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

Actual source code: test11.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:   Vec            v0;              /* initial vector */
     29:   Mat            A;               /* operator matrix */
     30:   EPS            eps;             /* eigenproblem solver context */
     31:   ST             st;              /* spectral transformation associated */
     32:   PetscReal      tol=1000*PETSC_MACHINE_EPSILON;
     33:   PetscScalar    target=0.5;
     34:   PetscInt       N,m=15,nev;
     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);
     71:   EPSSetTolerances(eps,tol,PETSC_DEFAULT);

     73:   /*
     74:      Set the custom comparing routine in order to obtain the eigenvalues
     75:      closest to the target on the right only
     76:   */
     77:   EPSSetEigenvalueComparison(eps,MyEigenSort,&target);

     79:   /*
     80:      Set solver parameters at runtime
     81:   */
     82:   EPSSetFromOptions(eps);

     84:   /*
     85:      Set the preconditioner based on A - target * I
     86:   */
     87:   EPSGetST(eps,&st);
     88:   STSetShift(st,target);

     90:   /*
     91:      Set the initial vector. This is optional, if not done the initial
     92:      vector is set to random values
     93:   */
     94:   MatCreateVecs(A,&v0,NULL);
     95:   VecSet(v0,1.0);
     96:   EPSSetInitialSpace(eps,1,&v0);

     98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     99:                       Solve the eigensystem
    100:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    102:   EPSSolve(eps);
    103:   EPSGetDimensions(eps,&nev,NULL,NULL);
    104:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

    106:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    107:                     Display solution and clean up
    108:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    110:   EPSErrorView(eps,EPS_ERROR_RELATIVE,NULL);
    111:   EPSDestroy(&eps);
    112:   MatDestroy(&A);
    113:   VecDestroy(&v0);
    114:   SlepcFinalize();
    115:   return ierr;
    116: }

    118: PetscErrorCode MatMarkovModel(PetscInt m,Mat A)
    119: {
    120:   const PetscReal cst = 0.5/(PetscReal)(m-1);
    121:   PetscReal       pd,pu;
    122:   PetscInt        Istart,Iend,i,j,jmax,ix=0;
    123:   PetscErrorCode  ierr;

    126:   MatGetOwnershipRange(A,&Istart,&Iend);
    127:   for (i=1;i<=m;i++) {
    128:     jmax = m-i+1;
    129:     for (j=1;j<=jmax;j++) {
    130:       ix = ix + 1;
    131:       if (ix-1<Istart || ix>Iend) continue;  /* compute only owned rows */
    132:       if (j!=jmax) {
    133:         pd = cst*(PetscReal)(i+j-1);
    134:         /* north */
    135:         if (i==1) {
    136:           MatSetValue(A,ix-1,ix,2*pd,INSERT_VALUES);
    137:         } else {
    138:           MatSetValue(A,ix-1,ix,pd,INSERT_VALUES);
    139:         }
    140:         /* east */
    141:         if (j==1) {
    142:           MatSetValue(A,ix-1,ix+jmax-1,2*pd,INSERT_VALUES);
    143:         } else {
    144:           MatSetValue(A,ix-1,ix+jmax-1,pd,INSERT_VALUES);
    145:         }
    146:       }
    147:       /* south */
    148:       pu = 0.5 - cst*(PetscReal)(i+j-3);
    149:       if (j>1) {
    150:         MatSetValue(A,ix-1,ix-2,pu,INSERT_VALUES);
    151:       }
    152:       /* west */
    153:       if (i>1) {
    154:         MatSetValue(A,ix-1,ix-jmax-2,pu,INSERT_VALUES);
    155:       }
    156:     }
    157:   }
    158:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    159:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    160:   return(0);
    161: }

    163: /*
    164:     Function for user-defined eigenvalue ordering criterion.

    166:     Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
    167:     one of them as the preferred one according to the criterion.
    168:     In this example, the preferred value is the one closest to the target,
    169:     but on the right side.
    170: */
    171: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
    172: {
    173:   PetscScalar target = *(PetscScalar*)ctx;
    174:   PetscReal   da,db;
    175:   PetscBool   aisright,bisright;

    178:   if (PetscRealPart(target) < PetscRealPart(ar)) aisright = PETSC_TRUE;
    179:   else aisright = PETSC_FALSE;
    180:   if (PetscRealPart(target) < PetscRealPart(br)) bisright = PETSC_TRUE;
    181:   else bisright = PETSC_FALSE;
    182:   if (aisright == bisright) {
    183:     /* both are on the same side of the target */
    184:     da = SlepcAbsEigenvalue(ar-target,ai);
    185:     db = SlepcAbsEigenvalue(br-target,bi);
    186:     if (da < db) *r = -1;
    187:     else if (da > db) *r = 1;
    188:     else *r = 0;
    189:   } else if (aisright && !bisright) *r = -1; /* 'a' is on the right */
    190:   else *r = 1;  /* 'b' is on the right */
    191:   return(0);
    192: }

    194: /*TEST

    196:    testset:
    197:       args: -eps_nev 4
    198:       requires: !single
    199:       output_file: output/test11_1.out
    200:       test:
    201:          suffix: 1
    202:          args: -eps_type {{krylovschur arnoldi lapack}} -st_type sinvert
    203:       test:
    204:          suffix: 1_ks_cayley
    205:          args: -st_type cayley -st_cayley_antishift 1

    207:    test:
    208:       suffix: 2
    209:       args: -target 0.77 -eps_type gd -eps_nev 4 -eps_tol 1e-7 -eps_gd_krylov_start -eps_gd_blocksize 3
    210:       requires: double
    211:       filter: sed -e "s/[+-]0\.0*i//g"

    213: TEST*/