Actual source code: test9.c
slepc-3.18.3 2023-03-24
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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[] = "Eigenvalue problem associated with a Markov model of a random walk on a triangular grid. "
12: "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n"
13: "This example illustrates how the user can set the initial vector.\n\n"
14: "The command line options are:\n"
15: " -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";
17: #include <slepceps.h>
19: /*
20: User-defined routines
21: */
22: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
23: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);
25: /*
26: Check if computed eigenvectors have unit norm
27: */
28: PetscErrorCode CheckNormalizedVectors(EPS eps)
29: {
30: PetscInt i,nconv;
31: Mat A;
32: Vec xr,xi;
33: PetscReal error=0.0,normr;
34: #if !defined(PETSC_USE_COMPLEX)
35: PetscReal normi;
36: #endif
39: EPSGetConverged(eps,&nconv);
40: if (nconv>0) {
41: EPSGetOperators(eps,&A,NULL);
42: MatCreateVecs(A,&xr,&xi);
43: for (i=0;i<nconv;i++) {
44: EPSGetEigenvector(eps,i,xr,xi);
45: #if defined(PETSC_USE_COMPLEX)
46: VecNorm(xr,NORM_2,&normr);
47: error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
48: #else
49: VecNormBegin(xr,NORM_2,&normr);
50: VecNormBegin(xi,NORM_2,&normi);
51: VecNormEnd(xr,NORM_2,&normr);
52: VecNormEnd(xi,NORM_2,&normi);
53: error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
54: #endif
55: }
56: VecDestroy(&xr);
57: VecDestroy(&xi);
58: if (error>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
59: }
60: return 0;
61: }
63: int main(int argc,char **argv)
64: {
65: Vec v0; /* initial vector */
66: Mat A; /* operator matrix */
67: EPS eps; /* eigenproblem solver context */
68: PetscReal tol=0.5*PETSC_SMALL;
69: PetscInt N,m=15,nev;
70: PetscScalar origin=0.0;
71: PetscBool flg,delay,skipnorm=PETSC_FALSE;
74: SlepcInitialize(&argc,&argv,(char*)0,help);
76: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
77: N = m*(m+1)/2;
78: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m);
79: PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Compute the operator matrix that defines the eigensystem, Ax=kx
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: MatCreate(PETSC_COMM_WORLD,&A);
86: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
87: MatSetFromOptions(A);
88: MatSetUp(A);
89: MatMarkovModel(m,A);
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Create the eigensolver and set various options
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
95: /*
96: Create eigensolver context
97: */
98: EPSCreate(PETSC_COMM_WORLD,&eps);
100: /*
101: Set operators. In this case, it is a standard eigenvalue problem
102: */
103: EPSSetOperators(eps,A,NULL);
104: EPSSetProblemType(eps,EPS_NHEP);
105: EPSSetTolerances(eps,tol,PETSC_DEFAULT);
107: /*
108: Set the custom comparing routine in order to obtain the eigenvalues
109: closest to the target on the right only
110: */
111: EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);
113: /*
114: Set solver parameters at runtime
115: */
116: EPSSetFromOptions(eps);
117: PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg);
118: if (flg) {
119: EPSArnoldiGetDelayed(eps,&delay);
120: if (delay) PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n");
121: }
123: /*
124: Set the initial vector. This is optional, if not done the initial
125: vector is set to random values
126: */
127: MatCreateVecs(A,&v0,NULL);
128: VecSetValue(v0,0,-1.5,INSERT_VALUES);
129: VecSetValue(v0,1,2.1,INSERT_VALUES);
130: VecAssemblyBegin(v0);
131: VecAssemblyEnd(v0);
132: EPSSetInitialSpace(eps,1,&v0);
134: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135: Solve the eigensystem
136: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: EPSSolve(eps);
139: EPSGetDimensions(eps,&nev,NULL,NULL);
140: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Display solution and clean up
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
147: if (!skipnorm) CheckNormalizedVectors(eps);
148: EPSDestroy(&eps);
149: MatDestroy(&A);
150: VecDestroy(&v0);
151: SlepcFinalize();
152: return 0;
153: }
155: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
156: {
157: const PetscReal cst = 0.5/(PetscReal)(m-1);
158: PetscReal pd,pu;
159: PetscInt Istart,Iend,i,j,jmax,ix=0;
162: MatGetOwnershipRange(A,&Istart,&Iend);
163: for (i=1;i<=m;i++) {
164: jmax = m-i+1;
165: for (j=1;j<=jmax;j++) {
166: ix = ix + 1;
167: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
168: if (j!=jmax) {
169: pd = cst*(PetscReal)(i+j-1);
170: /* north */
171: if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
172: else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
173: /* east */
174: if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
175: else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
176: }
177: /* south */
178: pu = 0.5 - cst*(PetscReal)(i+j-3);
179: if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
180: /* west */
181: if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
182: }
183: }
184: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
185: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
186: return 0;
187: }
189: /*
190: Function for user-defined eigenvalue ordering criterion.
