Actual source code: ex25.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[] = "Spectrum slicing on generalized symmetric eigenproblem.\n\n"
 12:   "The problem is similar to ex13.c.\n\n"
 13:   "The command line options are:\n"
 14:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 15:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n";

 17: #include <slepceps.h>

 19: int main(int argc,char **argv)
 20: {
 21:   Mat            A,B;         /* matrices */
 22:   EPS            eps;         /* eigenproblem solver context */
 23:   ST             st;          /* spectral transformation context */
 24:   KSP            ksp;
 25:   PC             pc;
 26:   EPSType        type;
 27:   PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,*inertias,ns;
 28:   PetscReal      inta,intb,*shifts;
 29:   PetscBool      flag,show=PETSC_FALSE,terse;
 30: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
 31:   Mat            F;
 32: #endif

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

 36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 37:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
 38:   PetscOptionsGetBool(NULL,NULL,"-show_inertias",&show,NULL);
 39:   if (!flag) m=n;
 40:   N = n*m;
 41:   PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum slicing on GHEP, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m);

 43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 44:      Compute the matrices that define the eigensystem, Ax=kBx
 45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 52:   MatCreate(PETSC_COMM_WORLD,&B);
 53:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
 54:   MatSetFromOptions(B);
 55:   MatSetUp(B);

 57:   MatGetOwnershipRange(A,&Istart,&Iend);
 58:   for (II=Istart;II<Iend;II++) {
 59:     i = II/n; j = II-i*n;
 60:     if (i>0) MatSetValue(A,II,II-n,-1.0,INSERT_VALUES);
 61:     if (i<m-1) MatSetValue(A,II,II+n,-1.0,INSERT_VALUES);
 62:     if (j>0) MatSetValue(A,II,II-1,-1.0,INSERT_VALUES);
 63:     if (j<n-1) MatSetValue(A,II,II+1,-1.0,INSERT_VALUES);
 64:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
 65:     MatSetValue(B,II,II,4.0,INSERT_VALUES);
 66:   }

 68:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 69:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 70:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 71:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

 73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 74:                 Create the eigensolver and set various options
 75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 77:   /*
 78:      Create eigensolver context
 79:   */
 80:   EPSCreate(PETSC_COMM_WORLD,&eps);

 82:   /*
 83:      Set operators and set problem type
 84:   */
 85:   EPSSetOperators(eps,A,B);
 86:   EPSSetProblemType(eps,EPS_GHEP);

 88:   /*
 89:      Set interval for spectrum slicing
 90:   */
 91:   inta = 0.1;
 92:   intb = 0.2;
 93:   EPSSetInterval(eps,inta,intb);
 94:   EPSSetWhichEigenpairs(eps,EPS_ALL);

 96:   /*
 97:      Spectrum slicing requires Krylov-Schur
 98:   */
 99:   EPSSetType(eps,EPSKRYLOVSCHUR);

101:   /*
102:      Set shift-and-invert with Cholesky; select MUMPS if available
103:   */

105:   EPSGetST(eps,&st);
106:   STSetType(st,STSINVERT);
107:   EPSKrylovSchurGetKSP(eps,&ksp);
108:   KSPSetType(ksp,KSPPREONLY);
109:   KSPGetPC(ksp,&pc);
110:   PCSetType(pc,PCCHOLESKY);

112:   /*
113:      Use MUMPS if available.
114:      Note that in complex scalars we cannot use MUMPS for spectrum slicing,
115:      because MatGetInertia() is not available in that case.
116:   */
117: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
118:   EPSKrylovSchurSetDetectZeros(eps,PETSC_TRUE);  /* enforce zero detection */
119:   PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
120:   PCFactorSetUpMatSolverType(pc);
121:   /*
122:      Set several MUMPS options, the corresponding command-line options are:
123:      '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
124:      '-st_mat_mumps_icntl_24 1': detect null pivots in factorization (for the case that a shift is equal to an eigenvalue)
125:      '-st_mat_mumps_cntl_3 <tol>': a tolerance used for null pivot detection (must be larger than machine epsilon)

127:      Note: depending on the interval, it may be necessary also to increase the workspace:
128:      '-st_mat_mumps_icntl_14 <percentage>': increase workspace with a percentage (50, 100 or more)
129:   */
130:   PCFactorGetMatrix(pc,&F);
131:   MatMumpsSetIcntl(F,13,1);
132:   MatMumpsSetIcntl(F,24,1);
133:   MatMumpsSetCntl(F,3,1e-12);
134: #endif

136:   /*
137:      Set solver parameters at runtime
138:   */
139:   EPSSetFromOptions(eps);

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:                       Solve the eigensystem
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144:   EPSSetUp(eps);
145:   if (show) {
146:     EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
147:     PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n");
148:     for (i=0;i<ns;i++) PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]);
149:     PetscPrintf(PETSC_COMM_WORLD,"\n");
150:     PetscFree(shifts);
151:     PetscFree(inertias);
152:   }
153:   EPSSolve(eps);
154:   if (show) {
155:     EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
156:     PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n");
157:     for (i=0;i<ns;i++) PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]);
158:     PetscPrintf(PETSC_COMM_WORLD,"\n");
159:     PetscFree(shifts);
160:     PetscFree(inertias);
161:   }

163:   /*
164:      Show eigenvalues in interval and print solution
165:   */
166:   EPSGetType(eps,&type);
167:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
168:   EPSGetDimensions(eps,&nev,NULL,NULL);
169:   EPSGetInterval(eps,&inta,&intb);
170:   PetscPrintf(PETSC_COMM_WORLD," %" PetscInt_FMT " eigenvalues found in [%g, %g]\n",nev,(double)inta,(double)intb);

172:   /*
173:      Show detailed info unless -terse option is given by user
174:    */
175:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
176:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
177:   else {
178:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
179:     EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
180:     EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
181:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
182:   }

184:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
185:                     Clean up
186:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
187:   EPSDestroy(&eps);
188:   MatDestroy(&A);
189:   MatDestroy(&B);
190:   SlepcFinalize();
191:   return 0;
192: }

194: /*TEST

196:    testset:
197:       args: -terse
198:       test:
199:          requires: !mumps
200:       test:
201:          requires: mumps !complex

203: TEST*/