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*/