192: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
193: one of them as the preferred one according to the criterion.
194: In this example, the preferred value is the one furthest away from the origin.
195: */
196: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
197: {
198: PetscScalar origin = *(PetscScalar*)ctx;
199: PetscReal d;
202: d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
203: *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
204: return 0;
205: }
207: /*TEST
209: testset:
210: args: -eps_nev 4
211: output_file: output/test9_1.out
212: test:
213: suffix: 1
214: args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 7 -eps_max_it 300
215: test:
216: suffix: 1_gd
217: args: -eps_type gd -st_pc_type none
218: test:
219: suffix: 1_gd2
220: args: -eps_type gd -eps_gd_double_expansion -st_pc_type none
222: test:
223: suffix: 2
224: args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_max_it 1500
225: requires: double
226: output_file: output/test9_1.out
228: test:
229: suffix: 3
230: nsize: 2
231: args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm
232: requires: !single
233: output_file: output/test9_3.out
235: test:
236: suffix: 4
237: args: -eps_nev 4 -eps_true_residual
238: requires: !single
239: output_file: output/test9_1.out
241: test:
242: suffix: 5
243: args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2
244: filter: sed -e "s/[+-]0\.0*i//g"
245: requires: !single
247: test:
248: suffix: 5_arpack
249: args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10
250: requires: arpack !single
251: output_file: output/test9_5.out
253: testset:
254: args: -eps_type ciss -eps_tol 1e-9 -rg_type ellipse -rg_ellipse_center 0.55 -rg_ellipse_radius 0.05 -rg_ellipse_vscale 0.1 -eps_ciss_usest 0 -eps_all
255: requires: !single
256: output_file: output/test9_6.out
257: test:
258: suffix: 6
259: test:
260: suffix: 6_hankel
261: args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 64
262: test:
263: suffix: 6_cheby
264: args: -eps_ciss_quadrule chebyshev
265: test:
266: suffix: 6_hankel_cheby
267: args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 64
268: test:
269: suffix: 6_refine
270: args: -eps_ciss_moments 4 -eps_ciss_blocksize 5 -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 2
271: test:
272: suffix: 6_bcgs
273: args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type sor -eps_ciss_integration_points 12
275: test:
276: suffix: 6_cheby_interval
277: args: -eps_type ciss -eps_tol 1e-9 -rg_type interval -rg_interval_endpoints 0.5,0.6 -eps_ciss_quadrule chebyshev -eps_ciss_usest 0 -eps_all
278: requires: !single
279: output_file: output/test9_6.out
281: testset:
282: args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values
283: filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"
284: test:
285: suffix: 7_real
286: requires: !single !complex
287: test:
288: suffix: 7
289: requires: !single complex
291: test:
292: suffix: 8
293: args: -eps_nev 4 -eps_ncv 7 -eps_view_values draw -eps_monitor draw::draw_lg
294: requires: x
295: output_file: output/test9_1.out
297: test:
298: suffix: 5_ksphpddm
299: args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10
300: requires: hpddm
301: output_file: output/test9_5.out
303: test:
304: suffix: 5_pchpddm
305: args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10
306: requires: hpddm
307: output_file: output/test9_5.out
309: TEST*/