1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
| !****************************************************
! 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
|
