Actual source code: ex27.c
slepc-3.8.2 2017-12-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2017, 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[] = "Simple nonlinear eigenproblem using the NLEIGS solver.\n\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = matrix dimension.\n"
14: " -split <0/1>, to select the split form in the problem definition (enabled by default)\n";
16: /*
17: Solve T(lambda)x=0 using NLEIGS solver
18: with T(lambda) = -D+sqrt(lambda)*I
19: where D is the Laplacian operator in 1 dimension
20: and with the interpolation interval [.01,16]
21: */
23: #include <slepcnep.h>
25: /*
26: User-defined routines
27: */
28: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
29: PetscErrorCode ComputeSingularities(NEP,PetscInt*,PetscScalar*,void*);
31: int main(int argc,char **argv)
32: {
33: NEP nep; /* nonlinear eigensolver context */
34: Mat F,A[2];
35: NEPType type;
36: PetscInt n=100,nev,Istart,Iend,i;
38: PetscBool terse,split=PETSC_TRUE;
39: RG rg;
40: FN f[2];
41: PetscScalar coeffs;
43: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
44: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
45: PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL);
46: PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%D%s\n\n",n,split?" (in split form)":"");
48: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
49: Create nonlinear eigensolver context
50: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
52: NEPCreate(PETSC_COMM_WORLD,&nep);
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Select the NLEIGS solver and set required options for it
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: NEPSetType(nep,NEPNLEIGS);
59: NEPNLEIGSSetSingularitiesFunction(nep,ComputeSingularities,NULL);
60: NEPGetRG(nep,&rg);
61: RGSetType(rg,RGINTERVAL);
62: #if defined(PETSC_USE_COMPLEX)
63: RGIntervalSetEndpoints(rg,0.01,16.0,-0.001,0.001);
64: #else
65: RGIntervalSetEndpoints(rg,0.01,16.0,0,0);
66: #endif
67: NEPSetTarget(nep,1.1);
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Define the nonlinear problem
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
73: if (split) {
74: /*
75: Create matrices for the split form
76: */
77: MatCreate(PETSC_COMM_WORLD,&A[0]);
78: MatSetSizes(A[0],PETSC_DECIDE,PETSC_DECIDE,n,n);
79: MatSetFromOptions(A[0]);
80: MatSetUp(A[0]);
81: MatGetOwnershipRange(A[0],&Istart,&Iend);
82: for (i=Istart;i<Iend;i++) {
83: if (i>0) { MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES); }
84: if (i<n-1) { MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES); }
85: MatSetValue(A[0],i,i,-2.0,INSERT_VALUES);
86: }
87: MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY);
88: MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY);
90: MatCreate(PETSC_COMM_WORLD,&A[1]);
91: MatSetSizes(A[1],PETSC_DECIDE,PETSC_DECIDE,n,n);
92: MatSetFromOptions(A[1]);
93: MatSetUp(A[1]);
94: MatAssemblyBegin(A[1],MAT_FINAL_ASSEMBLY);
95: MatAssemblyEnd(A[1],MAT_FINAL_ASSEMBLY);
96: MatShift(A[1],1.0);
98: /*
99: Define funcions for the split form
100: */
101: FNCreate(PETSC_COMM_WORLD,&f[0]);
102: FNSetType(f[0],FNRATIONAL);
103: coeffs = 1.0;
104: FNRationalSetNumerator(f[0],1,&coeffs);
105: FNCreate(PETSC_COMM_WORLD,&f[1]);
106: FNSetType(f[1],FNSQRT);
107: NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN);
109: } else {
110: /*
111: Callback form: create matrix and set Function evaluation routine
112: */
113: MatCreate(PETSC_COMM_WORLD,&F);
114: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
115: MatSetFromOptions(F);
116: MatSeqAIJSetPreallocation(F,3,NULL);
117: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
118: MatSetUp(F);
119: NEPSetFunction(nep,F,F,FormFunction,NULL);
120: }
122: /*
123: Set solver parameters at runtime
124: */
125: NEPSetFromOptions(nep);
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Solve the eigensystem
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130: NEPSolve(nep);
131: NEPGetType(nep,&type);
132: PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
133: NEPGetDimensions(nep,&nev,NULL,NULL);
134: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
136: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137: Display solution and clean up
138: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140: /* show detailed info unless -terse option is given by user */
141: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
142: if (terse) {
143: NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL);
144: } else {
145: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
146: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
147: NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
148: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
149: }
150: NEPDestroy(&nep);
151: if (split) {
152: MatDestroy(&A[0]);
153: MatDestroy(&A[1]);
154: FNDestroy(&f[0]);
155: FNDestroy(&f[1]);
156: } else {
157: MatDestroy(&F);
158: }
159: SlepcFinalize();
160: return ierr;
161: }
163: /* ------------------------------------------------------------------- */
164: /*
165: FormFunction - Computes Function matrix T(lambda)
166: */
167: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
168: {
170: PetscInt i,n,col[3],Istart,Iend;
171: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
172: PetscScalar value[3],t;
175: /*
176: Compute Function entries and insert into matrix
177: */
178: t = PetscSqrtScalar(lambda);
179: MatGetSize(fun,&n,NULL);
180: MatGetOwnershipRange(fun,&Istart,&Iend);
181: if (Istart==0) FirstBlock=PETSC_TRUE;
182: if (Iend==n) LastBlock=PETSC_TRUE;
183: value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
184: for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
185: col[0]=i-1; col[1]=i; col[2]=i+1;
186: MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES);
187: }
188: if (LastBlock) {
189: i=n-1; col[0]=n-2; col[1]=n-1;
190: MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES);
191: }
192: if (FirstBlock) {
193: i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
194: MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES);
195: }
197: /*
198: Assemble matrix
199: */
200: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
201: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
202: if (fun != B) {
203: MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
204: MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
205: }
206: return(0);
207: }
209: /*
210: ComputeSingularities - Computes maxnp points (at most) in the complex plane where
211: the function T(.) is not analytic.
213: In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
214: */
215: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
216: {
217: PetscReal h;
218: PetscInt i;
221: h = 11.0/(*maxnp-1);
222: xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
223: for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
224: return(0);
225: }