Actual source code: test12.c
slepc-3.17.2 2022-08-09
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*/