796 lines
49 KiB
Fortran
796 lines
49 KiB
Fortran
! ==============================================================================
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! 通过 gfortran ./test.f90 -o ./run && ./run 运行
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! 程序名：
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! 第9章习题，及书上例题
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! 目的:
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!
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! 修订记录:
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! 日期 编程者 改动描述
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! =================== ============= =====================================
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! 2021-05-06 18:56:24 Sola 例9-1 模仿正常的上三角解法
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! 2021-05-07 00:20:30 Sola 例9-1 高斯-亚当消元法(书上解法确实好)
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! 2021-05-07 17:48:03 Sola 习题9-4 判断程序正误
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! 2021-05-07 18:00:54 Sola 习题9-5 判断输出结果，跳过
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! 2021-05-07 19:17:23 Sola 习题9-6 矩阵乘法子程序, 显式结构
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! 2021-05-07 19:17:53 Sola 习题9-7 矩阵乘法子程序, 显式接口不定结构
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! 2021-05-07 19:20:11 Sola 习题9-8 用不定结构形参数组修改例9-1
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! 2021-05-07 20:22:22 Sola 习题9-9 测试图9-6的子程序
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! 2021-05-07 21:42:49 Sola 习题9-11 测试程序运行
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! 2021-05-07 21:59:54 Sola 习题9-12 修改测试程序
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! 2021-05-07 22:16:18 Sola 习题9-13 模拟掷色子
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! 2021-05-08 13:02:55 Sola 习题9-14 创建逐元过程运算
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! 2021-05-08 14:59:48 Sola 习题9-15 将9-14换成pure纯函数
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! 2021-05-09 00:52:48 Sola 习题9-16 高阶最小二乘回归
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! 2021-05-09 13:49:16 Sola 习题9-17 噪声值对拟合结果的影响
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! 2021-05-09 14:36:52 Sola 习题9-18 任意高阶最小二乘回归（9-16直接写了，跳过）
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! 2021-05-09 14:38:55 Sola 习题9-19 4阶最小二乘回归噪声影响
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! 2021-05-09 15:12:56 Sola 习题9-20 利用高阶最小二乘回归进行插值处理
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! 2021-05-09 15:24:01 Sola 习题9-21 推理，推理范围外的值
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! 程序结构:
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!
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! ==============================================================================
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! 模块：
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module Chapter9
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implicit none
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! 数据字典
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! 声明常数
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REAL, PARAMETER :: PI=3.14159265 ! PI值
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REAL, PARAMETER :: e=2.718281828459 ! 自然对数
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INTEGER, PARAMETER :: arrayLength=20 ! 数组基准长度
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! Example 9-1
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! real, dimension(:), allocatable :: arrayX
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! read, dimension(:, :), allocatable :: N
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integer :: m, n
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! 声明变量
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! 创建显式接口
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contains
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! subroutine SubName(varName1,varName2)
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! implicit none
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! ! 数据字典
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! end subroutine SubName
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! 上三角消元法
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! subroutine UpperTriangleElimination(matrixInput, arrayX, m, n)
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! implicit none
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! integer, intent(in) :: m, n ! 矩阵大小与X解向量长度
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! real, dimension(m, m+1), intent(inout) :: matrixInput ! 输入矩阵(输入)
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! real, dimension(n), intent(inout) :: arrayX ! 解向量(输入输出)
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! real, dimension(m+1) :: matrixTemp ! 临时向量, 用于矩阵行交换
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! integer :: i ! 局部变量: 循环参数
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! if ( m /= 1 ) then ! 如果矩阵行数不为1
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! if ( abs(matrixInput(1, 1)) < 1.0E-30 ) then ! 如果矩阵首位为0
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! do i = 2, m ! 从其余行选择不为0的交换
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! if ( abs(matrixInput(i, 1)) >= 1.0E-30 ) then
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! matrixTemp = matrixInput(i, :)
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! matrixInput(i, :) = matrixInput(1, :)
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! matrixInput(1, :) = matrixTemp
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! exit
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! end if
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! end do
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! end if
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! matrixInput(1, :) = matrixInput(1, :)/matrixInput(1, 1) ! 单位化矩阵第一行
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! do i = 2, m ! 消去其他行所有第一列的系数
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! matrixInput(i, :) = matrixInput(i, :) - matrixInput(1, :)*matrixInput(i, 1)
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! end do
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! if ( all(matrixInput(2:m, 2) == 0) ) then ! 检查第二列第二行到最后一行不为0
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! stop "输入矩阵不满秩，无法求解" ! 如果为0, 则输入矩阵不满秩, 无解
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! else
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! call GaussAdamElimination(matrixInput(2:m, 2:m+1), arrayX, m-1, n) ! 递归调用自身
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! end if
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! arrayX(n-m+1) = matrixInput(1, m+1) - matrixInput(1, 2:m)*arrayX(n-m+2:n) ! 计算当前位X值
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! else
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! arrayX(n) = matrixInput(1, m+1)/matrixInput(1, 1) ! 如果矩阵行数为1, 直接计算当前位X值
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! end if
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! end subroutine UpperTriangleElimination
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! 高斯亚当消元法 会破坏输入数组
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subroutine GaussAdamElimination(matrixInput, m, arrayX, maxLimit, error)
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implicit none
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integer, intent(in) :: m ! 输入的方程组数量
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integer, intent(in) :: maxLimit ! 矩阵大小与X解向量长度
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real, dimension(maxLimit, maxLimit), intent(inout) :: matrixInput ! 输入矩阵(输入)
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real, dimension(maxLimit), intent(inout) :: arrayX ! 输入常数向量, 输出X解向量
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integer, intent(out) :: error ! 错误值
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real :: temp ! 临时值, 用于数值交换
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integer :: maxLocate ! 最大值所在行
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integer :: i, n ! 局部变量: 循环参数
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do n = 1, m
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maxLocate = n ! 初始化绝对值最大的位置
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do i = n+1, m ! 执行最大支点技术，减少舍入误差
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if ( abs(matrixInput(i, n)) > abs(matrixInput(maxLocate, n)) ) then
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maxLocate = i
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end if
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end do
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if ( abs(matrixInput(maxLocate, n)) < 1.0E-30 ) then
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error = 1 ! 如果绝对值最大为0, 则矩阵不满秩, 无解
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return ! 退出运算
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end if
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if ( maxLocate /= n ) then ! 如果绝对值最大值位置发生了变化, 则交换
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do i = 1, m
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temp = matrixInput(maxLocate, i)
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matrixInput(maxLocate, i) = matrixInput(n, i)
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matrixInput(n, i) = temp
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end do
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temp = arrayX(maxLocate)
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arrayX(maxLocate) = arrayX(n)
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arrayX(n) = temp
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end if
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do i = 1, m ! 消去其他行所有第n列的系数
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if ( i /= n ) then
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temp = -matrixInput(i, n)/matrixInput(n, n) ! 这里务必要设置一个临时值保存数值, 不然会被修改
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matrixInput(i, :) = matrixInput(i, :) + matrixInput(n, :)*temp
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arrayX(i) = arrayX(i) + arrayX(n)*temp
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end if
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end do
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end do
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do i = 1, m ! 产生X的解向量
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arrayX(i) = arrayX(i)/matrixInput(i, i)
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matrixInput(i, i) = 1.
