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[] = "Computes the action of the square root of the 2-D Laplacian.\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"
 15:   "To draw the solution run with -mfn_view_solution draw -draw_pause -1\n\n";

 17: #include <slepcmfn.h>

 19: int main(int argc,char **argv)
 20: {
 21:   Mat            A;           /* problem matrix */
 22:   MFN            mfn;
 23:   FN             f;
 24:   PetscReal      norm,tol;
 25:   Vec            v,y,z;
 26:   PetscInt       N,n=10,m,Istart,Iend,i,j,II;
 27:   PetscBool      flag;

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

 32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 33:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
 34:   if (!flag) m=n;
 35:   N = n*m;
 36:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSquare root of Laplacian y=sqrt(A)*e_1, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

 38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 39:                  Compute the discrete 2-D Laplacian, A
 40:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 46:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
 47:   for (II=Istart;II<Iend;II++) {
 48:     i = II/n; j = II-i*n;
 49:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
 50:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
 51:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
 52:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
 53:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
 54:   }

 56:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
 57:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

 59:   /* set symmetry flag so that solver can exploit it */
 60:   PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));

 62:   /* set v = e_1 */
 63:   PetscCall(MatCreateVecs(A,NULL,&v));
 64:   PetscCall(VecSetValue(v,0,1.0,INSERT_VALUES));
 65:   PetscCall(VecAssemblyBegin(v));
 66:   PetscCall(VecAssemblyEnd(v));
 67:   PetscCall(VecDuplicate(v,&y));
 68:   PetscCall(VecDuplicate(v,&z));

 70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 71:              Create the solver, set the matrix and the function
 72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 73:   PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
 74:   PetscCall(MFNSetOperator(mfn,A));
 75:   PetscCall(MFNGetFN(mfn,&f));
 76:   PetscCall(FNSetType(f,FNSQRT));
 77:   PetscCall(MFNSetErrorIfNotConverged(mfn,PETSC_TRUE));
 78:   PetscCall(MFNSetFromOptions(mfn));

 80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 81:                       First solve: y=sqrt(A)*v
 82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 84:   PetscCall(MFNSolve(mfn,v,y));
 85:   PetscCall(VecNorm(y,NORM_2,&norm));
 86:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Intermediate vector has norm %g\n",(double)norm));

 88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 89:              Second solve: z=sqrt(A)*y and compare against A*v
 90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 92:   PetscCall(MFNSolve(mfn,y,z));
 93:   PetscCall(MFNGetTolerances(mfn,&tol,NULL));

 95:   PetscCall(MatMult(A,v,y));   /* overwrite y */
 96:   PetscCall(VecAXPY(y,-1.0,z));
 97:   PetscCall(VecNorm(y,NORM_2,&norm));

 99:   if (norm<tol) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error norm is less than the requested tolerance\n\n"));
100:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error norm larger than tolerance: %3.1e\n\n",(double)norm));

102:   /*
103:      Free work space
104:   */
105:   PetscCall(MFNDestroy(&mfn));
106:   PetscCall(MatDestroy(&A));
107:   PetscCall(VecDestroy(&v));
108:   PetscCall(VecDestroy(&y));
109:   PetscCall(VecDestroy(&z));
110:   PetscCall(SlepcFinalize());
111:   return 0;
112: }

114: /*TEST

116:    test:
117:       suffix: 1
118:       args: -mfn_tol 1e-4

120: TEST*/