Actual source code: ex41.c
slepc-3.23.1 2025-05-01
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[] = "Illustrates the computation of left eigenvectors.\n\n"
12: "The problem is the Markov model as in ex5.c.\n"
13: "The command line options are:\n"
14: " -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";
16: #include <slepceps.h>
18: /*
19: User-defined routines
20: */
21: PetscErrorCode MatMarkovModel(PetscInt,Mat);
22: PetscErrorCode ComputeResidualNorm(Mat,PetscBool,PetscScalar,PetscScalar,Vec,Vec,Vec,PetscReal*);
24: int main(int argc,char **argv)
25: {
26: Vec v0,w0; /* initial vectors */
27: Mat A; /* operator matrix */
28: EPS eps; /* eigenproblem solver context */
29: EPSType type;
30: PetscInt i,N,m=15,nconv;
31: PetscBool twosided;
32: PetscReal nrmr,nrml=0.0,re,im,lev;
33: PetscScalar *kr,*ki;
34: Vec t,*xr,*xi,*yr,*yi;
35: PetscMPIInt rank;
37: PetscFunctionBeginUser;
38: PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
40: PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
41: N = m*(m+1)/2;
42: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",N,m));
44: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: Compute the operator matrix that defines the eigensystem, Ax=kx
46: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
48: PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
49: PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
50: PetscCall(MatSetFromOptions(A));
51: PetscCall(MatMarkovModel(m,A));
52: PetscCall(MatCreateVecs(A,NULL,&t));
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Create the eigensolver and set various options
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
59: PetscCall(EPSSetOperators(eps,A,NULL));
60: PetscCall(EPSSetProblemType(eps,EPS_NHEP));
62: /* use a two-sided algorithm to compute left eigenvectors as well */
63: PetscCall(EPSSetTwoSided(eps,PETSC_TRUE));
65: /* allow user to change settings at run time */
66: PetscCall(EPSSetFromOptions(eps));
67: PetscCall(EPSGetTwoSided(eps,&twosided));
69: /*
70: Set the initial vectors. This is optional, if not done the initial
71: vectors are set to random values
72: */
73: PetscCall(MatCreateVecs(A,&v0,&w0));
74: PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
75: if (!rank) {
76: PetscCall(VecSetValue(v0,0,1.0,INSERT_VALUES));
77: PetscCall(VecSetValue(v0,1,1.0,INSERT_VALUES));
78: PetscCall(VecSetValue(v0,2,1.0,INSERT_VALUES));
79: PetscCall(VecSetValue(w0,0,2.0,INSERT_VALUES));
80: PetscCall(VecSetValue(w0,2,0.5,INSERT_VALUES));
81: }
82: PetscCall(VecAssemblyBegin(v0));
83: PetscCall(VecAssemblyBegin(w0));
84: PetscCall(VecAssemblyEnd(v0));
85: PetscCall(VecAssemblyEnd(w0));
86: PetscCall(EPSSetInitialSpace(eps,1,&v0));
87: PetscCall(EPSSetLeftInitialSpace(eps,1,&w0));
89: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
90: Solve the eigensystem
91: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: PetscCall(EPSSolve(eps));
95: /*
96: Optional: Get some information from the solver and display it
97: */
98: PetscCall(EPSGetType(eps,&type));
99: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
101: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: Display solution and clean up
103: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: /*
106: Get number of converged approximate eigenpairs
107: */
108: PetscCall(EPSGetConverged(eps,&nconv));
109: PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of converged eigenpairs: %" PetscInt_FMT "\n\n",nconv));
110: PetscCall(PetscMalloc2(nconv,&kr,nconv,&ki));
111: PetscCall(VecDuplicateVecs(t,nconv,&xr));
112: PetscCall(VecDuplicateVecs(t,nconv,&xi));
113: if (twosided) {
114: PetscCall(VecDuplicateVecs(t,nconv,&yr));
115: PetscCall(VecDuplicateVecs(t,nconv,&yi));
116: }
118: if (nconv>0) {
119: /*
120: Display eigenvalues and relative errors
121: */
122: PetscCall(PetscPrintf(PETSC_COMM_WORLD,
123: " k ||Ax-kx|| ||y'A-y'k||\n"
124: " ---------------- ------------------ ------------------\n"));
126: for (i=0;i<nconv;i++) {
127: /*
128: Get converged eigenpairs: i-th eigenvalue is stored in kr (real part) and
129: ki (imaginary part)
130: */
131: PetscCall(EPSGetEigenpair(eps,i,&kr[i],&ki[i],xr[i],xi[i]));
132: if (twosided) PetscCall(EPSGetLeftEigenvector(eps,i,yr[i],yi[i]));
133: /*
134: Compute the residual norms associated to each eigenpair
135: */
136: PetscCall(ComputeResidualNorm(A,PETSC_FALSE,kr[i],ki[i],xr[i],xi[i],t,&nrmr));
137: if (twosided) PetscCall(ComputeResidualNorm(A,PETSC_TRUE,kr[i],ki[i],yr[i],yi[i],t,&nrml));
139: #if defined(PETSC_USE_COMPLEX)
140: re = PetscRealPart(kr[i]);
141: im = PetscImaginaryPart(kr[i]);
142: #else
143: re = kr[i];
144: im = ki[i];
145: #endif
146: if (im!=0.0) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %8f%+8fi %12g %12g\n",(double)re,(double)im,(double)nrmr,(double)nrml));
147: else PetscCall(PetscPrintf(PETSC_COMM_WORLD," %12f %12g %12g\n",(double)re,(double)nrmr,(double)nrml));
148: }
149: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
150: /*
151: Check bi-orthogonality of eigenvectors
152: */
153: if (twosided) {
154: PetscCall(VecCheckOrthogonality(xr,nconv,yr,nconv,NULL,NULL,&lev));
155: if (lev<100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD," Level of bi-orthogonality of eigenvectors < 100*eps\n\n"));
156: else PetscCall(PetscPrintf(PETSC_COMM_WORLD," Level of bi-orthogonality of eigenvectors: %g\n\n",(double)lev));
157: }
158: }
160: PetscCall(EPSDestroy(&eps));
161: PetscCall(MatDestroy(&A));
162: PetscCall(VecDestroy(&v0));
163: PetscCall(VecDestroy(&w0));
164: PetscCall(VecDestroy(&t));
165: PetscCall(PetscFree2(kr,ki));
166: PetscCall(VecDestroyVecs(nconv,&xr));
167: PetscCall(VecDestroyVecs(nconv,&xi));
168: if (twosided) {
169: PetscCall(VecDestroyVecs(nconv,&yr));
170: PetscCall(VecDestroyVecs(nconv,&yi));
171: }
172: PetscCall(SlepcFinalize());
173: return 0;
174: }
176: /*
177: Matrix generator for a Markov model of a random walk on a triangular grid.
