Actual source code: test9.c
slepc-3.17.0 2022-03-31
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: PetscFunctionReturn(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;
73: SlepcInitialize(&argc,&argv,(char*)0,help);
75: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
76: N = m*(m+1)/2;
77: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m);
78: PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL);
80: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
81: Compute the operator matrix that defines the eigensystem, Ax=kx
82: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
84: MatCreate(PETSC_COMM_WORLD,&A);
85: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
86: MatSetFromOptions(A);
87: MatSetUp(A);
88: MatMarkovModel(m,A);
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Create the eigensolver and set various options
92: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: /*
95: Create eigensolver context
96: */
97: EPSCreate(PETSC_COMM_WORLD,&eps);
99: /*
100: Set operators. In this case, it is a standard eigenvalue problem
101: */
102: EPSSetOperators(eps,A,NULL);
103: EPSSetProblemType(eps,EPS_NHEP);
104: EPSSetTolerances(eps,tol,PETSC_DEFAULT);
106: /*
107: Set the custom comparing routine in order to obtain the eigenvalues
108: closest to the target on the right only
109: */
110: EPSSetEigenvalueComparison(eps,MyEigenSort,&origin);
112: /*
113: Set solver parameters at runtime
114: */
115: EPSSetFromOptions(eps);
116: PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg);
117: if (flg) {
118: EPSArnoldiGetDelayed(eps,&delay);
119: if (delay) PetscPrintf(PETSC_COMM_WORLD," Warning: delayed reorthogonalization may be unstable\n");
120: }
122: /*
123: Set the initial vector. This is optional, if not done the initial
124: vector is set to random values
125: */
126: MatCreateVecs(A,&v0,NULL);
127: VecSetValue(v0,0,-1.5,INSERT_VALUES);
128: VecSetValue(v0,1,2.1,INSERT_VALUES);
129: VecAssemblyBegin(v0);
130: VecAssemblyEnd(v0);
131: EPSSetInitialSpace(eps,1,&v0);
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Solve the eigensystem
135: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: EPSSolve(eps);
138: EPSGetDimensions(eps,&nev,NULL,NULL);
139: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Display solution and clean up
143: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
146: if (!skipnorm) CheckNormalizedVectors(eps);
147: EPSDestroy(&eps);
148: MatDestroy(&A);
149: VecDestroy(&v0);
150: SlepcFinalize();
151: return 0;
152: }
154: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
155: {
156: const PetscReal cst = 0.5/(PetscReal)(m-1);
157: PetscReal pd,pu;
158: PetscInt Istart,Iend,i,j,jmax,ix=0;
161: MatGetOwnershipRange(A,&Istart,&Iend);
162: for (i=1;i<=m;i++) {
163: jmax = m-i+1;
164: for (j=1;j<=jmax;j++) {
165: ix = ix + 1;
166: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
167: if (j!=jmax) {
168: pd = cst*(PetscReal)(i+j-1);
169: /* north */
170: if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
171: else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
172: /* east */
173: if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
174: else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
175: }
176: /* south */
177: pu = 0.5 - cst*(PetscReal)(i+j-3);
178: if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
179: /* west */
180: if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
181: }
182: }
183: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
184: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
185: PetscFunctionReturn(0);
186: }
188: /*
189: Function for user-defined eigenvalue ordering criterion.
191: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
192: one of them as the preferred one according to the criterion.
193: In this example, the preferred value is the one furthest away from the origin.
