Example description
!   H05AAF Example Program Text

!   Mark 27.1 Release. NAG Copyright 2020.
    Module h05aafe_mod

!     .. Use Statements ..
      Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Public                           :: calc_subset_score, free_subset_score
!     .. Parameters ..
      Integer, Parameter, Public       :: nin = 5, nout = 6
!     .. Derived Type Definitions ..
      Type, Public                     :: calc_subset_data
        Integer                        :: n, ldq, ldx
        Real (Kind=nag_wp)             :: tol
        Real (Kind=nag_wp), Allocatable :: x(:,:), y(:), b(:), cov(:), h(:),   &
                                          p(:), q(:,:), res(:), se(:), wk(:),  &
        Integer, Allocatable           :: isx(:)
        Character (1)                  :: mean, weight
      End Type calc_subset_data
      Subroutine calc_subset_score(m,drop,lz,z,la,a,bscore,cs)
!       Calculate the score associated with a particular set of feature
!       subsets.

!       M,DROP,LZ,Z,LA,A and BSCORE are all as described in the documentation
!       of H05AAF.

!       CS - Variable of type CALC_SUBSET_DATA that holds any additional data
!            required by this routine

!       This particular example finds the set, of a given size, of explanatory
!       variables that best fit a response variable when a linear regression
!       model is used. Therefore the feature set is the set of all the
!       explanatory variables and the best set of features is defined as set
!       of explanatory variables that gives the smallest residual sums of
!       squares.
!       See the documentation for G02DAF for details on linear regression
!       models.

!       .. Use Statements ..
        Use nag_library, Only: g02daf
!       .. Scalar Arguments ..
        Type (calc_subset_data), Intent (Inout) :: cs
        Integer, Intent (In)           :: drop, la, lz, m
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: bscore(:)
        Integer, Intent (In)           :: a(:), z(:)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: rss
        Integer                        :: i, idf, ifail, inv_drop, ip, irank
        Logical                        :: svd
        Character (200)                :: line
!       .. Intrinsic Procedures ..
        Intrinsic                      :: abs, allocated, count, max
!       .. Executable Statements ..

!       Allocate various arrays and read in the data if this is the first time
!       this routine has been called
        If (.Not. allocated(cs%x)) Then
!         Read in the number of observations for the data used in the linear
!         regression skipping any headings or blank lines
            Read (nin,*,Iostat=ifail) line
            If (ifail/=0) Then
            End If
            Read (line,*,Iostat=ifail) cs%n
            If (ifail==0) Then
            End If
          End Do

!         Read in the control parameters for the linear regression
          Read (nin,*) cs%tol

!         Read in the data
          cs%ldx = cs%n
          Allocate (cs%x(cs%ldx,m),cs%y(cs%n))
          Read (nin,*)(cs%x(i,1:m),cs%y(i),i=1,cs%n)

!         No intercept term and no weights
          cs%mean = 'Z'
          cs%weight = 'U'

!         Allocate memory required by the regression routine
          cs%ldq = cs%n
          Allocate (cs%b(m),cs%cov((m*m+m)/2),cs%h(cs%n),cs%p(m*(m+            &
            2)),cs%q(cs%ldq,m+1),cs%res(cs%n),cs%se(m),cs%wk(m*m+5*(m-         &
        End If

!       Set up the initial feature set.
!       If DROP = 0, this is the Null set (i.e. no features).
!       If DROP = 1 then this is the full set (i.e. all features)
        cs%isx(1:m) = drop

!       Add (if DROP = 0) or remove (if DROP = 1) the all the features
!       specified in Z
        inv_drop = abs(drop-1)
        Do i = 1, lz
          cs%isx(z(i)) = inv_drop
        End Do

        Do i = 1, max(la,1)
          If (la>0) Then
            If (i>1) Then
!             Reset the feature altered at the last iteration
              cs%isx(a(i-1)) = drop
            End If

!           Add or drop the I'th feature in A
            cs%isx(a(i)) = inv_drop
          End If

          ip = count(cs%isx(1:m)==1)

!         Fit the regression model
          ifail = 0
          Call g02daf(cs%mean,cs%weight,cs%n,cs%x,cs%ldx,m,cs%isx,ip,cs%y,     &
            cs%wt,rss,idf,cs%b,cs%se,cs%cov,cs%res,cs%h,cs%q,cs%ldq,svd,irank, &

!         Return the score (the residual sums of squares)
          bscore(i) = rss
        End Do
      End Subroutine calc_subset_score
      Subroutine free_subset_score(cs)

