Actual source code: ex13.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[] = "Generalized Symmetric eigenproblem.\n\n"
12: "The problem is Ax = lambda Bx, with:\n"
13: " A = Laplacian operator in 2-D\n"
14: " B = diagonal matrix with all values equal to 4 except nulldim zeros\n\n"
15: "The command line options are:\n"
16: " -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
17: " -m <m>, where <m> = number of grid subdivisions in y dimension.\n"
18: " -nulldim <k>, where <k> = dimension of the nullspace of B.\n\n";
20: #include <slepceps.h>
22: int main(int argc,char **argv)
23: {
24: Mat A,B; /* matrices */
25: EPS eps; /* eigenproblem solver context */
26: ST st; /* spectral transformation context */
27: EPSType type;
28: PetscInt N,n=10,m,Istart,Iend,II,nev,i,j,nulldim=0;
29: PetscBool flag,terse;
32: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
34: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
35: PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
36: if (!flag) m=n;
37: N = n*m;
38: PetscOptionsGetInt(NULL,NULL,"-nulldim",&nulldim,NULL);
39: PetscPrintf(PETSC_COMM_WORLD,"\nGeneralized Symmetric Eigenproblem, N=%D (%Dx%D grid), null(B)=%D\n\n",N,n,m,nulldim);
41: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
42: Compute the matrices that define the eigensystem, Ax=kBx
43: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
45: MatCreate(PETSC_COMM_WORLD,&A);
46: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
47: MatSetFromOptions(A);
48: MatSetUp(A);
50: MatCreate(PETSC_COMM_WORLD,&B);
51: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
52: MatSetFromOptions(B);
53: MatSetUp(B);
55: MatGetOwnershipRange(A,&Istart,&Iend);
56: for (II=Istart;II<Iend;II++) {
57: i = II/n; j = II-i*n;
58: if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
59: if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
60: if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
61: if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
62: MatSetValue(A,II,II,4.0,INSERT_VALUES);
63: if (II>=nulldim) { MatSetValue(B,II,II,4.0,INSERT_VALUES); }
64: }
66: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
67: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
68: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
69: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
71: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
72: Create the eigensolver and set various options
73: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
75: /*
76: Create eigensolver context
77: */
78: EPSCreate(PETSC_COMM_WORLD,&eps);
80: /*
81: Set operators. In this case, it is a generalized eigenvalue problem
82: */
83: EPSSetOperators(eps,A,B);
84: EPSSetProblemType(eps,EPS_GHEP);
86: /*
87: Set solver parameters at runtime
88: */
89: EPSSetFromOptions(eps);
91: PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSBLOPEX,EPSLOBPCG,EPSRQCG,"");
92: if (flag) {
93: EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL);
94: } else {
95: /*
96: Select portion of spectrum
97: */
98: EPSSetTarget(eps,0.0);
99: EPSSetWhichEigenpairs(eps,EPS_TARGET_MAGNITUDE);
100: /*
101: Use shift-and-invert to avoid solving linear systems with a singular B
102: in case nulldim>0
103: */
104: PetscObjectTypeCompareAny((PetscObject)eps,&flag,EPSGD,EPSJD,"");
105: if (!flag) {
106: EPSGetST(eps,&st);
107: STSetType(st,STSINVERT);
108: }
109: }
111: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
112: Solve the eigensystem
113: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
115: EPSSolve(eps);
117: /*
118: Optional: Get some information from the solver and display it
119: */
120: EPSGetType(eps,&type);
121: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
122: EPSGetDimensions(eps,&nev,NULL,NULL);
123: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
125: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126: Display solution and clean up
127: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
129: /* show detailed info unless -terse option is given by user */
130: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
131: if (terse) {
132: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
133: } else {
134: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
135: EPSReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
136: EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
137: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
138: }
139: EPSDestroy(&eps);
140: MatDestroy(&A);
141: MatDestroy(&B);
142: SlepcFinalize();
143: return ierr;
144: }
146: /*TEST
148: test:
149: suffix: 1
150: args: -eps_nev 4 -eps_ncv 22 -eps_tol 1e-5 -terse
152: test:
153: suffix: 2
154: args: -n 110 -nulldim 6 -eps_nev 4 -eps_ncv 18 -eps_tol 1e-5 -eps_purify 1 -st_type sinvert -terse
155: requires: !single
157: TEST*/