Actual source code: ex27f90.F90

slepc-3.11.2 2019-07-30
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  1: !
  2: !  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3: !  SLEPc - Scalable Library for Eigenvalue Problem Computations
  4: !  Copyright (c) 2002-2019, 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> ./ex27f90 [-help] [-n <n>] [all SLEPc options]
 11: !
 12: !  Description: Simple NLEIGS example. Fortran90 equivalent of ex27.c
 13: !
 14: !  The command line options are:
 15: !    -n <n>, where <n> = matrix dimension
 16: !
 17: ! ----------------------------------------------------------------------
 18: !   Solve T(lambda)x=0 using NLEIGS solver
 19: !      with T(lambda) = -D+sqrt(lambda)*I
 20: !      where D is the Laplacian operator in 1 dimension
 21: !      and with the interpolation interval [.01,16]
 22: ! ----------------------------------------------------------------------
 23: !
 24: PROGRAM main
 25: #include <slepc/finclude/slepcnep.h>
 26:   USE slepcnep
 27:   implicit none

 29: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 30: !     Declarations
 31: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 33:   NEP                :: nep
 34:   Mat                :: A(2),F,J
 35:   NEPType            :: ntype
 36:   PetscInt           :: n=100,nev,Istart,Iend,i,col,one,two,three
 37:   PetscErrorCode     :: ierr
 38:   PetscBool          :: terse,flg,split=PETSC_TRUE
 39:   PetscReal          :: ia,ib,ic,id
 40:   RG                 :: rg
 41:   FN                 :: fn(2)
 42:   PetscScalar        :: coeffs,sigma,done
 43:   CHARACTER(LEN=128) :: string

 45:   ! NOTE: Any user-defined Fortran routines (such as ComputeSingularities)
 46:   !       MUST be declared as external.
 47:   external ComputeSingularities, FormFunction, FormJacobian

 49: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 50: !     Beginning of program
 51: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 53:   call SlepcInitialize(PETSC_NULL_CHARACTER,ierr)
 54:   if (ierr .ne. 0) then
 55:     print*,'SlepcInitialize failed'
 56:     stop
 57:   end if
 58:   call PetscOptionsGetInt(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,"-n",n,flg,ierr);CHKERRA(ierr)
 59:   call PetscOptionsGetBool(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,"-split",split,flg,ierr);CHKERRA(ierr)
 60:   if (split) then
 61:      write(string,*) 'Square root eigenproblem, n=',n,' (split-form)\n'
 62:   else
 63:      write(string,*) 'Square root eigenproblem, n=',n,'\n'
 64:   end if
 65:   call PetscPrintf(PETSC_COMM_WORLD,trim(string),ierr);CHKERRA(ierr)
 66:   done  = 1.0
 67:   one   = 1
 68:   two   = 2
 69:   three = 3
 70:   
 71: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72: !     Create nonlinear eigensolver context and set options
 73: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 75:   call NEPCreate(PETSC_COMM_WORLD,nep,ierr);CHKERRA(ierr)
 76:   call NEPSetType(nep,NEPNLEIGS,ierr);CHKERRA(ierr)
 77:   call NEPNLEIGSSetSingularitiesFunction(nep,ComputeSingularities,0,ierr);CHKERRA(ierr)
 78:   call NEPGetRG(nep,rg,ierr);CHKERRA(ierr)
 79:   call RGSetType(rg,RGINTERVAL,ierr);CHKERRA(ierr)
 80:   ia = 0.01
 81:   ib = 16.0
 82: #if defined(PETSC_USE_COMPLEX)
 83:   ic = -0.001
 84:   id = 0.001
 85: #else
 86:   ic = 0.0
 87:   id = 0.0
 88: #endif
 89:   call RGIntervalSetEndpoints(rg,ia,ib,ic,id,ierr);CHKERRA(ierr)
 90:   sigma = 1.1
 91:   call NEPSetTarget(nep,sigma,ierr);CHKERRA(ierr)

