Actual source code: ex20f.F90

slepc-3.22.2 2024-12-02
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  1: !
  2: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3: !  SLEPc - Scalable Library for Eigenvalue Problem Computations
  4: !  Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
  5: !
  6: !  This file is part of SLEPc.
  7: !  SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: !
 10: !  Program usage: mpiexec -n <np> ./ex20f [-n <n>] [SLEPc opts]
 11: !
 12: !  Description: Simple 1-D nonlinear eigenproblem. Fortran90 equivalent of ex20.c
 13: !
 14: !  The command line options are:
 15: !    -n <n>, where <n> = number of grid subdivisions
 16: !
 17: ! ----------------------------------------------------------------------
 18: !  Solve 1-D PDE
 19: !           -u'' = lambda*u
 20: !  on [0,1] subject to
 21: !           u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
 22: ! ----------------------------------------------------------------------
 23: !

 25: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 26: !     User-defined application context
 27: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 28:       module UserModule
 29: #include <slepc/finclude/slepcnep.h>
 30:       use slepcnep
 31:       type User
 32:         PetscScalar kappa
 33:         PetscReal   h
 34:       end type User
 35:       end module

 37:       program main
 38: #include <slepc/finclude/slepcnep.h>
 39:       use UserModule
 40:       implicit none

 42: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43: !     Declarations
 44: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 45: !
 46: !  Variables:
 47: !     nep       nonlinear eigensolver context
 48: !     x         eigenvector
 49: !     lambda    eigenvalue
 50: !     F,J       Function and Jacobian matrices
 51: !     ctx       user-defined context

 53:       NEP            nep
 54:       Vec            x, v(1)
 55:       PetscScalar    lambda
 56:       Mat            F, J
 57:       type(User)     ctx
 58:       NEPType        tname
 59:       PetscInt       n, i, k, nev, its, maxit, nconv, three, one
 60:       PetscReal      tol, norm
 61:       PetscScalar    alpha
 62:       PetscMPIInt    rank
 63:       PetscBool      flg
 64:       PetscErrorCode ierr
 65: !  Note: Any user-defined Fortran routines (such as FormJacobian)
 66: !  MUST be declared as external.
 67:       external       FormFunction, FormJacobian

 69: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 70: !     Beginning of program
 71: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 73:       PetscCallA(SlepcInitialize(PETSC_NULL_CHARACTER,ierr))
 74:       PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
 75:       n = 128
 76:       PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-n',n,flg,ierr))
 77:       if (rank .eq. 0) then
 78:         write(*,'(/A,I4)') 'Nonlinear Eigenproblem, n =',n
 79:       endif

 81:       ctx%h = 1.0/real(n)
 82:       ctx%kappa = 1.0

 84:       three = 3
 85:       one = 1

 87: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 88: !     Create matrix data structure to hold the Function and the Jacobian
 89: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 91:       PetscCallA(MatCreate(PETSC_COMM_WORLD,F,ierr))
 92:       PetscCallA(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n,ierr))
 93:       PetscCallA(MatSetFromOptions(F,ierr))
 94:       PetscCallA(MatSeqAIJSetPreallocation(F,three,PETSC_NULL_INTEGER_ARRAY,ierr))
 95:       PetscCallA(MatMPIAIJSetPreallocation(F,three,PETSC_NULL_INTEGER_ARRAY,one,PETSC_NULL_INTEGER_ARRAY,ierr))

 97:       PetscCallA(MatCreate(PETSC_COMM_WORLD,J,ierr))
 98:       PetscCallA(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n,ierr))
 99:       PetscCallA(MatSetFromOptions(J,ierr))
100:       PetscCallA(MatSeqAIJSetPreallocation(J,three,PETSC_NULL_INTEGER_ARRAY,ierr))
101:       PetscCallA(MatMPIAIJSetPreallocation(J,three,PETSC_NULL_INTEGER_ARRAY,one,PETSC_NULL_INTEGER_ARRAY,ierr))

103: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: !     Create the eigensolver and set various options
105: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

107: !     ** Create eigensolver context
108:       PetscCallA(NEPCreate(PETSC_COMM_WORLD,nep,ierr))

110: !     ** Set routines for evaluation of Function and Jacobian
111:       PetscCallA(NEPSetFunction(nep,F,F,FormFunction,ctx,ierr))
112:       PetscCallA(NEPSetJacobian(nep,J,FormJacobian,ctx,ierr))

