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[] = "Tests the case when both arguments of MFNSolve() are the same Vec.\n\n"
 12:   "The command line options are:\n"
 13:   "  -t <sval>, where <sval> = scalar value that multiplies the argument.\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\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;
 25:   PetscScalar    t=0.3;
 26:   PetscInt       N,n=25,m,Istart,Iend,II,i,j;
 27:   PetscBool      flag;
 28:   Vec            v,y;

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

 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(PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL));
 38:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMatrix exponential y=exp(t*A)*e, of the 2-D Laplacian, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

 40:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 41:                          Build the 2-D Laplacian
 42:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 48:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
 49:   for (II=Istart;II<Iend;II++) {
 50:     i = II/n; j = II-i*n;
 51:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
 52:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
 53:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
 54:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
 55:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
 56:   }

 58:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
 59:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));

 61:   /* set v = ones(n,1) */
 62:   PetscCall(MatCreateVecs(A,&v,&y));
 63:   PetscCall(VecSet(v,1.0));

 65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 66:                 Create the solver and set various options
 67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 69:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f));
 70:   PetscCall(FNSetType(f,FNEXP));

 72:   PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
 73:   PetscCall(MFNSetOperator(mfn,A));
 74:   PetscCall(MFNSetFN(mfn,f));
 75:   PetscCall(MFNSetErrorIfNotConverged(mfn,PETSC_TRUE));
 76:   PetscCall(MFNSetFromOptions(mfn));

 78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79:                       Solve the problem, y=exp(t*A)*v
 80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 82:   PetscCall(FNSetScale(f,t,1.0));
 83:   PetscCall(MFNSolve(mfn,v,y));
 84:   PetscCall(VecNorm(y,NORM_2,&norm));
 85:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm));

 87:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 88:            Repeat the computation in two steps, overwriting v:
 89:               v=exp(0.5*t*A)*v,  v=exp(0.5*t*A)*v
 90:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 92:   PetscCall(FNSetScale(f,0.5*t,1.0));
 93:   PetscCall(MFNSolve(mfn,v,v));
 94:   PetscCall(MFNSolve(mfn,v,v));
 95:   /* compute norm of difference */
 96:   PetscCall(VecAXPY(y,-1.0,v));
 97:   PetscCall(VecNorm(y,NORM_2,&norm));
 98:   if (norm<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is <100*eps\n\n"));
 99:   else PetscCall(PetscPrintf(PETSC_COMM_WORLD," The norm of the difference is %g\n\n",(double)norm));

101:   /*
102:      Free work space
103:   */
104:   PetscCall(MFNDestroy(&mfn));
105:   PetscCall(FNDestroy(&f));
106:   PetscCall(MatDestroy(&A));
107:   PetscCall(VecDestroy(&v));
108:   PetscCall(VecDestroy(&y));
109:   PetscCall(SlepcFinalize());
110:   return 0;
111: }

113: /*TEST

115:    testset:
116:       args: -mfn_type {{krylov expokit}}
117:       output_file: output/test2_1.out
118:       test:
119:          suffix: 1
120:       test:
121:          suffix: 1_cuda
122:          args: -mat_type aijcusparse
123:          requires: cuda

125:    test:
126:       suffix: 3
127:       args: -mfn_type expokit -t 0.6 -mfn_ncv 24
128:       requires: !__float128

130: TEST*/