 93: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94: !     Define the nonlinear problem
 95: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 97:   if (split) then
 98:      ! ** Create matrices for the split form
 99:      call MatCreate(PETSC_COMM_WORLD,A(1),ierr);CHKERRA(ierr)
100:      call MatSetSizes(A(1),PETSC_DECIDE,PETSC_DECIDE,n,n,ierr);CHKERRA(ierr)
101:      call MatSetFromOptions(A(1),ierr);CHKERRA(ierr)
102:      call MatSetUp(A(1),ierr);CHKERRA(ierr)
103:      call MatGetOwnershipRange(A(1),Istart,Iend,ierr);CHKERRA(ierr)
104:      coeffs = -2.0
105:      do i=Istart,Iend-1
106:         if (i.gt.0) then
107:            col = i-1
108:            call MatSetValue(A(1),i,col,done,INSERT_VALUES,ierr);CHKERRA(ierr)
109:         end if
110:         if (i.lt.n-1) then
111:            col = i+1
112:            call MatSetValue(A(1),i,col,done,INSERT_VALUES,ierr);CHKERRA(ierr)
113:         end if
114:         call MatSetValue(A(1),i,i,coeffs,INSERT_VALUES,ierr);CHKERRA(ierr)
115:      end do
116:      call MatAssemblyBegin(A(1),MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)
117:      call MatAssemblyEnd(A(1),MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)

119:      call MatCreate(PETSC_COMM_WORLD,A(2),ierr);CHKERRA(ierr)
120:      call MatSetSizes(A(2),PETSC_DECIDE,PETSC_DECIDE,n,n,ierr);CHKERRA(ierr)
121:      call MatSetFromOptions(A(2),ierr);CHKERRA(ierr)
122:      call MatSetUp(A(2),ierr);CHKERRA(ierr)
123:      call MatAssemblyBegin(A(2),MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)
124:      call MatAssemblyEnd(A(2),MAT_FINAL_ASSEMBLY,ierr);CHKERRA(ierr)
125:      call MatShift(A(2),done,ierr);CHKERRA(ierr)

127:      ! ** Define funcions for the split form
128:      call FNCreate(PETSC_COMM_WORLD,fn(1),ierr);CHKERRA(ierr)
129:      call FNSetType(fn(1),FNRATIONAL,ierr);CHKERRA(ierr)
130:      call FNRationalSetNumerator(fn(1),one,done,ierr);CHKERRA(ierr)
131:      call FNCreate(PETSC_COMM_WORLD,fn(2),ierr);CHKERRA(ierr)
132:      call FNSetType(fn(2),FNSQRT,ierr);CHKERRA(ierr)
133:      call NEPSetSplitOperator(nep,two,A,fn,SUBSET_NONZERO_PATTERN,ierr);CHKERRA(ierr)
134:   else
135:     ! ** Callback form: create matrix and set Function evaluation routine
136:     call MatCreate(PETSC_COMM_WORLD,F,ierr);CHKERRA(ierr)
137:     call MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n,ierr);CHKERRA(ierr)
138:     call MatSetFromOptions(F,ierr);CHKERRA(ierr)
139:     call MatSeqAIJSetPreallocation(F,three,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
140:     call MatMPIAIJSetPreallocation(F,three,PETSC_NULL_INTEGER,one,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
141:     Call MatSetUp(F,ierr);CHKERRA(ierr)
142:     call NEPSetFunction(nep,F,F,FormFunction,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)

144:     call MatCreate(PETSC_COMM_WORLD,J,ierr);CHKERRA(ierr)
145:     call MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n,ierr);CHKERRA(ierr)
146:     call MatSetFromOptions(J,ierr);CHKERRA(ierr)
147:     call MatSeqAIJSetPreallocation(J,one,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
148:     call MatMPIAIJSetPreallocation(J,one,PETSC_NULL_INTEGER,one,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
149:     call MatSetUp(J,ierr);CHKERRA(ierr)
150:     call NEPSetJacobian(nep,J,FormJacobian,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
151:   end if

