Date: 2021-09-20T09:43:42+00:00

Actual source code: test12.c
slepc-3.15.2 2021-09-20
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2021, 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 DSNEP.\n\n";

     13: #include <slepcds.h>

     15: int main(int argc,char **argv)
     16: {
     18:   DS             ds;
     19:   FN             f1,f2,f3,funs[3],qfun;
     20:   SlepcSC        sc;
     21:   PetscScalar    *Id,*A,*B,*wr,*wi,*X,coeffs[2];
     22:   PetscReal      tau=0.001,h,a=20,xi,re,im,nrm,aux;
     23:   PetscInt       i,j,n=10,ld,nev,nfun;
     24:   PetscViewer    viewer;
     25:   PetscBool      verbose;

     27:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     28:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     29:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     30:   PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type NEP - dimension %D, tau=%g.\n",n,(double)tau);
     31:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);

     33:   /* Create DS object */
     34:   DSCreate(PETSC_COMM_WORLD,&ds);
     35:   DSSetType(ds,DSNEP);
     36:   DSSetFromOptions(ds);

     38:   /* Set functions (prior to DSAllocate) */
     39:   FNCreate(PETSC_COMM_WORLD,&f1);
     40:   FNSetType(f1,FNRATIONAL);
     41:   coeffs[0] = -1.0; coeffs[1] = 0.0;
     42:   FNRationalSetNumerator(f1,2,coeffs);

     44:   FNCreate(PETSC_COMM_WORLD,&f2);
     45:   FNSetType(f2,FNRATIONAL);
     46:   coeffs[0] = 1.0;
     47:   FNRationalSetNumerator(f2,1,coeffs);

     49:   FNCreate(PETSC_COMM_WORLD,&f3);
     50:   FNSetType(f3,FNEXP);
     51:   FNSetScale(f3,-tau,1.0);

     53:   funs[0] = f1;
     54:   funs[1] = f2;
     55:   funs[2] = f3;
     56:   DSNEPSetFN(ds,3,funs);

     58:   /* Set dimensions */
     59:   ld = n+2;  /* test leading dimension larger than n */
     60:   DSAllocate(ds,ld);
     61:   DSSetDimensions(ds,n,0,0,0);

     63:   /* Set up viewer */
     64:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     65:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
     66:   DSView(ds,viewer);
     67:   PetscViewerPopFormat(viewer);
     68:   if (verbose) {
     69:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
     70:   }

     72:   /* Show info about functions */
     73:   DSNEPGetNumFN(ds,&nfun);
     74:   for (i=0;i<nfun;i++) {
     75:     PetscPrintf(PETSC_COMM_WORLD,"Function %D:\n",i);
     76:     DSNEPGetFN(ds,i,&qfun);
     77:     FNView(qfun,NULL);
     78:   }

     80:   /* Fill matrices */
     81:   DSGetArray(ds,DS_MAT_E0,&Id);
     82:   for (i=0;i<n;i++) Id[i+i*ld]=1.0;
     83:   DSRestoreArray(ds,DS_MAT_E0,&Id);
     84:   h = PETSC_PI/(PetscReal)(n+1);
     85:   DSGetArray(ds,DS_MAT_E1,&A);
     86:   for (i=0;i<n;i++) A[i+i*ld]=-2.0/(h*h)+a;
     87:   for (i=1;i<n;i++) {
     88:     A[i+(i-1)*ld]=1.0/(h*h);
     89:     A[(i-1)+i*ld]=1.0/(h*h);
     90:   }
     91:   DSRestoreArray(ds,DS_MAT_E1,&A);
     92:   DSGetArray(ds,DS_MAT_E2,&B);
     93:   for (i=0;i<n;i++) {
     94:     xi = (i+1)*h;
     95:     B[i+i*ld] = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
     96:   }
     97:   DSRestoreArray(ds,DS_MAT_E2,&B);

     99:   if (verbose) {
    100:     PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
    101:     DSView(ds,viewer);
    102:   }

    104:   /* Solve */
    105:   PetscMalloc2(n,&wr,n,&wi);
    106:   DSGetSlepcSC(ds,&sc);
    107:   sc->comparison    = SlepcCompareLargestMagnitude;
    108:   sc->comparisonctx = NULL;
    109:   sc->map           = NULL;
    110:   sc->mapobj        = NULL;
    111:   DSSolve(ds,wr,wi);
    112:   DSSort(ds,wr,wi,NULL,NULL,NULL);

    114:   if (verbose) {
    115:     PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
    116:     DSView(ds,viewer);
    117:   }

    119:   /* Print first eigenvalue */
    120:   PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalue =\n");
    121:   nev = 1;
    122:   for (i=0;i<nev;i++) {
    123: #if defined(PETSC_USE_COMPLEX)
    124:     re = PetscRealPart(wr[i]);
    125:     im = PetscImaginaryPart(wr[i]);
    126: #else
    127:     re = wr[i];
    128:     im = wi[i];
    129: #endif
    130:     if (PetscAbs(im)<1e-10) {
    131:       PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)re);
    132:     } else {
    133:       PetscViewerASCIIPrintf(viewer,"  %.5f%+.5fi\n",(double)re,(double)im);
    134:     }
    135:   }

    137:   /* Eigenvectors */
    138:   DSVectors(ds,DS_MAT_X,NULL,NULL);
    139:   j = 0;
    140:   nrm = 0.0;
    141:   DSGetArray(ds,DS_MAT_X,&X);
    142:   for (i=0;i<n;i++) {
    143: #if defined(PETSC_USE_COMPLEX)
    144:     aux = PetscAbsScalar(X[i+j*ld]);
    145: #else
    146:     if (PetscAbs(wi[j])==0.0) aux = PetscAbsScalar(X[i+j*ld]);
    147:     else aux = SlepcAbsEigenvalue(X[i+j*ld],X[i+(j+1)*ld]);
    148: #endif
    149:     nrm += aux*aux;
    150:   }
    151:   DSRestoreArray(ds,DS_MAT_X,&X);
    152:   nrm = PetscSqrtReal(nrm);
    153:   PetscPrintf(PETSC_COMM_WORLD,"Norm of eigenvector = %.3f\n",(double)nrm);
    154:   if (verbose) {
    155:     PetscPrintf(PETSC_COMM_WORLD,"After vectors - - - - - - - - -\n");
    156:     DSView(ds,viewer);
    157:   }

    159:   PetscFree2(wr,wi);
    160:   FNDestroy(&f1);
    161:   FNDestroy(&f2);
    162:   FNDestroy(&f3);
    163:   DSDestroy(&ds);
    164:   SlepcFinalize();
    165:   return ierr;
    166: }

    168: /*TEST

    170:    test:
    171:       suffix: 1

    173: TEST*/