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 DSPEP.\n\n";

 13: #include <slepcds.h>

 15: int main(int argc,char **argv)
 16: {
 17:   DS             ds;
 18:   SlepcSC        sc;
 19:   Mat            X;
 20:   Vec            x0;
 21:   PetscScalar    *K,*C,*M,*wr,*wi,z=1.0;
 22:   PetscReal      re,im,nrm,*pbc;
 23:   PetscInt       i,j,n=10,d=2,ld;
 24:   PetscViewer    viewer;
 25:   PetscBool      verbose;

 27:   PetscFunctionBeginUser;
 28:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
 29:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 30:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type PEP - n=%" PetscInt_FMT ".\n",n));
 31:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));

 33:   /* Create DS object */
 34:   PetscCall(DSCreate(PETSC_COMM_WORLD,&ds));
 35:   PetscCall(DSSetType(ds,DSPEP));
 36:   PetscCall(DSSetFromOptions(ds));
 37:   PetscCall(DSPEPSetDegree(ds,d));

 39:   /* Set dimensions */
 40:   ld = n+2;  /* test leading dimension larger than n */
 41:   PetscCall(DSAllocate(ds,ld));
 42:   PetscCall(DSSetDimensions(ds,n,0,0));

 44:   /* Set up viewer */
 45:   PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer));
 46:   PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL));
 47:   PetscCall(DSView(ds,viewer));
 48:   PetscCall(PetscViewerPopFormat(viewer));
 49:   if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB));

 51:   /* Fill matrices */
 52:   PetscCall(DSGetArray(ds,DS_MAT_E0,&K));
 53:   for (i=0;i<n-1;i++) K[i+i*ld] = 2.0*n;
 54:   K[n-1+(n-1)*ld] = 1.0*n;
 55:   for (i=1;i<n;i++) {
 56:     K[i+(i-1)*ld] = -1.0*n;
 57:     K[(i-1)+i*ld] = -1.0*n;
 58:   }
 59:   PetscCall(DSRestoreArray(ds,DS_MAT_E0,&K));
 60:   PetscCall(DSGetArray(ds,DS_MAT_E1,&C));
 61:   C[n-1+(n-1)*ld] = 2.0*PETSC_PI/z;
 62:   PetscCall(DSRestoreArray(ds,DS_MAT_E1,&C));
 63:   PetscCall(DSGetArray(ds,DS_MAT_E2,&M));
 64:   for (i=0;i<n-1;i++) M[i+i*ld] = -4.0*PETSC_PI*PETSC_PI/n;
 65:   M[i+i*ld] = -2.0*PETSC_PI*PETSC_PI/n;
 66:   PetscCall(DSRestoreArray(ds,DS_MAT_E2,&M));

 68:   if (verbose) {
 69:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
 70:     PetscCall(DSView(ds,viewer));
 71:   }

 73:   /* Solve */
 74:   PetscCall(PetscMalloc2(d*n,&wr,d*n,&wi));
 75:   PetscCall(DSGetSlepcSC(ds,&sc));
 76:   sc->comparison    = SlepcCompareLargestReal;
 77:   sc->comparisonctx = NULL;
 78:   sc->map           = NULL;
 79:   sc->mapobj        = NULL;
 80:   PetscCall(DSSolve(ds,wr,wi));
 81:   PetscCall(DSSort(ds,wr,wi,NULL,NULL,NULL));
 82:   if (verbose) {
 83:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n"));
 84:     PetscCall(DSView(ds,viewer));
 85:   }

 87:   /* Print polynomial coefficients */
 88:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Polynomial coefficients (alpha,beta,gamma) =\n"));
 89:   PetscCall(DSPEPGetCoefficients(ds,&pbc));
 90:   for (j=0;j<3;j++) {
 91:     for (i=0;i<d+1;i++) PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f",(double)pbc[j+3*i]));
 92:     PetscCall(PetscViewerASCIIPrintf(viewer,"\n"));
 93:   }
 94:   PetscCall(PetscFree(pbc));

 96:   /* Print eigenvalues */
 97:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n"));
 98:   for (i=0;i<d*n;i++) {
 99: #if defined(PETSC_USE_COMPLEX)
100:     re = PetscRealPart(wr[i]);
101:     im = PetscImaginaryPart(wr[i]);
102: #else
103:     re = wr[i];
104:     im = wi[i];
105: #endif
106:     if (PetscAbs(im)<1e-10) PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)re));
107:     else PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f%+.5fi\n",(double)re,(double)im));
108:   }

110:   /* Eigenvectors */
111:   PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL));  /* all eigenvectors */
112:   PetscCall(DSGetMat(ds,DS_MAT_X,&X));
113:   PetscCall(MatCreateVecs(X,NULL,&x0));
114:   PetscCall(MatGetColumnVector(X,x0,0));
115:   PetscCall(VecNorm(x0,NORM_2,&nrm));
116:   PetscCall(DSRestoreMat(ds,DS_MAT_X,&X));
117:   PetscCall(VecDestroy(&x0));
118:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of 1st vector = %.3f\n",(double)nrm));
119:   if (verbose) {
120:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"After vectors - - - - - - - - -\n"));
121:     PetscCall(DSView(ds,viewer));
122:   }

124:   PetscCall(PetscFree2(wr,wi));
125:   PetscCall(DSDestroy(&ds));
126:   PetscCall(SlepcFinalize());
127:   return 0;
128: }

130: /*TEST

132:    test:
133:       suffix: 1
134:       requires: !single

136: TEST*/