Actual source code: ex32.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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[] = "Solves a Lypunov equation with the 2-D Laplacian.\n\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
14: " -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";
16: #include <slepclme.h>
18: int main(int argc,char **argv)
19: {
20: Mat A; /* problem matrix */
21: Mat C,C1; /* right-hand side */
22: Mat X,X1; /* solution */
23: LME lme;
24: PetscReal tol,errest,error;
25: PetscScalar *u;
26: PetscInt N,n=10,m,Istart,Iend,II,maxit,its,ncv,i,j,rank=0;
27: PetscErrorCode ierr;
28: PetscBool flag;
29: LMEConvergedReason reason;
31: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
33: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
34: PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
35: if (!flag) m=n;
36: N = n*m;
37: PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL);
38: PetscPrintf(PETSC_COMM_WORLD,"\nLyapunov equation, N=%D (%Dx%D grid)\n\n",N,n,m);
40: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: Create the 2-D Laplacian, A
42: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
44: MatCreate(PETSC_COMM_WORLD,&A);
45: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
46: MatSetFromOptions(A);
47: MatSetUp(A);
48: MatGetOwnershipRange(A,&Istart,&Iend);
49: for (II=Istart;II<Iend;II++) {
50: i = II/n; j = II-i*n;
51: if (i>0) { MatSetValue(A,II,II-n,1.0,INSERT_VALUES); }
52: if (i<m-1) { MatSetValue(A,II,II+n,1.0,INSERT_VALUES); }
53: if (j>0) { MatSetValue(A,II,II-1,1.0,INSERT_VALUES); }
54: if (j<n-1) { MatSetValue(A,II,II+1,1.0,INSERT_VALUES); }
55: MatSetValue(A,II,II,-4.0,INSERT_VALUES);
56: }
57: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
58: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Create a low-rank Mat to store the right-hand side C = C1*C1'
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: MatCreate(PETSC_COMM_WORLD,&C1);
65: MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,N,2);
66: MatSetType(C1,MATDENSE);
67: MatSetUp(C1);
68: MatGetOwnershipRange(C1,&Istart,&Iend);
69: MatDenseGetArray(C1,&u);
70: for (i=Istart;i<Iend;i++) {
71: if (i<N/2) u[i-Istart] = 1.0;
72: if (i==0) u[i+Iend-2*Istart] = -2.0;
73: if (i==1) u[i+Iend-2*Istart] = -1.0;
74: if (i==2) u[i+Iend-2*Istart] = -1.0;
75: }
76: MatDenseRestoreArray(C1,&u);
77: MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
78: MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);
79: MatCreateLRC(NULL,C1,NULL,NULL,&C);
80: MatDestroy(&C1);
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Create the solver and set various options
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: /*
86: Create the matrix equation solver context
87: */
88: LMECreate(PETSC_COMM_WORLD,&lme);
90: /*
91: Set the type of equation
92: */
93: LMESetProblemType(lme,LME_LYAPUNOV);
95: /*
96: Set the matrix coefficients, the right-hand side, and the solution.
97: In this case, it is a Lyapunov equation A*X+X*A'=-C where both
98: C and X are symmetric and low-rank, C=C1*C1', X=X1*X1'
99: */
100: LMESetCoefficients(lme,A,NULL,NULL,NULL);
101: LMESetRHS(lme,C);
103: if (rank) { /* Create X only if the user has specified a nonzero value of rank */
104: PetscPrintf(PETSC_COMM_WORLD," Computing a solution with prescribed rank=%d\n",rank);
105: MatCreate(PETSC_COMM_WORLD,&X1);
106: MatSetSizes(X1,PETSC_DECIDE,PETSC_DECIDE,N,rank);
107: MatSetType(X1,MATDENSE);
108: MatSetUp(X1);
109: MatAssemblyBegin(X1,MAT_FINAL_ASSEMBLY);
110: MatAssemblyEnd(X1,MAT_FINAL_ASSEMBLY);
111: MatCreateLRC(NULL,X1,NULL,NULL,&X);
112: MatDestroy(&X1);
113: LMESetSolution(lme,X);
114: MatDestroy(&X);
115: }
117: /*
118: (Optional) Set other solver options
119: */
120: LMESetTolerances(lme,1e-07,PETSC_DEFAULT);
122: /*
123: Set solver parameters at runtime
124: */
125: LMESetFromOptions(lme);
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Solve the matrix equation, A*X+X*A'=-C
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: LMESolve(lme);
132: LMEGetConvergedReason(lme,&reason);
133: if (reason<0) SETERRQ(PETSC_COMM_WORLD,1,"Solver did not converge");
135: if (!rank) { /* X1 was created by the solver, so extract it and see how many columns it has */
136: LMEGetSolution(lme,&X);
137: MatLRCGetMats(X,NULL,&X1,NULL,NULL);
138: MatGetSize(X1,NULL,&rank);
139: PetscPrintf(PETSC_COMM_WORLD," The solver has computed a solution with rank=%d\n",rank);
140: }
142: /*
143: Optional: Get some information from the solver and display it
144: */
145: LMEGetIterationNumber(lme,&its);
146: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
147: LMEGetDimensions(lme,&ncv);
148: PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %D\n",ncv);
149: LMEGetTolerances(lme,&tol,&maxit);
150: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Compute residual error
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156: LMEGetErrorEstimate(lme,&errest);
157: PetscPrintf(PETSC_COMM_WORLD," Error estimate reported by the solver: %.4g\n",(double)errest);
158: LMEComputeError(lme,&error);
159: PetscPrintf(PETSC_COMM_WORLD," Computed residual norm: %.4g\n\n",(double)error);
161: /*
162: Free work space
163: */
164: LMEDestroy(&lme);
165: MatDestroy(&A);
166: MatDestroy(&C);
167: SlepcFinalize();
168: return ierr;
169: }
171: /*TEST
173: test:
174: suffix: 1
175: requires: !single
177: TEST*/