Actual source code: test9.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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: int main(int argc,char **argv)
 26: {
 27:   Vec            v0;              /* initial vector */
 28:   Mat            A;               /* operator matrix */
 29:   EPS            eps;             /* eigenproblem solver context */
 30:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
 31:   PetscInt       N,m=15,nev;
 32:   PetscScalar    origin=0.0;
 33:   PetscBool      flg,delay;

 36:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 38:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 39:   N = m*(m+1)/2;
 40:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n\n",N,m);

 42:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43:      Compute the operator matrix that defines the eigensystem, Ax=kx
 44:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 46:   MatCreate(PETSC_COMM_WORLD,&A);
 47:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 48:   MatSetFromOptions(A);
 49:   MatSetUp(A);
 50:   MatMarkovModel(m,A);

 52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 53:                 Create the eigensolver and set various options
 54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 56:   /*
 57:      Create eigensolver context
 58:   */
 59:   EPSCreate(PETSC_COMM_WORLD,&eps);

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

 68:   /*
 69:      Set the custom comparing routine in order to obtain the eigenvalues
 70:      closest to the target on the right only
 71:   */
 72:   EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);


 75:   /*
 76:      Set solver parameters at runtime
 77:   */
 78:   EPSSetFromOptions(eps);
 79:   PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg);
 80:   if (flg) {
 81:     EPSArnoldiGetDelayed(eps,&delay);
 82:     if (delay) {
 83:       PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n");
 84:     }
 85:   }

 87:   /*
 88:      Set the initial vector. This is optional, if not done the initial
 89:      vector is set to random values
 90:   */
 91:   MatCreateVecs(A,&v0,NULL);
 92:   VecSetValue(v0,0,-1.5,INSERT_VALUES);
 93:   VecSetValue(v0,1,2.1,INSERT_VALUES);
 94:   VecAssemblyBegin(v0);
 95:   VecAssemblyEnd(v0);
 96:   EPSSetInitialSpace(eps,1,&v0);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:                       Solve the eigensystem
100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

102:   EPSSolve(eps);
103:   EPSGetDimensions(eps,&nev,NULL,NULL);
104:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107:                     Display solution and clean up
108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

110:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
111:   EPSDestroy(&eps);
112:   MatDestroy(&A);
113:   VecDestroy(&v0);
114:   SlepcFinalize();
115:   return ierr;
116: }

118: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
119: {
120:   const PetscReal cst = 0.5/(PetscReal)(m-1);
121:   PetscReal       pd,pu;
122:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
123:   PetscErrorCode  ierr;

126:   MatGetOwnershipRange(A,&Istart,&Iend);
127:   for (i=1;i<=m;i++) {
128:     jmax = m-i+1;
129:     for (j=1;j<=jmax;j++) {
130:       ix = ix + 1;
131:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
132:       if (j!=jmax) {
133:         pd = cst*(PetscReal)(i+j-1);
134:         /* north */
135:         if (i==1) {
136:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
137:         } else {
138:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
139:         }
140:         /* east */
141:         if (j==1) {
142:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
143:         } else {
144:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
145:         }
146:       }
147:       /* south */
148:       pu = 0.5 - cst*(PetscReal)(i+j-3);
149:       if (j>1) {
150:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
151:       }
152:       /* west */
153:       if (i>1) {
154:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
155:       }
156:     }
157:   }
158:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
159:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
160:   return(0);
161: }

163: /*
164:     Function for user-defined eigenvalue ordering criterion.

166:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
167:     one of them as the preferred one according to the criterion.
168:     In this example, the preferred value is the one furthest to the origin.
169: */
170: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
171: {
172:   PetscScalar origin = *(PetscScalar*)ctx;
173:   PetscReal   d;

176:   d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
177:   *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
178:   return(0);
179: }

181: /*TEST

183:    testset:
184:       args: -eps_nev 4
185:       requires: !single
186:       output_file: output/test9_1.out
187:       test:
188:          suffix: 1
189:          args: -eps_type {{krylovschur arnoldi}} -eps_ncv 7 -eps_max_it 300
190:       test:
191:          suffix: 1_more
192:          args: -eps_type {{gd lapack}}
193:       test:
194:          suffix: 1_gd2
195:          args: -eps_type gd -eps_gd_double_expansion

197:    test:
198:       suffix: 2
199:       args: -eps_balance {{none oneside twoside}} -eps_nev 4 -eps_ncv 7 -eps_max_it 500
200:       requires: !single
201:       output_file: output/test9_1.out

203:    test:
204:       suffix: 3
205:       nsize: 2
206:       args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}}
207:       requires: !single
208:       output_file: output/test9_3.out

210:    test:
211:       suffix: 4
212:       args: -eps_nev 4 -eps_true_residual
213:       requires: !single
214:       output_file: output/test9_1.out

216:    test:
217:       suffix: 5
218:       args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -eps_jd_minv 2
219:       requires: !single !complex

221:    testset:
222:       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
223:       requires: !single
224:       output_file: output/test9_6.out
225:       test:
226:          suffix: 6
227:       test:
228:          suffix: 6_hankel
229:          args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6
230:       test:
231:          suffix: 6_cheby
232:          args: -eps_ciss_quadrule chebyshev
233:       test:
234:          suffix: 6_hankel_cheby
235:          args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev
236:       test:
237:          suffix: 6_refine
238:          args: -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 1
239:       test:
240:          suffix: 6_bcgs
241:          args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type sor

243: TEST*/