Actual source code: ex12.c

slepc-3.21.1 2024-04-26
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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[] = "Compute all eigenvalues in an interval of a symmetric-definite problem.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

 16: #include <slepceps.h>

 18: int main(int argc,char **argv)
 19: {
 20:   Mat            A,B;         /* matrices */
 21:   EPS            eps;         /* eigenproblem solver context */
 22:   ST             st;          /* spectral transformation context */
 23:   KSP            ksp;
 24:   PC             pc;
 25:   PetscInt       N,n=35,m,Istart,Iend,II,nev,i,j,k,*inertias;
 26:   PetscBool      flag,showinertia=PETSC_TRUE;
 27:   PetscReal      int0,int1,*shifts;

 29:   PetscFunctionBeginUser;
 30:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

 32:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-showinertia",&showinertia,NULL));
 33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 34:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
 35:   if (!flag) m=n;
 36:   N = n*m;
 37:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSymmetric-definite problem with two intervals, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:      Compute the matrices that define the eigensystem, Ax=kBx
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 43:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
 44:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
 45:   PetscCall(MatSetFromOptions(A));

 47:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
 48:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N));
 49:   PetscCall(MatSetFromOptions(B));

 51:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
 52:   for (II=Istart;II<Iend;II++) {
 53:     i = II/n; j = II-i*n;
 54:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
 55:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
 56:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
 57:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
 58:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
 59:     PetscCall(MatSetValue(B,II,II,2.0,INSERT_VALUES));
 60:   }
 61:   if (Istart==0) {
 62:     PetscCall(MatSetValue(B,0,0,6.0,INSERT_VALUES));
 63:     PetscCall(MatSetValue(B,0,1,-1.0,INSERT_VALUES));
 64:     PetscCall(MatSetValue(B,1,0,-1.0,INSERT_VALUES));
 65:     PetscCall(MatSetValue(B,1,1,1.0,INSERT_VALUES));
 66:   }

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

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

 77:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
 78:   PetscCall(EPSSetOperators(eps,A,B));
 79:   PetscCall(EPSSetProblemType(eps,EPS_GHEP));

 81:   /*
 82:      Set first interval and other settings for spectrum slicing
 83:   */
 84:   PetscCall(EPSSetType(eps,EPSKRYLOVSCHUR));
 85:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_ALL));
 86:   PetscCall(EPSSetInterval(eps,1.1,1.3));
 87:   PetscCall(EPSGetST(eps,&st));
 88:   PetscCall(STSetType(st,STSINVERT));
 89:   PetscCall(EPSKrylovSchurGetKSP(eps,&ksp));
 90:   PetscCall(KSPGetPC(ksp,&pc));
 91:   PetscCall(KSPSetType(ksp,KSPPREONLY));
 92:   PetscCall(PCSetType(pc,PCCHOLESKY));
 93:   PetscCall(EPSSetFromOptions(eps));

 95:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 96:                  Solve for first interval and display info
 97:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 99:   PetscCall(EPSSolve(eps));
100:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
101:   PetscCall(EPSGetInterval(eps,&int0,&int1));
102:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Found %" PetscInt_FMT " eigenvalues in interval [%g,%g]\n",nev,(double)int0,(double)int1));
103:   if (showinertia) {
104:     PetscCall(EPSKrylovSchurGetInertias(eps,&k,&shifts,&inertias));
105:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Used %" PetscInt_FMT " shifts (inertia):\n",k));
106:     for (i=0;i<k;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD," .. %g (%" PetscInt_FMT ")\n",(double)shifts[i],inertias[i]));
107:     PetscCall(PetscFree(shifts));
108:     PetscCall(PetscFree(inertias));
109:   }

111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
112:                  Solve for second interval and display info
113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114:   PetscCall(EPSSetInterval(eps,1.499,1.6));
115:   PetscCall(EPSSolve(eps));
116:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
117:   PetscCall(EPSGetInterval(eps,&int0,&int1));
118:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Found %" PetscInt_FMT " eigenvalues in interval [%g,%g]\n",nev,(double)int0,(double)int1));
119:   if (showinertia) {
120:     PetscCall(EPSKrylovSchurGetInertias(eps,&k,&shifts,&inertias));
121:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Used %" PetscInt_FMT " shifts (inertia):\n",k));
122:     for (i=0;i<k;i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD," .. %g (%" PetscInt_FMT ")\n",(double)shifts[i],inertias[i]));
123:     PetscCall(PetscFree(shifts));
124:     PetscCall(PetscFree(inertias));
125:   }

127:   PetscCall(EPSDestroy(&eps));
128:   PetscCall(MatDestroy(&A));
129:   PetscCall(MatDestroy(&B));
130:   PetscCall(SlepcFinalize());
131:   return 0;
132: }

134: /*TEST

136:    test:
137:       suffix: 1
138:       args: -showinertia 0 -eps_error_relative
139:       requires: !single

141: TEST*/