Actual source code: ex47.c

slepc-3.22.2 2024-12-02
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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[] = "Shows how to recover symmetry when solving a GHEP as non-symmetric.\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: /*
 19:    User context for shell matrix
 20: */
 21: typedef struct {
 22:   KSP       ksp;
 23:   Mat       B;
 24:   Vec       w;
 25: } CTX_SHELL;

 27: /*
 28:     Matrix-vector product function for user matrix
 29:        y <-- A^{-1}*B*x
 30:     The matrix A^{-1}*B*x is not symmetric, but it is self-adjoint with respect
 31:     to the B-inner product. Here we assume A is symmetric and B is SPD.
 32:  */
 33: PetscErrorCode MatMult_Sinvert0(Mat S,Vec x,Vec y)
 34: {
 35:   CTX_SHELL      *ctx;

 37:   PetscFunctionBeginUser;
 38:   PetscCall(MatShellGetContext(S,&ctx));
 39:   PetscCall(MatMult(ctx->B,x,ctx->w));
 40:   PetscCall(KSPSolve(ctx->ksp,ctx->w,y));
 41:   PetscFunctionReturn(PETSC_SUCCESS);
 42: }

 44: int main(int argc,char **argv)
 45: {
 46:   Mat               A,B,S;      /* matrices */
 47:   EPS               eps;        /* eigenproblem solver context */
 48:   BV                bv;
 49:   Vec               *X,v;
 50:   PetscReal         lev=0.0,tol=1000*PETSC_MACHINE_EPSILON;
 51:   PetscInt          N,n=45,m,Istart,Iend,II,i,j,nconv;
 52:   PetscBool         flag;
 53:   CTX_SHELL         *ctx;

 55:   PetscFunctionBeginUser;
 56:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
 57:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 58:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
 59:   if (!flag) m=n;
 60:   N = n*m;
 61:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

 63:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 64:          Compute the matrices that define the eigensystem, Ax=kBx
 65:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 67:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
 68:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
 69:   PetscCall(MatSetFromOptions(A));

 71:   PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
 72:   PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N));
 73:   PetscCall(MatSetFromOptions(B));

 75:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
 76:   for (II=Istart;II<Iend;II++) {
 77:     i = II/n; j = II-i*n;
 78:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
 79:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
 80:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
 81:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
 82:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
 83:     PetscCall(MatSetValue(B,II,II,2.0/PetscLogScalar(II+2),INSERT_VALUES));
 84:   }

 86:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
 87:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
 88:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
 89:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
 90:   PetscCall(MatCreateVecs(B,&v,NULL));

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:               Create a shell matrix S = A^{-1}*B
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 95:   PetscCall(PetscNew(&ctx));
 96:   PetscCall(KSPCreate(PETSC_COMM_WORLD,&ctx->ksp));
 97:   PetscCall(KSPSetOperators(ctx->ksp,A,A));
 98:   PetscCall(KSPSetTolerances(ctx->ksp,tol,PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
 99:   PetscCall(KSPSetFromOptions(ctx->ksp));
100:   ctx->B = B;
101:   PetscCall(MatCreateVecs(A,&ctx->w,NULL));
102:   PetscCall(MatCreateShell(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,(void*)ctx,&S));
103:   PetscCall(MatShellSetOperation(S,MATOP_MULT,(void(*)(void))MatMult_Sinvert0));

105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106:                 Create the eigensolver and set various options
107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

109:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
110:   PetscCall(EPSSetOperators(eps,S,NULL));
111:   PetscCall(EPSSetProblemType(eps,EPS_HEP));  /* even though S is not symmetric */
112:   PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT));
113:   PetscCall(EPSSetFromOptions(eps));

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
116:                       Solve the eigensystem
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

119:   PetscCall(EPSSetUp(eps));   /* explicitly call setup */
120:   PetscCall(EPSGetBV(eps,&bv));
121:   PetscCall(BVSetMatrix(bv,B,PETSC_FALSE));  /* set inner product matrix to recover symmetry */
122:   PetscCall(EPSSolve(eps));

124:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125:                  Display solution and check B-orthogonality
126:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

128:   PetscCall(EPSGetTolerances(eps,&tol,NULL));
129:   PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
130:   PetscCall(EPSGetConverged(eps,&nconv));
131:   if (nconv>1) {
132:     PetscCall(VecDuplicateVecs(v,nconv,&X));
133:     for (i=0;i<nconv;i++) PetscCall(EPSGetEigenvector(eps,i,X[i],NULL));
134:     PetscCall(VecCheckOrthonormality(X,nconv,NULL,nconv,B,NULL,&lev));
135:     if (lev<10*tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality below the tolerance\n"));
136:     else PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Level of orthogonality: %g\n",(double)lev));
137:     PetscCall(VecDestroyVecs(nconv,&X));
138:   }

140:   PetscCall(EPSDestroy(&eps));
141:   PetscCall(MatDestroy(&A));
142:   PetscCall(MatDestroy(&B));
143:   PetscCall(VecDestroy(&v));
144:   PetscCall(KSPDestroy(&ctx->ksp));
145:   PetscCall(VecDestroy(&ctx->w));
146:   PetscCall(PetscFree(ctx));
147:   PetscCall(MatDestroy(&S));
148:   PetscCall(SlepcFinalize());
149:   return 0;
150: }

152: /*TEST

154:    test:
155:       args: -n 18 -eps_nev 4 -eps_max_it 1500
156:       requires: !single

158: TEST*/