Actual source code: ex27.c

slepc-3.17.1 2022-04-11
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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[] = "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:   SlepcInitialize(&argc,&argv,(char*)0,help);
 44:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 45:   PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL);
 46:   PetscPrintf(PETSC_COMM_WORLD,"\nSquare root eigenproblem, n=%" PetscInt_FMT "%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:     MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&A[1]);

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

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

115:     MatCreate(PETSC_COMM_WORLD,&J);
116:     MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
117:     MatSetFromOptions(J);
118:     MatSeqAIJSetPreallocation(J,1,NULL);
119:     MatMPIAIJSetPreallocation(J,1,NULL,1,NULL);
120:     MatSetUp(J);
121:     NEPSetJacobian(nep,J,FormJacobian,NULL);
122:   }

124:   /*
125:      Set solver parameters at runtime
126:   */
127:   NEPSetFromOptions(nep);

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

138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139:                     Display solution and clean up
140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

142:   /* show detailed info unless -terse option is given by user */
143:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
144:   if (terse) NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL);
145:   else {
146:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
147:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
148:     NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
149:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
150:   }
151:   NEPDestroy(&nep);
152:   if (split) {
153:     MatDestroy(&A[0]);
154:     MatDestroy(&A[1]);
155:     FNDestroy(&f[0]);
156:     FNDestroy(&f[1]);
157:   } else {
158:     MatDestroy(&F);
159:     MatDestroy(&J);
160:   }
161:   SlepcFinalize();
162:   return 0;
163: }

165: /* ------------------------------------------------------------------- */
166: /*
167:    FormFunction - Computes Function matrix  T(lambda)
168: */
169: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
170: {
171:   PetscInt       i,n,col[3],Istart,Iend;
172:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
173:   PetscScalar    value[3],t;

176:   /*
177:      Compute Function entries and insert into matrix
178:   */
179:   t = PetscSqrtScalar(lambda);
180:   MatGetSize(fun,&n,NULL);
181:   MatGetOwnershipRange(fun,&Istart,&Iend);
182:   if (Istart==0) FirstBlock=PETSC_TRUE;
183:   if (Iend==n) LastBlock=PETSC_TRUE;
184:   value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
185:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
186:     col[0]=i-1; col[1]=i; col[2]=i+1;
187:     MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES);
188:   }
189:   if (LastBlock) {
190:     i=n-1; col[0]=n-2; col[1]=n-1;
191:     MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES);
192:   }
193:   if (FirstBlock) {
194:     i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
195:     MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES);
196:   }

198:   /*
199:      Assemble matrix
200:   */
201:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
202:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
203:   if (fun != B) {
204:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
205:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
206:   }
207:   PetscFunctionReturn(0);
208: }

210: /* ------------------------------------------------------------------- */
211: /*
212:    FormJacobian - Computes Jacobian matrix  T'(lambda)
213: */
214: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
215: {
216:   Vec            d;

219:   MatCreateVecs(jac,&d,NULL);
220:   VecSet(d,0.5/PetscSqrtScalar(lambda));
221:   MatDiagonalSet(jac,d,INSERT_VALUES);
222:   VecDestroy(&d);
223:   PetscFunctionReturn(0);
224: }

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

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

239:   h = 11.0/(*maxnp-1);
240:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
241:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
242:   PetscFunctionReturn(0);
243: }

245: /*TEST

247:    testset:
248:       args: -nep_nev 3 -terse
249:       output_file: output/ex27_1.out
250:       requires: !single
251:       filter: sed -e "s/[+-]0\.0*i//g"
252:       test:
253:          suffix: 1
254:          args: -nep_nleigs_interpolation_degree 90
255:       test:
256:          suffix: 3
257:          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
258:       test:
259:          suffix: 5
260:          args: -mat_type aijcusparse
261:          requires: cuda

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

280:    testset:
281:       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
282:       requires: complex !single
283:       output_file: output/ex27_7.out
284:       timeoutfactor: 2
285:       test:
286:          suffix: 7
287:       test:
288:          suffix: 7_par
289:          nsize: 2
290:          args: -nep_ciss_partitions 2

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

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

315: TEST*/