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

Actual source code: test12.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 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],qfun;
     19:   SlepcSC        sc;
     20:   PetscScalar    *Id,*A,*B,*wr,*wi,*X,*W,coeffs[2],auxr,alpha;
     21:   PetscReal      tol,tau=0.001,radius=10,h,a=20,xi,re,im,nrm,aux;
     22:   PetscInt       i,j,ii,jj,k,n=10,ld,nev,nfun;
     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:   PetscScalar    auxi;
     29: #endif

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

     38:   /* Create DS object */
     39:   DSCreate(PETSC_COMM_WORLD,&ds);
     40:   DSSetType(ds,DSNEP);
     41:   tol  = 1000*n*PETSC_MACHINE_EPSILON;
     42:   DSNEPSetRefine(ds,tol,PETSC_DECIDE);
     43:   DSSetFromOptions(ds);

     45:   /* Set functions (prior to DSAllocate) */
     46:   FNCreate(PETSC_COMM_WORLD,&f1);
     47:   FNSetType(f1,FNRATIONAL);
     48:   coeffs[0] = -1.0; coeffs[1] = 0.0;
     49:   FNRationalSetNumerator(f1,2,coeffs);

     51:   FNCreate(PETSC_COMM_WORLD,&f2);
     52:   FNSetType(f2,FNRATIONAL);
     53:   coeffs[0] = 1.0;
     54:   FNRationalSetNumerator(f2,1,coeffs);

     56:   FNCreate(PETSC_COMM_WORLD,&f3);
     57:   FNSetType(f3,FNEXP);
     58:   FNSetScale(f3,-tau,1.0);

     60:   funs[0] = f1;
     61:   funs[1] = f2;
     62:   funs[2] = f3;
     63:   DSNEPSetFN(ds,3,funs);

     65:   /* Set dimensions */
     66:   ld = n+2;  /* test leading dimension larger than n */
     67:   DSAllocate(ds,ld);
     68:   DSSetDimensions(ds,n,0,0);

     70:   /* Set region (used only in method=1) */
     71:   RGCreate(PETSC_COMM_WORLD,&rg);
     72:   RGSetType(rg,RGELLIPSE);
     73:   RGEllipseSetParameters(rg,0.0,radius,1.0);
     74:   DSNEPSetRG(ds,rg);
     75:   RGDestroy(&rg);

     77:   /* Set up viewer */
     78:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
     79:   PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
     80:   DSView(ds,viewer);
     81:   PetscViewerPopFormat(viewer);
     82:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

     84:   /* Show info about functions */
     85:   DSNEPGetNumFN(ds,&nfun);
     86:   for (i=0;i<nfun;i++) {
     87:     PetscPrintf(PETSC_COMM_WORLD,"Function %" PetscInt_FMT ":\n",i);
     88:     DSNEPGetFN(ds,i,&qfun);
     89:     FNView(qfun,NULL);
     90:   }

     92:   /* Fill matrices */
     93:   DSGetArray(ds,DS_MAT_E0,&Id);
     94:   for (i=0;i<n;i++) Id[i+i*ld]=1.0;
     95:   DSRestoreArray(ds,DS_MAT_E0,&Id);
     96:   h = PETSC_PI/(PetscReal)(n+1);
     97:   DSGetArray(ds,DS_MAT_E1,&A);
     98:   for (i=0;i<n;i++) A[i+i*ld]=-2.0/(h*h)+a;
     99:   for (i=1;i<n;i++) {
    100:     A[i+(i-1)*ld]=1.0/(h*h);
    101:     A[(i-1)+i*ld]=1.0/(h*h);
    102:   }
    103:   DSRestoreArray(ds,DS_MAT_E1,&A);
    104:   DSGetArray(ds,DS_MAT_E2,&B);
    105:   for (i=0;i<n;i++) {
    106:     xi = (i+1)*h;
    107:     B[i+i*ld] = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
    108:   }
    109:   DSRestoreArray(ds,DS_MAT_E2,&B);

    111:   if (verbose) {
    112:     PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
    113:     DSView(ds,viewer);
    114:   }

    116:   /* Solve */
    117:   PetscCalloc2(n,&wr,n,&wi);
    118:   DSGetSlepcSC(ds,&sc);
    119:   sc->comparison    = SlepcCompareLargestMagnitude;
    120:   sc->comparisonctx = NULL;
    121:   sc->map           = NULL;
    122:   sc->mapobj        = NULL;
    123:   DSSolve(ds,wr,wi);
    124:   DSSort(ds,wr,wi,NULL,NULL,NULL);

    126:   if (verbose) {
    127:     PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");
    128:     DSView(ds,viewer);
    129:   }
    130:   DSGetDimensions(ds,NULL,NULL,NULL,&nev);

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

    185: /*TEST

    187:    testset:
    188:       test:
    189:          filter: grep -v "solving the problem"
    190:          suffix: 1
    191:       test:
    192:          suffix: 2
    193:          args: -ds_method 1 -radius 10 -ds_nep_refine_its 1
    194:          filter: grep -v "solving the problem" | sed -e "s/[+-]0\.0*i//g" | sed -e "s/37411/37410/" | sed -e "s/tolerance [0-9]\.[0-9]*e[+-]\([0-9]*\)/tolerance removed/" | sed -e "s/tolerance [0-9]\.\([0-9]*\)/tolerance removed/"
    195:          requires: complex

    197: TEST*/