Actual source code: ex23.c

slepc-3.20.1 2023-11-27
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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[] = "Computes exp(t*A)*v for a matrix associated with a Markov model.\n\n"
 12:   "The command line options are:\n"
 13:   "  -t <t>, where <t> = time parameter (multiplies the matrix).\n"
 14:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n"
 15:   "To draw the solution run with -mfn_view_solution draw -draw_pause -1\n\n";

 17: #include <slepcmfn.h>

 19: /*
 20:    User-defined routines
 21: */
 22: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

 24: int main(int argc,char **argv)
 25: {
 26:   Mat                A;           /* problem matrix */
 27:   MFN                mfn;
 28:   FN                 f;
 29:   PetscReal          tol,norm;
 30:   PetscScalar        t=2.0;
 31:   Vec                v,y;
 32:   PetscInt           N,m=15,ncv,maxit,its;
 33:   MFNConvergedReason reason;

 35:   PetscFunctionBeginUser;
 36:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

 38:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
 39:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL));
 40:   N = m*(m+1)/2;
 41:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov y=exp(t*A)*e_1, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));

 43:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 44:             Compute the transition probability matrix, A
 45:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 47:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
 48:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
 49:   PetscCall(MatSetFromOptions(A));
 50:   PetscCall(MatSetUp(A));
 51:   PetscCall(MatMarkovModel(m,A));

 53:   /* set v = e_1 */
 54:   PetscCall(MatCreateVecs(A,NULL,&y));
 55:   PetscCall(MatCreateVecs(A,NULL,&v));
 56:   PetscCall(VecSetValue(v,0,1.0,INSERT_VALUES));
 57:   PetscCall(VecAssemblyBegin(v));
 58:   PetscCall(VecAssemblyEnd(v));

 60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 61:                 Create the solver and set various options
 62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 63:   /*
 64:      Create matrix function solver context
 65:   */
 66:   PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));

 68:   /*
 69:      Set operator matrix, the function to compute, and other options
 70:   */
 71:   PetscCall(MFNSetOperator(mfn,A));
 72:   PetscCall(MFNGetFN(mfn,&f));
 73:   PetscCall(FNSetType(f,FNEXP));
 74:   PetscCall(FNSetScale(f,t,1.0));
 75:   PetscCall(MFNSetTolerances(mfn,1e-07,PETSC_DEFAULT));

 77:   /*
 78:      Set solver parameters at runtime
 79:   */
 80:   PetscCall(MFNSetFromOptions(mfn));

 82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 83:                       Solve the problem, y=exp(t*A)*v
 84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 86:   PetscCall(MFNSolve(mfn,v,y));
 87:   PetscCall(MFNGetConvergedReason(mfn,&reason));
 88:   PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
 89:   PetscCall(VecNorm(y,NORM_2,&norm));

 91:   /*
 92:      Optional: Get some information from the solver and display it
 93:   */
 94:   PetscCall(MFNGetIterationNumber(mfn,&its));
 95:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
 96:   PetscCall(MFNGetDimensions(mfn,&ncv));
 97:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
 98:   PetscCall(MFNGetTolerances(mfn,&tol,&maxit));
 99:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:                     Display solution and clean up
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm));

106:   /*
107:      Free work space
108:   */
109:   PetscCall(MFNDestroy(&mfn));
110:   PetscCall(MatDestroy(&A));
111:   PetscCall(VecDestroy(&v));
112:   PetscCall(VecDestroy(&y));
113:   PetscCall(SlepcFinalize());
114:   return 0;
115: }

117: /*
118:     Matrix generator for a Markov model of a random walk on a triangular grid.
119:     See ex5.c for additional details.
120: */
121: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
122: {
123:   const PetscReal cst = 0.5/(PetscReal)(m-1);
124:   PetscReal       pd,pu;
125:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

127:   PetscFunctionBeginUser;
128:   PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
129:   for (i=1;i<=m;i++) {
130:     jmax = m-i+1;
131:     for (j=1;j<=jmax;j++) {
132:       ix = ix + 1;
133:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
134:       if (j!=jmax) {
135:         pd = cst*(PetscReal)(i+j-1);
136:         /* north */
137:         if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
138:         else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
139:         /* east */
140:         if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
141:         else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
142:       }
143:       /* south */
144:       pu = 0.5 - cst*(PetscReal)(i+j-3);
145:       if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
146:       /* west */
147:       if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
148:     }
149:   }
150:   PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
151:   PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
152:   PetscFunctionReturn(PETSC_SUCCESS);
153: }

155: /*TEST

157:    test:
158:       suffix: 1
159:       args: -mfn_ncv 6

161: TEST*/