0);
132:   EPSSetInitialSpace(eps,1,&v0);

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:                       Solve the eigensystem
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

138:   EPSSolve(eps);
139:   EPSGetDimensions(eps,&nev,NULL,NULL);
140:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143:                     Display solution and clean up
144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

146:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
147:   if (!skipnorm) CheckNormalizedVectors(eps);
148:   EPSDestroy(&eps);
149:   MatDestroy(&A);
150:   VecDestroy(&v0);
151:   SlepcFinalize();
152:   return 0;
153: }

155: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
156: {
157:   const PetscReal cst = 0.5/(PetscReal)(m-1);
158:   PetscReal       pd,pu;
159:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

162:   MatGetOwnershipRange(A,&Istart,&Iend);
163:   for (i=1;i<=m;i++) {
164:     jmax = m-i+1;
165:     for (j=1;j<=jmax;j++) {
166:       ix = ix + 1;
167:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
168:       if (j!=jmax) {
169:         pd = cst*(PetscReal)(i+j-1);
170:         /* north */
171:         if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
172:         else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
173:         /* east */
174:         if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
175:         else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
176:       }
177:       /* south */
178:       pu = 0.5 - cst*(PetscReal)(i+j-3);
179:       if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
180:       /* west */
181:       if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
182:     }
183:   }
184:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
185:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
186:   return 0;
187: }

189: /*
190:     Function for user-defined eigenvalue ordering criterion.

192:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
193:     one of them as the preferred one according to the criterion.
194:     In this example, the preferred value is the one furthest away from the origin.
195: */
196: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
197: {
198:   PetscScalar origin = *(PetscScalar*)ctx;
199:   PetscReal   d;

202:   d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
203:   *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
204:   return 0;
205: }

207: /*TEST

209:    testset:
210:       args: -eps_nev 4
211:       output_file: output/test9_1.out
212:       test:
213:          suffix: 1
214:          args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 7 -eps_max_it 300
215:       test:
216:          suffix: 1_gd
217:          args: -eps_type gd -st_pc_type none
218:       test:
219:          suffix: 1_gd2
220:          args: -eps_type gd -eps_gd_double_expansion -st_pc_type none

222:    test:
223:       suffix: 2
224:       args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_max_it 1500
225:       requires: double
226:       output_file: output/test9_1.out

228:    test:
229:       suffix: 3
230:       nsize: 2
231:       args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm
232:       requires: !single
233:       output_file: output/test9_3.out

235:    test:
236:       suffix: 4
237:       args: -eps_nev 4 -eps_true_residual
238:       requires: !single
239:       output_file: output/test9_1.out

241:    test:
242:       suffix: 5
243:       args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2
244:       filter: sed -e "s/[+-]0\.0*i//g"
245:       requires: !single

247:    test:
248:       suffix: 5_arpack
249:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10
250:       requires: arpack !single
251:       output_file: output/test9_5.out

253:    testset:
254:       args: -eps_type ciss -eps_tol 1e-9 -rg_type ellipse -rg_ellipse_center 0.55 -rg_ellipse_radius 0.05 -rg_ellipse_vscale 0.1 -eps_ciss_usest 0 -eps_all
255:       requires: !single
256:       output_file: output/test9_6.out
257:       test:
258:          suffix: 6
259:       test:
260:          suffix: 6_hankel
261:          args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 64
262:       test:
263:          suffix: 6_cheby
264:          args: -eps_ciss_quadrule chebyshev
265:       test:
266:          suffix: 6_hankel_cheby
267:          args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 64
268:       test:
269:          suffix: 6_refine
270:          args: -eps_ciss_moments 4 -eps_ciss_blocksize 5 -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 2
271:       test:
272:          suffix: 6_bcgs
273:          args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type sor -eps_ciss_integration_points 12

275:    test:
276:       suffix: 6_cheby_interval
277:       args: -eps_type ciss -eps_tol 1e-9 -rg_type interval -rg_interval_endpoints 0.5,0.6 -eps_ciss_quadrule chebyshev -eps_ciss_usest 0 -eps_all
278:       requires: !single
279:       output_file: output/test9_6.out

281:    testset:
282:       args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values
283:       filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"
284:       test:
285:          suffix: 7_real
286:          requires: !single !complex
287:       test:
288:          suffix: 7
289:          requires: !single complex

291:    test:
292:       suffix: 8
293:       args: -eps_nev 4 -eps_ncv 7 -eps_view_values draw -eps_monitor draw::draw_lg
294:       requires: x
295:       output_file: output/test9_1.out

297:    test:
298:       suffix: 5_ksphpddm
299:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10
300:       requires: hpddm
301:       output_file: output/test9_5.out

303:    test:
304:       suffix: 5_pchpddm
305:       args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10
306:       requires: hpddm
307:       output_file: output/test9_5.out

309: TEST*/