Actual source code: ex18.c

slepc-3.18.3 2023-03-24
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  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:   Mat            A;               /* operator matrix */
 29:   EPS            eps;             /* eigenproblem solver context */
 30:   EPSType        type;
 31:   PetscScalar    target=0.5;
 32:   PetscInt       N,m=15,nev;
 33:   PetscBool      terse;
 34:   PetscViewer    viewer;
 35:   char           str[50];

 38:   SlepcInitialize(&argc,&argv,(char*)0,help);

 40:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 41:   N = m*(m+1)/2;
 42:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n",N,m);
 43:   PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
 44:   SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE);
 45:   PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);

 47:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48:      Compute the operator matrix that defines the eigensystem, Ax=kx
 49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 51:   MatCreate(PETSC_COMM_WORLD,&A);
 52:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 53:   MatSetFromOptions(A);
 54:   MatSetUp(A);
 55:   MatMarkovModel(m,A);

 57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 58:                 Create the eigensolver and set various options
 59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 61:   /*
 62:      Create eigensolver context
 63:   */
 64:   EPSCreate(PETSC_COMM_WORLD,&eps);

 66:   /*
 67:      Set operators. In this case, it is a standard eigenvalue problem
 68:   */
 69:   EPSSetOperators(eps,A,NULL);
 70:   EPSSetProblemType(eps,EPS_NHEP);

 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:                       Solve the eigensystem
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 87:   EPSSolve(eps);

 89:   /*
 90:      Optional: Get some information from the solver and display it
 91:   */
 92:   EPSGetType(eps,&type);
 93:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
 94:   EPSGetDimensions(eps,&nev,NULL,NULL);
 95:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

 97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 98:                     Display solution and clean up
 99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

101:   /* show detailed info unless -terse option is given by user */
102:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
103:   if (terse) EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
104:   else {
105:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
106:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
107:     EPSConvergedReasonView(eps,viewer);
108:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
109:     PetscViewerPopFormat(viewer);
110:   }
111:   EPSDestroy(&eps);
112:   MatDestroy(&A);
113:   SlepcFinalize();
114:   return 0;
115: }

117: /*
118:     Matrix generator for a Markov model of a random walk on a triangular grid.

120:     This subroutine generates a test matrix that models a random walk on a
121:     triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
122:     FORTRAN subroutine to calculate the dominant invariant subspaces of a real
123:     matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
124:     papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
125:     (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
126:     algorithms. The transpose of the matrix  is stochastic and so it is known
127:     that one is an exact eigenvalue. One seeks the eigenvector of the transpose
128:     associated with the eigenvalue unity. The problem is to calculate the steady
129:     state probability distribution of the system, which is the eigevector
130:     associated with the eigenvalue one and scaled in such a way that the sum all
131:     the components is equal to one.

133:     Note: the code will actually compute the transpose of the stochastic matrix
134:     that contains the transition probabilities.
135: */
136: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
137: {
138:   const PetscReal cst = 0.5/(PetscReal)(m-1);
139:   PetscReal       pd,pu;
140:   PetscInt        Istart,Iend,i,j,jmax,ix=0;

143:   MatGetOwnershipRange(A,&Istart,&Iend);
144:   for (i=1;i<=m;i++) {
145:     jmax = m-i+1;
146:     for (j=1;j<=jmax;j++) {
147:       ix = ix + 1;
148:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
149:       if (j!=jmax) {
150:         pd = cst*(PetscReal)(i+j-1);
151:         /* north */
152:         if (i==1) MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
153:         else MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
154:         /* east */
155:         if (j==1) MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
156:         else MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
157:       }
158:       /* south */
159:       pu = 0.5 - cst*(PetscReal)(i+j-3);
160:       if (j>1) MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
161:       /* west */
162:       if (i>1) MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
163:     }
164:   }
165:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
166:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
167:   return 0;
168: }

170: /*
171:     Function for user-defined eigenvalue ordering criterion.

173:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
174:     one of them as the preferred one according to the criterion.
175:     In this example, the preferred value is the one closest to the target,
176:     but on the right side.
177: */
178: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
179: {
180:   PetscScalar target = *(PetscScalar*)ctx;
181:   PetscReal   da,db;
182:   PetscBool   aisright,bisright;

185:   if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
186:   else aisright = PETSC_FALSE;
187:   if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
188:   else bisright = PETSC_FALSE;
189:   if (aisright == bisright) {
190:     /* both are on the same side of the target */
191:     da = SlepcAbsEigenvalue(ar-target,ai);
192:     db = SlepcAbsEigenvalue(br-target,bi);
193:     if (da < db) *r = -1;
194:     else if (da > db) *r = 1;
195:     else *r = 0;
196:   } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
197:   else *r = 1;  /* 'b' is on the right */
198:   return 0;
199: }

201: /*TEST

203:    test:
204:       suffix: 1
205:       args: -eps_nev 4 -terse
206:       requires: !single
207:       filter: sed -e "s/[+-]0\.0*i//g"

209: TEST*/