Date: 2022-08-09T09:05:23+00:00

Actual source code: test23.c
slepc-3.17.2 2022-08-09
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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[] = "Test interface functions of DSNEP.\n\n";

     13: #include <slepcds.h>

     15: int main(int argc,char **argv)
     16: {
     17:   DS             ds;
     18:   FN             f1,f2,f3,funs[3];
     19:   SlepcSC        sc;
     20:   PetscScalar    *Id,*A,*B,*wr,*wi,*X,*W,coeffs[2],auxr,alpha;
     21:   PetscReal      tau=0.001,h,a=20,xi,re,im,nrm,aux;
     22:   PetscInt       i,j,ii,jj,k,n=10,ld,nev,nfun,midx,ip,rits,meth,spls;
     23:   PetscViewer    viewer;
     24:   PetscBool      verbose;
     25:   RG             rg;
     26:   DSMatType      mat[3]={DS_MAT_E0,DS_MAT_E1,DS_MAT_E2};
     27: #if defined(PETSC_USE_COMPLEX)
     28:   PetscBool      flg;
     29: #else
     30:   PetscScalar    auxi;
     31: #endif

     33:   SlepcInitialize(&argc,&argv,(char*)0,help);
     34:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     35:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
     36:   PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type NEP - dimension %" PetscInt_FMT ", tau=%g.\n",n,(double)tau);
     37:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);

     39:   /* Create DS object and set options */
     40:   DSCreate(PETSC_COMM_WORLD,&ds);
     41:   DSSetType(ds,DSNEP);
     42: #if defined(PETSC_USE_COMPLEX)
     43:   DSSetMethod(ds,1);  /* contour integral */
     44: #endif
     45:   DSNEPGetRG(ds,&rg);
     46:   RGSetType(rg,RGELLIPSE);
     47:   DSNEPSetMinimality(ds,1);
     48:   DSNEPSetIntegrationPoints(ds,16);
     49:   DSNEPSetRefine(ds,PETSC_DEFAULT,2);
     50:   DSNEPSetSamplingSize(ds,25);
     51:   DSSetFromOptions(ds);

     53:   /* Print current options */
     54:   DSGetMethod(ds,&meth);
     55: #if defined(PETSC_USE_COMPLEX)
     57:   RGIsTrivial(rg,&flg);
     59: #endif

     61:   DSNEPGetMinimality(ds,&midx);
     62:   DSNEPGetIntegrationPoints(ds,&ip);
     63:   DSNEPGetRefine(ds,NULL,&rits);
     64:   DSNEPGetSamplingSize(ds,&spls);
     65:   if (meth==1) {
     66:     PetscPrintf(PETSC_COMM_WORLD,"Contour integral method with %" PetscInt_FMT " integration points, minimality index %" PetscInt_FMT ", and sampling size %" PetscInt_FMT "\n",ip,midx,spls);
     67:     if (rits) PetscPrintf(PETSC_COMM_WORLD,"Doing %" PetscInt_FMT " iterations of Newton refinement\n",rits);
     68:   }

     70:   /* Set functions (prior to DSAllocate) */
     71:   FNCreate(PETSC_COMM_WORLD,&f1);
     72:   FNSetType(f1,FNRATIONAL);
     73:   coeffs[0] = -1.0; coeffs[1] = 0.0;
     74:   FNRationalSetNumerator(f1,2,coeffs);

     76:   FNCreate(PETSC_COMM_WORLD,&f2);
     77:   FNSetType(f2,FNRATIONAL);
     78:   coeffs[0] = 1.0;
     79:   FNRationalSetNumerator(f2,1,coeffs);

     81:   FNCreate(PETSC_COMM_WORLD,&f3);
     82:   FNSetType(f3,FNEXP);
     83:   FNSetScale(f3,-tau,1.0);

     85:   funs[0] = f1;
     86:   funs[1] = f2;
     87:   funs[2] = f3;
     88:   DSNEPSetFN(ds,3,funs);

     90:   /* Set dimensions */
     91:   ld = n;
     92:   DSAllocate(ds,ld);
     93:   DSSetDimensions(ds,n,0,0);

     95:   /* Set up viewer */
     96:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     97:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
     98:   PetscViewerPopFormat(viewer);
     99:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

