Actual source code: ex23.c

slepc-3.7.0 2016-05-16
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2016, 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(t*A)*v for a matrix associated with a Markov model.\n\n"
 23:   "The command line options are:\n"
 24:   "  -t <t>, where <t> = time parameter (multiplies the matrix).\n\n"
 25:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

 27: #include <slepcmfn.h>

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

 36: int main(int argc,char **argv)
 37: {
 38:   Mat                A;           /* problem matrix */
 39:   MFN                mfn;
 40:   FN                 f;
 41:   PetscReal          tol,norm;
 42:   PetscScalar        t=2.0;
 43:   Vec                v,y;
 44:   PetscInt           N,m=15,ncv,maxit,its;
 45:   PetscErrorCode     ierr;
 46:   PetscBool          draw_sol;
 47:   MFNConvergedReason reason;

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

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

 56:   PetscOptionsHasName(NULL,NULL,"-draw_sol",&draw_sol);

 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 59:             Compute the transition probability matrix, A
 60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 98:                       Solve the problem, y=exp(t*A)*v
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

101:   MFNSolve(mfn,v,y);
102:   MFNGetConvergedReason(mfn,&reason);
103:   if (reason<0) SETERRQ(PETSC_COMM_WORLD,1,"Solver did not converge");
104:   VecNorm(y,NORM_2,&norm);
105:   
106:   /*
107:      Optional: Get some information from the solver and display it
108:   */
109:   MFNGetIterationNumber(mfn,&its);
110:   PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
111:   MFNGetDimensions(mfn,&ncv);
112:   PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %D\n",ncv);
113:   MFNGetTolerances(mfn,&tol,&maxit);
114:   PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);

116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
117:                     Display solution and clean up
118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119:   PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm);
120:   if (draw_sol) {
121:     PetscViewerDrawSetPause(PETSC_VIEWER_DRAW_WORLD,-1);
122:     VecView(y,PETSC_VIEWER_DRAW_WORLD);
123:   }

125:   /* 
126:      Free work space
127:   */
128:   MFNDestroy(&mfn);
129:   MatDestroy(&A);
130:   VecDestroy(&v);
131:   VecDestroy(&y);
132:   SlepcFinalize();
133:   return ierr;
134: }

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

150:   MatGetOwnershipRange(A,&Istart,&Iend);
151:   for (i=1;i<=m;i++) {
152:     jmax = m-i+1;
153:     for (j=1;j<=jmax;j++) {
154:       ix = ix + 1;
155:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
156:       if (j!=jmax) {
157:         pd = cst*(PetscReal)(i+j-1);
158:         /* north */
159:         if (i==1) {
160:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
161:         } else {
162:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
163:         }
164:         /* east */
165:         if (j==1) {
166:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
167:         } else {
168:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
169:         }
170:       }
171:       /* south */
172:       pu = 0.5 - cst*(PetscReal)(i+j-3);
173:       if (j>1) {
174:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
175:       }
176:       /* west */
177:       if (i>1) {
178:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
179:       }
180:     }
181:   }
182:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
183:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
184:   return(0);
185: }