!       .. Scalar Arguments ..
        Type (calc_subset_data), Intent (Inout) :: cs
!       .. Intrinsic Procedures ..
        Intrinsic                      :: allocated
!       .. Executable Statements ..
        If (allocated(cs%x)) Then
          Deallocate (cs%x)
        End If
        If (allocated(cs%y)) Then
          Deallocate (cs%y)
        End If
        If (allocated(cs%b)) Then
          Deallocate (cs%b)
        End If
        If (allocated(cs%cov)) Then
          Deallocate (cs%cov)
        End If
        If (allocated(cs%h)) Then
          Deallocate (cs%h)
        End If
        If (allocated(cs%p)) Then
          Deallocate (cs%p)
        End If
        If (allocated(cs%q)) Then
          Deallocate (cs%q)
        End If
        If (allocated(cs%res)) Then
          Deallocate (cs%res)
        End If
        If (allocated(cs%se)) Then
          Deallocate (cs%se)
        End If
        If (allocated(cs%wk)) Then
          Deallocate (cs%wk)
        End If
        If (allocated(cs%wt)) Then
          Deallocate (cs%wt)
        End If
        If (allocated(cs%isx)) Then
          Deallocate (cs%isx)
        End If
      End Subroutine free_subset_score
    End Module h05aafe_mod

    Program h05aafe

!     .. Use Statements ..
      Use h05aafe_mod, Only: calc_subset_data, calc_subset_score,              &
                             free_subset_score, nin, nout
      Use nag_library, Only: h05aaf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Type (calc_subset_data)          :: cs
      Real (Kind=nag_wp)               :: gamma
      Integer                          :: cnt, drop, i, ifail, ip, irevcm, j,  &
                                          la, licomm, lrcomm, lz, m, mincnt,   &
                                          mincr, mip, nbest
!     .. Local Arrays ..
      Real (Kind=nag_wp)               :: acc(2)
      Real (Kind=nag_wp), Allocatable  :: bscore(:), rcomm(:)
      Integer, Allocatable             :: a(:), bz(:,:), ibz(:), icomm(:),     &
      Logical, Allocatable             :: mask(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, pack
!     .. Executable Statements ..
      Write (nout,*) 'H05AAF Example Program Results'
      Write (nout,*)

!     Skip headings in data file
      Read (nin,*)
      Read (nin,*)

!     Read in the problem size
      Read (nin,*) m, ip, nbest

!     Read in the control parameters for the subset selection
      Read (nin,*) mincr, mincnt, gamma, acc(1:2)

!     Allocate memory required by the subset selection routine
      mip = m - ip
      Allocate (z(mip),a(max(nbest,m)),bz(mip,nbest),bscore(max(nbest,m)))

!     Allocate dummy communication arrays, as we will query the required size
      licomm = 2
      lrcomm = 0
      Allocate (icomm(licomm),rcomm(lrcomm))

!     Query the required length for the communication arrays
      irevcm = 0
      ifail = 1
      Call h05aaf(irevcm,mincr,m,ip,nbest,drop,lz,z,la,a,bscore,bz,mincnt,     &

!     Extract the required sizes from the communication array
      licomm = icomm(1)
      lrcomm = icomm(2)

!     Reallocate communication arrays to the correct size
      Deallocate (icomm,rcomm)
      Allocate (icomm(licomm),rcomm(lrcomm))

!     Initialize reverse communication control flag
      irevcm = 0

!     Call the reverse communication best subset routine in a loop.
!     The loop should terminate when IRECVM = 0 on exit
      cnt = 0
rev_lp: Do
        ifail = -1
        Call h05aaf(irevcm,mincr,m,ip,nbest,drop,lz,z,la,a,bscore,bz,mincnt,   &
        If (irevcm==0) Then
          If (ifail==0 .Or. ifail==53) Then
!           No error, or a warning was issued
            Exit rev_lp
!           An error occurred
            Go To 100
          End If
        End If

!       Calculate and return the score for the required models and keep track
!       of the number of subsets evaluated
        cnt = cnt + max(1,la)
        Call calc_subset_score(m,drop,lz,z,la,a,bscore,cs)

      End Do rev_lp

      Call free_subset_score(cs)

!     Titles
      Write (nout,99999) '    Score        Feature Subset'
      Write (nout,99999) '    -----        --------------'

!     Display the best subsets and corresponding scores. H05AAF returns a list
!     of features excluded from the best subsets, so this is inverted to give
!     the set of features included in each subset
      Allocate (ibz(m),mask(m))
      ibz(1:m) = (/(i,i=1,m)/)
      Do i = 1, la
        mask(1:m) = .True.
        Do j = 1, mip
          mask(bz(j,i)) = .False.
        End Do
        Write (nout,99998) bscore(i), pack(ibz,mask)
      End Do

      Write (nout,*)
      If (ifail==53) Then
        Write (nout,99997) nbest,                                              &
          ' subsets of the requested size do not exist, only ', la,            &
          ' are displayed.'
      End If
      Write (nout,99996) cnt, ' subsets evaluated in total'

100   Continue

99999 Format (1X,A)
99998 Format (1X,E12.5,100(1X,I5))
99997 Format (1X,I0,A,I0,A)
99996 Format (1X,I0,A)

    End Program h05aafe