Actual source code: test23.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 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:   PetscFunctionBeginUser;
     34:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
     35:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     36:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
     37:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type NEP - dimension %" PetscInt_FMT ", tau=%g.\n",n,(double)tau));
     38:   PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose));

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

     54:   /* Print current options */
     55:   PetscCall(DSGetMethod(ds,&meth));
     56: #if defined(PETSC_USE_COMPLEX)
     57:   PetscCheck(meth==1,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"This example requires ds_method=1");
     58:   PetscCall(RGIsTrivial(rg,&flg));
     59:   PetscCheck(!flg,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"Must at least set the radius of the ellipse");
     60: #endif

     62:   PetscCall(DSNEPGetMinimality(ds,&midx));
     63:   PetscCall(DSNEPGetIntegrationPoints(ds,&ip));
     64:   PetscCall(DSNEPGetRefine(ds,NULL,&rits));
     65:   PetscCall(DSNEPGetSamplingSize(ds,&spls));
     66:   if (meth==1) {
     67:     PetscCall(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));
     68:     if (rits) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Doing %" PetscInt_FMT " iterations of Newton refinement\n",rits));
     69:   }

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

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

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

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

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

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

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

    121:   if (verbose) {
    122:     PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n"));
    123:     PetscCall(DSView(ds,viewer));
    124:   }

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

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

    142:   /* Print computed eigenvalues */
    143:   PetscCall(DSNEPGetNumFN(ds,&nfun));
    144:   PetscCall(PetscMalloc1(ld*ld,&W));
    145:   PetscCall(DSVectors(ds,DS_MAT_X,NULL,NULL));
    146:   PetscCall(DSGetArray(ds,DS_MAT_X,&X));
    147:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalues =\n"));
    148:   for (i=0;i<nev;i++) {
    149: #if defined(PETSC_USE_COMPLEX)
    150:     re = PetscRealPart(wr[i]);
    151:     im = PetscImaginaryPart(wr[i]);
    152: #else
    153:     re = wr[i];
    154:     im = wi[i];
    155: #endif
    156:     /* Residual */
    157:     PetscCall(PetscArrayzero(W,ld*ld));
    158:     for (k=0;k<nfun;k++) {
    159:       PetscCall(FNEvaluateFunction(funs[k],wr[i],&alpha));
    160:       PetscCall(DSGetArray(ds,mat[k],&A));
    161:       for (jj=0;jj<n;jj++) for (ii=0;ii<n;ii++) W[jj*ld+ii] += alpha*A[jj*ld+ii];
    162:       PetscCall(DSRestoreArray(ds,mat[k],&A));
    163:     }
    164:     nrm = 0.0;
    165:     for (k=0;k<n;k++) {
    166:       auxr = 0.0;
    167: #if !defined(PETSC_USE_COMPLEX)
    168:       auxi = 0.0;
    169: #endif
    170:       for (j=0;j<n;j++) {
    171:         auxr += W[k+j*ld]*X[i*ld+j];
    172: #if !defined(PETSC_USE_COMPLEX)
    173:         if (PetscAbs(wi[j])!=0.0) auxi += W[k+j*ld]*X[(i+1)*ld+j];
    174: #endif
    175:       }
    176:       aux = SlepcAbsEigenvalue(auxr,auxi);
    177:       nrm += aux*aux;
    178:     }
    179:     nrm = PetscSqrtReal(nrm);
    180:     if (nrm>1000*n*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the residual norm of the %" PetscInt_FMT "-th computed eigenpair %g\n",i,(double)nrm));
    181:     if (PetscAbs(im)<1e-10) PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f\n",(double)re));
    182:     else PetscCall(PetscViewerASCIIPrintf(viewer,"  %.5f%+.5fi\n",(double)re,(double)im));
    183:   }
    184:   PetscCall(PetscFree(W));
    185:   PetscCall(DSRestoreArray(ds,DS_MAT_X,&X));
    186:   PetscCall(DSRestoreArray(ds,DS_MAT_W,&W));
    187:   PetscCall(PetscFree2(wr,wi));
    188:   PetscCall(FNDestroy(&f1));
    189:   PetscCall(FNDestroy(&f2));
    190:   PetscCall(FNDestroy(&f3));
    191:   PetscCall(DSDestroy(&ds));
    192:   PetscCall(SlepcFinalize());
    193:   return 0;
    194: }

    196: /*TEST

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

    208: TEST*/