Actual source code: ex27.c

slepc-3.21.1 2024-04-26
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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.
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 FormJacobian(NEP,PetscScalar,Mat,void*);
30: PetscErrorCode ComputeSingularities(NEP,PetscInt*,PetscScalar*,void*);

32: int main(int argc,char **argv)
33: {
34:   NEP            nep;             /* nonlinear eigensolver context */
35:   Mat            F,J,A[2];
36:   NEPType        type;
37:   PetscInt       n=100,nev,Istart,Iend,i;
38:   PetscBool      terse,split=PETSC_TRUE;
39:   RG             rg;
40:   FN             f[2];
41:   PetscScalar    coeffs;

43:   PetscFunctionBeginUser;
44:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
46:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL));
47:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%" PetscInt_FMT "%s\n\n",n,split?" (in split form)":""));

49:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
50:      Create nonlinear eigensolver context
51:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

53:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));

55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
56:      Select the NLEIGS solver and set required options for it
57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

59:   PetscCall(NEPSetType(nep,NEPNLEIGS));
60:   PetscCall(NEPNLEIGSSetSingularitiesFunction(nep,ComputeSingularities,NULL));
61:   PetscCall(NEPGetRG(nep,&rg));
62:   PetscCall(RGSetType(rg,RGINTERVAL));
63: #if defined(PETSC_USE_COMPLEX)
64:   PetscCall(RGIntervalSetEndpoints(rg,0.01,16.0,-0.001,0.001));
65: #else
66:   PetscCall(RGIntervalSetEndpoints(rg,0.01,16.0,0,0));
67: #endif
68:   PetscCall(NEPSetTarget(nep,1.1));

70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71:      Define the nonlinear problem
72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

74:   if (split) {
75:     /*
76:        Create matrices for the split form
77:     */
78:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[0]));
79:     PetscCall(MatSetSizes(A[0],PETSC_DECIDE,PETSC_DECIDE,n,n));
80:     PetscCall(MatSetFromOptions(A[0]));
81:     PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
82:     for (i=Istart;i<Iend;i++) {
83:       if (i>0) PetscCall(MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES));
84:       if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES));
85:       PetscCall(MatSetValue(A[0],i,i,-2.0,INSERT_VALUES));
86:     }
87:     PetscCall(MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY));
88:     PetscCall(MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY));

90:     PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&A[1]));

92:     /*
93:        Define functions for the split form
94:      */
95:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f[0]));
96:     PetscCall(FNSetType(f[0],FNRATIONAL));
97:     coeffs = 1.0;
98:     PetscCall(FNRationalSetNumerator(f[0],1,&coeffs));
99:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f[1]));
100:     PetscCall(FNSetType(f[1],FNSQRT));
101:     PetscCall(NEPSetSplitOperator(nep,2,A,f,SUBSET_NONZERO_PATTERN));

103:   } else {
104:     /*
105:        Callback form: create matrix and set Function evaluation routine
106:      */
107:     PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
108:     PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
109:     PetscCall(MatSetFromOptions(F));
110:     PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
111:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
112:     PetscCall(NEPSetFunction(nep,F,F,FormFunction,NULL));

114:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
115:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
116:     PetscCall(MatSetFromOptions(J));
117:     PetscCall(MatSeqAIJSetPreallocation(J,1,NULL));
118:     PetscCall(MatMPIAIJSetPreallocation(J,1,NULL,1,NULL));
119:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,NULL));
120:   }

122:   /*
123:      Set solver parameters at runtime
124:   */
125:   PetscCall(NEPSetFromOptions(nep));

127:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128:                       Solve the eigensystem
129:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
130:   PetscCall(NEPSolve(nep));
131:   PetscCall(NEPGetType(nep,&type));
132:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type));
133:   PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
134:   PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

136:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
137:                     Display solution and clean up
138:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

140:   /* show detailed info unless -terse option is given by user */
141:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
142:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL));
143:   else {
144:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
145:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
146:     PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
147:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
148:   }
149:   PetscCall(NEPDestroy(&nep));
150:   if (split) {
151:     PetscCall(MatDestroy(&A[0]));
152:     PetscCall(MatDestroy(&A[1]));
153:     PetscCall(FNDestroy(&f[0]));
154:     PetscCall(FNDestroy(&f[1]));
155:   } else {
156:     PetscCall(MatDestroy(&F));
157:     PetscCall(MatDestroy(&J));
158:   }
159:   PetscCall(SlepcFinalize());
160:   return 0;
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: {
169:   PetscInt       i,n,col[3],Istart,Iend;
170:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
171:   PetscScalar    value[3],t;

