Actual source code: ex23.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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:   PetscErrorCode     ierr;
 34:   MFNConvergedReason reason;

 36:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

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

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

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

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

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

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

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

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

 86:   MFNSolve(mfn,v,y);
 87:   MFNGetConvergedReason(mfn,&reason);
 88:   if (reason<0) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
 89:   VecNorm(y,NORM_2,&norm);

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

101:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:                     Display solution and clean up
103:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104:   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:   MFNDestroy(&mfn);
110:   MatDestroy(&A);
111:   VecDestroy(&v);
112:   VecDestroy(&y);
113:   SlepcFinalize();
114:   return ierr;
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;
126:   PetscErrorCode  ierr;

129:   MatGetOwnershipRange(A,&Istart,&Iend);
130:   for (i=1;i<=m;i++) {
131:     jmax = m-i+1;
132:     for (j=1;j<=jmax;j++) {
133:       ix = ix + 1;
134:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
135:       if (j!=jmax) {
136:         pd = cst*(PetscReal)(i+j-1);
137:         /* north */
138:         if (i==1) {
139:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
140:         } else {
141:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
142:         }
143:         /* east */
144:         if (j==1) {
145:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
146:         } else {
147:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
148:         }
149:       }
150:       /* south */
151:       pu = 0.5 - cst*(PetscReal)(i+j-3);
152:       if (j>1) {
153:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
154:       }
155:       /* west */
156:       if (i>1) {
157:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
158:       }
159:     }
160:   }
161:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
162:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
163:   return(0);
164: }

166: /*TEST

168:    test:
169:       suffix: 1
170:       args: -mfn_ncv 6

172: TEST*/