153:   call NEPSetFromOptions(nep,ierr);CHKERRA(ierr)

155: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: !     Solve the eigensystem
157: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

159:   call NEPSolve(nep,ierr);CHKERRA(ierr)
160:   call NEPGetType(nep,ntype,ierr);CHKERRA(ierr)
161:   write(string,*) 'Solution method: ',ntype,'\n'
162:   call PetscPrintf(PETSC_COMM_WORLD,trim(string),ierr);CHKERRA(ierr)
163:   call NEPGetDimensions(nep,nev,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
164:   write(string,*) 'Number of requested eigenvalues:',nev,'\n'
165:   call PetscPrintf(PETSC_COMM_WORLD,trim(string),ierr);CHKERRA(ierr)

167: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
168: !     Display solution and clean up
169: ! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

171:   ! ** show detailed info unless -terse option is given by user
172:   call PetscOptionsHasName(PETSC_NULL_OPTIONS,PETSC_NULL_CHARACTER,'-terse',terse,ierr);CHKERRA(ierr)
173:   if (terse) then
174:     call NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_NULL_VIEWER,ierr);CHKERRA(ierr)
175:   else
176:     call PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL,ierr);CHKERRA(ierr)
177:     call NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD,ierr);CHKERRA(ierr)
178:     call NEPErrorView(nep,NEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD,ierr);CHKERRA(ierr)
179:     call PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD,ierr);CHKERRA(ierr)
180:   end if
181:   
182:   if (split) then
183:     call MatDestroy(A(1),ierr);CHKERRA(ierr)
184:     call MatDestroy(A(2),ierr);CHKERRA(ierr)
185:     call FNDestroy(fn(1),ierr);CHKERRA(ierr)
186:     call FNDestroy(fn(2),ierr);CHKERRA(ierr)
187:   else
188:     call MatDestroy(F,ierr);CHKERRA(ierr)
189:     call MatDestroy(J,ierr);CHKERRA(ierr)
190:   end if
191:   call NEPDestroy(nep,ierr)
192:   call SlepcFinalize(ierr)

194: END PROGRAM main

196: ! --------------------------------------------------------------
197: !
198: !   FormFunction - Computes Function matrix  T(lambda)
199: !
200: SUBROUTINE FormFunction(nep,lambda,fun,B,ctx,ierr)
201: #include <slepc/finclude/slepcnep.h>
202:   use slepcnep
203:   implicit none

205:   NEP            :: nep
206:   PetscScalar    :: lambda,val(0:2),t
207:   Mat            :: fun,B
208:   PetscInt       :: ctx,i,n,col(0:2),Istart,Iend,Istart0,Iend0,one,two,three
209:   PetscErrorCode :: ierr
210:   PetscBool      :: FirstBlock=PETSC_FALSE, LastBlock=PETSC_FALSE

212:   one   = 1
213:   two   = 2
214:   three = 3

216:   ! ** Compute Function entries and insert into matrix
217:   t = sqrt(lambda)
218:   call MatGetSize(fun,n,PETSC_NULL_INTEGER,ierr);CHKERRA(ierr)
219:   call MatGetOwnershipRange(fun,Istart,Iend,ierr);CHKERRA(ierr)
220:   if (Istart.eq.0) FirstBlock=PETSC_TRUE;
221:   if (Iend.eq.n) LastBlock=PETSC_TRUE;
222:   val(0)=1.0; val(1)=t-2.0; val(2)=1.0;

224:   Istart0 = Istart
225:   if (FirstBlock) Istart0 = Istart+1
226:   Iend0 = Iend
227:   if (LastBlock) Iend0 = Iend-1