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end do
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error = 0
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end subroutine GaussAdamElimination
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end module Chapter9
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! ==============================================================================
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! 主程序：
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program ProName
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! use ModName
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implicit none
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! 数据字典
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! 声明常量
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! 声明变量
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! 变量初始化
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! 数据输入
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! 运算过程
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! 结果输出
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! call Exercises9_4
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! call Exercises9_6
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! call Exercises9_8
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! call Exercises9_9
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! call Exercises9_11
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! call Exercises9_12
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! call Exercises9_13
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! call Exercises9_14
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! call Exercises9_15
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! call Exercises9_16
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end program ProName
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! ==============================================================================
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! 子程序
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! subroutine SubName(varName1,varName2)
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! use MouName
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! implicit none
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! Type, intent(inout) :: varName
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! end subroutine SubName
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! ==============================================================================
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! 函数
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! function FunName(varName1,varName2)
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! use MouName
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! implicit none
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! end function FunName
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! ==============================================================================
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! 习题9-4 判断程序正误
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subroutine Exercises9_4
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implicit none
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real :: a=3., b=4., output
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integer :: i=0
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call sub1(a, I, output)
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write(*,*) 'The output is', output
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contains
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subroutine sub1(x, j, junk)
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real, intent(in) :: x
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integer, intent(in) :: j
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real, intent(out) :: junk
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junk = (x-j)/b
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end subroutine sub1
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end subroutine Exercises9_4
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subroutine Exercises9_6
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implicit none
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real, dimension(:, :), allocatable :: arrayInput1, arrayInput2, arrayResult ! 输入输出矩阵
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integer :: errorLevel ! 错误码
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integer :: i ! 循环参数
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! 9-6 a
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allocate(arrayInput1(3, 3), stat=errorLevel) ! 分配数组
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if (errorLevel /= 0) print *, "arrayInput1: Allocation request denied"
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allocate(arrayInput2(3, 3), stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayInput2: Allocation request denied"
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allocate(arrayResult(3, 3), stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayResult: Allocation request denied"
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arrayInput1(1, :) = (/ 2., -1., 2./) ! 定义数组
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arrayInput1(2, :) = (/-1., -3., 4./)
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arrayInput1(3, :) = (/ 2., 4., 2./)
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arrayInput2(1, :) = (/ 1., 2., 3./)
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arrayInput2(2, :) = (/ 2., 1., 2./)
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arrayInput2(3, :) = (/ 3., 2., 1./)
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call MatrixMultplication(arrayInput1, 3, 3, arrayInput2, 3, 3, arrayResult, errorLevel) ! 调用子程序计算矩阵乘积
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if (errorLevel /= 0) print *, "无法进行矩阵乘法"
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write(*,'(3F8.2)') (arrayResult(i, :), i = 1, 3) ! 输出计算结果
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arrayResult(:,:) = matmul(arrayInput1, arrayInput2) ! 调用内部函数计算矩阵乘积
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write(*,'(3F8.2)') (arrayResult(i, :), i = 1, 3) ! 输出计算结果
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call MatrixMul(arrayInput1, arrayInput2, arrayResult, errorLevel) ! 调用子程序计算矩阵乘积
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if (errorLevel /= 0) print *, "无法进行矩阵乘法"
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write(*,'(3F8.2)') (arrayResult(i, :), i = 1, 3) ! 输出计算结果
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if (allocated(arrayResult)) deallocate(arrayResult, stat=errorLevel) ! 释放数组
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if (errorLevel /= 0) print *, "arrayResult: Deallocation request denied"
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if (allocated(arrayInput2)) deallocate(arrayInput2, stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayInput2: Deallocation request denied"
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if (allocated(arrayInput1)) deallocate(arrayInput1, stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayInput1: Deallocation request denied"
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! 9-6 b
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allocate(arrayInput1(4, 3), stat=errorLevel) ! 分配数组
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if (errorLevel /= 0) print *, "arrayInput1: Allocation request denied"
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allocate(arrayInput2(3, 1), stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayInput2: Allocation request denied"
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allocate(arrayResult(4, 1), stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayResult: Allocation request denied"
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arrayInput1(1, :) = (/ 1., -1., -2./) ! 定义数组
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arrayInput1(2, :) = (/ 2., 2., 0./)
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arrayInput1(3, :) = (/ 3., 3., 3./)
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arrayInput1(4, :) = (/ 5., 4., 4./)
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arrayInput2(:, 1) = (/-2., 5., 2./)
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call MatrixMultplication(arrayInput1, 4, 3, arrayInput2, 3, 1, arrayResult, errorLevel) ! 调用子程序计算矩阵乘积
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if (errorLevel /= 0) print *, "无法进行矩阵乘法"
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write(*,'(F8.2)') (arrayResult(i, :), i = 1, 4) ! 输出计算结果
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arrayResult(:,:) = matmul(arrayInput1, arrayInput2) ! 调用内部函数计算矩阵乘积
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write(*,'(F8.2)') (arrayResult(i, :), i = 1, 4) ! 输出计算结果
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call MatrixMul(arrayInput1, arrayInput2, arrayResult, errorLevel) ! 调用子程序计算矩阵乘积
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if (errorLevel /= 0) print *, "无法进行矩阵乘法"
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write(*,'(F8.2)') (arrayResult(i, :), i = 1, 4) ! 输出计算结果