114: !     ** Customize nonlinear solver
115:       tol = 1e-9
116:       PetscCallA(NEPSetTolerances(nep,tol,PETSC_CURRENT_INTEGER,ierr))
117:       k = 1
118:       PetscCallA(NEPSetDimensions(nep,k,PETSC_DETERMINE_INTEGER,PETSC_DETERMINE_INTEGER,ierr))

120: !     ** Set solver parameters at runtime
121:       PetscCallA(NEPSetFromOptions(nep,ierr))

123: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124: !     Solve the eigensystem
125: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

127: !     ** Evaluate initial guess
128:       PetscCallA(MatCreateVecs(F,x,PETSC_NULL_VEC,ierr))
129:       PetscCallA(VecDuplicate(x,v(1),ierr))
130:       alpha = 1.0
131:       PetscCallA(VecSet(v(1),alpha,ierr))
132:       k = 1
133:       PetscCallA(NEPSetInitialSpace(nep,k,v,ierr))
134:       PetscCallA(VecDestroy(v(1),ierr))

136: !     ** Call the solver
137:       PetscCallA(NEPSolve(nep,ierr))
138:       PetscCallA(NEPGetIterationNumber(nep,its,ierr))
139:       if (rank .eq. 0) then
140:         write(*,'(A,I3)') ' Number of NEP iterations =',its
141:       endif

143: !     ** Optional: Get some information from the solver and display it
144:       PetscCallA(NEPGetType(nep,tname,ierr))
145:       if (rank .eq. 0) then
146:         write(*,'(A,A10)') ' Solution method: ',tname
147:       endif
148:       PetscCallA(NEPGetDimensions(nep,nev,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr))
149:       if (rank .eq. 0) then
150:         write(*,'(A,I4)') ' Number of requested eigenvalues:',nev
151:       endif
152:       PetscCallA(NEPGetTolerances(nep,tol,maxit,ierr))
153:       if (rank .eq. 0) then
154:         write(*,'(A,F12.9,A,I5)') ' Stopping condition: tol=',tol,', maxit=',maxit
155:       endif

157: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158: !     Display solution and clean up
159: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

161:       PetscCallA(NEPGetConverged(nep,nconv,ierr))
162:       if (rank .eq. 0) then
163:         write(*,'(A,I2/)') ' Number of converged approximate eigenpairs:',nconv
164:       endif

166: !     ** Display eigenvalues and relative errors
167:       if (nconv .gt. 0) then
168:         if (rank .eq. 0) then
169:           write(*,*) '        k              ||T(k)x||'
170:           write(*,*) '----------------- ------------------'
171:         endif
172:         do i=0,nconv-1
173: !         ** Get converged eigenpairs: (in this example they are always real)
174:           PetscCallA(NEPGetEigenpair(nep,i,lambda,PETSC_NULL_SCALAR,x,PETSC_NULL_VEC,ierr))

176: !         ** Compute residual norm and error
177:           PetscCallA(NEPComputeError(nep,i,NEP_ERROR_RELATIVE,norm,ierr))
178:           if (rank .eq. 0) then
179:             write(*,'(1P,E15.4,E18.4)') PetscRealPart(lambda), norm
180:           endif
181:         enddo
182:         if (rank .eq. 0) then
183:           write(*,*)
184:         endif
185:       endif

187:       PetscCallA(NEPDestroy(nep,ierr))
188:       PetscCallA(MatDestroy(F,ierr))
189:       PetscCallA(MatDestroy(J,ierr))
190:       PetscCallA(VecDestroy(x,ierr))
191:       PetscCallA(SlepcFinalize(ierr))
192:       end

194: ! ---------------  Evaluate Function matrix  T(lambda)  ----------------

196:       subroutine FormFunction(nep,lambda,fun,B,ctx,ierr)
197:       use UserModule
198:       implicit none
199:       NEP            nep
200:       PetscScalar    lambda, A(3), c, d
201:       Mat            fun,B
202:       type(User)     ctx
203:       PetscReal      h
204:       PetscInt       i, n, j(3), Istart, Iend, one, two, three
205:       PetscErrorCode ierr

