Actual source code: ex1.c
2: static char help[] = "Solves a standard symmetric eigenproblem corresponding to the Laplacian operator in 1 dimension.\n\n"
3: "The command line options are:\n\n"
4: " -n <n>, where <n> = number of grid subdivisions = matrix dimension.\n\n";
6: #include slepceps.h
10: int main( int argc, char **argv )
11: {
12: Mat A; /* operator matrix */
13: EPS eps; /* eigenproblem solver context */
14: EPSType type;
15: PetscReal error, tol,re, im;
16: PetscScalar kr, ki;
17: int n=30, nev, ierr, maxit, i, its, nconv,
18: col[3], Istart, Iend, FirstBlock=0, LastBlock=0;
19: PetscScalar value[3];
21: SlepcInitialize(&argc,&argv,(char*)0,help);
23: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
24: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Laplacian Eigenproblem, n=%d\n\n",n);
25:
27: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
28: Compute the operator matrix that defines the eigensystem, Ax=kx
29: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
31: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,&A);
32: MatSetFromOptions(A);
33:
34: MatGetOwnershipRange(A,&Istart,&Iend);
35: if (Istart==0) FirstBlock=PETSC_TRUE;
36: if (Iend==n) LastBlock=PETSC_TRUE;
37: value[0]=-1.0; value[1]=2.0; value[2]=-1.0;
38: for( i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++ ) {
39: col[0]=i-1; col[1]=i; col[2]=i+1;
40: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
41: }
42: if (LastBlock) {
43: i=n-1; col[0]=n-2; col[1]=n-1;
44: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
45: }
46: if (FirstBlock) {
47: i=0; col[0]=0; col[1]=1; value[0]=2.0; value[1]=-1.0;
48: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
49: }
51: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
52: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Create the eigensolver and set various options
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: /*
59: Create eigensolver context
60: */
61: EPSCreate(PETSC_COMM_WORLD,&eps);
63: /*
64: Set operators. In this case, it is a standard eigenvalue problem
65: */
66: EPSSetOperators(eps,A,PETSC_NULL);
68: /*
69: Set solver parameters at runtime
70: */
71: EPSSetFromOptions(eps);
73: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
74: Solve the eigensystem
75: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
77: EPSSolve(eps);
78: EPSGetIterationNumber(eps, &its);
79: PetscPrintf(PETSC_COMM_WORLD," Number of iterations of the method: %d\n",its);
80:
81: /*
82: Optional: Get some information from the solver and display it
83: */
84: EPSGetType(eps,&type);
85: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
86: EPSGetDimensions(eps,&nev,PETSC_NULL);
87: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %d\n",nev);
88:
89: EPSGetTolerances(eps,&tol,&maxit);
90: PetscPrintf(PETSC_COMM_WORLD," Stopping condition: tol=%.4g, maxit=%d\n",tol,maxit);
91:
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Display solution and clean up
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: /*
99: Get number of converged approximate eigenpairs
100: */
101: EPSGetConverged(eps,&nconv);
102: PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %d\n\n",nconv);
103:
105: if (nconv>0) {
106: /*
107: Display eigenvalues and relative errors
108: */
109: PetscPrintf(PETSC_COMM_WORLD,
110: " k ||Ax-kx||/||kx||\n"
111: " ----------------- ------------------\n" );
113: for( i=0; i<nconv; i++ ) {
114: /*
115: Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
116: ki (imaginary part)
117: */
118: EPSGetEigenpair(eps,i,&kr,&ki,PETSC_NULL,PETSC_NULL);
119: /*
120: Compute the relative error associated to each eigenpair
121: */
122: EPSComputeRelativeError(eps,i,&error);
124: #ifdef PETSC_USE_COMPLEX
125: re = PetscRealPart(kr);
126: im = PetscImaginaryPart(kr);
127: #else
128: re = kr;
129: im = ki;
130: #endif
131: if (im!=0.0) {
132: PetscPrintf(PETSC_COMM_WORLD," %9f%+9f j %12f\n",re,im,error);
133: } else {
134: PetscPrintf(PETSC_COMM_WORLD," %12f %12f\n",re,error);
135: }
136: }
137: PetscPrintf(PETSC_COMM_WORLD,"\n" );
138: }
139:
140: /*
141: Free work space
142: */
143: EPSDestroy(eps);
144: MatDestroy(A);
145: SlepcFinalize();
146: return 0;
147: }