Date: 2026-03-31T13:23:04+00:00

Actual source code: butterfly.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: */
     10: /*
     11:    This example implements one of the problems found at
     12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     13:        The University of Manchester.
     14:    The details of the collection can be found at:
     15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     18:    The butterfly problem is a quartic PEP with T-even structure.
     19: */

     21: static char help[] = "Quartic polynomial eigenproblem with T-even structure.\n\n"
     22:   "The command line options are:\n"
     23:   "  -m <m>, grid size, the dimension of the matrices is n=m*m.\n"
     24:   "  -c <array>, problem parameters, must be 10 comma-separated real values.\n\n";

     26: #include <slepcpep.h>

     28: #define NMAT 5

     30: int main(int argc,char **argv)
     31: {
     32:   Mat            A[NMAT];         /* problem matrices */
     33:   PEP            pep;             /* polynomial eigenproblem solver context */
     34:   PetscInt       n,m=8,k,II,Istart,Iend,i,j;
     35:   PetscReal      c[10] = { 0.6, 1.3, 1.3, 0.1, 0.1, 1.2, 1.0, 1.0, 1.2, 1.0 };
     36:   PetscBool      flg;
     37:   PetscBool      terse;

     39:   PetscFunctionBeginUser;
     40:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     42:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     43:   n = m*m;
     44:   k = 10;
     45:   PetscCall(PetscOptionsGetRealArray(NULL,NULL,"-c",c,&k,&flg));
     46:   PetscCheck(!flg || k==10,PETSC_COMM_WORLD,PETSC_ERR_USER,"The number of parameters -c should be 10, you provided %" PetscInt_FMT,k);
     47:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nButterfly problem, n=%" PetscInt_FMT " (m=%" PetscInt_FMT ")\n\n",n,m));

     49:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     50:                      Compute the polynomial matrices
     51:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     53:   /* initialize matrices */
     54:   for (i=0;i<NMAT;i++) {
     55:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
     56:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
     57:     PetscCall(MatSetFromOptions(A[i]));
     58:   }
     59:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

     61:   /* A0 */
     62:   for (II=Istart;II<Iend;II++) {
     63:     i = II/m; j = II-i*m;
     64:     PetscCall(MatSetValue(A[0],II,II,4.0*c[0]/6.0+4.0*c[1]/6.0,INSERT_VALUES));
     65:     if (j>0) PetscCall(MatSetValue(A[0],II,II-1,c[0]/6.0,INSERT_VALUES));
     66:     if (j<m-1) PetscCall(MatSetValue(A[0],II,II+1,c[0]/6.0,INSERT_VALUES));
     67:     if (i>0) PetscCall(MatSetValue(A[0],II,II-m,c[1]/6.0,INSERT_VALUES));
     68:     if (i<m-1) PetscCall(MatSetValue(A[0],II,II+m,c[1]/6.0,INSERT_VALUES));
     69:   }

     71:   /* A1 */
     72:   for (II=Istart;II<Iend;II++) {
     73:     i = II/m; j = II-i*m;
     74:     if (j>0) PetscCall(MatSetValue(A[1],II,II-1,c[2],INSERT_VALUES));
     75:     if (j<m-1) PetscCall(MatSetValue(A[1],II,II+1,-c[2],INSERT_VALUES));
     76:     if (i>0) PetscCall(MatSetValue(A[1],II,II-m,c[3],INSERT_VALUES));
     77:     if (i<m-1) PetscCall(MatSetValue(A[1],II,II+m,-c[3],INSERT_VALUES));
     78:   }

     80:   /* A2 */
     81:   for (II=Istart;II<Iend;II++) {
     82:     i = II/m; j = II-i*m;
     83:     PetscCall(MatSetValue(A[2],II,II,-2.0*c[4]-2.0*c[5],INSERT_VALUES));
     84:     if (j>0) PetscCall(MatSetValue(A[2],II,II-1,c[4],INSERT_VALUES));
     85:     if (j<m-1) PetscCall(MatSetValue(A[2],II,II+1,c[4],INSERT_VALUES));
     86:     if (i>0) PetscCall(MatSetValue(A[2],II,II-m,c[5],INSERT_VALUES));
     87:     if (i<m-1) PetscCall(MatSetValue(A[2],II,II+m,c[5],INSERT_VALUES));
     88:   }

