Actual source code: test11.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[] = "Solves the same problem as in ex5, but with a user-defined sorting criterion."
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 a custom spectrum selection.\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: */
23: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);
24: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);
26: int main(int argc,char **argv)
27: {
28: Vec v0; /* initial vector */
29: Mat A; /* operator matrix */
30: EPS eps; /* eigenproblem solver context */
31: ST st; /* spectral transformation associated */
32: PetscReal tol=PETSC_SMALL;
33: PetscScalar target=0.5;
34: PetscInt N,m=15,nev;
35: char str[50];
37: SlepcInitialize(&argc,&argv,(char*)0,help);
39: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
40: N = m*(m+1)/2;
41: PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m);
42: PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
43: SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE);
44: PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);
46: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47: Compute the operator matrix that defines the eigensystem, Ax=kx
48: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
50: MatCreate(PETSC_COMM_WORLD,&A);
51: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
52: MatSetFromOptions(A);
53: MatSetUp(A);
54: MatMarkovModel(m,A);
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Create the eigensolver and set various options
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: /*
61: Create eigensolver context
62: */
63: EPSCreate(PETSC_COMM_WORLD,&eps);
65: /*
66: Set operators. In this case, it is a standard eigenvalue problem
67: */
68: EPSSetOperators(eps,A,NULL);
69: EPSSetProblemType(eps,EPS_NHEP);
70: EPSSetTolerances(eps,tol,PETSC_DEFAULT);
72: /*
73: Set the custom comparing routine in order to obtain the eigenvalues
74: closest to the target on the right only
75: */
76: EPSSetEigenvalueComparison(eps,MyEigenSort,&target);
78: /*
79: Set solver parameters at runtime
80: */
81: EPSSetFromOptions(eps);
83: /*
84: Set the preconditioner based on A - target * I
85: */
86: EPSGetST(eps,&st);
87: STSetShift(st,target);
89: /*
90: Set the initial vector. This is optional, if not done the initial
91: vector is set to random values
92: */
93: MatCreateVecs(A,&v0,NULL);
94: VecSet(v0,1.0);
95: EPSSetInitialSpace(eps,1,&v0);
97: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98: Solve the eigensystem
99: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: EPSSolve(eps);
102: EPSGetDimensions(eps,&nev,NULL,NULL);
103: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
105: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106: Display solution and clean up
107: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109: EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
110: EPSDestroy(&eps);
111: MatDestroy(&A);
112: VecDestroy(&v0);
113: SlepcFinalize();
114: return 0;
115: }
117: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
118: {
119: const PetscReal cst = 0.5/(PetscReal)(m-1);
120: PetscReal pd,pu;
121: PetscInt Istart,Iend,i,j,jmax,ix=0;
124: MatGetOwnershipRange(A,&Istart,&Iend);
125: for (i=1;i<=m;i++) {
126: jmax = m-i+1;
127: for (j=1;j<=jmax;j++) {
128: ix = ix + 1;
129: if (ix-1<Istart || ix>Iend) continue; /* compute only owned rows */
130: if (j!=jmax) {
131: pd = cst*(PetscReal)(i+j-1);
132: /* north */
133: if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
134: else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
135: /* east */
136: if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
137: else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
138: }
139: /* south */
140: pu = 0.5 - cst*(PetscReal)(i+j-3);
141: if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
142: /* west */
143: if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
144: }
145: }
146: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
147: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
148: PetscFunctionReturn(0);
149: }
151: /*
152: Function for user-defined eigenvalue ordering criterion.
154: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
155: one of them as the preferred one according to the criterion.
156: In this example, the preferred value is the one closest to the target,
157: but on the right side.
158: */
159: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
160: {
161: PetscScalar target = *(PetscScalar*)ctx;
162: PetscReal da,db;
163: PetscBool aisright,bisright;
166: if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
167: else aisright = PETSC_FALSE;
168: if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
169: else bisright = PETSC_FALSE;
170: if (aisright == bisright) {
171: /* both are on the same side of the target */
172: da = SlepcAbsEigenvalue(ar-target,ai);
173: db = SlepcAbsEigenvalue(br-target,bi);
174: if (da < db) *r = -1;
175: else if (da > db) *r = 1;
176: else *r = 0;
177: } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
178: else *r = 1; /* 'b' is on the right */
179: PetscFunctionReturn(0);
180: }
182: /*TEST
184: testset:
185: args: -eps_nev 4
186: requires: !single
187: output_file: output/test11_1.out
188: test:
189: suffix: 1
190: args: -eps_type {{krylovschur arnoldi lapack}} -st_type sinvert
191: test:
192: suffix: 1_ks_cayley
193: args: -st_type cayley -st_cayley_antishift 1
195: test:
196: suffix: 2
197: args: -target 0.77 -eps_type gd -eps_nev 4 -eps_tol 1e-7 -eps_gd_krylov_start -eps_gd_blocksize 3
198: requires: double
199: filter: sed -e "s/[+-]0\.0*i//g"
201: TEST*/