Actual source code: test17.c

slepc-3.19.0 2023-03-31
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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[] = "Tests a user-provided preconditioner.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
 14:   "  -tau <tau>, where <tau> is the delay parameter.\n"
 15:   "  -a <a>, where <a> is the coefficient that multiplies u in the equation.\n"
 16:   "  -split <0/1>, to select the split form in the problem definition (enabled by default).\n";

 18: /* Based on ex22.c (delay) */

 20: #include <slepcnep.h>

 22: /*
 23:    User-defined application context
 24: */
 25: typedef struct {
 26:   PetscScalar tau;
 27:   PetscReal   a;
 28: } ApplicationCtx;

 30: /*
 31:    Create problem matrices in split form
 32: */
 33: PetscErrorCode BuildSplitMatrices(PetscInt n,PetscReal a,Mat *Id,Mat *A,Mat *B)
 34: {
 35:   PetscInt       i,Istart,Iend;
 36:   PetscReal      h,xi;
 37:   PetscScalar    b;

 39:   PetscFunctionBeginUser;
 40:   h = PETSC_PI/(PetscReal)(n+1);

 42:   /* Identity matrix */
 43:   PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,Id));
 44:   PetscCall(MatSetOption(*Id,MAT_HERMITIAN,PETSC_TRUE));

 46:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
 47:   PetscCall(MatCreate(PETSC_COMM_WORLD,A));
 48:   PetscCall(MatSetSizes(*A,PETSC_DECIDE,PETSC_DECIDE,n,n));
 49:   PetscCall(MatSetFromOptions(*A));
 50:   PetscCall(MatSetUp(*A));
 51:   PetscCall(MatGetOwnershipRange(*A,&Istart,&Iend));
 52:   for (i=Istart;i<Iend;i++) {
 53:     if (i>0) PetscCall(MatSetValue(*A,i,i-1,1.0/(h*h),INSERT_VALUES));
 54:     if (i<n-1) PetscCall(MatSetValue(*A,i,i+1,1.0/(h*h),INSERT_VALUES));
 55:     PetscCall(MatSetValue(*A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
 56:   }
 57:   PetscCall(MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY));
 58:   PetscCall(MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY));
 59:   PetscCall(MatSetOption(*A,MAT_HERMITIAN,PETSC_TRUE));

 61:   /* B = diag(b(xi)) */
 62:   PetscCall(MatCreate(PETSC_COMM_WORLD,B));
 63:   PetscCall(MatSetSizes(*B,PETSC_DECIDE,PETSC_DECIDE,n,n));
 64:   PetscCall(MatSetFromOptions(*B));
 65:   PetscCall(MatSetUp(*B));
 66:   PetscCall(MatGetOwnershipRange(*B,&Istart,&Iend));
 67:   for (i=Istart;i<Iend;i++) {
 68:     xi = (i+1)*h;
 69:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
 70:     PetscCall(MatSetValue(*B,i,i,b,INSERT_VALUES));
 71:   }
 72:   PetscCall(MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY));
 73:   PetscCall(MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY));
 74:   PetscCall(MatSetOption(*B,MAT_HERMITIAN,PETSC_TRUE));
 75:   PetscFunctionReturn(PETSC_SUCCESS);
 76: }

 78: /*
 79:    Create preconditioner matrices (only Ap=diag(A))
 80: */
 81: PetscErrorCode BuildSplitPreconditioner(PetscInt n,PetscReal a,Mat *Ap)
 82: {
 83:   PetscInt       i,Istart,Iend;
 84:   PetscReal      h;

 86:   PetscFunctionBeginUser;
 87:   h = PETSC_PI/(PetscReal)(n+1);

