Actual source code: ex27.c

slepc-3.20.1 2023-11-27
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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:   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(MatSetUp(A[0]));
 82:     PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));
 83:     for (i=Istart;i<Iend;i++) {
 84:       if (i>0) PetscCall(MatSetValue(A[0],i,i-1,1.0,INSERT_VALUES));
 85:       if (i<n-1) PetscCall(MatSetValue(A[0],i,i+1,1.0,INSERT_VALUES));
 86:       PetscCall(MatSetValue(A[0],i,i,-2.0,INSERT_VALUES));
 87:     }
 88:     PetscCall(MatAssemblyBegin(A[0],MAT_FINAL_ASSEMBLY));
 89:     PetscCall(MatAssemblyEnd(A[0],MAT_FINAL_ASSEMBLY));

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

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

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

116:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
117:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
118:     PetscCall(MatSetFromOptions(J));
119:     PetscCall(MatSeqAIJSetPreallocation(J,1,NULL));
120:     PetscCall(MatMPIAIJSetPreallocation(J,1,NULL,1,NULL));
121:     PetscCall(MatSetUp(J));
122:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,NULL));
123:   }

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

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

139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140:                     Display solution and clean up
141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

143:   /* show detailed info unless -terse option is given by user */
144:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
145:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,NULL));
146:   else {
147:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
148:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
149:     PetscCall(NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
150:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
151:   }
152:   PetscCall(NEPDestroy(&nep));
153:   if (split) {
154:     PetscCall(MatDestroy(&A[0]));
155:     PetscCall(MatDestroy(&A[1]));
156:     PetscCall(FNDestroy(&f[0]));
157:     PetscCall(FNDestroy(&f[1]));
158:   } else {
159:     PetscCall(MatDestroy(&F));
160:     PetscCall(MatDestroy(&J));
161:   }
162:   PetscCall(SlepcFinalize());
163:   return 0;
164: }

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

176:   PetscFunctionBeginUser;
177:   /*
178:      Compute Function entries and insert into matrix
179:   */
180:   t = PetscSqrtScalar(lambda);
181:   PetscCall(MatGetSize(fun,&n,NULL));
182:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
183:   if (Istart==0) FirstBlock=PETSC_TRUE;
184:   if (Iend==n) LastBlock=PETSC_TRUE;
185:   value[0]=1.0; value[1]=t-2.0; value[2]=1.0;
186:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
187:     col[0]=i-1; col[1]=i; col[2]=i+1;
188:     PetscCall(MatSetValues(fun,1,&i,3,col,value,INSERT_VALUES));
189:   }
190:   if (LastBlock) {
191:     i=n-1; col[0]=n-2; col[1]=n-1;
192:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
193:   }
194:   if (FirstBlock) {
195:     i=0; col[0]=0; col[1]=1; value[0]=t-2.0; value[1]=1.0;
196:     PetscCall(MatSetValues(fun,1,&i,2,col,value,INSERT_VALUES));
197:   }

199:   /*
200:      Assemble matrix
201:   */
202:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
203:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
204:   if (fun != B) {
205:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
206:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
207:   }
208:   PetscFunctionReturn(PETSC_SUCCESS);
209: }

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

219:   PetscFunctionBeginUser;
220:   PetscCall(MatCreateVecs(jac,&d,NULL));
221:   PetscCall(VecSet(d,0.5/PetscSqrtScalar(lambda)));
222:   PetscCall(MatDiagonalSet(jac,d,INSERT_VALUES));
223:   PetscCall(VecDestroy(&d));
224:   PetscFunctionReturn(PETSC_SUCCESS);
225: }

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

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

239:   PetscFunctionBeginUser;
240:   h = 11.0/(*maxnp-1);
241:   xi[0] = -1e-5; xi[*maxnp-1] = -1e+6;
242:   for (i=1;i<*maxnp-1;i++) xi[i] = -PetscPowReal(10,-5+h*i);
243:   PetscFunctionReturn(PETSC_SUCCESS);
244: }

246: /*TEST

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

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

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

293:    testset:
294:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 8 -rg_ellipse_radius .7 -rg_ellipse_vscale 0.1 -terse
295:       requires: complex
296:       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/"
297:       output_file: output/ex27_7.out
298:       timeoutfactor: 2
299:       test:
300:          suffix: 8
301:       test:
302:          suffix: 8_parallel
303:          nsize: 4
304:          args: -nep_ciss_partitions 4 -ds_parallel distributed
305:       test:
306:          suffix: 8_hpddm
307:          args: -nep_ciss_ksp_type hpddm
308:          requires: hpddm

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

316: TEST*/