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: }