Actual source code: test9.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[] = "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: {
31: PetscInt i,nconv;
32: Mat A;
33: Vec xr,xi;
34: PetscReal error=0.0,normr;
35: #if !defined(PETSC_USE_COMPLEX)
36: PetscReal normi;
37: #endif
40: EPSGetConverged(eps,&nconv);
41: if (nconv>0) {
42: EPSGetOperators(eps,&A,NULL);
43: MatCreateVecs(A,&xr,&xi);
44: for (i=0;i<nconv;i++) {
45: EPSGetEigenvector(eps,i,xr,xi);
46: #if defined(PETSC_USE_COMPLEX)
47: VecNorm(xr,NORM_2,&normr);
48: error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
49: #else
50: VecNormBegin(xr,NORM_2,&normr);
51: VecNormBegin(xi,NORM_2,&normi);
52: VecNormEnd(xr,NORM_2,&normr);
53: VecNormEnd(xi,NORM_2,&normi);
54: error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
55: #endif
56: }
57: VecDestroy(&xr);
58: VecDestroy(&xi);
59: if (error>100*PETSC_MACHINE_EPSILON) {
60: PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error);
61: }
62: }
63: return(0);
64: }
66: int main(int argc,char **argv)
67: {
68: Vec v0; /* initial vector */
69: Mat A; /* operator matrix */
70: EPS eps; /* eigenproblem solver context */
71: PetscReal tol=0.5*PETSC_SMALL;
72: PetscInt N,m=15,nev;
73: PetscScalar origin=0.0;
74: PetscBool flg,delay,skipnorm=PETSC_FALSE;
77: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
79: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
80: N = m*(m+1)/2;
81: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n\n",N,m);
82: PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Compute the operator matrix that defines the eigensystem, Ax=kx
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: MatCreate(PETSC_COMM_WORLD,&A);
89: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
90: MatSetFromOptions(A);
91: MatSetUp(A);
92: MatMarkovModel(m,A);
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Create the eigensolver and set various options
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: /*
99: Create eigensolver context
100: */
101: EPSCreate(PETSC_COMM_WORLD,&eps);
103: /*
104: Set operators. In this case, it is a standard eigenvalue problem
105: */
106: EPSSetOperators(eps,A,NULL);
107: EPSSetProblemType(eps,EPS_NHEP);
108: EPSSetTolerances(eps,tol,PETSC_DEFAULT);
110: /*
111: Set the custom comparing routine in order to obtain the eigenvalues
112: closest to the target on the right only
113: */
114: EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);
116: /*
117: Set solver parameters at runtime
118: */
119: EPSSetFromOptions(eps);
120: PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg);
121: if (flg) {
122: EPSArnoldiGetDelayed(eps,&delay);
123: if (delay) {
124: PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n");
125: }
126: }
128: /*
129: Set the initial vector. This is optional, if not done the initial
130: vector is set to random values
131: */
132: MatCreateVecs(A,&v0,NULL);
133: VecSetValue(v0,0,-1.5,INSERT_VALUES);
134: VecSetValue(v0,1,2.1,INSERT_VALUES);
135: VecAssemblyBegin(v0);
136: VecAssemblyEnd(v0);
137: EPSSetInitialSpace(eps,1,&v0);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Solve the eigensystem
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: EPSSolve(eps);
144: EPSGetDimensions(eps,&nev,NULL,NULL);
145: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
147: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148: Display solution and clean up
149: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
152: if (!skipnorm) { CheckNormalizedVectors(eps); }
153: EPSDestroy(&eps);
154: MatDestroy(&A);
155: VecDestroy(&v0);
156: SlepcFinalize();
157: return ierr;
158: }
160: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
161: {
162: const PetscReal cst = 0.5/(PetscReal)(m-1);
163: PetscReal pd,pu;
164: PetscInt Istart,Iend,i,j,jmax,ix=0;
165: PetscErrorCode ierr;
168: MatGetOwnershipRange(A,&Istart,&Iend);
169: for (i=1;i<=m;i++) {
170: jmax = m-i+1;
171: for (j=1;j<=jmax;j++) {
172: ix = ix + 1;
173: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
174: if (j!=jmax) {
175: pd = cst*(PetscReal)(i+j-1);
176: /* north */
177: if (i==1) {
178: MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
179: } else {
180: MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
181: }
182: /* east */
183: if (j==1) {
184: MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
185: } else {
186: MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
187: }
188: }
189: /* south */
190: pu = 0.5 - cst*(PetscReal)(i+j-3);
191: if (j>1) {
192: MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
193: }
194: /* west */
195: if (i>1) {
196: MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
197: }
198: }
199: }
200: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
201: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
202: return(0);
203: }
205: /*
206: Function for user-defined eigenvalue ordering criterion.
208: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
209: one of them as the preferred one according to the criterion.
210: In this example, the preferred value is the one furthest away from the origin.
211: */
212: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
213: {
214: PetscScalar origin = *(PetscScalar*)ctx;
215: PetscReal d;
218: d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
219: *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
220: return(0);
221: }
223: /*TEST
225: testset:
226: args: -eps_nev 4
227: output_file: output/test9_1.out
228: test:
229: suffix: 1
230: args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 7 -eps_max_it 300
231: test:
232: suffix: 1_gd
233: args: -eps_type gd -st_pc_type none
234: test:
235: suffix: 1_gd2
236: args: -eps_type gd -eps_gd_double_expansion -st_pc_type none
238: test:
239: suffix: 2
240: args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_ncv 7 -eps_max_it 1500
241: requires: double
242: output_file: output/test9_1.out
244: test:
245: suffix: 3
246: nsize: 2
247: args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm
248: requires: !single
249: output_file: output/test9_3.out
251: test:
252: suffix: 4
253: args: -eps_nev 4 -eps_true_residual
254: requires: !single
255: output_file: output/test9_1.out
257: test:
258: suffix: 5
259: args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2
260: filter: sed -e "s/[+-]0\.0*i//g"
261: requires: !single
263: test:
264: suffix: 5_arpack
265: args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10
266: requires: arpack !single
267: output_file: output/test9_5.out
269: testset:
270: 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
271: requires: !single
272: output_file: output/test9_6.out
273: test:
274: suffix: 6
275: test:
276: suffix: 6_hankel
277: args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 64
278: test:
279: suffix: 6_cheby
280: args: -eps_ciss_quadrule chebyshev
281: test:
282: suffix: 6_hankel_cheby
283: args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 64
284: test:
285: suffix: 6_refine
286: args: -eps_ciss_moments 4 -eps_ciss_blocksize 5 -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 2
287: test:
288: suffix: 6_bcgs
289: args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type sor -eps_ciss_integration_points 12
291: test:
292: suffix: 6_cheby_interval
293: 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
294: requires: !single
295: output_file: output/test9_6.out
297: testset:
298: args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values
299: filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"
300: test:
301: suffix: 7_real
302: requires: !single !complex
303: test:
304: suffix: 7
305: requires: !single complex
307: test:
308: suffix: 8
309: args: -eps_nev 4 -eps_ncv 7 -eps_view_values draw -eps_monitor draw::draw_lg
310: requires: x
311: output_file: output/test9_1.out
313: test:
314: suffix: 5_ksphpddm
315: args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10
316: requires: hpddm
317: output_file: output/test9_5.out
319: test:
320: suffix: 5_pchpddm
321: args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10
322: requires: hpddm
323: output_file: output/test9_5.out
325: TEST*/