Actual source code: ex32.c
slepc-3.14.2 2021-02-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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: 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: PetscOptionsGetScalar(NULL,NULL,"-sigma",&sigma,NULL);
38: PetscOptionsGetInt(NULL,NULL,"-rank",&rank,NULL);
39: PetscPrintf(PETSC_COMM_WORLD,"\nLyapunov equation, N=%D (%Dx%D grid)\n\n",N,n,m);
41: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42: Create the 2-D Laplacian, A
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45: MatCreate(PETSC_COMM_WORLD,&A);
46: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
47: MatSetFromOptions(A);
48: MatSetUp(A);
49: MatGetOwnershipRange(A,&Istart,&Iend);
50: for (II=Istart;II<Iend;II++) {
51: i = II/n; j = II-i*n;
52: if (i>0) { MatSetValue(A,II,II-n,1.0,INSERT_VALUES); }
53: if (i<m-1) { MatSetValue(A,II,II+n,1.0,INSERT_VALUES); }
54: if (j>0) { MatSetValue(A,II,II-1,1.0,INSERT_VALUES); }
55: if (j<n-1) { MatSetValue(A,II,II+1,1.0,INSERT_VALUES); }
56: MatSetValue(A,II,II,-4.0-sigma,INSERT_VALUES);
57: }
58: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
59: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
61: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
62: Create a low-rank Mat to store the right-hand side C = C1*C1'
63: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
65: MatCreate(PETSC_COMM_WORLD,&C1);
66: MatSetSizes(C1,PETSC_DECIDE,PETSC_DECIDE,N,2);
67: MatSetType(C1,MATDENSE);
68: MatSetUp(C1);
69: MatGetOwnershipRange(C1,&Istart,&Iend);
70: MatDenseGetArray(C1,&u);
71: for (i=Istart;i<Iend;i++) {
72: if (i<N/2) u[i-Istart] = 1.0;
73: if (i==0) u[i+Iend-2*Istart] = -2.0;
74: if (i==1) u[i+Iend-2*Istart] = -1.0;
75: if (i==2) u[i+Iend-2*Istart] = -1.0;
76: }
77: MatDenseRestoreArray(C1,&u);
78: MatAssemblyBegin(C1,MAT_FINAL_ASSEMBLY);
79: MatAssemblyEnd(C1,MAT_FINAL_ASSEMBLY);
80: MatCreateLRC(NULL,C1,NULL,NULL,&C);
81: MatDestroy(&C1);
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Create the solver and set various options
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: /*
87: Create the matrix equation solver context
88: */
89: LMECreate(PETSC_COMM_WORLD,&lme);
91: /*
92: Set the type of equation
93: */
94: LMESetProblemType(lme,LME_LYAPUNOV);
96: /*
97: Set the matrix coefficients, the right-hand side, and the solution.
98: In this case, it is a Lyapunov equation A*X+X*A'=-C where both
99: C and X are symmetric and low-rank, C=C1*C1', X=X1*X1'
100: */
101: LMESetCoefficients(lme,A,NULL,NULL,NULL);
102: LMESetRHS(lme,C);
104: if (rank) { /* Create X only if the user has specified a nonzero value of rank */
105: PetscPrintf(PETSC_COMM_WORLD," Computing a solution with prescribed rank=%d\n",rank);
106: MatCreate(PETSC_COMM_WORLD,&X1);
107: MatSetSizes(X1,PETSC_DECIDE,PETSC_DECIDE,N,rank);
108: MatSetType(X1,MATDENSE);
109: MatSetUp(X1);
110: MatAssemblyBegin(X1,MAT_FINAL_ASSEMBLY);
111: MatAssemblyEnd(X1,MAT_FINAL_ASSEMBLY);
112: MatCreateLRC(NULL,X1,NULL,NULL,&X);
113: MatDestroy(&X1);
114: LMESetSolution(lme,X);
115: MatDestroy(&X);
116: }
118: /*
119: (Optional) Set other solver options
120: */
121: LMESetTolerances(lme,1e-07,PETSC_DEFAULT);
123: /*
124: Set solver parameters at runtime
125: */
126: LMESetFromOptions(lme);
128: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129: Solve the matrix equation, A*X+X*A'=-C
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: LMESolve(lme);
133: LMEGetConvergedReason(lme,&reason);
134: if (reason<0) SETERRQ(PETSC_COMM_WORLD,1,"Solver did not converge");
136: if (!rank) { /* X1 was created by the solver, so extract it and see how many columns it has */
137: LMEGetSolution(lme,&X);
138: MatLRCGetMats(X,NULL,&X1,NULL,NULL);
139: MatGetSize(X1,NULL,&rank);
140: PetscPrintf(PETSC_COMM_WORLD," The solver has computed a solution with rank=%d\n",rank);
141: }
143: /*
144: Optional: Get some information from the solver and display it
145: */
146: LMEGetIterationNumber(lme,&its);
147: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %D\n",its);
148: LMEGetDimensions(lme,&ncv);
149: PetscPrintf(PETSC_COMM_WORLD," Subspace dimension: %D\n",ncv);
150: LMEGetTolerances(lme,&tol,&maxit);
151: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%D\n",(double)tol,maxit);
153: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154: Compute residual error
155: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157: LMEGetErrorEstimate(lme,&errest);
158: PetscPrintf(PETSC_COMM_WORLD," Error estimate reported by the solver: %.4g\n",(double)errest);
159: if (n<=150) {
160: LMEComputeError(lme,&error);
161: PetscPrintf(PETSC_COMM_WORLD," Computed residual norm: %.4g\n\n",(double)error);
162: } else {
163: PetscPrintf(PETSC_COMM_WORLD," Matrix too large to compute residual norm\n\n");
164: }
166: /*
167: Free work space
168: */
169: LMEDestroy(&lme);
170: MatDestroy(&A);
171: MatDestroy(&C);
172: SlepcFinalize();
173: return ierr;
174: }
176: /*TEST
178: test:
179: suffix: 1
180: requires: !single
182: test:
183: suffix: 2
184: args: -rank 40
185: requires: !single
187: TEST*/