Actual source code: ex18.c

      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.\n\n"
     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];

     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,m));
     43:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL));
     44:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),target,PETSC_FALSE));
     45:   PetscCall(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:   PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
     52:   PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N));
     53:   PetscCall(MatSetFromOptions(A));
     54:   PetscCall(MatMarkovModel(m,A));

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:                 Create the eigensolver and set various options
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     60:   /*
     61:      Create eigensolver context
     62:   */
     63:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));

     65:   /*
     66:      Set operators. In this case, it is a standard eigenvalue problem
     67:   */
     68:   PetscCall(EPSSetOperators(eps,A,NULL));
     69:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));

     71:   /*
     72:      Set the custom comparing routine in order to obtain the eigenvalues
     73:      closest to the target on the right only
     74:   */
     75:   PetscCall(EPSSetEigenvalueComparison(eps,MyEigenSort,&target));

     77:   /*
     78:      Set solver parameters at runtime
     79:   */
     80:   PetscCall(EPSSetFromOptions(eps));

     82:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     83:                       Solve the eigensystem
     84:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     86:   PetscCall(EPSSolve(eps));

     88:   /*
     89:      Optional: Get some information from the solver and display it
     90:   */
     91:   PetscCall(EPSGetType(eps,&type));
     92:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type));
     93:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
     94:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                     Display solution and clean up
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    116: /*
    117:     Matrix generator for a Markov model of a random walk on a triangular grid.

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

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

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

    169: /*
    170:     Function for user-defined eigenvalue ordering criterion.

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

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

    200: /*TEST

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

    208: TEST*/