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if (allocated(arrayResult)) deallocate(arrayResult, stat=errorLevel) ! 释放数组
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if (errorLevel /= 0) print *, "arrayResult: Deallocation request denied"
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if (allocated(arrayInput2)) deallocate(arrayInput2, stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayInput2: Deallocation request denied"
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if (allocated(arrayInput1)) deallocate(arrayInput1, stat=errorLevel)
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if (errorLevel /= 0) print *, "arrayInput1: Deallocation request denied"
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contains
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! 矩阵乘法子程序, 显式结构
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subroutine MatrixMultplication(array1, x1, y1, array2, x2, y2, array3, errorLevel)
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integer, intent(in) :: x1, y1, x2, y2 ! 矩阵大小
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real, dimension(x1, y1), intent(in) :: array1 ! 矩阵1
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real, dimension(x2, y2), intent(in) :: array2 ! 矩阵2
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real, dimension(x1, y2), intent(out) :: array3 ! 输出矩阵
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integer, intent(out) :: errorLevel ! 错误代码
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integer :: i, j, k ! 循环参数
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if ( y1 /= x2 ) then ! 判断乘法是否可行
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errorLevel = 1 ! 不可行, 错误码=1
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return ! 退出
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end if
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array3 = 0. ! 初始化输出矩阵
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! forall(i = 1:x1, j = 1:y1, k = 1:y2) ! forall结构计算
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! array3(i, k) = array1(i, j)*array2(j, k) + array3(i, k)
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! end forall
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do i = 1, x1 ! do嵌套计算
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do j = 1, y1
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do k = 1, y2
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array3(i, k) = array1(i, j)*array2(j, k) + array3(i, k)
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end do
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end do
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end do
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errorLevel = 0 ! 运算完成, 错误码=0
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end subroutine MatrixMultplication
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! 矩阵乘法子程序, 显式接口不定结构
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subroutine MatrixMul(array1, array2, array3, errorLevel)
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real, dimension(:, :), intent(in) :: array1 ! 矩阵1
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real, dimension(:, :), intent(in) :: array2 ! 矩阵2
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real, dimension(:, :), intent(out) :: array3 ! 输出矩阵
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integer, intent(out) :: errorLevel ! 错误代码
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integer :: i, j, k ! 循环参数
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if ( size(array1, 2) /= size(array2, 1) ) then ! 判断乘法是否可行
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errorLevel = 1 ! 不可行, 错误码=1
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return ! 退出
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end if
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array3 = 0. ! 初始化输出矩阵
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! forall(i = 1:x1, j = 1:y1, k = 1:y2) ! forall结构计算
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! array3(i, k) = array1(i, j)*array2(j, k) + array3(i, k)
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! end forall
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do i = 1, size(array1, 1) ! do嵌套计算
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do j = 1, size(array1, 2)
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do k = 1, size(array2, 2)
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array3(i, k) = array1(i, j)*array2(j, k) + array3(i, k)
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end do
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end do
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end do
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errorLevel = 0 ! 运算完成, 错误码=0
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end subroutine MatrixMul
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end subroutine Exercises9_6
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! 习题9-8
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subroutine Exercises9_8
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implicit none
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real, dimension(3, 3) :: arrayInput1, arrayInput2 ! 输入矩阵
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real, dimension(3) :: arrayX1, arrayX2 ! 常数向量
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integer :: errorLevel ! 错误码
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integer :: i ! 循环参数
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arrayInput1(1, :) = (/ 1.0, 1.0, 1.0/) ! 输入数据1
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arrayInput1(2, :) = (/ 2.0, 1.0, 1.0/)
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arrayInput1(3, :) = (/ 1.0, 3.0, 2.0/)
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arrayX1(:) = (/ 1.0, 2.0, 4.0/)
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arrayInput2(1, :) = (/ 1.0, 1.0, 1.0/) ! 输入数据2
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arrayInput2(2, :) = (/ 2.0, 6.0, 4.0/)
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arrayInput2(3, :) = (/ 1.0, 3.0, 2.0/)
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arrayX2(:) = (/ 1.0, 8.0, 4.0/)
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call GAEli(arrayInput1, arrayX1, errorLevel) ! 调用子程序解方程组
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if (errorLevel /= 0) then
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write(*,*) 'Error!' ! 如果无解, 输出错误
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else
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write(*,'(4F8.2)') (arrayInput1(i, :), arrayX1(i), i = 1, 3) ! 如果有解, 输出计算后的矩阵
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end if
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call GAEli(arrayInput2, arrayX2, errorLevel) ! 调用子程序解方程组
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if (errorLevel /= 0) then
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write(*,*) 'Error!' ! 如果无解, 输出错误
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else
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write(*,'(4F8.2)') (arrayInput2(i, :), arrayX2(i), i = 1, 3) ! 如果有解, 输出计算后的矩阵
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end if
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contains
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! 高斯亚当消元法, 不定结构, 破坏输入矩阵
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subroutine GAEli(matrixInput, arrayX, errorLevel)
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implicit none
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real, dimension(:, :), intent(inout) :: matrixInput ! 输入矩阵(输入)
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real, dimension(:), intent(inout) :: arrayX ! 输入常数向量, 输出X解向量
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integer, intent(out) :: errorLevel ! 错误值
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real :: temp ! 临时值, 用于数值交换
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integer :: maxLocate ! 最大值所在行
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integer :: i, n, m ! 局部变量: 循环参数
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m = size(matrixInput, 1)
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do n = 1, m
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maxLocate = n ! 初始化绝对值最大的位置
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do i = n+1, m ! 执行最大支点技术，减少舍入误差
|
||
if ( abs(matrixInput(i, n)) > abs(matrixInput(maxLocate, n)) ) then
|
||
maxLocate = i
|
||
end if
|
||
end do
|
||
if ( abs(matrixInput(maxLocate, n)) < 1.0E-30 ) then
|
||
errorLevel = 1 ! 如果绝对值最大为0, 则矩阵不满秩, 无解
|
||
return ! 退出运算
|
||
end if
|
||
if ( maxLocate /= n ) then ! 如果绝对值最大值位置发生了变化, 则交换
|
||
do i = 1, m
|
||
temp = matrixInput(maxLocate, i)
|
||
matrixInput(maxLocate, i) = matrixInput(n, i)
|
||
matrixInput(n, i) = temp
|
||
end do
|
||
temp = arrayX(maxLocate)
|
||
arrayX(maxLocate) = arrayX(n)
|
||
arrayX(n) = temp
|
||
end if
|
||
do i = 1, m ! 消去其他行所有第n列的系数
|
||
if ( i /= n ) then
|
||
temp = -matrixInput(i, n)/matrixInput(n, n) ! 这里务必要设置一个临时值保存数值, 不然会被修改
|
||
matrixInput(i, :) = matrixInput(i, :) + matrixInput(n, :)*temp
|
||
arrayX(i) = arrayX(i) + arrayX(n)*temp
|
||
end if
|
||
end do
|
||
end do
|
||
do i = 1, m ! 产生X的解向量
|
||
arrayX(i) = arrayX(i)/matrixInput(i, i)
|
||
matrixInput(i, i) = 1.