229:   do i=Istart0,Iend0-1
230:      col(0) = i-1
231:      col(1) = i
232:      col(2) = i+1
233:      call MatSetValues(fun,one,i,three,col,val,INSERT_VALUES,ierr);CHKERRA(ierr)
234:   end do

236:   if (LastBlock) then
237:      i = n-1
238:      col(0) = n-2
239:      col(1) = n-1
240:      val(0) = 1.0
241:      val(1) = t-2.0
242:      call MatSetValues(fun,one,i,two,col,val,INSERT_VALUES,ierr);CHKERRA(ierr)
243:   end if

245:   if (FirstBlock) then
246:      i = 0
247:      col(0) = 0
248:      col(1) = 1
249:      val(0) = t-2.0
250:      val(1) = 1.0
251:      call MatSetValues(fun,one,i,two,col,val,INSERT_VALUES,ierr);CHKERRA(ierr)
252:   end if

254:   ! ** Assemble matrix
255:   call MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
256:   call MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
257:   call MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)
258:   call MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY,ierr);CHKERRQ(ierr)

260: END SUBROUTINE FormFunction

262: ! --------------------------------------------------------------
263: !
264: !   FormJacobian - Computes Jacobian matrix  T'(lambda)
265: !
266: SUBROUTINE FormJacobian(nep,lambda,jac,ctx,ierr)
267: #include <slepc/finclude/slepcnep.h>
268:   USE slepcnep
269:   implicit none

271:   NEP            :: nep
272:   PetscScalar    :: lambda,t
273:   Mat            :: jac
274:   PetscInt       :: ctx
275:   PetscErrorCode :: ierr
276:   Vec            :: d

278:   call MatCreateVecs(jac,d,PETSC_NULL_VEC,ierr);CHKERRA(ierr)
279:   t = 0.5/sqrt(lambda)
280:   call VecSet(d,t,ierr);CHKERRA(ierr)
281:   call MatDiagonalSet(jac,d,INSERT_VALUES,ierr);CHKERRA(ierr)
282:   calL VecDestroy(d,ierr);CHKERRA(ierr)

284: END SUBROUTINE FormJacobian

286: ! --------------------------------------------------------------
287: !
288: !  ComputeSingularities - This is a user-defined routine to compute maxnp
289: !  points (at most) in the complex plane where the function T(.) is not analytic.
290: !
291: !  In this case, we discretize the singularity region (-inf,0)~(-10e+6,-10e-6)
292: !
293: !  Input Parameters:
294: !    nep   - nonlinear eigensolver context
295: !    maxnp - on input number of requested points in the discretization (can be set)
296: !    xi    - computed values of the discretization
297: !    dummy - optional user-defined monitor context (unused here)
298: !
299: SUBROUTINE ComputeSingularities(nep,maxnp,xi,dummy,ierr)
300: #include <slepc/finclude/slepcnep.h>
301:   use slepcnep
302:   implicit none

304:   NEP            :: nep
305:   PetscInt       :: maxnp, dummy
306:   PetscScalar    :: xi(0:maxnp-1)
307:   PetscErrorCode :: ierr
308:   PetscReal      :: h
309:   PetscInt       :: i

311:   h = 11.0/real(maxnp-1)
312:   xi(0) = -1e-5
313:   xi(maxnp-1) = -1e+6
314:   do i=1,maxnp-2
315:      xi(i) = -10**(-5+h*i)
316:   end do

318: END SUBROUTINE ComputeSingularities

320: !/*TEST
321: !
322: !   test:
323: !      suffix: 1
324: !      args: -nep_nev 3 -nep_nleigs_interpolation_degree 90 -terse
325: !      requires: !single
326: !
327: !   test:
328: !      suffix: 2
329: !      args: -split 0 -nep_nev 3 -nep_nleigs_interpolation_degree 90 -terse
330: !      requires: !single
331: !
332: !TEST*/