Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 :
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";
16 :
17 : #include <slepcmfn.h>
18 :
19 : /*
20 : User-defined routines
21 : */
22 : PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
23 :
24 1 : int main(int argc,char **argv)
25 : {
26 1 : Mat A; /* problem matrix */
27 1 : MFN mfn;
28 1 : FN f;
29 1 : PetscReal tol,norm;
30 1 : PetscScalar t=2.0;
31 1 : Vec v,y;
32 1 : PetscInt N,m=15,ncv,maxit,its;
33 1 : MFNConvergedReason reason;
34 :
35 1 : PetscFunctionBeginUser;
36 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
37 :
38 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
39 1 : PetscCall(PetscOptionsGetScalar(NULL,NULL,"-t",&t,NULL));
40 1 : N = m*(m+1)/2;
41 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov y=exp(t*A)*e_1, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));
42 :
43 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44 : Compute the transition probability matrix, A
45 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
46 :
47 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
48 1 : PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
49 1 : PetscCall(MatSetFromOptions(A));
50 1 : PetscCall(MatMarkovModel(m,A));
51 :
52 : /* set v = e_1 */
53 1 : PetscCall(MatCreateVecs(A,NULL,&y));
54 1 : PetscCall(MatCreateVecs(A,NULL,&v));
55 1 : PetscCall(VecSetValue(v,0,1.0,INSERT_VALUES));
56 1 : PetscCall(VecAssemblyBegin(v));
57 1 : PetscCall(VecAssemblyEnd(v));
58 :
59 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60 : Create the solver and set various options
61 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62 : /*
63 : Create matrix function solver context
64 : */
65 1 : PetscCall(MFNCreate(PETSC_COMM_WORLD,&mfn));
66 :
67 : /*
68 : Set operator matrix, the function to compute, and other options
69 : */
70 1 : PetscCall(MFNSetOperator(mfn,A));
71 1 : PetscCall(MFNGetFN(mfn,&f));
72 1 : PetscCall(FNSetType(f,FNEXP));
73 1 : PetscCall(FNSetScale(f,t,1.0));
74 1 : PetscCall(MFNSetTolerances(mfn,1e-07,PETSC_DEFAULT));
75 :
76 : /*
77 : Set solver parameters at runtime
78 : */
79 1 : PetscCall(MFNSetFromOptions(mfn));
80 :
81 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82 : Solve the problem, y=exp(t*A)*v
83 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84 :
85 1 : PetscCall(MFNSolve(mfn,v,y));
86 1 : PetscCall(MFNGetConvergedReason(mfn,&reason));
87 1 : PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
88 1 : PetscCall(VecNorm(y,NORM_2,&norm));
89 :
90 : /*
91 : Optional: Get some information from the solver and display it
92 : */
93 1 : PetscCall(MFNGetIterationNumber(mfn,&its));
94 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
95 1 : PetscCall(MFNGetDimensions(mfn,&ncv));
96 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
97 1 : PetscCall(MFNGetTolerances(mfn,&tol,&maxit));
98 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));
99 :
100 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101 : Display solution and clean up
102 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed vector at time t=%.4g has norm %g\n\n",(double)PetscRealPart(t),(double)norm));
104 :
105 : /*
106 : Free work space
107 : */
108 1 : PetscCall(MFNDestroy(&mfn));
109 1 : PetscCall(MatDestroy(&A));
110 1 : PetscCall(VecDestroy(&v));
111 1 : PetscCall(VecDestroy(&y));
112 1 : PetscCall(SlepcFinalize());
113 : return 0;
114 : }
115 :
116 : /*
117 : Matrix generator for a Markov model of a random walk on a triangular grid.
118 : See ex5.c for additional details.
119 : */
120 1 : PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
121 : {
122 1 : const PetscReal cst = 0.5/(PetscReal)(m-1);
123 1 : PetscReal pd,pu;
124 1 : PetscInt Istart,Iend,i,j,jmax,ix=0;
125 :
126 1 : PetscFunctionBeginUser;
127 1 : PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
128 16 : for (i=1;i<=m;i++) {
129 15 : jmax = m-i+1;
130 135 : for (j=1;j<=jmax;j++) {
131 120 : ix = ix + 1;
132 120 : if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
133 120 : if (j!=jmax) {
134 105 : pd = cst*(PetscReal)(i+j-1);
135 : /* north */
136 105 : if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
137 91 : else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
138 : /* east */
139 105 : if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
140 91 : else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
141 : }
142 : /* south */
143 120 : pu = 0.5 - cst*(PetscReal)(i+j-3);
144 120 : if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
145 : /* west */
146 120 : if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
147 : }
148 : }
149 1 : PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
150 1 : PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
151 1 : PetscFunctionReturn(PETSC_SUCCESS);
152 : }
153 :
154 : /*TEST
155 :
156 : test:
157 : suffix: 1
158 : args: -mfn_ncv 6
159 :
160 : TEST*/
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