Date: 2021-02-01T14:42:03+00:00

Actual source code: ex18.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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;
     36:   char           str[50];

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

     40:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     41:   N = m*(m+1)/2;
     42:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\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: %D\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) {
    104:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    105:   } else {
    106:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    107:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    108:     EPSConvergedReasonView(eps,viewer);
    109:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
    110:     PetscViewerPopFormat(viewer);
    111:   }
    112:   EPSDestroy(&eps);
    113:   MatDestroy(&A);
    114:   SlepcFinalize();
    115:   return ierr;
    116: }

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

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

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

    145:   MatGetOwnershipRange(A,&Istart,&Iend);
    146:   for (i=1;i<=m;i++) {
    147:     jmax = m-i+1;
    148:     for (j=1;j<=jmax;j++) {
    149:       ix = ix + 1;
    150:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    151:       if (j!=jmax) {
    152:         pd = cst*(PetscReal)(i+j-1);
    153:         /* north */
    154:         if (i==1) {
    155:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    156:         } else {
    157:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    158:         }
    159:         /* east */
    160:         if (j==1) {
    161:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    162:         } else {
    163:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    164:         }
    165:       }
    166:       /* south */
    167:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    168:       if (j>1) {
    169:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    170:       }
    171:       /* west */
    172:       if (i>1) {
    173:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    174:       }
    175:     }
    176:   }
    177:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    178:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    179:   return(0);
    180: }

    182: /*
    183:     Function for user-defined eigenvalue ordering criterion.

    185:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    186:     one of them as the preferred one according to the criterion.
    187:     In this example, the preferred value is the one closest to the target,
    188:     but on the right side.
    189: */
    190: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    191: {
    192:   PetscScalar target = *(PetscScalar*)ctx;
    193:   PetscReal   da,db;
    194:   PetscBool   aisright,bisright;

    197:   if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
    198:   else aisright = PETSC_FALSE;
    199:   if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
    200:   else bisright = PETSC_FALSE;
    201:   if (aisright == bisright) {
    202:     /* both are on the same side of the target */
    203:     da = SlepcAbsEigenvalue(ar-target,ai);
    204:     db = SlepcAbsEigenvalue(br-target,bi);
    205:     if (da < db) *r = -1;
    206:     else if (da > db) *r = 1;
    207:     else *r = 0;
    208:   } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
    209:   else *r = 1;  /* 'b' is on the right */
    210:   return(0);
    211: }

    213: /*TEST

    215:    test:
    216:       suffix: 1
    217:       args: -eps_nev 4 -terse
    218:       requires: !single

    220: TEST*/