|
||
end do
|
||
errorLevel = 0
|
||
end subroutine GAEli
|
||
end subroutine Exercises9_8
|
||
! 习题9-8
|
||
subroutine Exercises9_9
|
||
implicit none
|
||
real, dimension(3, 3) :: arrayInput1, arrayInput2 ! 输入矩阵
|
||
real, dimension(3) :: arrayX1, arrayX2 ! 常数向量
|
||
integer :: errorLevel ! 错误码
|
||
integer :: i ! 循环参数
|
||
arrayInput1(1, :) = (/ 1.0, 1.0, 1.0/) ! 输入数据1
|
||
arrayInput1(2, :) = (/ 2.0, 1.0, 1.0/)
|
||
arrayInput1(3, :) = (/ 1.0, 3.0, 2.0/)
|
||
arrayX1(:) = (/ 1.0, 2.0, 4.0/)
|
||
arrayInput2(1, :) = (/ 1.0, 1.0, 1.0/) ! 输入数据2
|
||
arrayInput2(2, :) = (/ 2.0, 6.0, 4.0/)
|
||
arrayInput2(3, :) = (/ 1.0, 3.0, 2.0/)
|
||
arrayX2(:) = (/ 1.0, 8.0, 4.0/)
|
||
call GAEli1(arrayInput1, arrayX1, errorLevel) ! 调用子程序解方程组
|
||
if (errorLevel /= 0) then
|
||
write(*,*) 'Error!' ! 如果无解, 输出错误
|
||
else
|
||
write(*,'(A, I1, A, F6.2)') ('x', i, ' = ', arrayX1(i), i = 1, 3) ! 如果有解, 输出各解
|
||
end if
|
||
call GAEli1(arrayInput2, arrayX2, errorLevel) ! 调用子程序解方程组
|
||
if (errorLevel /= 0) then
|
||
write(*,*) 'Error!' ! 如果无解, 输出错误
|
||
else
|
||
write(*,'(A, I1, F6.2)') ('x', i, ' = ', arrayX2(i), i = 1, 3) ! 如果有解, 输出各解
|
||
end if
|
||
contains
|
||
! 高斯-亚当消元法，不破坏输入矩阵
|
||
subroutine GAEli1(matrixInput1, arrayX, errorLevel)
|
||
implicit none
|
||
real, dimension(:, :), intent(inout) :: matrixInput1 ! 输入矩阵(输入)
|
||
real, dimension(size(matrixInput1, 1), size(matrixInput1, 2)) :: matrixInput
|
||
! 运算矩阵
|
||
real, dimension(:), intent(inout) :: arrayX ! 输入常数向量, 输出X解向量
|
||
integer, intent(out) :: errorLevel ! 错误值
|
||
real :: temp ! 临时值, 用于数值交换
|
||
integer :: maxLocate ! 最大值所在行
|
||
integer :: i, n, m ! 局部变量: 循环参数
|
||
matrixInput = matrixInput1
|
||
m = size(matrixInput, 1)
|
||
do n = 1, m
|
||
maxLocate = n ! 初始化绝对值最大的位置
|
||
do i = n+1, m ! 执行最大支点技术，减少舍入误差
|
||
if ( abs(matrixInput(i, n)) > abs(matrixInput(maxLocate, n)) ) then
|
||
maxLocate = i
|
||
end if
|
||
end do
|
||
if ( abs(matrixInput(maxLocate, n)) < 1.0E-30 ) then
|
||
errorLevel = 1 ! 如果绝对值最大为0, 则矩阵不满秩, 无解
|
||
return ! 退出运算
|
||
end if
|
||
if ( maxLocate /= n ) then ! 如果绝对值最大值位置发生了变化, 则交换
|
||
do i = 1, m
|
||
temp = matrixInput(maxLocate, i)
|
||
matrixInput(maxLocate, i) = matrixInput(n, i)
|
||
matrixInput(n, i) = temp
|
||
end do
|
||
temp = arrayX(maxLocate)
|
||
arrayX(maxLocate) = arrayX(n)
|
||
arrayX(n) = temp
|
||
end if
|
||
do i = 1, m ! 消去其他行所有第n列的系数
|
||
if ( i /= n ) then
|
||
temp = -matrixInput(i, n)/matrixInput(n, n) ! 这里务必要设置一个临时值保存数值, 不然会被修改
|
||
matrixInput(i, :) = matrixInput(i, :) + matrixInput(n, :)*temp
|
||
arrayX(i) = arrayX(i) + arrayX(n)*temp
|
||
end if
|
||
end do
|
||
end do
|
||
do i = 1, m ! 产生X的解向量
|
||
arrayX(i) = arrayX(i)/matrixInput(i, i)
|
||
matrixInput(i, i) = 1.
