Fortran 95 source code to compute multiple regression equations.(2d)

regression_multi_2d.f95

!****************************************************
! 重回帰式計算（説明（独立）変数2個、2次多項式モデル）
! * y = b0 + b1x1 + b2x2 + b3x1x2 + b4x1^2 + b5x2^2
! * y = b0 + b1x1 + b2x2 + b3x3 + b4x4 + b5x5
!   (x3 = x1x2, x4 = x1^2, x5 = x2^2)
!   ということ。

!   date          name            version
!   2019.06.27    mk-mode.com     1.00 新規作成
!
! Copyright(C) 2019 mk-mode.com All Rights Reserved.
!****************************************************
!
module const
  ! SP: 単精度(4), DP: 倍精度(8)
  integer,     parameter :: SP = kind(1.0)
  integer(SP), parameter :: DP = selected_real_kind(2 * precision(1.0_SP))
end module const

module comp
  use const
  implicit none
  private
  public :: calc_reg_multi_2d

contains
  ! 重回帰式計算
  ! * 説明変数2個、2次多項式モデル
  ! * y = b0 + b1x1 + b2x2 + b3x1x2 + b4x1^2 + b5x2^2
  ! * y = b0 + b1x1 + b2x2 + b3x3 + b4x4 + b5x5
  !   (x3 = x1x2, x4 = x1^2, x5 = x2^2)
  !
  ! :param(in)  real(8) x(:, 2): 説明変数配列
  ! :param(in)  real(8)    y(:): 目的変数配列
  ! :param(out) real(8)       c: 定数
  ! :param(out) real(8)    v(5): 係数
  subroutine calc_reg_multi_2d(x, y, c, v)
    implicit none
    real(DP), intent(in)  :: x(:, :), y(:)
    real(DP), intent(out) :: c, v(5)
    integer(SP) :: s_x1, s_x2, s_y
    real(DP)    :: mtx(6, 7)
    real(DP), allocatable :: x1(:), x2(:), x3(:), x4(:), x5(:)

    s_x1 = size(x(:, 1))
    s_x2 = size(x(:, 2))
    s_y  = size(y)
    if (s_x1 == 0 .or. s_x2 == 0 .or. s_y == 0) then
      print *, "[ERROR] array size == 0"
      stop
    end if
    if (s_x1 /= s_y .or. s_x2 /= s_y) then
      print *, "[ERROR] size(X) != size(Y)"
      stop
    end if
    allocate(x1(s_x1))
    allocate(x2(s_x1))
    allocate(x3(s_x1))
    allocate(x4(s_x1))
    allocate(x5(s_x1))

