Actual source code: ex25.c
slepc-3.16.2 2022-02-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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;
31: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
32: Mat F;
33: #endif
35: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
37: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
38: PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);
39: PetscOptionsGetBool(NULL,NULL,"-show_inertias",&show,NULL);
40: if (!flag) m=n;
41: N = n*m;
42: PetscPrintf(PETSC_COMM_WORLD,"\nSpectrum slicing on GHEP, N=%D (%Dx%D grid)\n\n",N,n,m);
44: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: Compute the matrices that define the eigensystem, Ax=kBx
46: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
48: MatCreate(PETSC_COMM_WORLD,&A);
49: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
50: MatSetFromOptions(A);
51: MatSetUp(A);
53: MatCreate(PETSC_COMM_WORLD,&B);
54: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,N,N);
55: MatSetFromOptions(B);
56: MatSetUp(B);
58: MatGetOwnershipRange(A,&Istart,&Iend);
59: for (II=Istart;II<Iend;II++) {
60: i = II/n; j = II-i*n;
61: if (i>0) { MatSetValue(A,II,II-n,-1.0,INSERT_VALUES); }
62: if (i<m-1) { MatSetValue(A,II,II+n,-1.0,INSERT_VALUES); }
63: if (j>0) { MatSetValue(A,II,II-1,-1.0,INSERT_VALUES); }
64: if (j<n-1) { MatSetValue(A,II,II+1,-1.0,INSERT_VALUES); }
65: MatSetValue(A,II,II,4.0,INSERT_VALUES);
66: MatSetValue(B,II,II,4.0,INSERT_VALUES);
67: }
69: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
70: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
71: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
72: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
74: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
75: Create the eigensolver and set various options
76: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
78: /*
79: Create eigensolver context
80: */
81: EPSCreate(PETSC_COMM_WORLD,&eps);
83: /*
84: Set operators and set problem type
85: */
86: EPSSetOperators(eps,A,B);
87: EPSSetProblemType(eps,EPS_GHEP);
89: /*
90: Set interval for spectrum slicing
91: */
92: inta = 0.1;
93: intb = 0.2;
94: EPSSetInterval(eps,inta,intb);
95: EPSSetWhichEigenpairs(eps,EPS_ALL);
97: /*
98: Spectrum slicing requires Krylov-Schur
99: */
100: EPSSetType(eps,EPSKRYLOVSCHUR);
102: /*
103: Set shift-and-invert with Cholesky; select MUMPS if available
104: */
106: EPSGetST(eps,&st);
107: STSetType(st,STSINVERT);
108: EPSKrylovSchurGetKSP(eps,&ksp);
109: KSPSetType(ksp,KSPPREONLY);
110: KSPGetPC(ksp,&pc);
111: PCSetType(pc,PCCHOLESKY);
113: /*
114: Use MUMPS if available.
115: Note that in complex scalars we cannot use MUMPS for spectrum slicing,
116: because MatGetInertia() is not available in that case.
117: */
118: #if defined(PETSC_HAVE_MUMPS) && !defined(PETSC_USE_COMPLEX)
119: EPSKrylovSchurSetDetectZeros(eps,PETSC_TRUE); /* enforce zero detection */
120: PCFactorSetMatSolverType(pc,MATSOLVERMUMPS);
121: PCFactorSetUpMatSolverType(pc);
122: /*
123: Set several MUMPS options, the corresponding command-line options are:
124: '-st_mat_mumps_icntl_13 1': turn off ScaLAPACK for matrix inertia
125: '-st_mat_mumps_icntl_24 1': detect null pivots in factorization (for the case that a shift is equal to an eigenvalue)
126: '-st_mat_mumps_cntl_3 <tol>': a tolerance used for null pivot detection (must be larger than machine epsilon)
128: Note: depending on the interval, it may be necessary also to increase the workspace:
129: '-st_mat_mumps_icntl_14 <percentage>': increase workspace with a percentage (50, 100 or more)
130: */
131: PCFactorGetMatrix(pc,&F);
132: MatMumpsSetIcntl(F,13,1);
133: MatMumpsSetIcntl(F,24,1);
134: MatMumpsSetCntl(F,3,1e-12);
135: #endif
137: /*
138: Set solver parameters at runtime
139: */
140: EPSSetFromOptions(eps);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Solve the eigensystem
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: EPSSetUp(eps);
146: if (show) {
147: EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
148: PetscPrintf(PETSC_COMM_WORLD,"Subintervals (after setup):\n");
149: for (i=0;i<ns;i++) { PetscPrintf(PETSC_COMM_WORLD,"Shift %g Inertia %D \n",(double)shifts[i],inertias[i]); }
150: PetscPrintf(PETSC_COMM_WORLD,"\n");
151: PetscFree(shifts);
152: PetscFree(inertias);
153: }
154: EPSSolve(eps);
155: if (show) {
156: EPSKrylovSchurGetInertias(eps,&ns,&shifts,&inertias);
157: PetscPrintf(PETSC_COMM_WORLD,"All shifts (after solve):\n");
158: for (i=0;i<ns;i++) { PetscPrintf(PETSC_COMM_WORLD,"Shift %g Inertia %D \n",(double)shifts[i],inertias[i]); }
159: PetscPrintf(PETSC_COMM_WORLD,"\n");
160: PetscFree(shifts);
161: PetscFree(inertias);
162: }
164: /*
165: Show eigenvalues in interval and print solution
166: */
167: EPSGetType(eps,&type);
168: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
169: EPSGetDimensions(eps,&nev,NULL,NULL);
170: EPSGetInterval(eps,&inta,&intb);
171: PetscPrintf(PETSC_COMM_WORLD," %D eigenvalues found in [%g, %g]\n",nev,(double)inta,(double)intb);
173: /*
174: Show detailed info unless -terse option is given by user
175: */
176: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
177: if (terse) {
178: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
179: } else {
180: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
181: EPSConvergedReasonView(eps,PETSC_VIEWER_STDOUT_WORLD);
182: EPSErrorView(eps,EPS_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
183: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
184: }
186: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: Clean up
188: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
189: EPSDestroy(&eps);
190: MatDestroy(&A);
191: MatDestroy(&B);
192: SlepcFinalize();
193: return ierr;
194: }
196: /*TEST
198: testset:
199: args: -terse
200: test:
201: requires: !mumps
202: test:
203: requires: mumps !complex
205: TEST*/