|
||
end do
|
||
errorLevel = 0
|
||
end subroutine GAEli1
|
||
end subroutine Exercises9_9
|
||
! 习题9-11 9-12
|
||
subroutine Exercises9_11
|
||
implicit none
|
||
real, allocatable, dimension(:) :: a
|
||
integer :: istat
|
||
allocate(a(6), stat=istat)
|
||
a = (/ 1., 2., 3., 4., 5., 6./)
|
||
write(*,'(A, 6F4.1)') 'Main: Array a before call = ', a
|
||
call test_alloc(a)
|
||
write(*,'(A, 6F4.1)') 'Main: Array a after call = ', a
|
||
contains
|
||
subroutine test_alloc(array)
|
||
real, dimension(:), allocatable, intent(inout) :: array
|
||
integer :: i
|
||
integer :: istat
|
||
if (allocated(array)) then
|
||
write(*,'(A)') 'Sub: the array is allocated'
|
||
write(*,'(A, 6F4.1)') 'Sub: Array on entry = ', array
|
||
else
|
||
write(*,*) 'In sub: the array is not allocated'
|
||
end if
|
||
if (allocated(array)) then
|
||
deallocate(array, stat=istat)
|
||
end if
|
||
allocate(array(5), stat=istat)
|
||
do i = 1, 5
|
||
array(i) = 6 - i
|
||
end do
|
||
write(*,'(A, 6F4.1)') 'Sub: Array on exit = ', array
|
||
end subroutine test_alloc
|
||
end subroutine Exercises9_11
|
||
! 习题9-13 掷色子
|
||
subroutine Exercises9_13
|
||
implicit none
|
||
integer :: x, y ! 定义俩变量
|
||
call throw(x, y) ! 获取俩随机值
|
||
write(*,*) x, y ! 打印
|
||
contains
|
||
subroutine throw(random1, random2) ! out属性形参可以作为参数传递给过程
|
||
integer, intent(out) :: random1, random2 ! 定义俩变量储存随机数
|
||
call die(random1) ! 获取第一个随机数
|
||
call die(random2) ! 获取第二个随机数
|
||
end subroutine throw
|
||
subroutine die(random)
|
||
integer, intent(out) :: random ! 定义随机整数
|
||
real :: temp ! 随机数临时值
|
||
call random_seed() ! 根据时间日期获取随机数种子
|
||
call random_number(temp) ! 获取一个[0,1)的随机数给临时值
|
||
random = int(temp*6) + 1 ! 变化其区间为[1,7), 并向下取整
|
||
end subroutine die
|
||
end subroutine Exercises9_13
|
||
! 创建逐元过程运算, 这种过程内函数, 直接在函数体写定义, 调用部分可以不考虑
|
||
subroutine Exercises9_14
|
||
implicit none
|
||
real, parameter :: PI=3.14159265 ! PI值
|
||
real, dimension(2, 3) :: array1, array2, array3 ! 计算用数组
|
||
integer :: i ! 循环参数
|
||
array1(1, :) = (/ 10.0, 20.0, 30.0/) ! 定义输入数组
|
||
array1(2, :) = (/ 40.0, 50.0, 60.0/)
|
||
array2 = FunSin(array1) ! 计算值
|
||
write(*,1) '计算得到正弦值为:', (array2(i, :), i = 1, 2) ! 输出计算值, 以下相同
|
||
array3 = FunAsin(array2)
|
||
write(*,1) '计算得到反正弦值为:', (array3(i, :), i = 1, 2)
|
||
array2 = FunCos(array1)
|
||
write(*,1) '计算得到余弦值为:', (array2(i, :), i = 1, 2)
|
||
array3 = FunAcos(array2)
|
||
write(*,1) '计算得到反余弦值为:', (array3(i, :), i = 1, 2)
|
||
array2 = FunTan(array1)
|
||
write(*,1) '计算得到正切为:', (array2(i, :), i = 1, 2)
|
||
array3 = FunAtan(array2)
|
||
write(*,1) '计算得到反正切为:', (array3(i, :), i = 1, 2)
|
||
1 format(1X, A,/& ! 输出格式
|
||
&1X, 3F8.2,/&
|
||
&1X, 3F8.2)
|
||
contains
|
||
elemental function FunSin(degree) ! 定义函数
|
||
real, intent(in) :: degree ! 定义输入变量
|
||
real :: FunSin ! 定义函数输出类型
|
||
FunSin = sin(degree/360.*2*PI) ! 计算输出值, 以下相同
|
||
end function FunSin
|
||
elemental function FunCos(degree)
|
||
real, intent(in) :: degree
|
||
real :: FunCos
|
||
FunCos = cos(degree/360.*2*PI)
|
||
end function FunCos
|
||
elemental function FunTan(degree)
|
||
real, intent(in) :: degree
|
||
real :: FunTan
|
||
FunTan = tan(degree/360.*2*PI)
|
||
end function FunTan
|
||
elemental function FunAsin(value)
|
||
real, intent(in) :: value
|
||
real :: FunAsin
|
||
FunAsin = asin(value)*360./(2.*PI)
|
||
end function FunAsin
|
||
elemental function FunAcos(value)
|
||
real, intent(in) :: value
|
||
real :: FunAcos
|
||
FunAcos = acos(value)*360./(2.*PI)
|
||
end function FunAcos
|
||
elemental function FunAtan(value)
|
||
real, intent(in) :: value
|
||
real :: FunAtan
|
||
FunAtan = atan(value)*360./(2.*PI)
|
||
end function FunAtan
|
||
end subroutine Exercises9_14
|
||
! 习题9-15 将9-14的内容修改为纯函数
|
||