207: !     ** Compute Function entries and insert into matrix
208:       PetscCall(MatGetSize(fun,n,PETSC_NULL_INTEGER,ierr))
209:       PetscCall(MatGetOwnershipRange(fun,Istart,Iend,ierr))
210:       h = ctx%h
211:       c = ctx%kappa/(lambda-ctx%kappa)
212:       d = n
213:       one = 1
214:       two = 2
215:       three = 3

217: !     ** Boundary points
218:       if (Istart .eq. 0) then
219:         i = 0
220:         j(1) = 0
221:         j(2) = 1
222:         A(1) = 2.0*(d-lambda*h/3.0)
223:         A(2) = -d-lambda*h/6.0
224:         PetscCall(MatSetValues(fun,one,[i],two,j,A,INSERT_VALUES,ierr))
225:         Istart = Istart + 1
226:       endif

228:       if (Iend .eq. n) then
229:         i = n-1
230:         j(1) = n-2
231:         j(2) = n-1
232:         A(1) = -d-lambda*h/6.0
233:         A(2) = d-lambda*h/3.0+lambda*c
234:         PetscCall(MatSetValues(fun,one,[i],two,j,A,INSERT_VALUES,ierr))
235:         Iend = Iend - 1
236:       endif

238: !     ** Interior grid points
239:       do i=Istart,Iend-1
240:         j(1) = i-1
241:         j(2) = i
242:         j(3) = i+1
243:         A(1) = -d-lambda*h/6.0
244:         A(2) = 2.0*(d-lambda*h/3.0)
245:         A(3) = -d-lambda*h/6.0
246:         PetscCall(MatSetValues(fun,one,[i],three,j,A,INSERT_VALUES,ierr))
247:       enddo

249: !     ** Assemble matrix
250:       PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY,ierr))
251:       PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY,ierr))

253:       end

255: ! ---------------  Evaluate Jacobian matrix  T'(lambda)  ---------------

257:       subroutine FormJacobian(nep,lambda,jac,ctx,ierr)
258:       use UserModule
259:       implicit none
260:       NEP            nep
261:       PetscScalar    lambda, A(3), c
262:       Mat            jac
263:       type(User)     ctx
264:       PetscReal      h
265:       PetscInt       i, n, j(3), Istart, Iend, one, two, three
266:       PetscErrorCode ierr

268: !     ** Compute Jacobian entries and insert into matrix
269:       PetscCall(MatGetSize(jac,n,PETSC_NULL_INTEGER,ierr))
270:       PetscCall(MatGetOwnershipRange(jac,Istart,Iend,ierr))
271:       h = ctx%h
272:       c = ctx%kappa/(lambda-ctx%kappa)
273:       one = 1
274:       two = 2
275:       three = 3

277: !     ** Boundary points
278:       if (Istart .eq. 0) then
279:         i = 0
280:         j(1) = 0
281:         j(2) = 1
282:         A(1) = -2.0*h/3.0
283:         A(2) = -h/6.0
284:         PetscCall(MatSetValues(jac,one,[i],two,j,A,INSERT_VALUES,ierr))
285:         Istart = Istart + 1
286:       endif

288:       if (Iend .eq. n) then
289:         i = n-1
290:         j(1) = n-2
291:         j(2) = n-1
292:         A(1) = -h/6.0
293:         A(2) = -h/3.0-c*c
294:         PetscCall(MatSetValues(jac,one,[i],two,j,A,INSERT_VALUES,ierr))
295:         Iend = Iend - 1
296:       endif

298: !     ** Interior grid points
299:       do i=Istart,Iend-1
300:         j(1) = i-1
301:         j(2) = i
302:         j(3) = i+1
303:         A(1) = -h/6.0
304:         A(2) = -2.0*h/3.0
305:         A(3) = -h/6.0
306:         PetscCall(MatSetValues(jac,one,[i],three,j,A,INSERT_VALUES,ierr))
307:       enddo

309: !     ** Assemble matrix
310:       PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY,ierr))
311:       PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY,ierr))

313:       end

315: !/*TEST
316: !
317: !   test:
318: !      suffix: 1
319: !      args: -nep_target 4
320: !      filter: sed -e "s/[0-9]\.[0-9]*E-[0-9]*/removed/g" -e "s/ Number of NEP iterations = [ 0-9]*/ Number of NEP iterations = /"
321: !      requires: !single
322: !
323: !TEST*/