    101:   /* Fill matrices */
    102:   DSGetArray(ds,DS_MAT_E0,&Id);
    103:   for (i=0;i<n;i++) Id[i+i*ld]=1.0;
    104:   DSRestoreArray(ds,DS_MAT_E0,&Id);
    105:   h = PETSC_PI/(PetscReal)(n+1);
    106:   DSGetArray(ds,DS_MAT_E1,&A);
    107:   for (i=0;i<n;i++) A[i+i*ld]=-2.0/(h*h)+a;
    108:   for (i=1;i<n;i++) {
    109:     A[i+(i-1)*ld]=1.0/(h*h);
    110:     A[(i-1)+i*ld]=1.0/(h*h);
    111:   }
    112:   DSRestoreArray(ds,DS_MAT_E1,&A);
    113:   DSGetArray(ds,DS_MAT_E2,&B);
    114:   for (i=0;i<n;i++) {
    115:     xi = (i+1)*h;
    116:     B[i+i*ld] = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    117:   }
    118:   DSRestoreArray(ds,DS_MAT_E2,&B);

    120:   if (verbose) {
    121:     PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
    122:     DSView(ds,viewer);
    123:   }

    125:   /* Solve */
    126:   PetscCalloc2(n,&wr,n,&wi);
    127:   DSGetSlepcSC(ds,&sc);
    128:   sc->comparison    = SlepcCompareLargestMagnitude;
    129:   sc->comparisonctx = NULL;
    130:   sc->map           = NULL;
    131:   sc->mapobj        = NULL;
    132:   DSSolve(ds,wr,wi);
    133:   DSSort(ds,wr,wi,NULL,NULL,NULL);

    135:   if (verbose) {
    136:     PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
    137:     DSView(ds,viewer);
    138:   }
    139:   DSGetDimensions(ds,NULL,NULL,NULL,&nev);

    141:   /* Print computed eigenvalues */
    142:   DSNEPGetNumFN(ds,&nfun);
    143:   PetscMalloc1(ld*ld,&W);
    144:   DSVectors(ds,DS_MAT_X,NULL,NULL);
    145:   DSGetArray(ds,DS_MAT_X,&X);
    146:   PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n");
    147:   for (i=0;i<nev;i++) {
    148: #if defined(PETSC_USE_COMPLEX)
    149:     re = PetscRealPart(wr[i]);
    150:     im = PetscImaginaryPart(wr[i]);
    151: #else
    152:     re = wr[i];
    153:     im = wi[i];
    154: #endif
    155:     /* Residual */
    156:     PetscArrayzero(W,ld*ld);
    157:     for (k=0;k<nfun;k++) {
    158:       FNEvaluateFunction(funs[k],wr[i],&alpha);
    159:       DSGetArray(ds,mat[k],&A);
    160:       for (jj=0;jj<n;jj++) for (ii=0;ii<n;ii++) W[jj*ld+ii] += alpha*A[jj*ld+ii];
    161:       DSRestoreArray(ds,mat[k],&A);
    162:     }
    163:     nrm = 0.0;
    164:     for (k=0;k<n;k++) {
    165:       auxr = 0.0;
    166: #if !defined(PETSC_USE_COMPLEX)
    167:       auxi = 0.0;
    168: #endif
    169:       for (j=0;j<n;j++) {
    170:         auxr += W[k+j*ld]*X[i*ld+j];
    171: #if !defined(PETSC_USE_COMPLEX)
    172:         if (PetscAbs(wi[j])!=0.0) auxi += W[k+j*ld]*X[(i+1)*ld+j];
    173: #endif
    174:       }
    175:       aux = SlepcAbsEigenvalue(auxr,auxi);
    176:       nrm += aux*aux;
    177:     }
    178:     nrm = PetscSqrtReal(nrm);
    179:     if (nrm>1000*n*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the residual norm of the %" PetscInt_FMT "-th computed eigenpair %g\n",i,(double)nrm);
    180:     if (PetscAbs(im)<1e-10) PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)re);
    181:     else PetscViewerASCIIPrintf(viewer,"  %.5f%+.5fi\n",(double)re,(double)im);
    182:   }
    183:   PetscFree(W);
    184:   DSRestoreArray(ds,DS_MAT_X,&X);
    185:   DSRestoreArray(ds,DS_MAT_W,&W);
    186:   PetscFree2(wr,wi);
    187:   FNDestroy(&f1);
    188:   FNDestroy(&f2);
    189:   FNDestroy(&f3);
    190:   DSDestroy(&ds);
    191:   SlepcFinalize();
    192:   return 0;
    193: }

    195: /*TEST

    197:    testset:
    198:       test:
    199:          suffix: 1
    200:          requires: !complex
    201:       test:
    202:          suffix: 2
    203:          args: -ds_nep_rg_ellipse_radius 10
    204:          filter: sed -e "s/[+-]0\.0*i//g" | sed -e "s/37411/37410/"
    205:          requires: complex

    207: TEST*/