Date: 2013-09-02T10:08:27+00:00

Actual source code: ex23.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Computes exp(A)*v for a matrix associated with a Markov model.\n\n"
     23:   "The command line options are:\n"
     24:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

     26: #include <slepcmfn.h>

     28: /*
     29:    User-defined routines
     30: */
     31: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     35: int main(int argc,char **argv)
     36: {
     37:   Mat                A;           /* problem matrix */
     38:   MFN                mfn;
     39:   PetscReal          tol,norm;
     40:   PetscScalar        t;
     41:   Vec                v,y;
     42:   PetscInt           N,m=15,ncv,maxit,its;
     43:   PetscErrorCode     ierr;
     44:   PetscBool          draw_sol;
     45:   MFNConvergedReason reason;

     47:   SlepcInitialize(&argc,&argv,(char*)0,help);

     49:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
     50:   N = m*(m+1)/2;
     51:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov y=exp(t*A)*e_1, N=%D (m=%D)\n\n",N,m);

     53:   PetscOptionsHasName(PETSC_NULL,"-draw_sol",&draw_sol);

     55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     56:             Compute the transition probability matrix, A
     57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     59:   MatCreate(PETSC_COMM_WORLD,&A);
     60:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     61:   MatSetFromOptions(A);
     62:   MatSetUp(A);
     63:   MatMarkovModel(m,A);

     65:   /* set v = e_1 */
     66:   MatGetVecs(A,PETSC_NULL,&y);
     67:   MatGetVecs(A,PETSC_NULL,&v);
     68:   VecSetValue(v,1,1.0,INSERT_VALUES);
     69:   VecAssemblyBegin(v);
     70:   VecAssemblyEnd(v);

     72:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     73:                 Create the solver and set various options
     74:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     75:   /*
     76:      Create matrix function solver context
     77:   */
     78:   MFNCreate(PETSC_COMM_WORLD,&mfn);

     80:   /*
     81:      Set operator matrix, the function to compute, and other options
     82:   */
     83:   MFNSetOperator(mfn,A);
     84:   MFNSetFunction(mfn,SLEPC_FUNCTION_EXP);
     85:   MFNSetTolerances(mfn,1e-07,PETSC_DEFAULT);

     87:   /*
     88:      Set solver parameters at runtime
     89:   */
     90:   MFNSetFromOptions(mfn);

     92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     93:                       Solve the problem, y=exp(A)*v
     94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     96:   MFNSolve(mfn,v,y);
     97:   MFNGetConvergedReason(mfn,&reason);
     98:   if (reason!=MFN_CONVERGED_TOL) SETERRQ(PETSC_COMM_WORLD,1,"Solver did not converge");
     99:   VecNorm(y,NORM_2,&norm);
    100:
    101:   /*
    102:      Optional: Get some information from the solver and display it
    103:   */
    104:   MFNGetIterationNumber(mfn,&its);
    105:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
    106:   MFNGetDimensions(mfn,&ncv);
    107:   PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %D\n",ncv);
    108:   MFNGetTolerances(mfn,&tol,&maxit);
    109:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4G, maxit=%D\n",tol,maxit);

    111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    112:                     Display solution and clean up
    113:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    114:   MFNGetScaleFactor(mfn,&t);
    115:   PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4G has norm %G\n\n",PetscRealPart(t),norm);
    116:   if (draw_sol) {
    117:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
    118:     VecView(y,PETSC_VIEWER_DRAW_WORLD);
    119:   }

    121:   /*
    122:      Free work space
    123:   */
    124:   MFNDestroy(&mfn);
    125:   MatDestroy(&A);
    126:   VecDestroy(&v);
    127:   VecDestroy(&y);
    128:   SlepcFinalize();
    129:   return 0;
    130: }

    134: /*
    135:     Matrix generator for a Markov model of a random walk on a triangular grid.
    136:     See ex5.c for additional details.
    137: */
    138: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    139: {
    140:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    141:   PetscReal       pd,pu;
    142:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    143:   PetscErrorCode  ierr;

    146:   MatGetOwnershipRange(A,&Istart,&Iend);
    147:   for (i=1;i<=m;i++) {
    148:     jmax = m-i+1;
    149:     for (j=1;j<=jmax;j++) {
    150:       ix = ix + 1;
    151:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    152:       if (j!=jmax) {
    153:         pd = cst*(PetscReal)(i+j-1);
    154:         /* north */
    155:         if (i==1) {
    156:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    157:         } else {
    158:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    159:         }
    160:         /* east */
    161:         if (j==1) {
    162:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    163:         } else {
    164:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    165:         }
    166:       }
    167:       /* south */
    168:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    169:       if (j>1) {
    170:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    171:       }
    172:       /* west */
    173:       if (i>1) {
    174:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    175:       }
    176:     }
    177:   }
    178:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    179:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    180:   return(0);
    181: }