 89:   /* Ap = diag(A) */
 90:   PetscCall(MatCreate(PETSC_COMM_WORLD,Ap));
 91:   PetscCall(MatSetSizes(*Ap,PETSC_DECIDE,PETSC_DECIDE,n,n));
 92:   PetscCall(MatSetFromOptions(*Ap));
 93:   PetscCall(MatSetUp(*Ap));
 94:   PetscCall(MatGetOwnershipRange(*Ap,&Istart,&Iend));
 95:   for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(*Ap,i,i,-2.0/(h*h)+a,INSERT_VALUES));
 96:   PetscCall(MatAssemblyBegin(*Ap,MAT_FINAL_ASSEMBLY));
 97:   PetscCall(MatAssemblyEnd(*Ap,MAT_FINAL_ASSEMBLY));
 98:   PetscCall(MatSetOption(*Ap,MAT_HERMITIAN,PETSC_TRUE));
 99:   PetscFunctionReturn(PETSC_SUCCESS);
100: }

102: /*
103:    Compute Function matrix  T(lambda)
104: */
105: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
106: {
107:   ApplicationCtx *user = (ApplicationCtx*)ctx;
108:   PetscInt       i,n,Istart,Iend;
109:   PetscReal      h,xi;
110:   PetscScalar    b;

112:   PetscFunctionBeginUser;
113:   PetscCall(MatGetSize(fun,&n,NULL));
114:   h = PETSC_PI/(PetscReal)(n+1);
115:   PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
116:   for (i=Istart;i<Iend;i++) {
117:     if (i>0) PetscCall(MatSetValue(fun,i,i-1,1.0/(h*h),INSERT_VALUES));
118:     if (i<n-1) PetscCall(MatSetValue(fun,i,i+1,1.0/(h*h),INSERT_VALUES));
119:     xi = (i+1)*h;
120:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
121:     PetscCall(MatSetValue(fun,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
122:     if (B!=fun) PetscCall(MatSetValue(B,i,i,-lambda-2.0/(h*h)+user->a+PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
123:   }
124:   PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
125:   PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
126:   if (fun != B) {
127:     PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
128:     PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
129:   }
130:   PetscFunctionReturn(PETSC_SUCCESS);
131: }

133: /*
134:    Compute Jacobian matrix  T'(lambda)
135: */
136: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
137: {
138:   ApplicationCtx *user = (ApplicationCtx*)ctx;
139:   PetscInt       i,n,Istart,Iend;
140:   PetscReal      h,xi;
141:   PetscScalar    b;

143:   PetscFunctionBeginUser;
144:   PetscCall(MatGetSize(jac,&n,NULL));
145:   h = PETSC_PI/(PetscReal)(n+1);
146:   PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
147:   for (i=Istart;i<Iend;i++) {
148:     xi = (i+1)*h;
149:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
150:     PetscCall(MatSetValue(jac,i,i,-1.0-user->tau*PetscExpScalar(-user->tau*lambda)*b,INSERT_VALUES));
151:   }
152:   PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
153:   PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
154:   PetscFunctionReturn(PETSC_SUCCESS);
155: }

157: int main(int argc,char **argv)
158: {
159:   NEP            nep;             /* nonlinear eigensolver context */
160:   Mat            Id,A,B,Ap,J,F,P; /* problem matrices */
161:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
162:   ApplicationCtx ctx;             /* user-defined context */
163:   Mat            mats[3];
164:   FN             funs[3];
165:   PetscScalar    coeffs[2];
166:   PetscInt       n=128;
167:   PetscReal      tau=0.001,a=20;
168:   PetscBool      split=PETSC_TRUE;

170:   PetscFunctionBeginUser;
171:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
172:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
173:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
174:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-a",&a,NULL));
175:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-split",&split,NULL));
176:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g, a=%g\n\n",n,(double)tau,(double)a));

178:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
179:               Create nonlinear eigensolver and solve the problem
180:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

182:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
183:   if (split) {
184:     PetscCall(BuildSplitMatrices(n,a,&Id,&A,&B));
185:     /* f1=-lambda */
186:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
187:     PetscCall(FNSetType(f1,FNRATIONAL));
188:     coeffs[0] = -1.0; coeffs[1] = 0.0;
189:     PetscCall(FNRationalSetNumerator(f1,2,coeffs));
190:     /* f2=1.0 */
191:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
192:     PetscCall(FNSetType(f2,FNRATIONAL));
193:     coeffs[0] = 1.0;
194:     PetscCall(FNRationalSetNumerator(f2,1,coeffs));
195:     /* f3=exp(-tau*lambda) */
196:     PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
197:     PetscCall(FNSetType(f3,FNEXP));
198:     PetscCall(FNSetScale(f3,-tau,1.0));
199:     mats[0] = A;  funs[0] = f2;
200:     mats[1] = Id; funs[1] = f1;
201:     mats[2] = B;  funs[2] = f3;
202:     PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
203:     PetscCall(BuildSplitPreconditioner(n,a,&Ap));
204:     mats[0] = Ap;
205:     mats[1] = Id;
206:     mats[2] = B;
207:     PetscCall(NEPSetSplitPreconditioner(nep,3,mats,SAME_NONZERO_PATTERN));
208:   } else {
209:     /* callback form  */
210:     ctx.tau = tau;
211:     ctx.a   = a;
212:     PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
213:     PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
214:     PetscCall(MatSetFromOptions(F));
215:     PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
216:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
217:     PetscCall(MatSetUp(F));
218:     PetscCall(MatDuplicate(F,MAT_DO_NOT_COPY_VALUES,&P));
219:     PetscCall(NEPSetFunction(nep,F,P,FormFunction,&ctx));
220:     PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
221:     PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
222:     PetscCall(MatSetFromOptions(J));
223:     PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
224:     PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
225:     PetscCall(MatSetUp(J));
226:     PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));
227:   }

229:   /* Set solver parameters at runtime */
230:   PetscCall(NEPSetFromOptions(nep));

232:   /* Solve the eigensystem */
233:   PetscCall(NEPSolve(nep));
234:   PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));

236:   PetscCall(NEPDestroy(&nep));
237:   if (split) {
238:     PetscCall(MatDestroy(&Id));
239:     PetscCall(MatDestroy(&A));
240:     PetscCall(MatDestroy(&B));
241:     PetscCall(MatDestroy(&Ap));
242:     PetscCall(FNDestroy(&f1));
243:     PetscCall(FNDestroy(&f2));
244:     PetscCall(FNDestroy(&f3));
245:   } else {
246:     PetscCall(MatDestroy(&F));
247:     PetscCall(MatDestroy(&P));
248:     PetscCall(MatDestroy(&J));
249:   }
250:   PetscCall(SlepcFinalize());
251:   return 0;
252: }

254: /*TEST

256:    testset:
257:       args: -a 90000 -nep_nev 2
258:       requires: double !defined(PETSCTEST_VALGRIND)
259:       output_file: output/test17_1.out
260:       timeoutfactor: 2
261:       test:
262:          suffix: 1
263:          args: -nep_type slp -nep_two_sided {{0 1}} -split {{0 1}}

265:    testset:
266:       args: -nep_nev 2 -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7
267:       requires: !single
268:       output_file: output/test17_2.out
269:       filter: sed -e "s/[+-]0\.0*i//g"
270:       test:
271:          suffix: 2_interpol
272:          args: -nep_type interpol -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type sor -nep_tol 1e-6 -nep_interpol_st_ksp_rtol 1e-7
273:       test:
274:          suffix: 2_nleigs
275:          args: -nep_type nleigs -split {{0 1}}
276:          requires: complex
277:       test:
278:          suffix: 2_nleigs_real
279:          args: -nep_type nleigs -rg_interval_endpoints .5,15 -split {{0 1}} -nep_nleigs_ksp_type tfqmr
280:          requires: !complex

282:    testset:
283:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -rg_ellipse_vscale 0.1 -nep_ciss_ksp_type bcgs -nep_ciss_pc_type sor
284:       output_file: output/test17_3.out
285:       requires: complex !single !defined(PETSCTEST_VALGRIND)
286:       test:
287:          suffix: 3
288:          args: -split {{0 1}}
289:       test:
290:          suffix: 3_par
291:          nsize: 2
292:          args: -nep_ciss_partitions 2

294: TEST*/