    x1 = x(:, 1)
    x2 = x(:, 2)
    x3 = x1 * x2
    x4 = x1 * x1
    x5 = x2 * x2
    ! 左辺・対角成分
    mtx(1, 1) = s_x1
    mtx(2, 2) = sum(x1 * x1)
    mtx(3, 3) = sum(x2 * x2)
    mtx(4, 4) = sum(x3 * x3)
    mtx(5, 5) = sum(x4 * x4)
    mtx(6, 6) = sum(x5 * x5)
    ! 左辺・右上成分
    mtx(1, 2) = sum(x1)
    mtx(1, 3) = sum(x2)
    mtx(1, 4) = sum(x3)
    mtx(1, 5) = sum(x4)
    mtx(1, 6) = sum(x5)
    mtx(2, 3) = sum(x1 * x2)
    mtx(2, 4) = sum(x1 * x3)
    mtx(2, 5) = sum(x1 * x4)
    mtx(2, 6) = sum(x1 * x5)
    mtx(3, 4) = sum(x2 * x3)
    mtx(3, 5) = sum(x2 * x4)
    mtx(3, 6) = sum(x2 * x5)
    mtx(4, 5) = sum(x3 * x4)
    mtx(4, 6) = sum(x3 * x5)
    mtx(5, 6) = sum(x4 * x5)
    ! 左辺・左下成分
    mtx(2, 1) = mtx(1, 2)
    mtx(3, 1) = mtx(1, 3)
    mtx(3, 2) = mtx(2, 3)
    mtx(4, 1) = mtx(1, 4)
    mtx(4, 2) = mtx(2, 4)
    mtx(4, 3) = mtx(3, 4)
    mtx(5, 1) = mtx(1, 5)
    mtx(5, 2) = mtx(2, 5)
    mtx(5, 3) = mtx(3, 5)
    mtx(5, 4) = mtx(4, 5)
    mtx(6, 1) = mtx(1, 6)
    mtx(6, 2) = mtx(2, 6)
    mtx(6, 3) = mtx(3, 6)
    mtx(6, 4) = mtx(4, 6)
    mtx(6, 5) = mtx(5, 6)
    ! 右辺
    mtx(1, 7) = sum(     y)
    mtx(2, 7) = sum(x1 * y)
    mtx(3, 7) = sum(x2 * y)
    mtx(4, 7) = sum(x3 * y)
    mtx(5, 7) = sum(x4 * y)
    mtx(6, 7) = sum(x5 * y)
    deallocate(x1)
    deallocate(x2)
    deallocate(x3)
    deallocate(x4)
    deallocate(x5)
    call gauss_e(6, mtx)
    c = mtx(1, 7)
    v = mtx(2:6, 7)
  end subroutine calc_reg_multi_2d

  ! Gaussian elimination
  !
  ! :param(in)    integer(4)     n: 元数
  ! :param(inout) real(8) a(n,n+1): 係数配列
  subroutine gauss_e(n, a)
    implicit none
    integer(SP), intent(in)    :: n
    real(DP),    intent(inout) :: a(n, n + 1)
    integer(SP) :: i, j
    real(DP)    :: d

    ! 前進消去
    do j = 1, n - 1
      do i = j + 1, n
        d = a(i, j) / a(j, j)
        a(i, j+1:n+1) = a(i, j+1:n+1) - a(j, j+1:n+1) * d
      end do
    end do

    ! 後退代入
    do i = n, 1, -1
      d = a(i, n + 1)
      do j = i + 1, n
        d = d - a(i, j) * a(j, n + 1)
      end do
      a(i, n + 1) = d / a(i, i)
    end do
  end subroutine gauss_e
end module comp

program regression_multi_2d
  use const
  use comp
  implicit none
  character(9), parameter :: F_INP = "input.txt"
  integer(SP),  parameter :: UID   = 10
  real(DP)    :: c, v(5)
  integer(SP) :: n, i
  character(20) :: f
  real(DP), allocatable :: x(:, :), y(:)

  ! IN ファイル OPEN
  open (UID, file = F_INP, status = "old")

  ! データ数読み込み
  read (UID, *) n

  ! 配列用メモリ確保
  allocate(x(n, 2))
  allocate(y(n))

  ! データ読み込み
  do i = 1, n
    read (UID, *) x(i, :), y(i)
  end do
  write (f, '("(A, ", I0, "F8.2, A)")') n
  print f, "説明変数 X(1) = (", x(:, 1), ")"
  print f, "説明変数 X(2) = (", x(:, 2), ")"
  print f, "目的変数    Y = (", y, ")"
  print '(A)', "---"

  ! IN ファイル CLOSE
  close (UID)

  call calc_reg_multi_2d(x, y, c, v)
  print '(A, F14.8)', "定数項 = ", c
  print '(A, F14.8)', "係数-1 = ", v(1)
  print '(A, F14.8)', "係数-2 = ", v(2)
  print '(A, F14.8)', "係数-3 = ", v(3)
  print '(A, F14.8)', "係数-4 = ", v(4)
  print '(A, F14.8)', "係数-5 = ", v(5)

  ! 配列用メモリ解放
  deallocate(x)
  deallocate(y)
end program regression_multi_2d