Date: 2017-05-17T08:26:22+00:00

Actual source code: ex18.c
slepc-3.7.4 2017-05-17
Report Typos and Errors

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */

     22: static char help[] = "Solves the same problem as in ex5, but with a user-defined sorting criterion."
     23:   "It is a standard nonsymmetric eigenproblem with real eigenvalues and the rightmost eigenvalue is known to be 1.\n"
     24:   "This example illustrates how the user can set a custom spectrum selection.\n\n"
     25:   "The command line options are:\n"
     26:   "  -m <m>, where <m> = number of grid subdivisions in each dimension.\n\n";

     28: #include <slepceps.h>

     30: /*
     31:    User-defined routines
     32: */

     34: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx);
     35: PetscErrorCode MatMarkovModel(PetscInt m,Mat A);

     39: int main(int argc,char **argv)
     40: {
     41:   Mat            A;               /* operator matrix */
     42:   EPS            eps;             /* eigenproblem solver context */
     43:   EPSType        type;
     44:   PetscScalar    target=0.5;
     45:   PetscInt       N,m=15,nev;
     46:   PetscBool      terse;
     47:   PetscViewer    viewer;
     49:   char           str[50];

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

     53:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
     54:   N = m*(m+1)/2;
     55:   PetscPrintf(PETSC_COMM_WORLD,"\nMarkov Model, N=%D (m=%D)\n",N,m);
     56:   PetscOptionsGetScalar(NULL,NULL,"-target",&target,NULL);
     57:   SlepcSNPrintfScalar(str,50,target,PETSC_FALSE);
     58:   PetscPrintf(PETSC_COMM_WORLD,"Searching closest eigenvalues to the right of %s.\n\n",str);

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:      Compute the operator matrix that defines the eigensystem, Ax=kx
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     64:   MatCreate(PETSC_COMM_WORLD,&A);
     65:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
     66:   MatSetFromOptions(A);
     67:   MatSetUp(A);
     68:   MatMarkovModel(m,A);

     70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     71:                 Create the eigensolver and set various options
     72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     74:   /*
     75:      Create eigensolver context
     76:   */
     77:   EPSCreate(PETSC_COMM_WORLD,&eps);

     79:   /*
     80:      Set operators. In this case, it is a standard eigenvalue problem
     81:   */
     82:   EPSSetOperators(eps,A,NULL);
     83:   EPSSetProblemType(eps,EPS_NHEP);

     85:   /*
     86:      Set the custom comparing routine in order to obtain the eigenvalues
     87:      closest to the target on the right only
     88:   */
     89:   EPSSetEigenvalueComparison(eps,MyEigenSort,&target);

     91:   /*
     92:      Set solver parameters at runtime
     93:   */
     94:   EPSSetFromOptions(eps);

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                       Solve the eigensystem
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    100:   EPSSolve(eps);

    102:   /*
    103:      Optional: Get some information from the solver and display it
    104:   */
    105:   EPSGetType(eps,&type);
    106:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    107:   EPSGetDimensions(eps,&nev,NULL,NULL);
    108:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:                     Display solution and clean up
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    114:   /* show detailed info unless -terse option is given by user */
    115:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    116:   if (terse) {
    117:     EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    118:   } else {
    119:     PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
    120:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
    121:     EPSReasonView(eps,viewer);
    122:     EPSErrorView(eps,EPS_ERROR_RELATIVE,viewer);
    123:     PetscViewerPopFormat(viewer);
    124:   }
    125:   EPSDestroy(&eps);
    126:   MatDestroy(&A);
    127:   SlepcFinalize();
    128:   return ierr;
    129: }

    133: /*
    134:     Matrix generator for a Markov model of a random walk on a triangular grid.

    136:     This subroutine generates a test matrix that models a random walk on a
    137:     triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
    138:     FORTRAN subroutine to calculate the dominant invariant subspaces of a real
    139:     matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
    140:     papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
    141:     (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
    142:     algorithms. The transpose of the matrix  is stochastic and so it is known
    143:     that one is an exact eigenvalue. One seeks the eigenvector of the transpose
    144:     associated with the eigenvalue unity. The problem is to calculate the steady
    145:     state probability distribution of the system, which is the eigevector
    146:     associated with the eigenvalue one and scaled in such a way that the sum all
    147:     the components is equal to one.

    149:     Note: the code will actually compute the transpose of the stochastic matrix
    150:     that contains the transition probabilities.
    151: */
    152: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    153: {
    154:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    155:   PetscReal       pd,pu;
    156:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    157:   PetscErrorCode  ierr;

    160:   MatGetOwnershipRange(A,&Istart,&Iend);
    161:   for (i=1;i<=m;i++) {
    162:     jmax = m-i+1;
    163:     for (j=1;j<=jmax;j++) {
    164:       ix = ix + 1;
    165:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    166:       if (j!=jmax) {
    167:         pd = cst*(PetscReal)(i+j-1);
    168:         /* north */
    169:         if (i==1) {
    170:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    171:         } else {
    172:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    173:         }
    174:         /* east */
    175:         if (j==1) {
    176:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    177:         } else {
    178:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    179:         }
    180:       }
    181:       /* south */
    182:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    183:       if (j>1) {
    184:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    185:       }
    186:       /* west */
    187:       if (i>1) {
    188:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    189:       }
    190:     }
    191:   }
    192:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    193:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    194:   return(0);
    195: }

    199: /*
    200:     Function for user-defined eigenvalue ordering criterion.

    202:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    203:     one of them as the preferred one according to the criterion.
    204:     In this example, the preferred value is the one closest to the target,
    205:     but on the right side.
    206: */
    207: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    208: {
    209:   PetscScalar target = *(PetscScalar*)ctx;
    210:   PetscReal   da,db;
    211:   PetscBool   aisright,bisright;

    214:   if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
    215:   else aisright = PETSC_FALSE;
    216:   if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
    217:   else bisright = PETSC_FALSE;
    218:   if (aisright == bisright) {
    219:     /* both are on the same side of the target */
    220:     da = SlepcAbsEigenvalue(ar-target,ai);
    221:     db = SlepcAbsEigenvalue(br-target,bi);
    222:     if (da < db) *r = -1;
    223:     else if (da > db) *r = 1;
    224:     else *r = 0;
    225:   } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
    226:   else *r = 1;  /* 'b' is on the right */
    227:   return(0);
    228: }