Actual source code: ex23.c

slepc-3.6.1 2015-09-03
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2015, 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:   FN                 f;
 40:   PetscReal          tol,norm;
 41:   PetscScalar        t=2.0;
 42:   Vec                v,y;
 43:   PetscInt           N,m=15,ncv,maxit,its;
 44:   PetscErrorCode     ierr;
 45:   PetscBool          draw_sol;
 46:   MFNConvergedReason reason;

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

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

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

 57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 58:             Compute the transition probability matrix, A
 59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

 67:   /* set v = e_1 */
 68:   MatCreateVecs(A,PETSC_NULL,&y);
 69:   MatCreateVecs(A,PETSC_NULL,&v);
 70:   VecSetValue(v,0,1.0,INSERT_VALUES);
 71:   VecAssemblyBegin(v);
 72:   VecAssemblyEnd(v);

 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 75:                 Create the solver and set various options
 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 77:   /* 
 78:      Create matrix function solver context
 79:   */
 80:   MFNCreate(PETSC_COMM_WORLD,&mfn);

 82:   /* 
 83:      Set operator matrix, the function to compute, and other options
 84:   */
 85:   MFNSetOperator(mfn,A);
 86:   MFNGetFN(mfn,&f);
 87:   FNSetType(f,FNEXP);
 88:   FNSetScale(f,t,1.0);  
 89:   MFNSetTolerances(mfn,1e-07,PETSC_DEFAULT);

 91:   /*
 92:      Set solver parameters at runtime
 93:   */
 94:   MFNSetFromOptions(mfn);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 97:                       Solve the problem, y=exp(A)*v
 98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
116:                     Display solution and clean up
117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
118:   PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm);
119:   if (draw_sol) {
120:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
121:     VecView(y,PETSC_VIEWER_DRAW_WORLD);
122:   }

124:   /* 
125:      Free work space
126:   */
127:   MFNDestroy(&mfn);
128:   MatDestroy(&A);
129:   VecDestroy(&v);
130:   VecDestroy(&y);
131:   SlepcFinalize();
132:   return 0;
133: }

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

149:   MatGetOwnershipRange(A,&Istart,&Iend);
150:   for (i=1;i<=m;i++) {
151:     jmax = m-i+1;
152:     for (j=1;j<=jmax;j++) {
153:       ix = ix + 1;
154:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
155:       if (j!=jmax) {
156:         pd = cst*(PetscReal)(i+j-1);
157:         /* north */
158:         if (i==1) {
159:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
160:         } else {
161:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
162:         }
163:         /* east */
164:         if (j==1) {
165:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
166:         } else {
167:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
168:         }
169:       }
170:       /* south */
171:       pu = 0.5 - cst*(PetscReal)(i+j-3);
172:       if (j>1) {
173:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
174:       }
175:       /* west */
176:       if (i>1) {
177:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
178:       }
179:     }
180:   }
181:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
182:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
183:   return(0);
184: }