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20210519-第13章习题.f90
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20210519-第13章习题.f90
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! ==============================================================================
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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13章习题
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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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! 2021-05-19 21:36:27 Sola 习题13-1 上一章写过了
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! 2021-05-19 21:36:44 Sola 习题13-2 递归函数和子程序计算阶乘
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! 2021-05-19 22:06:42 Sola 习题13-3 验证例题13-2的子程序
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! 2021-05-19 22:30:37 Sola 习题13-4 ~ 习题13-18 跳过
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! 2021-05-19 22:56:02 Sola 习题13-19 极坐标复数
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! 2021-05-19 23:21:36 Sola 习题13-20 复数的极坐标乘除
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! 2021-05-19 23:40:41 Sola 习题13-21 ~ 习题13-22 跳过
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! 2021-05-19 23:42:15 Sola 习题13-23 ...之前就是这么写的
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! 2021-05-19 23:44:46 Sola 习题13-24 跳过
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! 程序结构:
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!
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! ==============================================================================
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! 主程序：
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program Chapter13
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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 Exercises13_2
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! call Exercises13_3
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! call Exercises13_19
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! call Exercises13_20
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end program Chapter13
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! ==============================================================================
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! 习题13-2 递归函数和子程序计算阶乘
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subroutine Exercises13_2
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implicit none
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interface
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subroutine SubFactorial(n, result)
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implicit none
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integer, intent(in) :: n
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integer, intent(out) :: result
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integer :: temp
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end subroutine SubFactorial
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recursive function FunFactorial(n) result(result)
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implicit none
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integer, intent(in) :: n
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integer :: result
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end function FunFactorial
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end interface
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integer :: result
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call SubFactorial(5, result)
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write(*, *) "通过子程序计算5的阶乘为： ", result
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write(*, *) "通过函数计算10的阶乘为： ", FunFactorial(10)
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end subroutine Exercises13_2
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! 阶乘运算子程序
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recursive subroutine SubFactorial(n, result)
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implicit none
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integer, intent(in) :: n
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integer, intent(out) :: result
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integer :: temp
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if ( n >= 1 ) then
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call SubFactorial(n-1, temp)
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result = n*temp
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else
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result = 1
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end if
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end subroutine SubFactorial
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! 阶乘运算函数
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recursive function FunFactorial(n) result(result)
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implicit none
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integer, intent(in) :: n
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integer :: result
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if ( n >= 1 ) then
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result = n*FunFactorial(n-1)
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else
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result = 1
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end if
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end function FunFactorial
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! 习题13-3 验证例题13-2子程序, 求极值
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subroutine Exercises13_3
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implicit none
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interface
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subroutine Extremes(a, n, maxVal, posMaxVal, minVal, posMinVal)
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implicit none
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integer, intent(in) :: n
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real, intent(in), dimension(n) :: a
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real, intent(out), optional :: maxVal
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integer, intent(out), optional :: posMaxVal
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real, intent(out), optional :: minVal
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integer, intent(out), optional :: posMinVal
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end subroutine Extremes
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end interface
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real, dimension(18) :: input
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integer :: maxLoc, minLoc
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real :: maxValue, minValue
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input = (/ 3., 4., 0., 1., 2., 1., 1., 9., 9., 8., 0., 7., 2., 0., 7., 3., 3., 3./)
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call Extremes(input, 18, minVal=minValue, maxVal=maxValue, posMinVal=minLoc, posMaxVal=maxLoc)
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write(*, *) "数组在第", maxLoc, "位取到最大值", maxValue
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write(*, *) "数组在第", minLoc, "位取到最小值", minValue
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end subroutine Exercises13_3
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subroutine Extremes(a, n, maxVal, posMaxVal, minVal, posMinVal)
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implicit none
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integer, intent(in) :: n
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real, intent(in), dimension(n) :: a
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real, intent(out), optional :: maxVal
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integer, intent(out), optional :: posMaxVal
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real, intent(out), optional :: minVal
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integer, intent(out), optional :: posMinVal
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integer :: i
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real :: realMax
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integer :: posMax
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real :: realMin
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integer :: posMin
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realMax = a(1)
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posMax = 1
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realMin = a(1)
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posMin = 1
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do i = 2, n
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if ( a(i) > realMax ) then
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realMax = a(i)
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posMax = i
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end if
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if ( a(i) < realMin ) then
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realMin = a(i)
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posMin = i
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end if
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end do
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if ( present(maxVal) ) maxVal = realMax
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if ( present(posMaxVal) ) posMaxVal = posMax
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if ( present(minVal) ) minVal = realMin
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if ( present(posMinVal) ) posMinVal = posMin
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end subroutine Extremes
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! 习题13-19 极坐标复数
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module Exercises13_19_Mod
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implicit none
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interface assignment(=)
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module procedure Complex2Polar
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module procedure Polar2Complex
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end interface
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interface operator(*)
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module procedure PolarMul
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end interface
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interface operator(/)
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module procedure PolarDiv
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end interface
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type :: polar
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real :: z
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real :: theta
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end type
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private
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! private :: Complex2Polar, Polar2Complex
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public :: assignment(=), polar, operator(*), operator(/)
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contains
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subroutine Complex2Polar(result, input)
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implicit none
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type(polar), intent(out) :: result
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complex, intent(in) :: input
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result%z = cabs(input)
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result%theta = atan(aimag(input)/real(input))
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end subroutine
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subroutine Polar2Complex(result, input)
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implicit none
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complex, intent(out) :: result
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type(polar), intent(in) :: input
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result = cmplx(input%z*cos(input%theta), input%z*sin(input%theta))
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end subroutine
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function PolarMul(var1, var2) result(result)
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implicit none
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type(polar), intent(in) :: var1, var2
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type(polar) :: result
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result%z = var1%z*var2%z
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result%theta = mod(var1%theta + var2%theta + 3.141593, 3.141593*2) - 3.141593
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end function PolarMul
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function PolarDiv(var1, var2) result(result)
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implicit none
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type(polar), intent(in) :: var1, var2
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type(polar) :: result
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result%z = var1%z/var2%z
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result%theta = mod(var1%theta - var2%theta + 3.141593, 3.141593*2) - 3.141593
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end function PolarDiv
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end module Exercises13_19_Mod
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subroutine Exercises13_19
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use Exercises13_19_Mod, only: assignment(=), polar
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implicit none
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type(polar) :: a
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complex :: b
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b = (1.0, 2.0)
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a = b
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b = a
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write(*, *) "计算得到的极坐标形式为", a, "; 计算得到的直角坐标形式为", b
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end subroutine Exercises13_19
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! 习题13-20 复数的极坐标乘除
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subroutine Exercises13_20
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use Exercises13_19_Mod, only: polar, operator(*), operator(/), assignment(=)
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implicit none
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complex :: a, b
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type(polar) :: c, d
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a = (1.0, 1.0)
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b = (1.0,-1.0)
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c = a
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d = b
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write(*, *) "c的初始值为: ", c, "; d的初始值为: ", d
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write(*, *) "c*d的结果为: ", c*d, "; c/d的结果为: ", c/d
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end subroutine Exercises13_20
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