Actual source code: test9.c
slepc-3.22.1 2024-10-28
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
38: PetscFunctionBeginUser;
39: PetscCall(EPSGetConverged(eps,&nconv));
40: if (nconv>0) {
41: PetscCall(EPSGetOperators(eps,&A,NULL));
42: PetscCall(MatCreateVecs(A,&xr,&xi));
43: for (i=0;i<nconv;i++) {
44: PetscCall(EPSGetEigenvector(eps,i,xr,xi));
45: #if defined(PETSC_USE_COMPLEX)
46: PetscCall(VecNorm(xr,NORM_2,&normr));
47: error = PetscMax(error,PetscAbsReal(normr-PetscRealConstant(1.0)));
48: #else
49: PetscCall(VecNormBegin(xr,NORM_2,&normr));
50: PetscCall(VecNormBegin(xi,NORM_2,&normi));
51: PetscCall(VecNormEnd(xr,NORM_2,&normr));
52: PetscCall(VecNormEnd(xi,NORM_2,&normi));
53: error = PetscMax(error,PetscAbsReal(SlepcAbsEigenvalue(normr,normi)-PetscRealConstant(1.0)));
54: #endif
55: }
56: PetscCall(VecDestroy(&xr));
57: PetscCall(VecDestroy(&xi));
58: if (error>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Vectors are not normalized. Error=%g\n",(double)error));
59: }
60: PetscFunctionReturn(PETSC_SUCCESS);
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: PetscFunctionBeginUser;
74: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
76: PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
77: N = m*(m+1)/2;
78: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));
79: PetscCall(PetscOptionsGetBool(NULL,NULL,"-skipnorm",&skipnorm,NULL));
81: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
82: Compute the operator matrix that defines the eigensystem, Ax=kx
83: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
85: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
86: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
87: PetscCall(MatSetFromOptions(A));
88: PetscCall(MatMarkovModel(m,A));
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Create the eigensolver and set various options
92: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: /*
95: Create eigensolver context
96: */
97: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
99: /*
100: Set operators. In this case, it is a standard eigenvalue problem
101: */
102: PetscCall(EPSSetOperators(eps,A,NULL));
103: PetscCall(EPSSetProblemType(eps,EPS_NHEP));
104: PetscCall(EPSSetTolerances(eps,tol,PETSC_CURRENT));
106: /*
107: Set the custom comparing routine in order to obtain the eigenvalues
108: closest to the target on the right only
109: */
110: PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&origin));
112: /*
113: Set solver parameters at runtime
114: */
115: PetscCall(EPSSetFromOptions(eps));
116: PetscCall(PetscObjectTypeCompare((PetscObject)eps,EPSARNOLDI,&flg));
117: if (flg) {
118: PetscCall(EPSArnoldiGetDelayed(eps,&delay));
119: if (delay) PetscCall(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: PetscCall(MatCreateVecs(A,&v0,NULL));
127: PetscCall(VecSetValue(v0,0,-1.5,INSERT_VALUES));
128: PetscCall(VecSetValue(v0,1,2.1,INSERT_VALUES));
129: PetscCall(VecAssemblyBegin(v0));
130: PetscCall(VecAssemblyEnd(v0));
131: PetscCall(EPSSetInitialSpace(eps,1,&v0));
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Solve the eigensystem
135: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: PetscCall(EPSSolve(eps));
138: PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
139: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Display solution and clean up
143: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145: PetscCall(EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL));
146: if (!skipnorm) PetscCall(CheckNormalizedVectors(eps));
147: PetscCall(EPSDestroy(&eps));
148: PetscCall(MatDestroy(&A));
149: PetscCall(VecDestroy(&v0));
150: PetscCall(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;
160: PetscFunctionBeginUser;
161: PetscCall(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) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
171: else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
172: /* east */
173: if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
174: else PetscCall(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) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
179: /* west */
180: if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
181: }
182: }
183: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
184: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
185: PetscFunctionReturn(PETSC_SUCCESS);
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;
200: PetscFunctionBeginUser;
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(PETSC_SUCCESS);
204: }
206: /*TEST
208: testset:
209: args: -eps_nev 4
210: output_file: output/test9_1.out
211: filter: sed -e "s/97136/97137/g"
212: test:
213: suffix: 1
214: args: -eps_type {{krylovschur arnoldi lapack}} -eps_ncv 8 -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 ilu -eps_ciss_integration_points 8
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*/