Actual source code: ex32.c
slepc-3.21.0 2024-03-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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 shifted 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,sigma=0.0;
26: PetscInt N,n=10,m,Istart,Iend,II,maxit,its,ncv,i,j,rank=0;
27: PetscBool flag;
28: LMEConvergedReason reason;
30: PetscFunctionBeginUser;
31: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
33: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
34: PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag));
35: if (!flag) m=n;
36: N = n*m;
37: PetscCall(PetscOptionsGetScalar(NULL,NULL,"-sigma",&sigma,NULL));
38: PetscCall(PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL));
39: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nLyapunov equation, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));
41: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42: Create the 2-D Laplacian, A
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
46: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
47: PetscCall(MatSetFromOptions(A));
48: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
49: for (II=Istart;II<Iend;II++) {
50: i = II/n; j = II-i*n;
51: if (i>0) PetscCall(MatSetValue(A,II,II-n,1.0,INSERT_VALUES));
52: if (i<m-1) PetscCall(MatSetValue(A,II,II+n,1.0,INSERT_VALUES));
53: if (j>0) PetscCall(MatSetValue(A,II,II-1,1.0,INSERT_VALUES));
54: if (j<n-1) PetscCall(MatSetValue(A,II,II+1,1.0,INSERT_VALUES));
55: PetscCall(MatSetValue(A,II,II,-4.0-sigma,INSERT_VALUES));
56: }
57: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
58: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Create a low-rank Mat to store the right-hand side C = C1*C1'
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: PetscCall(MatCreate(PETSC_COMM_WORLD,&C1));
65: PetscCall(MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,N,2));
66: PetscCall(MatSetType(C1,MATDENSE));
67: PetscCall(MatGetOwnershipRange(C1,&Istart,&Iend));
68: PetscCall(MatDenseGetArray(C1,&u));
69: for (i=Istart;i<Iend;i++) {
70: if (i<N/2) u[i-Istart] = 1.0;
71: if (i==0) u[i+Iend-2*Istart] = -2.0;
72: if (i==1) u[i+Iend-2*Istart] = -1.0;
73: if (i==2) u[i+Iend-2*Istart] = -1.0;
74: }
75: PetscCall(MatDenseRestoreArray(C1,&u));
76: PetscCall(MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY));
77: PetscCall(MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY));
78: PetscCall(MatCreateLRC(NULL,C1,NULL,NULL,&C));
79: PetscCall(MatDestroy(&C1));
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Create the solver and set various options
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: /*
85: Create the matrix equation solver context
86: */
87: PetscCall(LMECreate(PETSC_COMM_WORLD,&lme));
89: /*
90: Set the type of equation
91: */
92: PetscCall(LMESetProblemType(lme,LME_LYAPUNOV));
94: /*
95: Set the matrix coefficients, the right-hand side, and the solution.
96: In this case, it is a Lyapunov equation A*X+X*A'=-C where both
97: C and X are symmetric and low-rank, C=C1*C1', X=X1*X1'
98: */
99: PetscCall(LMESetCoefficients(lme,A,NULL,NULL,NULL));
100: PetscCall(LMESetRHS(lme,C));
102: if (rank) { /* Create X only if the user has specified a nonzero value of rank */
103: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computing a solution with prescribed rank=%" PetscInt_FMT "\n",rank));
104: PetscCall(MatCreate(PETSC_COMM_WORLD,&X1));
105: PetscCall(MatSetSizes(X1,PETSC_DECIDE,PETSC_DECIDE,N,rank));
106: PetscCall(MatSetType(X1,MATDENSE));
107: PetscCall(MatAssemblyBegin(X1,MAT_FINAL_ASSEMBLY));
108: PetscCall(MatAssemblyEnd(X1,MAT_FINAL_ASSEMBLY));
109: PetscCall(MatCreateLRC(NULL,X1,NULL,NULL,&X));
110: PetscCall(MatDestroy(&X1));
111: PetscCall(LMESetSolution(lme,X));
112: PetscCall(MatDestroy(&X));
113: }
115: /*
116: (Optional) Set other solver options
117: */
118: PetscCall(LMESetTolerances(lme,1e-07,PETSC_DEFAULT));
120: /*
121: Set solver parameters at runtime
122: */
123: PetscCall(LMESetFromOptions(lme));
125: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126: Solve the matrix equation, A*X+X*A'=-C
127: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129: PetscCall(LMESolve(lme));
130: PetscCall(LMEGetConvergedReason(lme,&reason));
131: PetscCheck(reason>=0,PETSC_COMM_WORLD,PETSC_ERR_CONV_FAILED,"Solver did not converge");
133: if (!rank) { /* X1 was created by the solver, so extract it and see how many columns it has */
134: PetscCall(LMEGetSolution(lme,&X));
135: PetscCall(MatLRCGetMats(X,NULL,&X1,NULL,NULL));
136: PetscCall(MatGetSize(X1,NULL,&rank));
137: PetscCall(PetscPrintf(PETSC_COMM_WORLD," The solver has computed a solution with rank=%" PetscInt_FMT "\n",rank));
138: }
140: /*
141: Optional: Get some information from the solver and display it
142: */
143: PetscCall(LMEGetIterationNumber(lme,&its));
144: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %" PetscInt_FMT "\n",its));
145: PetscCall(LMEGetDimensions(lme,&ncv));
146: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %" PetscInt_FMT "\n",ncv));
147: PetscCall(LMEGetTolerances(lme,&tol,&maxit));
148: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%" PetscInt_FMT "\n",(double)tol,maxit));
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Compute residual error
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
154: PetscCall(LMEGetErrorEstimate(lme,&errest));
155: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Error estimate reported by the solver: %.4g\n",(double)errest));
156: if (n<=150) {
157: PetscCall(LMEComputeError(lme,&error));
158: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Computed residual norm: %.4g\n\n",(double)error));
159: } else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Matrix too large to compute residual norm\n\n"));
161: /*
162: Free work space
163: */
164: PetscCall(LMEDestroy(&lme));
165: PetscCall(MatDestroy(&A));
166: PetscCall(MatDestroy(&C));
167: PetscCall(SlepcFinalize());
168: return 0;
169: }
171: /*TEST
173: test:
174: suffix: 1
175: requires: !single
177: test:
178: suffix: 2
179: args: -rank 40
180: requires: !single
182: TEST*/