Actual source code: test2.c

slepc-3.20.2 2024-03-15
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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[] = "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));
 47:   PetscCall(MatSetUp(A));

 49:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
 50:   for (II=Istart;II<Iend;II++) {
 51:     i = II/n; j = II-i*n;
 52:     if (i>0) PetscCall(MatSetValue(A,II,II-n,-1.0,INSERT_VALUES));
 53:     if (i<m-1) PetscCall(MatSetValue(A,II,II+n,-1.0,INSERT_VALUES));
 54:     if (j>0) PetscCall(MatSetValue(A,II,II-1,-1.0,INSERT_VALUES));
 55:     if (j<n-1) PetscCall(MatSetValue(A,II,II+1,-1.0,INSERT_VALUES));
 56:     PetscCall(MatSetValue(A,II,II,4.0,INSERT_VALUES));
 57:   }

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

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

 67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 68:                 Create the solver and set various options
 69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 71:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f));
 72:   PetscCall(FNSetType(f,FNEXP));

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

 80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 81:                       Solve the problem, y=exp(t*A)*v
 82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 89:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 90:            Repeat the computation in two steps, overwriting v:
 91:               v=exp(0.5*t*A)*v,  v=exp(0.5*t*A)*v
 92:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

103:   /*
104:      Free work space
105:   */
106:   PetscCall(MFNDestroy(&mfn));
107:   PetscCall(FNDestroy(&f));
108:   PetscCall(MatDestroy(&A));
109:   PetscCall(VecDestroy(&v));
110:   PetscCall(VecDestroy(&y));
111:   PetscCall(SlepcFinalize());
112:   return 0;
113: }

115: /*TEST

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

127:    test:
128:       suffix: 3
129:       args: -mfn_type expokit -t 0.6 -mfn_ncv 35
130:       requires: !__float128

132: TEST*/