Date: 2026-03-09T09:12:12+00:00

Actual source code: test9.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: */

     11: static char help[] = "Test DSGHEP.\n\n";

     13: #include <slepcds.h>

     15: /*
     16:    Compute the norm of the j-th column of matrix mat in ds
     17:  */
     18: PetscErrorCode ComputeNorm(DS ds,DSMatType mat,PetscInt j,PetscReal *onrm)
     19: {
     20:   PetscScalar    *X;
     21:   PetscReal      aux,nrm=0.0;
     22:   PetscInt       i,n,ld;

     24:   PetscFunctionBeginUser;
     25:   PetscCall(DSGetLeadingDimension(ds,&ld));
     26:   PetscCall(DSGetDimensions(ds,&n,NULL,NULL,NULL));
     27:   PetscCall(DSGetArray(ds,mat,&X));
     28:   for (i=0;i<n;i++) {
     29:     aux = PetscAbsScalar(X[i+j*ld]);
     30:     nrm += aux*aux;
     31:   }
     32:   PetscCall(DSRestoreArray(ds,mat,&X));
     33:   *onrm = PetscSqrtReal(nrm);
     34:   PetscFunctionReturn(PETSC_SUCCESS);
     35: }

     37: int main(int argc,char **argv)
     38: {
     39:   DS             ds;
     40:   SlepcSC        sc;
     41:   PetscReal      re;
     42:   PetscScalar    *A,*B,*eig;
     43:   PetscReal      nrm;
     44:   PetscInt       i,j,n=10,ld;
     45:   PetscViewer    viewer;
     46:   PetscBool      verbose;

     48:   PetscFunctionBeginUser;
     49:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     50:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     51:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solve a System of type GHEP - dimension %" PetscInt_FMT ".\n",n));
     52:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));

     54:   /* Create DS object */
     55:   PetscCall(DSCreate(PETSC_COMM_WORLD,&ds));
     56:   PetscCall(DSSetType(ds,DSGHEP));
     57:   PetscCall(DSSetFromOptions(ds));
     58:   ld = n+2;  /* test leading dimension larger than n */
     59:   PetscCall(DSAllocate(ds,ld));
     60:   PetscCall(DSSetDimensions(ds,n,0,0));

     62:   /* Set up viewer */
     63:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
     64:   PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
     65:   PetscCall(DSView(ds,viewer));
     66:   PetscCall(PetscViewerPopFormat(viewer));
     67:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

     69:   /* Fill with a symmetric Toeplitz matrix */
     70:   PetscCall(DSGetArray(ds,DS_MAT_A,&A));
     71:   PetscCall(DSGetArray(ds,DS_MAT_B,&B));
     72:   for (i=0;i<n;i++) A[i+i*ld]=2.0;
     73:   for (j=1;j<3;j++) {
     74:     for (i=0;i<n-j;i++) { A[i+(i+j)*ld]=1.0; A[(i+j)+i*ld]=1.0; }
     75:   }
     76:   for (j=1;j<3;j++) { A[0+j*ld]=-1.0*(j+2); A[j+0*ld]=-1.0*(j+2); }
     77:   /* Diagonal matrix */
     78:   for (i=0;i<n;i++) B[i+i*ld]=0.1*(i+1);
     79:   PetscCall(DSRestoreArray(ds,DS_MAT_A,&A));
     80:   PetscCall(DSRestoreArray(ds,DS_MAT_B,&B));
     81:   PetscCall(DSSetState(ds,DS_STATE_RAW));
     82:   if (verbose) {
     83:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
     84:     PetscCall(DSView(ds,viewer));
     85:   }

     87:   /* Solve */
     88:   PetscCall(PetscMalloc1(n,&eig));
     89:   PetscCall(PetscNew(&sc));
     90:   sc->comparison    = SlepcCompareLargestMagnitude;
     91:   sc->comparisonctx = NULL;
     92:   sc->map           = NULL;
     93:   sc->mapobj        = NULL;
     94:   PetscCall(DSSetSlepcSC(ds,sc));
     95:   PetscCall(DSSolve(ds,eig,NULL));
     96:   PetscCall(DSSort(ds,eig,NULL,NULL,NULL,NULL));
     97:   if (verbose) {
     98:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n"));
     99:     PetscCall(DSView(ds,viewer));
    100:   }

    102:   /* Print eigenvalues */
    103:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n"));
    104:   for (i=0;i<n;i++) {
    105:     re = PetscRealPart(eig[i]);
    106:     PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)re));
    107:   }

    109:   /* Eigenvectors */
    110:   j = 0;
    111:   PetscCall(DSVectors(ds,DS_MAT_X,&j,NULL));  /* all eigenvectors */
    112:   PetscCall(ComputeNorm(ds,DS_MAT_X,0,&nrm));
    113:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st vector = %.3f\n",(double)nrm));
    114:   PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL));  /* all eigenvectors */
    115:   if (verbose) {
    116:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After vectors - - - - - - - - -\n"));
    117:     PetscCall(DSView(ds,viewer));
    118:   }

    120:   PetscCall(PetscFree(eig));
    121:   PetscCall(PetscFree(sc));
    122:   PetscCall(DSDestroy(&ds));
    123:   PetscCall(SlepcFinalize());
    124:   return 0;
    125: }

    127: /*TEST

    129:    test:
    130:       suffix: 1
    131:       requires: !single

    133: TEST*/