173:   PetscFunctionBeginUser;
174:   /*
175:      Compute Function entries and insert into matrix
176:   */
177:   t = PetscSqrtScalar(lambda);
178:   PetscCall(MatGetSize(fun,&n,NULL));
179:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
180:   if (Istart==0) FirstBlock=PETSC_TRUE;
181:   if (Iend==n) LastBlock=PETSC_TRUE;
182:   value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
183:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
184:     col[0]=i-1; col[1]=i; col[2]=i+1;
185:     PetscCall(MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES));
186:   }
187:   if (LastBlock) {
188:     i=n-1; col[0]=n-2; col[1]=n-1;
189:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
190:   }
191:   if (FirstBlock) {
192:     i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
193:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
194:   }

196:   /*
197:      Assemble matrix
198:   */
199:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
200:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
201:   if (fun != B) {
202:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
203:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
204:   }
205:   PetscFunctionReturn(PETSC_SUCCESS);
206: }

208: /* ------------------------------------------------------------------- */
209: /*
210:    FormJacobian - Computes Jacobian matrix  T'(lambda)
211: */
212: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
213: {
214:   Vec            d;

216:   PetscFunctionBeginUser;
217:   PetscCall(MatCreateVecs(jac,&d,NULL));
218:   PetscCall(VecSet(d,0.5/PetscSqrtScalar(lambda)));
219:   PetscCall(MatDiagonalSet(jac,d,INSERT_VALUES));
220:   PetscCall(VecDestroy(&d));
221:   PetscFunctionReturn(PETSC_SUCCESS);
222: }

224: /* ------------------------------------------------------------------- */
225: /*
226:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
227:    the function T(.) is not analytic.

229:    In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
230: */
231: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
232: {
233:   PetscReal h;
234:   PetscInt  i;

236:   PetscFunctionBeginUser;
237:   h = 11.0/(*maxnp-1);
238:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
239:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
240:   PetscFunctionReturn(PETSC_SUCCESS);
241: }

243: /*TEST

245:    testset:
246:       args: -nep_nev 3 -terse
247:       output_file: output/ex27_1.out
248:       requires: !single
249:       filter: sed -e "s/[+-]0\.0*i//g"
250:       test:
251:          suffix: 1
252:          args: -nep_nleigs_interpolation_degree 90
253:       test:
254:          suffix: 3
255:          args: -nep_tol 1e-8 -nep_nleigs_rk_shifts 1.06,1.1,1.12,1.15 -nep_conv_norm -nep_nleigs_interpolation_degree 20
256:       test:
257:          suffix: 5
258:          args: -mat_type aijcusparse
259:          requires: cuda

261:    testset:
262:       args: -split 0 -nep_nev 3 -terse
263:       output_file: output/ex27_2.out
264:       filter: sed -e "s/[+-]0\.0*i//g"
265:       test:
266:          suffix: 2
267:          args: -nep_nleigs_interpolation_degree 90
268:          requires: !single
269:       test:
270:          suffix: 4
271:          args: -nep_nleigs_rk_shifts 1.06,1.1,1.12,1.15 -nep_nleigs_interpolation_degree 20
272:          requires: double
273:       test:
274:          suffix: 6
275:          args: -mat_type aijcusparse
276:          requires: cuda !single

278:    testset:
279:       args: -split 0 -nep_type ciss -nep_ciss_extraction {{ritz hankel caa}} -rg_type ellipse -rg_ellipse_center 8 -rg_ellipse_radius .7 -nep_ciss_moments 4 -rg_ellipse_vscale 0.1 -terse
280:       requires: complex !single
281:       output_file: output/ex27_7.out
282:       timeoutfactor: 2
283:       test:
284:          suffix: 7
285:       test:
286:          suffix: 7_par
287:          nsize: 2
288:          args: -nep_ciss_partitions 2

290:    testset:
291:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 8 -rg_ellipse_radius .7 -rg_ellipse_vscale 0.1 -terse
292:       requires: complex
293:       filter: sed -e "s/ (in split form)//" | sed -e "s/56925/56924/" | sed -e "s/60753/60754/" | sed -e "s/92630/92629/" | sed -e "s/24705/24706/"
294:       output_file: output/ex27_7.out
295:       timeoutfactor: 2
296:       test:
297:          suffix: 8
298:       test:
299:          suffix: 8_parallel
300:          nsize: 4
301:          args: -nep_ciss_partitions 4 -ds_parallel distributed
302:       test:
303:          suffix: 8_hpddm
304:          args: -nep_ciss_ksp_type hpddm
305:          requires: hpddm

307:    test:
308:       suffix: 9
309:       args: -nep_nev 4 -n 20 -terse
310:       requires: !single
311:       filter: sed -e "s/[+-]0\.0*i//g"

313: TEST*/
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