194: */
195: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
196: {
197: PetscScalar origin = *(PetscScalar*)ctx;
198: PetscReal d;
201: d = (SlepcAbsEigenvalue(br-origin,bi) - SlepcAbsEigenvalue(ar-origin,ai))/PetscMax(SlepcAbsEigenvalue(ar-origin,ai),SlepcAbsEigenvalue(br-origin,bi));
202: *r = d > PETSC_SQRT_MACHINE_EPSILON ? 1 : (d < -PETSC_SQRT_MACHINE_EPSILON ? -1 : PetscSign(PetscRealPart(br)));
203: PetscFunctionReturn(0);
204: }
206: /*TEST
208: testset:
209: args: -eps_nev 4
210: output_file: output/test9_1.out
211: test:
212: suffix: 1
213: args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 7 -eps_max_it 300
214: test:
215: suffix: 1_gd
216: args: -eps_type gd -st_pc_type none
217: test:
218: suffix: 1_gd2
219: args: -eps_type gd -eps_gd_double_expansion -st_pc_type none
221: test:
222: suffix: 2
223: args: -eps_balance {{none oneside twoside}} -eps_krylovschur_locking {{0 1}} -eps_nev 4 -eps_ncv 7 -eps_max_it 1500
224: requires: double
225: output_file: output/test9_1.out
227: test:
228: suffix: 3
229: nsize: 2
230: args: -eps_type arnoldi -eps_arnoldi_delayed -eps_largest_real -eps_nev 3 -eps_tol 1e-7 -bv_orthog_refine {{never ifneeded}} -skipnorm
231: requires: !single
232: output_file: output/test9_3.out
234: test:
235: suffix: 4
236: args: -eps_nev 4 -eps_true_residual
237: requires: !single
238: output_file: output/test9_1.out
240: test:
241: suffix: 5
242: args: -eps_type jd -eps_nev 3 -eps_target .5 -eps_harmonic -st_ksp_type bicg -st_pc_type lu -eps_jd_minv 2
243: filter: sed -e "s/[+-]0\.0*i//g"
244: requires: !single
246: test:
247: suffix: 5_arpack
248: args: -eps_nev 3 -st_type sinvert -eps_target .5 -eps_type arpack -eps_ncv 10
249: requires: arpack !single
250: output_file: output/test9_5.out
252: testset:
253: 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
254: requires: !single
255: output_file: output/test9_6.out
256: test:
257: suffix: 6
258: test:
259: suffix: 6_hankel
260: args: -eps_ciss_extraction hankel -eps_ciss_spurious_threshold 1e-6 -eps_ncv 64
261: test:
262: suffix: 6_cheby
263: args: -eps_ciss_quadrule chebyshev
264: test:
265: suffix: 6_hankel_cheby
266: args: -eps_ciss_extraction hankel -eps_ciss_quadrule chebyshev -eps_ncv 64
267: test:
268: suffix: 6_refine
269: args: -eps_ciss_moments 4 -eps_ciss_blocksize 5 -eps_ciss_refine_inner 1 -eps_ciss_refine_blocksize 2
270: test:
271: suffix: 6_bcgs
272: args: -eps_ciss_realmats -eps_ciss_ksp_type bcgs -eps_ciss_pc_type sor -eps_ciss_integration_points 12
274: test:
275: suffix: 6_cheby_interval
276: 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
277: requires: !single
278: output_file: output/test9_6.out
280: testset:
281: args: -eps_nev 4 -eps_two_sided -eps_view_vectors ::ascii_info -eps_view_values
282: filter: sed -e "s/\(0x[0-9a-fA-F]*\)/objectid/"
283: test:
284: suffix: 7_real
285: requires: !single !complex
286: test:
287: suffix: 7
288: requires: !single complex
290: test:
291: suffix: 8
292: args: -eps_nev 4 -eps_ncv 7 -eps_view_values draw -eps_monitor draw::draw_lg
293: requires: x
294: output_file: output/test9_1.out
296: test:
297: suffix: 5_ksphpddm
298: args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_ksp_type hpddm -st_ksp_hpddm_type gcrodr -eps_ncv 10
299: requires: hpddm
300: output_file: output/test9_5.out
302: test:
303: suffix: 5_pchpddm
304: args: -eps_nev 3 -st_type sinvert -eps_target .5 -st_pc_type hpddm -st_pc_hpddm_coarse_pc_type lu -eps_ncv 10
305: requires: hpddm
306: output_file: output/test9_5.out
308: TEST*/