subroutine Exercises9_15
|
||
implicit none
|
||
real, parameter :: PI=3.14159265 ! PI值
|
||
real, dimension(2, 3) :: array1, array2, array3 ! 计算用数组
|
||
integer :: i ! 循环参数
|
||
array1(1, :) = (/ 10.0, 20.0, 30.0/) ! 定义输入数组
|
||
array1(2, :) = (/ 40.0, 50.0, 60.0/)
|
||
array2 = FunSin(array1) ! 计算值
|
||
write(*,1) '计算得到正弦值为:', (array2(i, :), i = 1, 2) ! 输出计算值, 以下相同
|
||
array3 = FunAsin(array2)
|
||
write(*,1) '计算得到反正弦值为:', (array3(i, :), i = 1, 2)
|
||
array2 = FunCos(array1)
|
||
write(*,1) '计算得到余弦值为:', (array2(i, :), i = 1, 2)
|
||
array3 = FunAcos(array2)
|
||
write(*,1) '计算得到反余弦值为:', (array3(i, :), i = 1, 2)
|
||
array2 = FunTan(array1)
|
||
write(*,1) '计算得到正切为:', (array2(i, :), i = 1, 2)
|
||
array3 = FunAtan(array2)
|
||
write(*,1) '计算得到反正切为:', (array3(i, :), i = 1, 2)
|
||
1 format(1X, A,/& ! 输出格式
|
||
&1X, 3F8.2,/&
|
||
&1X, 3F8.2)
|
||
contains
|
||
pure function FunSin(degree)
|
||
real, intent(in), dimension(:, :) :: degree
|
||
real, dimension(size(degree, 1), size(degree, 2)) :: FunSin
|
||
FunSin = sin(degree/360.*2*PI)
|
||
end function FunSin
|
||
pure function FunCos(degree)
|
||
real, intent(in), dimension(:, :) :: degree
|
||
real, dimension(size(degree, 1), size(degree, 2)) :: FunCos
|
||
FunCos = cos(degree/360.*2*PI)
|
||
end function FunCos
|
||
pure function FunTan(degree)
|
||
real, intent(in), dimension(:, :) :: degree
|
||
real, dimension(size(degree, 1), size(degree, 2)) :: FunTan
|
||
FunTan = tan(degree/360.*2*PI)
|
||
end function FunTan
|
||
pure function FunAsin(value)
|
||
real, intent(in), dimension(:, :) :: value
|
||
real, dimension(size(value, 1), size(value, 2)) :: FunAsin
|
||
FunAsin = asin(value)*360./(2.*PI)
|
||
end function FunAsin
|
||
pure function FunAcos(value)
|
||
real, intent(in), dimension(:, :) :: value
|
||
real, dimension(size(value, 1), size(value, 2)) :: FunAcos
|
||
FunAcos = acos(value)*360./(2.*PI)
|
||
end function FunAcos
|
||
pure function FunAtan(value)
|
||
real, intent(in), dimension(:, :) :: value
|
||
real, dimension(size(value, 1), size(value, 2)) :: FunAtan
|
||
FunAtan = atan(value)*360./(2.*PI)
|
||
end function FunAtan
|
||
end subroutine Exercises9_15
|
||
! 习题9-16 高阶最小二乘回归 首先第一个，发现了解多元一次方程组程序的错误，第二，发现了总之，很多很多错误，很有意义的一道题
|
||
subroutine Exercises9_16
|
||
implicit none
|
||
real, dimension(:), allocatable :: pointX, pointY ! 坐标(x, y)
|
||
real, dimension(:), allocatable :: arrayCoefficient ! 系数向量
|
||
integer :: errorLevel ! 错误码
|
||
integer :: i ! 循环参数
|
||
real :: temp
|
||
open(unit=1, status='scratch', iostat=errorLevel) ! 打开临时文件
|
||
if ( errorLevel /= 0 ) stop "打开临时文件失败" ! 判断打开状态
|
||
write(1, '(A)') & ! 输入数据
|
||
&' 0.167, 0.333, 0.500, 0.667, 0.833, 1.000, 1.167, 1.333, 1.500&
|
||
&, 1.667, 1.833, 2.000, 2.167, 2.333, 2.500, 2.667, 2.833, 3.000',&
|
||
&' 49.9, 52.2, 50.6, 47.0, 47.7, 42.3, 37.9, 38.2, 38.0, 33.8, 26.7, 24.8, 22.0, 16.5, 14.0, 5.6, 2.9, 0.8',&
|
||
&' -5.1,-12.9,-15.1, -6.8,-12.3,-18.0, -5.7, -6.3,-12.7,-13.7,-26.7,-31.3,-22.9,-25.6,-25.7,-25.2,-35.0,-27.9'
|
||
rewind(unit=1, iostat=errorLevel) ! 回到初始行
|
||
if ( errorLevel /= 0 ) stop "读取临时文件失败" ! 判断执行状态
|
||
allocate(pointX(18), stat=errorLevel) ! 分配数组
|
||
if (errorLevel /= 0) print *, "pointX: Allocation request denied" ! 判断分配结果, 下同
|
||
allocate(pointY(18), stat=errorLevel)
|
||
if (errorLevel /= 0) print *, "pointY: Allocation request denied"
|
||
allocate(arrayCoefficient(3), stat=errorLevel)
|
||
if (errorLevel /= 0) print *, "arrayCoefficient: Allocation request denied"
|
||
read(1, *) pointX, pointY ! 读取数据
|
||
close(unit=1, iostat=errorLevel) ! 关闭临时文件
|
||
if ( errorLevel /= 0 ) stop "关闭临时文件失败" ! 判断关闭状态
|
||
! write(*,'(18(F8.2, 1X))') pointX, pointY ! 输出读入值(供检验, 可注释)
|
||
