Fortran 选择案例 - Fortran

Fortran是一种高性能数值计算语言，广泛用于科学计算和工程领域。本文将介绍一些Fortran的应用场景，并提供相关代码示例。

1. 线性代数计算

Fortran在线性代数计算方面有着非常强大的功能，常常用于解决大规模线性方程组和最小二乘问题等。下面是一个Fortran实现的求解线性方程组的例子：

program solve_linear_equations
  implicit none
  integer, parameter :: n = 3
  real :: A(n,n), b(n), x(n)
  integer :: ipiv(n), info
  A = reshape([2, 1, -1, -3, -1, 2, -2, 1, 2], [n, n])
  b = [8, -11, -3]
  call sgesv(n, 1, A, n, ipiv, b, n, info)
  if (info == 0) then
    x = b
    write(*,*) "Solution: ", x
  else
    write(*,*) "Failed to solve the linear equations"
  endif
end program solve_linear_equations

2. 数值优化

Fortran还可以用于数值优化问题，例如寻找函数最小值或最大值。下面是一个使用Fortran实现的最小化函数的例子：

function func(x)
  real :: x, func
  func = (x - 3.14159)**2
end function func

program optimize_function
  implicit none
  real :: x0, f0, x1, f1, eps
  integer :: niter
  x0 = 0
  eps = 1e-6
  niter = 100
  do i = 1, niter
    f0 = func(x0)
    x1 = x0 - 0.01 * dfunc(x0) ! 根据导数更新x
    f1 = func(x1)
    if (abs(f1-f0) < eps) exit
    x0 = x1
  end do
  write(*,*) "Minimum point: (", x0, ",", func(x0), ")"
end program optimize_function

3. 并行计算

Fortran可以通过OpenMP和MPI等框架实现并行计算，加速程序运行。下面是一个使用MPI实现向量加法的例子：

program mpi_vector_addition
  implicit none
  include 'mpif.h'
  integer :: ierr, size, rank
  integer, parameter :: n = 100000
  real, dimension(n) :: a, b, c
  integer :: i
  call MPI_INIT(ierr)
  call MPI_COMM_SIZE(MPI_COMM_WORLD, size, ierr)
  call MPI_COMM_RANK(MPI_COMM_WORLD, rank, ierr)
  if (rank == 0) then
    a = 1.0
    b = 2.0
  endif
  call MPI_BCAST(a, n, MPI_REAL, 0, MPI_COMM_WORLD, ierr)
  call MPI_BCAST(b, n, MPI_REAL, 0, MPI_COMM_WORLD, ierr)
  do i = 1+(rank*n)/size, (rank+1)*n/size
    c(i) = a(i) + b(i)
  end do
  call MPI_ALLGATHER(c(1+(rank*n)/size), n/size, MPI_REAL, c, n/size, MPI_REAL, MPI_COMM_WORLD, ierr)
  call MPI_FINALIZE(ierr)
  ! 输出结果
end program mpi_vector_addition

以上是Fortran的一些应用场景和相关代码示例。仅供参考。