Actual source code: ex25.c
slepc-3.14.1 2020-12-08
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[] = "Spectrum slicing on generalized symmetric eigenproblem.\n\n"
12: "The problem is similar to ex13.c.\n\n"
13: "The command line options are:\n"
14: " -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
15: " -m <m>, where <m> = number of grid subdivisions in y dimension.\n";
17: #include <slepceps.h>
19: int main(int argc,char **argv)
20: {
21: Mat A,B; /* matrices */
22: EPS eps; /* eigenproblem solver context */
23: ST st; /* spectral transformation context */
24: KSP ksp;
25: PC pc;
26: EPSType type;
27: PetscInt N,n=10,m,Istart,Iend,II,nev,i,j,*inertias,ns;
28: PetscReal inta,intb,*shifts;
29: PetscBool flag,show=PETSC_FALSE,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: PetscOptionsGetBool(NULL,NULL,"-show_inertias",&show,NULL);
37: if (!flag) m=n;
38: N = n*m;
39: PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum slicing on GHEP, N=%D (%Dx%D grid)\n\n",N,n,m);
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: 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 and set problem type
82: */
83: EPSSetOperators(eps,A,B);
84: EPSSetProblemType(eps,EPS_GHEP);
86: /*
87: Set interval for spectrum slicing
88: */
89: inta = 0.1;
90: intb = 0.2;
91: EPSSetInterval(eps,inta,intb);
92: EPSSetWhichEigenpairs(eps,EPS_ALL);
94: /*
95: Spectrum slicing requires Krylov-Schur
96: */
97: EPSSetType(eps,EPSKRYLOVSCHUR);
99: /*
100: Set shift-and-invert with Cholesky; select MUMPS if available
101: */
103: EPSGetST(eps,&st);
104: STSetType(st,STSINVERT);
106: STGetKSP(st,&ksp);
107: KSPSetType(ksp,KSPPREONLY);
108: KSPGetPC(ksp,&pc);
109: PCSetType(pc,PCCHOLESKY);
111: /*
112: Use MUMPS if available.
113: Note that in complex scalars we cannot use MUMPS for spectrum slicing,
114: because MatGetInertia() is not available in that case.
115: */
116: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
117: EPSKrylovSchurSetDetectZeros(eps,PETSC_TRUE); /* enforce zero detection */
118: PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
119: /*
120: Add several MUMPS options (see ex43.c for a better way of setting them in program):
121: '-mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
122: '-mat_mumps_icntl_24 1': detect null pivots in factorization (for the case that a shift is equal to an eigenvalue)
123: '-mat_mumps_cntl_3 <tol>': a tolerance used for null pivot detection (must be larger than machine epsilon)
125: Note: depending on the interval, it may be necessary also to increase the workspace:
126: '-mat_mumps_icntl_14 <percentage>': increase workspace with a percentage (50, 100 or more)
127: */
128: PetscOptionsInsertString(NULL,"-mat_mumps_icntl_13 1 -mat_mumps_icntl_24 1 -mat_mumps_cntl_3 1e-12");
129: #endif
131: /*
132: Set solver parameters at runtime
133: */
134: EPSSetFromOptions(eps);
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Solve the eigensystem
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
139: EPSSetUp(eps);
140: if (show) {
141: EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
142: PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n");
143: for (i=0;i<ns;i++) { PetscPrintf(PETSC_COMM_WORLD,"Shift %g Inertia %D \n",(double)shifts[i],inertias[i]); }
144: PetscPrintf(PETSC_COMM_WORLD,"\n");
145: PetscFree(shifts);
146: PetscFree(inertias);
147: }
148: EPSSolve(eps);
149: if (show) {
150: EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
151: PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n");
152: for (i=0;i<ns;i++) { PetscPrintf(PETSC_COMM_WORLD,"Shift %g Inertia %D \n",(double)shifts[i],inertias[i]); }
153: PetscPrintf(PETSC_COMM_WORLD,"\n");
154: PetscFree(shifts);
155: PetscFree(inertias);
156: }
158: /*
159: Show eigenvalues in interval and print solution
160: */
161: EPSGetType(eps,&type);
162: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
163: EPSGetDimensions(eps,&nev,NULL,NULL);
164: EPSGetInterval(eps,&inta,&intb);
165: PetscPrintf(PETSC_COMM_WORLD," %D eigenvalues found in [%g, %g]\n",nev,(double)inta,(double)intb);
167: /*
168: Show detailed info unless -terse option is given by user
169: */
170: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
171: if (terse) {
172: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
173: } else {
174: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
175: EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
176: EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
177: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
178: }
180: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181: Clean up
182: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183: EPSDestroy(&eps);
184: MatDestroy(&A);
185: MatDestroy(&B);
186: SlepcFinalize();
187: return ierr;
188: }
190: /*TEST
192: testset:
193: args: -terse
194: test:
195: requires: !mumps
196: test:
197: requires: mumps !complex
199: TEST*/