call MultipleRegression(pointX, pointY, arrayCoefficient, 2, errorLevel) ! 计算参数值
|
||
write(*,*) '习题9-16'
|
||
write(*,1) arrayCoefficient ! 输出结果
|
||
1 format(1X, '(?) 计算得到的方程为：h = ', F8.2, ' + ', F8.2, ' t + ', F8.2, ' t^2')
|
||
! 习题9-17
|
||
write(*,*) '习题9-17'
|
||
call ShowNoise2( 0.0, 0.0, '(a)')
|
||
call ShowNoise2(-0.1, 0.1, '(b)')
|
||
call ShowNoise2(-0.5, 0.5, '(c)')
|
||
call ShowNoise2(-1.0, 1.0, '(d)')
|
||
! 习题9-19
|
||
write(*,*) '习题9-19'
|
||
arrayCoefficient = (/0.0, 0.0, 0.0, 0.0, 0.0/) ! 重定义系数向量长度
|
||
call ShowNoise4( 0.0, 0.0, '(a)')
|
||
call ShowNoise4(-0.1, 0.1, '(b)')
|
||
call ShowNoise4(-0.5, 0.5, '(c)')
|
||
call ShowNoise4(-1.0, 1.0, '(d)')
|
||
! 习题9-20
|
||
write(*,*) '习题9-20'
|
||
open(unit=1, status='scratch', iostat=errorLevel) ! 打开临时文件
|
||
if ( errorLevel /= 0 ) stop "打开临时文件失败" ! 判断打开状态
|
||
write(1, '(A)') & ! 输入数据
|
||
&' 0.00, 1.00, 2.00, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00',&
|
||
&'-23.22,-13.54, -4.14, -0.04, 3.92, 4.97, 3.96, -0.07, -5.67,-12.28,-20.25'
|
||
rewind(unit=1, iostat=errorLevel) ! 回到初始行
|
||
if ( errorLevel /= 0 ) stop "关闭临时文件失败" ! 判断关闭状态
|
||
pointX = (/(i, i = 1, 10)/) ! 重定义坐标x向量长度
|
||
pointY = pointX ! 重定义坐标y向量长度
|
||
read(1,*) pointX, pointY ! 赋值坐标(x, y)
|
||
close(unit=1, iostat=errorLevel) ! 关闭临时文件
|
||
arrayCoefficient = (/0.0, 0.0, 0.0/) ! 重定义系数向量长度
|
||
call MultipleRegression(pointX, pointY, arrayCoefficient, 2, errorLevel) ! 计算参数值
|
||
write(*,4) arrayCoefficient ! 输出结果
|
||
4 format(1X, '(?) 计算得到的方程为：y = ', F8.2, ' + ', F8.2, ' x + ', F8.2, ' x^2')
|
||
write(*,*) ' 当x0取3.5时，得到y0 = ', arrayCoefficient(1) + arrayCoefficient(2)*3.5 + arrayCoefficient(3)*3.5**2
|
||
! 习题9-21
|
||
write(*,*) '习题9-21'
|
||
open(unit=1, status='scratch', iostat=errorLevel) ! 打开临时文件
|
||
if ( errorLevel /= 0 ) stop "打开临时文件失败" ! 判断打开状态
|
||
write(1, '(A)') & ! 输入数据
|
||
&' 0.00, 1.00, 2.00, 3.00, 4.00, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00',&
|
||
&'-14.22,-10.54, -5.09, -3.12, 0.92, 3.79, 6.99, 8.95, 11.33, 14.71, 18.75'
|
||
rewind(unit=1, iostat=errorLevel) ! 回到初始行
|
||
if ( errorLevel /= 0 ) stop "关闭临时文件失败" ! 判断关闭状态
|
||
pointX = (/(i, i = 1, 10)/) ! 重定义坐标x向量长度
|
||
pointY = pointX ! 重定义坐标y向量长度
|
||
read(1,*) pointX, pointY ! 赋值坐标(x, y)
|
||
close(unit=1, iostat=errorLevel) ! 关闭临时文件
|
||
arrayCoefficient = (/0.0, 0.0, 0.0/) ! 重定义系数向量长度
|
||
call MultipleRegression(pointX, pointY, arrayCoefficient, 2, errorLevel) ! 计算参数值
|
||
write(*,4) arrayCoefficient ! 输出结果
|
||
write(*,*) ' 当x0取14.0时，得到y0 = ', arrayCoefficient(1) + arrayCoefficient(2)*14.0 + arrayCoefficient(3)*14.0**2
|
||
if ( errorLevel /= 0 ) stop "读取临时文件失败" ! 判断执行状态
|
||
if (allocated(arrayCoefficient)) deallocate(arrayCoefficient, stat=errorLevel) ! 释放数组
|
||
if (errorLevel /= 0) print *, "arrayCoefficient: Deallocation request denied" ! 判断释放结果, 下同
|
||
if (allocated(pointY)) deallocate(pointY, stat=errorLevel)
|
||
if (errorLevel /= 0) print *, "pointY: Deallocation request denied"
|
||
if (allocated(pointX)) deallocate(pointX, stat=errorLevel)
|
||
if (errorLevel /= 0) print *, "pointX: Deallocation request denied"
|
||
contains
|
||
! 构建输入方程和解向量
|
||
subroutine MultipleRegression(arrayX, arrayY, arrayResult, order, errorLevel)
|
||
real, dimension(:), intent(in) :: arrayX, arrayY ! 输入坐标(x, y)
|
||
integer, intent(in) :: order ! 拟合阶数
|
||
real, dimension(order+1), intent(out) :: arrayResult ! 系数向量(同时也充当了常数向量)
|
||
real, dimension(order+1, order+1) :: matrixCoefficient ! 系数矩阵
|
||
integer, intent(out) :: errorLevel ! 错误码(虽然主程序中没有做错误校验就是)
|
||
integer :: i, j ! 循环参数
|
||
if ( order < 1 ) then ! 判断阶数是否符合要求
|
||
errorLevel = 1
|
||
return
|
||
else
|
||
do i = 1, order+1 ! 各参数的偏导方程
|
||
do j = 1, order+1 ! 某一参数偏导数取0时, 各系数
|
||