179: This subroutine generates a test matrix that models a random walk on a
180: triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
181: FORTRAN subroutine to calculate the dominant invariant subspaces of a real
182: matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
183: papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
184: (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
185: algorithms. The transpose of the matrix is stochastic and so it is known
186: that one is an exact eigenvalue. One seeks the eigenvector of the transpose
187: associated with the eigenvalue unity. The problem is to calculate the steady
188: state probability distribution of the system, which is the eigevector
189: associated with the eigenvalue one and scaled in such a way that the sum all
190: the components is equal to one.
192: Note: the code will actually compute the transpose of the stochastic matrix
193: that contains the transition probabilities.
194: */
195: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
196: {
197: const PetscReal cst = 0.5/(PetscReal)(m-1);
198: PetscReal pd,pu;
199: PetscInt Istart,Iend,i,j,jmax,ix=0;
201: PetscFunctionBeginUser;
202: PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
203: for (i=1;i<=m;i++) {
204: jmax = m-i+1;
205: for (j=1;j<=jmax;j++) {
206: ix = ix + 1;
207: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
208: if (j!=jmax) {
209: pd = cst*(PetscReal)(i+j-1);
210: /* north */
211: if (i==1) PetscCall(MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES));
212: else PetscCall(MatSetValue(A,ix-1,ix,pd,INSERT_VALUES));
213: /* east */
214: if (j==1) PetscCall(MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES));
215: else PetscCall(MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES));
216: }
217: /* south */
218: pu = 0.5 - cst*(PetscReal)(i+j-3);
219: if (j>1) PetscCall(MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES));
220: /* west */
221: if (i>1) PetscCall(MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES));
222: }
223: }
224: PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
225: PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
226: PetscFunctionReturn(PETSC_SUCCESS);
227: }
229: /*
230: ComputeResidualNorm - Computes the norm of the residual vector
231: associated with an eigenpair.
233: Input Parameters:
234: trans - whether A' must be used instead of A
235: kr,ki - eigenvalue
236: xr,xi - eigenvector
237: u - work vector
238: */
239: PetscErrorCode ComputeResidualNorm(Mat A,PetscBool trans,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec u,PetscReal *norm)
240: {
241: #if !defined(PETSC_USE_COMPLEX)
242: PetscReal ni,nr;
243: #endif
244: PetscErrorCode (*matmult)(Mat,Vec,Vec) = trans? MatMultTranspose: MatMult;
246: PetscFunctionBegin;
247: #if !defined(PETSC_USE_COMPLEX)
248: if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) {
249: #endif
250: PetscCall((*matmult)(A,xr,u));
251: if (PetscAbsScalar(kr) > PETSC_MACHINE_EPSILON) PetscCall(VecAXPY(u,-kr,xr));
252: PetscCall(VecNorm(u,NORM_2,norm));
253: #if !defined(PETSC_USE_COMPLEX)
254: } else {
255: PetscCall((*matmult)(A,xr,u));
256: if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) {
257: PetscCall(VecAXPY(u,-kr,xr));
258: PetscCall(VecAXPY(u,ki,xi));
259: }
260: PetscCall(VecNorm(u,NORM_2,&nr));
261: PetscCall((*matmult)(A,xi,u));
262: if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) {
263: PetscCall(VecAXPY(u,-kr,xi));
264: PetscCall(VecAXPY(u,-ki,xr));
265: }
266: PetscCall(VecNorm(u,NORM_2,&ni));
267: *norm = SlepcAbsEigenvalue(nr,ni);
268: }
269: #endif
270: PetscFunctionReturn(PETSC_SUCCESS);
271: }
273: /*TEST
275: testset:
276: args: -st_type sinvert -eps_target 1.1 -eps_nev 4
277: filter: grep -v method | sed -e "s/[+-]0\.0*i//g" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
278: requires: !single
279: output_file: output/ex41_1.out
280: test:
281: suffix: 1
282: args: -eps_type {{power krylovschur}}
283: test:
284: suffix: 1_balance
285: args: -eps_balance {{oneside twoside}} -eps_ncv 17 -eps_krylovschur_locking 0
286: requires: !__float128
288: TEST*/