Date: 2023-09-05T10:18:45+00:00

Actual source code: embedgsvd.c
slepc-3.19.2 2023-09-05
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      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: */

     11: static char help[] = "Computes a GSVD associated with a complex network analysis problem.\n"
     12:   "The command line options are:\n"
     13:   "  -file <filename>, text file in TSV format containing undirected graph.\n"
     14:   "  -beta <beta>, optional decay parameter.\n\n";

     16: /*
     17:     Computes the Katz high-order proximity embedding of a graph via a partial GSVD.

     19:     [1] M. Ou et al. "Asymmetric transitivity preserving graph embedding" Proc. of
     20:         ACM SIGKDD 2016 - https://doi.org/10.1145/2939672.2939751
     21: */

     23: #include <slepcsvd.h>
     24: #include "network.h"

     26: PetscErrorCode SpectralRadius(Mat A,PetscReal *rho)
     27: {
     28:   EPS         eps;
     29:   PetscInt    nconv;
     30:   PetscScalar kr,ki;

     32:   PetscFunctionBeginUser;
     33:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
     34:   PetscCall(EPSSetOperators(eps,A,NULL));
     35:   PetscCall(EPSSetProblemType(eps,EPS_NHEP));
     36:   PetscCall(EPSSetDimensions(eps,1,PETSC_DEFAULT,PETSC_DEFAULT));
     37:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_MAGNITUDE));
     38:   PetscCall(EPSSetFromOptions(eps));
     39:   PetscCall(EPSSolve(eps));
     40:   PetscCall(EPSGetConverged(eps,&nconv));
     41:   *rho = 0.0;
     42:   if (nconv) {
     43:     PetscCall(EPSGetEigenvalue(eps,0,&kr,&ki));
     44:     *rho = SlepcAbsEigenvalue(kr,ki);
     45:   }
     46:   PetscCall(EPSDestroy(&eps));
     47:   PetscFunctionReturn(PETSC_SUCCESS);
     48: }

     50: int main(int argc,char **argv)
     51: {
     52:   Graph          graph;           /* directed graph */
     53:   Mat            A,B;             /* matrices */
     54:   SVD            svd;             /* singular value problem solver context */
     55:   PetscReal      beta=0.0,rho=0.0;
     56:   char           filename[PETSC_MAX_PATH_LEN];
     57:   PetscBool      flg,terse;

     59:   PetscFunctionBeginUser;
     60:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

     62:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     63:         Load graph and build adjacency matrix
     64:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     66:   PetscCall(PetscOptionsGetString(NULL,NULL,"-graph",filename,sizeof(filename),&flg));
     67:   PetscCheck(flg,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Must use -graph <name> to indicate a file containing the graph in TSV format");

     69:   PetscCall(GraphCreate(PETSC_COMM_WORLD,&graph));
     70:   PetscCall(GraphPreload(graph,filename));
     71:   PetscCheck(graph->type==GRAPH_DIRECTED,PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"A directed graph is required");
     72:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nGraph with %" PetscInt_FMT " vertices and %" PetscInt_FMT " edges.\n\n",graph->nvertices,graph->nedges));
     73:   if (graph->weight!=GRAPH_WEIGHT_UNWEIGHTED) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"WARNING: ignoring weights in input graph\n"));

     75:   PetscCall(GraphPreallocate(graph,filename));
     76:   PetscCall(GraphLoadUnweighted(graph,filename));

     78:   PetscCall(MatViewFromOptions(graph->adjacency,NULL,"-adjacency"));

     80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     81:       Build high-order proximity matrices (Katz): A=I-beta*G, B=beta*G
     82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     84:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-beta",&beta,NULL));
     85:   if (beta==0.0) {  /* compute decay parameter beta */
     86:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computing spectral radius...\n"));
     87:     PetscCall(SpectralRadius(graph->adjacency,&rho));
     88:     if (rho) {
     89:       beta = 0.8*rho;
     90:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Done, rho=%g, setting decay parameter beta=%g\n\n",(double)rho,(double)beta));
     91:     } else {
     92:       beta = 0.5;
     93:       PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Failed, using default decay parameter beta=%g\n\n",(double)beta));
     94:     }
     95:   }
     96:   PetscCall(MatDuplicate(graph->adjacency,MAT_COPY_VALUES,&A));
     97:   PetscCall(MatScale(A,-beta));
     98:   PetscCall(MatShift(A,1.0));
     99:   PetscCall(MatDuplicate(graph->adjacency,MAT_COPY_VALUES,&B));
    100:   PetscCall(MatScale(B,beta));

    102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    103:            Create the singular value solver and set various options
    104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    106:   PetscCall(SVDCreate(PETSC_COMM_WORLD,&svd));
    107:   PetscCall(SVDSetOperators(svd,A,B));
    108:   PetscCall(SVDSetProblemType(svd,SVD_GENERALIZED));
    109:   PetscCall(SVDSetType(svd,SVDTRLANCZOS));
    110:   PetscCall(SVDSetFromOptions(svd));

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                       Solve the problem and print solution
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    116:   PetscCall(SVDSolve(svd));

    118:   /* show detailed info unless -terse option is given by user */
    119:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    120:   if (terse) PetscCall(SVDErrorView(svd,SVD_ERROR_NORM,NULL));
    121:   else {
    122:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    123:     PetscCall(SVDConvergedReasonView(svd,PETSC_VIEWER_STDOUT_WORLD));
    124:     PetscCall(SVDErrorView(svd,SVD_ERROR_NORM,PETSC_VIEWER_STDOUT_WORLD));
    125:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    126:   }
    127:   PetscCall(SVDDestroy(&svd));
    128:   PetscCall(GraphDestroy(&graph));
    129:   PetscCall(MatDestroy(&A));
    130:   PetscCall(MatDestroy(&B));
    131:   PetscCall(SlepcFinalize());
    132:   return 0;
    133: }
    134: /*TEST

    136:    build:
    137:       depends: network.o

    139:    test:
    140:       args: -graph ${SLEPC_DIR}/share/slepc/datafiles/graphs/out.moreno_taro_taro -svd_nsv 4 -terse
    141:       filter: sed -e 's/4.38031/4.38032/' | sed -e 's/3.75089/3.7509/' | sed -e 's/3.00071/3.00072/'

    143: TEST*/