Actual source code: test2.c

slepc-3.17.0 2022-03-31
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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:   SlepcInitialize(&argc,&argv,(char*)0,help);

 32:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
 34:   if (!flag) m=n;
 35:   N = n*m;
 36:   PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL);
 37:   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);

 39:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40:                          Build the 2-D Laplacian
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

 66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 67:                 Create the solver and set various options
 68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

 79:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 80:                       Solve the problem, y=exp(t*A)*v
 81:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 88:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 89:            Repeat the computation in two steps, overwriting v:
 90:               v=exp(0.5*t*A)*v,  v=exp(0.5*t*A)*v
 91:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

114: /*TEST

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

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

131: TEST*/