matrixCoefficient(i, j) = sum(arrayX**(i+j-2)) ! 给各系数赋值
|
||
end do
|
||
arrayResult(i) = sum(arrayX**(i-1)*arrayY) ! 给常数向量赋值
|
||
end do
|
||
! write(*,'(3(F8.2, 1X))') matrixCoefficient, arrayResult ! 打印系数矩阵和常数向量(共检验, 可注释)
|
||
call GAEli1(matrixCoefficient, arrayResult, errorLevel) ! 计算系数值
|
||
end if
|
||
end subroutine MultipleRegression
|
||
! 调用方程组求解子程序，高斯-亚当消元法（不破坏输入数组）
|
||
subroutine GAEli1(matrixInput1, arrayX, errorLevel)
|
||
implicit none
|
||
real, dimension(:, :), intent(inout) :: matrixInput1 ! 输入矩阵(输入)
|
||
real, dimension(size(matrixInput1, 1), size(matrixInput1, 2)) :: matrixInput
|
||
! 运算矩阵
|
||
real, dimension(:), intent(inout) :: arrayX ! 输入常数向量, 输出X解向量
|
||
integer, intent(out) :: errorLevel ! 错误值
|
||
real :: temp ! 临时值, 用于数值交换
|
||
integer :: maxLocate ! 最大值所在行
|
||
integer :: i, n, m ! 局部变量: 循环参数
|
||
matrixInput = matrixInput1
|
||
m = size(matrixInput, 1)
|
||
do n = 1, m
|
||
maxLocate = n ! 初始化绝对值最大的位置
|
||
do i = n+1, m ! 执行最大支点技术，减少舍入误差
|
||
if ( abs(matrixInput(i, n)) > abs(matrixInput(maxLocate, n)) ) then
|
||
maxLocate = i
|
||
end if
|
||
end do
|
||
if ( abs(matrixInput(maxLocate, n)) < 1.0E-30 ) then
|
||
errorLevel = 1 ! 如果绝对值最大为0, 则矩阵不满秩, 无解
|
||
return ! 退出运算
|
||
end if
|
||
if ( maxLocate /= n ) then ! 如果绝对值最大值位置发生了变化, 则交换
|
||
do i = 1, m
|
||
temp = matrixInput(maxLocate, i)
|
||
matrixInput(maxLocate, i) = matrixInput(n, i)
|
||
matrixInput(n, i) = temp
|
||
end do
|
||
temp = arrayX(maxLocate)
|
||
arrayX(maxLocate) = arrayX(n)
|
||
arrayX(n) = temp
|
||
end if
|
||
do i = 1, m ! 消去其他行所有第n列的系数
|
||
if ( i /= n ) then
|
||
temp = -matrixInput(i, n)/matrixInput(n, n) ! 这里务必要设置一个临时值保存数值, 不然会被修改
|
||
matrixInput(i, :) = matrixInput(i, :) + matrixInput(n, :)*temp
|
||
arrayX(i) = arrayX(i) + arrayX(n)*temp
|
||
end if
|
||
end do
|
||
end do
|
||
do i = 1, m ! 产生X的解向量
|
||
arrayX(i) = arrayX(i)/matrixInput(i, i)
|
||
matrixInput(i, i) = 1.
|
||
end do
|
||
errorLevel = 0
|
||
end subroutine GAEli1
|
||
! 用于产生噪声值
|
||
subroutine Noise(value, lowerBound, upperBound)
|
||
real, intent(out) :: value ! 输出的随机数值
|
||
real, intent(in) :: lowerBound, upperBound ! 输出随机数值的上下界, 范围是[lowerBound, upperBound)
|
||
call random_seed() ! 根据当前时间日期计算随机数种子
|
||
call random_number(value) ! 计算随机数
|
||
value = lowerBound + value*( upperBound - lowerBound ) ! 重分布以适应范围
|
||
end subroutine Noise
|
||
! 用于计算习题9-17, 这里采用的是二阶回归
|
||
subroutine ShowNoise2(lowerBound, upperBound, tag)
|
||
real, intent(in) :: lowerBound, upperBound ! 噪声值上下界
|
||
character(len=3), intent(in) :: tag ! 当前题目标识符
|
||
pointX = (/0.0, 1.0, 2.0, 3.0, 4.0, 5.0/) ! 赋值坐标x
|
||
do i = 1, 6
|
||
call Noise(temp, lowerBound, upperBound) ! 产生噪声值
|
||
pointY(i) = pointX(i)**2 - 4*pointX(i) + 3 + temp ! 赋值坐标y
|
||
end do
|
||
call MultipleRegression(pointX, pointY, arrayCoefficient, 2, errorLevel)! 计算参数值
|
||
write(*,2) trim(tag), arrayCoefficient ! 输出结果
|
||
2 format(1X, A,' 计算得到的方程为：h = ', F8.2, ' + ', F8.2, ' t + ', F8.2, ' t^2')
|
||
end subroutine ShowNoise2
|
||
! 用于计算习题9-19, 这里采用的是四阶回归
|
||
subroutine ShowNoise4(lowerBound, upperBound, tag)
|
||
real, intent(in) :: lowerBound, upperBound ! 噪声值上下界
|
||
character(len=3), intent(in) :: tag ! 当前题目标识符
|
||
pointX = (/0.0, 1.0, 2.0, 3.0, 4.0, 5.0/) ! 赋值坐标x
|
||
do i = 1, 6
|
||
call Noise(temp, lowerBound, upperBound) ! 产生噪声值
|
||
pointY(i) = pointX(i)**4 - 3*pointX(i)**3 - 4*pointX(i)**2 + 2*pointX(i) + 3 + temp
|
||
end do ! 赋值坐标y
|
||
call MultipleRegression(pointX, pointY, arrayCoefficient, 4, errorLevel)! 计算参数值
|
||
write(*,3) trim(tag), arrayCoefficient ! 输出结果
|
||
3 format(1X, A,' 计算得到的方程为：h = ', F8.2, ' + ', F8.2, ' t + ', F8.2,&
|
||
& ' t^2 + ', F8.2, ' t^3 + ', F8.2, ' t^4')
|
||
end subroutine ShowNoise4
|
||
end subroutine Exercises9_16 |