我想使用Minpack(fortran)来估计S曲线的以下广义形式的D参数:y =(A-D)/(1 +(x ** B / C))+ D
想法是,在此应用程序中,用户提供A [始终强制为(0,0)通过的值为0],B和C,然后Minpack将为D找到一个值,以强制通过(1,y),其中y也由用户提供,但必须<=1。我可以使用下面的代码来完成此任务,但是,minpack声称实际上它似乎没有收敛,已。例如,在运行此代码并输入值1(在第一个提示符下)和0 4 0.1(在第二个提示符下)时,minpack返回info = 2,根据lmdif中的注释,这表示:
两个连续迭代之间的相对误差最多为xtol。
我很想注释掉第63行,但是我担心这很火...那里有经验丰富的minpack用户可以对此发表评论吗?第63行是这样的:
if (info /= 1) stop "failed to converge"
我是否滥用Minpack,即使它看起来收敛了(基于我在par中验证的值)?
module types
implicit none
private
public dp
integer, parameter :: dp=kind(0d0)
end module
module f_vals
DOUBLE PRECISION, SAVE, DIMENSION(:), POINTER:: fixed_vals
end module
module find_fit_module
! This module contains a general function find_fit() for a nonlinear least
! squares fitting. The function can fit any nonlinear expression to any data.
use minpack, only: lmdif1
use types, only: dp
implicit none
private
public find_fit
contains
subroutine find_fit(data_x, data_y, expr, pars)
! Fits the (data_x, data_y) arrays with the function expr(x, pars).
! The user can provide any nonlinear function 'expr' depending on any number of
! parameters 'pars' and it must return the evaluated expression on the
! array 'x'. The arrays 'data_x' and 'data_y' must have the same
! length.
real(dp), intent(in) :: data_x(:), data_y(:)
interface
function expr(x, pars) result(y)
use types, only: dp
implicit none
real(dp), intent(in) :: x(:), pars(:)
real(dp) :: y(size(x))
end function
end interface
real(dp), intent(inout) :: pars(:)
real(dp) :: tol, fvec(size(data_x))
integer :: iwa(size(pars)), info, m, n
real(dp), allocatable :: wa(:)
tol = sqrt(epsilon(1._dp))
!tol = 0.001
m = size(fvec)
n = size(pars)
allocate(wa(m*n + 5*n + m))
call lmdif1(fcn, m, n, pars, fvec, tol, info, iwa, wa, size(wa))
open(222, FILE='D_Value.txt')
write(222,4) pars(1)
4 format(E20.12)
close(222)
if (info /= 1) stop "failed to converge"
contains
subroutine fcn(m, n, x, fvec, iflag)
integer, intent(in) :: m, n, iflag
real(dp), intent(in) :: x(n)
real(dp), intent(out) :: fvec(m)
! Suppress compiler warning:
fvec(1) = iflag
fvec = data_y - expr(data_x, x)
end subroutine
end subroutine
end module
program snwdeplcrv
! Find a nonlinear fit of the form y = (A - D) / (1 + (x**B/C)) + D.
use find_fit_module, only: find_fit
use types, only: dp
use f_vals
implicit none
real(dp) :: pars(1), y_int_at_1
real(dp) :: y(1) = 1.0 ! Initialization of value to be reset by user (y: value of S-curve @ x=1)
real(dp) :: A, B, C
integer :: i
allocate(fixed_vals(3)) ! A, B, C parameters
pars = [1._dp] ! D parameter in S-curve function
! Read PEST-specified parameters
write(*,*) ' Enter value that S-curve should equal when SWE=1 (must be <= 1)'
read(*,*) y_int_at_1
if(y_int_at_1 > 1.0) y_int_at_1 = 1
y = y_int_at_1
! Read PEST-specified parameters
write(*,*) ' Enter S-curve parameters: A, B, & C. D parameter to be estimated '
read(*,*) A, B, C
fixed_vals(1) = A
fixed_vals(2) = B
fixed_vals(3) = C
call find_fit([(real(i, dp), i=1,size(y))], y, expression, pars)
print *, pars
contains
function expression(x, pars) result(y)
use f_vals
real(dp), intent(in) :: x(:), pars(:)
real(dp) :: y(size(x))
real(dp) :: A, B, C, D
A = fixed_vals(1)
B = fixed_vals(2)
C = fixed_vals(3)
D = pars(1)
y = (A - D) / (1 + (x**B / C)) + D
end function
end program