Date: 2016-03-29T14:58:24+00:00

Actual source code: test11.c
slepc-3.6.3 2016-03-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, 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:   Vec            v0;              /* initial vector */
     42:   Mat            A;               /* operator matrix */
     43:   EPS            eps;             /* eigenproblem solver context */
     44:   ST             st;              /* spectral transformation associated */
     45:   EPSType        type;
     46:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
     47:   PetscScalar    target=0.5;
     48:   PetscInt       N,m=15,nev;
     50:   char           str[50];

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

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

     61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     62:      Compute the operator matrix that defines the eigensystem, Ax=kx
     63:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     72:                 Create the eigensolver and set various options
     73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

     87:   /*
     88:      Set the custom comparing routine in order to obtain the eigenvalues
     89:      closest to the target on the right only
     90:   */
     91:   EPSSetEigenvalueComparison(eps,MyEigenSort,&target);

     93:   /*
     94:      Set solver parameters at runtime
     95:   */
     96:   EPSSetFromOptions(eps);

     98:   /*
     99:      Set the preconditioner based on A - target * I
    100:   */
    101:   EPSGetST(eps,&st);
    102:   STSetShift(st,target);

    104:   /*
    105:      Set the initial vector. This is optional, if not done the initial
    106:      vector is set to random values
    107:   */
    108:   MatCreateVecs(A,&v0,NULL);
    109:   VecSet(v0,1.0);
    110:   EPSSetInitialSpace(eps,1,&v0);

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                       Solve the eigensystem
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    116:   EPSSolve(eps);

    118:   /*
    119:      Optional: Get some information from the solver and display it
    120:   */
    121:   EPSGetType(eps,&type);
    122:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n\n",type);
    123:   EPSGetDimensions(eps,&nev,NULL,NULL);
    124:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    127:                     Display solution and clean up
    128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    130:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    131:   EPSDestroy(&eps);
    132:   MatDestroy(&A);
    133:   VecDestroy(&v0);
    134:   SlepcFinalize();
    135:   return 0;
    136: }

    140: /*
    141:     Matrix generator for a Markov model of a random walk on a triangular grid.

    143:     This subroutine generates a test matrix that models a random walk on a
    144:     triangular grid. This test example was used by G. W. Stewart ["{SRRIT} - a
    145:     FORTRAN subroutine to calculate the dominant invariant subspaces of a real
    146:     matrix", Tech. report. TR-514, University of Maryland (1978).] and in a few
    147:     papers on eigenvalue problems by Y. Saad [see e.g. LAA, vol. 34, pp. 269-295
    148:     (1980) ]. These matrices provide reasonably easy test problems for eigenvalue
    149:     algorithms. The transpose of the matrix  is stochastic and so it is known
    150:     that one is an exact eigenvalue. One seeks the eigenvector of the transpose
    151:     associated with the eigenvalue unity. The problem is to calculate the steady
    152:     state probability distribution of the system, which is the eigevector
    153:     associated with the eigenvalue one and scaled in such a way that the sum all
    154:     the components is equal to one.

    156:     Note: the code will actually compute the transpose of the stochastic matrix
    157:     that contains the transition probabilities.
    158: */
    159: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    160: {
    161:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    162:   PetscReal       pd,pu;
    163:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    164:   PetscErrorCode  ierr;

    167:   MatGetOwnershipRange(A,&Istart,&Iend);
    168:   for (i=1;i<=m;i++) {
    169:     jmax = m-i+1;
    170:     for (j=1;j<=jmax;j++) {
    171:       ix = ix + 1;
    172:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    173:       if (j!=jmax) {
    174:         pd = cst*(PetscReal)(i+j-1);
    175:         /* north */
    176:         if (i==1) {
    177:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    178:         } else {
    179:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    180:         }
    181:         /* east */
    182:         if (j==1) {
    183:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    184:         } else {
    185:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    186:         }
    187:       }
    188:       /* south */
    189:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    190:       if (j>1) {
    191:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    192:       }
    193:       /* west */
    194:       if (i>1) {
    195:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    196:       }
    197:     }
    198:   }
    199:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    200:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    201:   return(0);
    202: }

    206: /*
    207:     Function for user-defined eigenvalue ordering criterion.

    209:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    210:     one of them as the preferred one according to the criterion.
    211:     In this example, the preferred value is the one closest to the target,
    212:     but on the right side.
    213: */
    214: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    215: {
    216:   PetscScalar target = *(PetscScalar*)ctx;
    217:   PetscReal   da,db;
    218:   PetscBool   aisright,bisright;

    221:   if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
    222:   else aisright = PETSC_FALSE;
    223:   if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
    224:   else bisright = PETSC_FALSE;
    225:   if (aisright == bisright) {
    226:     /* both are on the same side of the target */
    227:     da = SlepcAbsEigenvalue(ar-target,ai);
    228:     db = SlepcAbsEigenvalue(br-target,bi);
    229:     if (da < db) *r = -1;
    230:     else if (da > db) *r = 1;
    231:     else *r = 0;
    232:   } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
    233:   else *r = 1;  /* 'b' is on the right */
    234:   return(0);
    235: }