     90:   /* A3 */
     91:   for (II=Istart;II<Iend;II++) {
     92:     i = II/m; j = II-i*m;
     93:     if (j>0) PetscCall(MatSetValue(A[3],II,II-1,c[6],INSERT_VALUES));
     94:     if (j<m-1) PetscCall(MatSetValue(A[3],II,II+1,-c[6],INSERT_VALUES));
     95:     if (i>0) PetscCall(MatSetValue(A[3],II,II-m,c[7],INSERT_VALUES));
     96:     if (i<m-1) PetscCall(MatSetValue(A[3],II,II+m,-c[7],INSERT_VALUES));
     97:   }

     99:   /* A4 */
    100:   for (II=Istart;II<Iend;II++) {
    101:     i = II/m; j = II-i*m;
    102:     PetscCall(MatSetValue(A[4],II,II,2.0*c[8]+2.0*c[9],INSERT_VALUES));
    103:     if (j>0) PetscCall(MatSetValue(A[4],II,II-1,-c[8],INSERT_VALUES));
    104:     if (j<m-1) PetscCall(MatSetValue(A[4],II,II+1,-c[8],INSERT_VALUES));
    105:     if (i>0) PetscCall(MatSetValue(A[4],II,II-m,-c[9],INSERT_VALUES));
    106:     if (i<m-1) PetscCall(MatSetValue(A[4],II,II+m,-c[9],INSERT_VALUES));
    107:   }

    109:   /* assemble matrices */
    110:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
    111:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

    113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    114:                 Create the eigensolver and solve the problem
    115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    117:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    118:   PetscCall(PEPSetOperators(pep,NMAT,A));
    119:   PetscCall(PEPSetFromOptions(pep));
    120:   PetscCall(PEPSolve(pep));

    122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    123:                     Display solution and clean up
    124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    126:   /* show detailed info unless -terse option is given by user */
    127:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    128:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    129:   else {
    130:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    131:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    132:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    133:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    134:   }
    135:   PetscCall(PEPDestroy(&pep));
    136:   for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
    137:   PetscCall(SlepcFinalize());
    138:   return 0;
    139: }

    141: /*TEST

    143:    testset:
    144:       args: -pep_nev 4 -st_type sinvert -pep_target 0.01 -terse
    145:       output_file: output/butterfly_1.out
    146:       test:
    147:          suffix: 1_toar
    148:          args: -pep_type toar -pep_toar_restart 0.3
    149:       test:
    150:          suffix: 1_linear
    151:          args: -pep_type linear

    153:    test:
    154:       suffix: 2
    155:       args: -pep_type {{toar linear}} -pep_nev 4 -terse
    156:       requires: double

    158:    testset:
    159:       args: -pep_type ciss -rg_type ellipse -rg_ellipse_center 1+.5i -rg_ellipse_radius .15 -terse
    160:       requires: complex
    161:       filter: sed -e "s/95386/95385/" | sed -e "s/91010/91009/" | sed -e "s/93092/93091/" | sed -e "s/96723/96724/" | sed -e "s/43015/43016/" | sed -e "s/53513/53514/"
    162:       output_file: output/butterfly_ciss.out
    163:       timeoutfactor: 2
    164:       test:
    165:          suffix: ciss_hankel
    166:          args: -pep_ciss_extraction hankel -pep_ciss_integration_points 60
    167:          requires: !single
    168:       test:
    169:          suffix: ciss_ritz
    170:          args: -pep_ciss_extraction ritz
    171:       test:
    172:          suffix: ciss_caa
    173:          args: -pep_ciss_extraction caa -pep_ciss_moments 4
    174:       test:
    175:          suffix: ciss_part
    176:          nsize: 2
    177:          args: -pep_ciss_partitions 2
    178:       test:
    179:          suffix: ciss_refine
    180:          args: -pep_ciss_refine_inner 1 -pep_ciss_refine_blocksize 1

    182:    testset:
    183:       args: -pep_type ciss -rg_type ellipse -rg_ellipse_center .5+.5i -rg_ellipse_radius .25 -pep_ciss_moments 4 -pep_ciss_blocksize 5 -pep_ciss_refine_blocksize 2 -terse
    184:       requires: complex double
    185:       filter: sed -e "s/46483/46484/" | sed -e "s/54946/54945/" | sed -e "s/48456/48457/" | sed -e "s/74117/74116/" | sed -e "s/37240/37241/"
    186:       output_file: output/butterfly_4.out
    187:       test:
    188:          suffix: 4
    189:       test:
    190:          suffix: 4_hankel
    191:          args: -pep_ciss_extraction hankel

    193: TEST*/