以上代码不调用IMSL算法库，实现UNLSF一样功能的函数

以下是一个不调用IMSL算法库，实现UNLSF算法功能的Fortran函数：

SUBROUTINE UNLSF(fcn, m, n, x0, fvec, fjac, tol, diag, qtf, info, errmsg)
  IMPLICIT NONE
  INTEGER, INTENT(IN) :: m, n
  REAL, DIMENSION(n), INTENT(INOUT) :: x0, diag, qtf
  REAL, DIMENSION(m), INTENT(OUT) :: fvec
  REAL, DIMENSION(m,n), INTENT(INOUT) :: fjac
  REAL, INTENT(IN) :: tol
  INTEGER, INTENT(OUT) :: info
  CHARACTER(LEN=*), INTENT(OUT) :: errmsg
  EXTERNAL :: fcn

  INTEGER :: maxiter, i, j, lmpar, iter, mode
  REAL :: fnorm, gnorm, pnorm, ratio, lambda, factor
  REAL :: epsmch, epsfcn, sqrt_eps, sum, temp
  REAL, DIMENSION(n) :: wa1, wa2, wa3
  REAL, DIMENSION(m) :: wa4
  REAL, DIMENSION(n,n) :: wa5
  REAL, DIMENSION(m,n+1) :: wa6
  REAL, DIMENSION(n+1) :: wa7

  epsmch = EPSILON(1.0)
  epsfcn = SQRT(epsmch)
  sqrt_eps = SQRT(epsmch)

  info = 0
  iter = 0

  CALL fcn(m, n, x0, fvec, fjac)

  fnorm = DNRM2(m, fvec, 1)
  gnorm = 0.0
  DO j = 1, n
    wa2(j) = 0.0
    DO i = 1, m
      wa2(j) = wa2(j) + fjac(i,j) * fvec(i)
    END DO
    gnorm = MAX(gnorm, ABS(wa2(j) / diag(j)))
  END DO

  IF (gnorm <= tol) THEN
    info = 1
    RETURN
  END IF

  DO j = 1, n
    wa3(j) = x0(j)
  END DO

  maxiter = MIN(50, MAX(1, n))
  lambda = 0.001
  mode = 1

  DO WHILE (iter < maxiter)
    iter = iter + 1

    CALL FDJAC2(fcn, m, n, x0, fvec, fjac, epsfcn, wa4, mode)

    DO j = 1, n
      wa2(j) = -fvec(j)
      DO i = 1, m
        wa2(j) = wa2(j) + fjac(i,j) * fvec(i)
      END DO
      wa1(j) = wa2(j) / sqrt_eps
      wa2(j) = diag(j) / sqrt_eps * wa2(j)
    END DO

    factor = 1.0
    DO WHILE (.TRUE.)
      CALL LMDIF1(n, x0, wa1, wa2, fjac, lmpar, wa1, wa2, wa4, wa5, wa6, wa7)

      DO j = 1, n
        wa3(j) = x0(j) - wa3(j)
        wa2(j) = wa1(j) * wa3(j)
      END DO

      pnorm = DNRM2(n, wa2, 1)

      IF (lmpar = 0) THEN
        ratio = 0.0
      ELSE
        ratio = ABS((fnorm - DNRM2(m, wa4, 1)) / lmpar)
      END IF

      IF (ratio < 0.1) THEN
        factor = 0.1
      ELSE IF (ratio < 0.7) THEN
        factor = MAX(factor, 0.1 / (1.0 - ratio))
      ELSE IF (ratio < 0.9) THEN
        factor = MAX(factor, 0.5 / (1.0 - ratio))
      ELSE IF (ratio < 1.0) THEN
        factor = MAX(factor, 0.9 / (1.0 - ratio))
      ELSE
        factor = 10.0
      END IF

      IF (lmpar = 0 .OR. ratio >= 0.9999) THEN
        CALL DAXPY(n, -1.0, wa3, 1, x0, 1)
        CALL COPY(n, x0, 1, wa3, 1)
        CALL fcn(m, n, x0, fvec, fjac)
        fnorm = DNRM2(m, fvec, 1)
        IF (fnorm < tol) THEN
          info = 1
          RETURN
        END IF
        lambda = lambda * MAX(0.1, factor)
        gnorm = 0.0
        DO j = 1, n
          wa2(j) = 0.0
          DO i = 1, m
            wa2(j) = wa2(j) + fjac(i,j) * fvec(i)
          END DO
          gnorm = MAX(gnorm, ABS(wa2(j) / diag(j)))
        END DO
        IF (gnorm < tol) THEN
          info = 1
          RETURN
        END IF
        mode = 2
        iter = 0
      ELSE
        lambda = lambda * factor
      END IF

      IF (lambda > 1.0E+10) THEN
        errmsg = "UNLSF failed to converge: too many iterations"
        RETURN
      END IF
    END DO
  END DO

  errmsg = "UNLSF failed to converge: too many iterations"
  RETURN
END SUBROUTINE UNLSF

这个函数使用了FDJAC2和LMDIF1等子程序来计算Jacobian矩阵和求解线性方程组，从而实现了UNLSF算法的功能。该代码中使用了一些数值计算的技巧，例如缩放因子、步长因子等，以提高算法的稳定性和求解效率。