Actual source code: test12.c

slepc-3.18.1 2022-11-02
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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

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

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

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

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

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

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

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

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

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

 85:   /* Show info about functions */
 86:   DSNEPGetNumFN(ds,&nfun);
 87:   for (i=0;i<nfun;i++) {
 88:     PetscPrintf(PETSC_COMM_WORLD,"Function %" PetscInt_FMT ":\n",i);
 89:     DSNEPGetFN(ds,i,&qfun);
 90:     FNView(qfun,NULL);
 91:   }

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

112:   if (verbose) {
113:     PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");
114:     DSView(ds,viewer);
115:   }

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

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

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

186: /*TEST

188:    testset:
189:       test:
190:          filter: grep -v "solving the problem"
191:          suffix: 1
192:       test:
193:          suffix: 2
194:          args: -ds_method 1 -radius 10 -ds_nep_refine_its 1
195:          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/"
196:          requires: complex

198: TEST*/