Actual source code: ex3.c
2: static char help[] = "Solves the same eigenproblem as in example ex2, but using a shell matrix. "
3: "The problem is a standard symmetric eigenproblem corresponding to the 2-D Laplacian operator.\n\n"
4: "The command line options are:\n\n"
5: " -n <n>, where <n> = number of grid subdivisions in both x and y dimensions.\n\n";
7: #include slepceps.h
8: #include "petscblaslapack.h"
10: /*
11: User-defined routines
12: */
13: extern int MatLaplacian2D_Mult( Mat A, Vec x, Vec y );
17: int main( int argc, char **argv )
18: {
19: Mat A; /* operator matrix */
20: EPS eps; /* eigenproblem solver context */
21: EPSType type;
22: PetscReal error, tol, re, im;
23: PetscScalar kr, ki;
24: int size, N, n=10, nev, ierr, maxit, i, its, nconv;
26: SlepcInitialize(&argc,&argv,(char*)0,help);
27: MPI_Comm_size(PETSC_COMM_WORLD,&size);
28: if (size != 1) SETERRQ(1,"This is a uniprocessor example only!");
30: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
31: N = n*n;
32: PetscPrintf(PETSC_COMM_WORLD,"\n2-D Laplacian Eigenproblem (matrix-free version), N=%d (%dx%d grid)\n\n",N,n,n);
34: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: Compute the operator matrix that defines the eigensystem, Ax=kx
36: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
38: MatCreateShell(PETSC_COMM_WORLD,N,N,N,N,&n,&A);
39: MatSetFromOptions(A);
40: MatShellSetOperation(A,MATOP_MULT,(void(*)())MatLaplacian2D_Mult);
41: MatShellSetOperation(A,MATOP_MULT_TRANSPOSE,(void(*)())MatLaplacian2D_Mult);
43: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
44: Create the eigensolver and set various options
45: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
47: /*
48: Create eigensolver context
49: */
50: EPSCreate(PETSC_COMM_WORLD,&eps);
52: /*
53: Set operators. In this case, it is a standard eigenvalue problem
54: */
55: EPSSetOperators(eps,A,PETSC_NULL);
56: EPSSetProblemType(eps,EPS_HEP);
58: /*
59: Set solver parameters at runtime
60: */
61: EPSSetFromOptions(eps);
63: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
64: Solve the eigensystem
65: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
67: EPSSolve(eps);
68: EPSGetIterationNumber(eps, &its);
69: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);
71: /*
72: Optional: Get some information from the solver and display it
73: */
74: EPSGetType(eps,&type);
75: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
76: EPSGetDimensions(eps,&nev,PETSC_NULL);
77: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
78: EPSGetTolerances(eps,&tol,&maxit);
79: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Display solution and clean up
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: /*
86: Get number of converged approximate eigenpairs
87: */
88: EPSGetConverged(eps,&nconv);
89: PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %d\n\n",nconv);
90:
92: if (nconv>0) {
93: /*
94: Display eigenvalues and relative errors
95: */
96: PetscPrintf(PETSC_COMM_WORLD,
97: " k ||Ax-kx||/||kx||\n"
98: " ----------------- ------------------\n" );
100: for( i=0; i<nconv; i++ ) {
101: /*
102: Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
103: ki (imaginary part)
104: */
105: EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
106: /*
107: Compute the relative error associated to each eigenpair
108: */
109: EPSComputeRelativeError(eps,i,&error);
111: #ifdef PETSC_USE_COMPLEX
112: re = PetscRealPart(kr);
113: im = PetscImaginaryPart(kr);
114: #else
115: re = kr;
116: im = ki;
117: #endif
118: if (im!=0.0) {
119: PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12f\n",re,im,error);
120: } else {
121: PetscPrintf(PETSC_COMM_WORLD," %12f %12f\n",re,error);
122: }
123: }
124: PetscPrintf(PETSC_COMM_WORLD,"\n" );
125: }
126:
127: /*
128: Free work space
129: */
130: EPSDestroy(eps);
131: MatDestroy(A);
132: SlepcFinalize();
133: return 0;
134: }
136: /*
137: Compute the matrix vector multiplication y<---T*x where T is a nx by nx
138: tridiagonal matrix with DD on the diagonal, DL on the subdiagonal, and
139: DU on the superdiagonal.
140: */
141: static void tv( int nx, PetscScalar *x, PetscScalar *y )
142: {
143: PetscScalar dd, dl, du;
144: int j;
146: dd = 4.0;
147: dl = -1.0;
148: du = -1.0;
150: y[0] = dd*x[0] + du*x[1];
151: for( j=1; j<nx-1; j++ )
152: y[j] = dl*x[j-1] + dd*x[j] + du*x[j+1];
153: y[nx-1] = dl*x[nx-2] + dd*x[nx-1];
154: }
158: /*
159: Matrix-vector product subroutine for the 2D Laplacian.
161: The matrix used is the 2 dimensional discrete Laplacian on unit square with
162: zero Dirichlet boundary condition.
163:
164: Computes y <-- A*x, where A is the block tridiagonal matrix
165:
166: | T -I |
167: |-I T -I |
168: A = | -I T |
169: | ... -I|
170: | -I T|
171:
172: The subroutine TV is called to compute y<--T*x.
173: */
174: int MatLaplacian2D_Mult( Mat A, Vec x, Vec y )
175: {
176: void *ctx;
177: int ierr, nx, lo, j, one=1;
178: PetscScalar *px, *py, dmone=-1.0;
179:
180: MatShellGetContext( A, &ctx );
181: nx = *(int *)ctx;
182: VecGetArray( x, &px );
183: VecGetArray( y, &py );
185: tv( nx, &px[0], &py[0] );
186: BLaxpy_( &nx, &dmone, &px[nx], &one, &py[0], &one );
188: for( j=2; j<nx; j++ ) {
189: lo = (j-1)*nx;
190: tv( nx, &px[lo], &py[lo]);
191: BLaxpy_( &nx, &dmone, &px[lo-nx], &one, &py[lo], &one );
192: BLaxpy_( &nx, &dmone, &px[lo+nx], &one, &py[lo], &one );
193: }
195: lo = (nx-1)*nx;
196: tv( nx, &px[lo], &py[lo]);
197: BLaxpy_( &nx, &dmone, &px[lo-nx], &one, &py[lo], &one );
199: VecRestoreArray( x, &px );
200: VecRestoreArray( y, &py );
202: return 0;
203: }