Actual source code: test12.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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*/