1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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;

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

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

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

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

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

 53:   MatGetOwnershipRange(A,&Istart,&Iend);
 54:   for (II=Istart;II<Iend;II++) {
 55:     i = II/n; j = II-i*n;
 56:     if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
 57:     if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
 58:     if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
 59:     if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
 60:     MatSetValue(A,II,II,4.0,INSERT_VALUES);
 61:     MatSetValue(B,II,II,2.0,INSERT_VALUES);
 62:   }
 63:   if (Istart==0) {
 64:     MatSetValue(B,0,0,6.0,INSERT_VALUES);
 65:     MatSetValue(B,0,1,-1.0,INSERT_VALUES);
 66:     MatSetValue(B,1,0,-1.0,INSERT_VALUES);
 67:     MatSetValue(B,1,1,1.0,INSERT_VALUES);
 68:   }

 70:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 71:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 72:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
 73:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);

 75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 76:                 Create the eigensolver and set various options
 77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 79:   EPSCreate(PETSC_COMM_WORLD,&eps);
 80:   EPSSetOperators(eps,A,B);
 81:   EPSSetProblemType(eps,EPS_GHEP);

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

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:                  Solve for first interval and display info
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

101:   EPSSolve(eps);
102:   EPSGetDimensions(eps,&nev,NULL,NULL);
103:   EPSGetInterval(eps,&int0,&int1);
104:   PetscPrintf(PETSC_COMM_WORLD," Found %D eigenvalues in interval [%g,%g]\n",nev,(double)int0,(double)int1);
105:   if (showinertia) {
106:     EPSKrylovSchurGetInertias(eps,&k,&shifts,&inertias);
107:     PetscPrintf(PETSC_COMM_WORLD," Used %D shifts (inertia):\n",k);
108:     for (i=0;i<k;i++) {
109:       PetscPrintf(PETSC_COMM_WORLD," .. %g (%D)\n",(double)shifts[i],inertias[i]);
110:     }
111:     PetscFree(shifts);
112:     PetscFree(inertias);
113:   }

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:                  Solve for second interval and display info
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
118:   EPSSetInterval(eps,1.499,1.6);
119:   EPSSolve(eps);
120:   EPSGetDimensions(eps,&nev,NULL,NULL);
121:   EPSGetInterval(eps,&int0,&int1);
122:   PetscPrintf(PETSC_COMM_WORLD," Found %D eigenvalues in interval [%g,%g]\n",nev,(double)int0,(double)int1);
123:   if (showinertia) {
124:     EPSKrylovSchurGetInertias(eps,&k,&shifts,&inertias);
125:     PetscPrintf(PETSC_COMM_WORLD," Used %D shifts (inertia):\n",k);
126:     for (i=0;i<k;i++) {
127:       PetscPrintf(PETSC_COMM_WORLD," .. %g (%D)\n",(double)shifts[i],inertias[i]);
128:     }
129:     PetscFree(shifts);
130:     PetscFree(inertias);
131:   }

133:   EPSDestroy(&eps);
134:   MatDestroy(&A);
135:   MatDestroy(&B);
136:   SlepcFinalize();
137:   return ierr;
138: }

140: /*TEST

142:    test:
143:       suffix: 1
144:       args: -showinertia 0 -eps_error_relative
145:       requires: !single

147: TEST*/