Actual source code: ex25.c

slepc-3.21.1 2024-04-26
Report Typos and Errors
  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:   PetscFunctionBeginUser;
 35:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

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

 44:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 45:      Compute the matrices that define the eigensystem, Ax=kBx
 46:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

 72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 73:                 Create the eigensolver and set various options
 74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 76:   /*
 77:      Create eigensolver context
 78:   */
 79:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

 81:   /*
 82:      Set operators and set problem type
 83:   */
 84:   PetscCall(EPSSetOperators(eps,A,B));
 85:   PetscCall(EPSSetProblemType(eps,EPS_GHEP));

 87:   /*
 88:      Set interval for spectrum slicing
 89:   */
 90:   inta = 0.1;
 91:   intb = 0.2;
 92:   PetscCall(EPSSetInterval(eps,inta,intb));
 93:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_ALL));

 95:   /*
 96:      Spectrum slicing requires Krylov-Schur
 97:   */
 98:   PetscCall(EPSSetType(eps,EPSKRYLOVSCHUR));

100:   /*
101:      Set shift-and-invert with Cholesky; select MUMPS if available
102:   */

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

111:   /*
112:      Use MUMPS if available.
113:      Note that in complex scalars we cannot use MUMPS for spectrum slicing,
114:      because MatGetInertia() is not available in that case.
115:   */
116: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
117:   PetscCall(EPSKrylovSchurSetDetectZeros(eps,PETSC_TRUE));  /* enforce zero detection */
118:   PetscCall(PCFactorSetMatSolverType(pc,MATSOLVERMUMPS));
119:   PetscCall(PCFactorSetUpMatSolverType(pc));
120:   /*
121:      Set several MUMPS options, the corresponding command-line options are:
122:      '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
123:      '-st_mat_mumps_icntl_24 1': detect null pivots in factorization (for the case that a shift is equal to an eigenvalue)
124:      '-st_mat_mumps_cntl_3 <tol>': a tolerance used for null pivot detection (must be larger than machine epsilon)

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

135:   /*
136:      Set solver parameters at runtime
137:   */
138:   PetscCall(EPSSetFromOptions(eps));

140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141:                       Solve the eigensystem
142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143:   PetscCall(EPSSetUp(eps));
144:   if (show) {
145:     PetscCall(EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias));
146:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n"));
147:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]));
148:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
149:     PetscCall(PetscFree(shifts));
150:     PetscCall(PetscFree(inertias));
151:   }
152:   PetscCall(EPSSolve(eps));
153:   if (show) {
154:     PetscCall(EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias));
155:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n"));
156:     for (i=0;i<ns;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Shift %g  Inertia %" PetscInt_FMT " \n",(double)shifts[i],inertias[i]));
157:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
158:     PetscCall(PetscFree(shifts));
159:     PetscCall(PetscFree(inertias));
160:   }

162:   /*
163:      Show eigenvalues in interval and print solution
164:   */
165:   PetscCall(EPSGetType(eps,&type));
166:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
167:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
168:   PetscCall(EPSGetInterval(eps,&inta,&intb));
169:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," %" PetscInt_FMT " eigenvalues found in [%g, %g]\n",nev,(double)inta,(double)intb));

171:   /*
172:      Show detailed info unless -terse option is given by user
173:    */
174:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
175:   if (terse) PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
176:   else {
177:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
178:     PetscCall(EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD));
179:     PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
180:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
181:   }

183:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
184:                     Clean up
185:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
186:   PetscCall(EPSDestroy(&eps));
187:   PetscCall(MatDestroy(&A));
188:   PetscCall(MatDestroy(&B));
189:   PetscCall(SlepcFinalize());
190:   return 0;
191: }

193: /*TEST

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

202: TEST*/