dfmin optif0

dfmin() function dfmin ( a::Real  , b::Real  , f::Function  , tol::Real  = 1.0e-10  ) Minimum of a single variable general nonlinear function Purpose dfmin finds a minimum of a function f(x) between the given values a and b. The method used is a combination of golden section search and successive parabolic interpolation. Convergence is never much slower than that for a Fibonacci search. If the function f has a continuous second derivative which is positive at the minimum (which is not at a or b), then convergence is superlinear, and usually of the order of about 1.324.... The function f is never evaluated at two points closer together than eps*abs(dfmin) + (tol/3), where eps is approximately the square root of the relative machine precision. If f is a unimodal function and the computed values of f are always unimodal when separated by at least eps*abs(xstar) + (tol/3), then dfmin approximates the abcissa of the global minimum of f on the interval [a, b] with an error less than 3*eps*abs(dfmin) + tol. If f is not unimodal, then dfmin may approximate a local, but perhaps non-global, minimum to the same accuracy. Returns (x, info) x (Float64): Abscissa approximating the point where f(x) attains a minimum on the interval [a, b]. info (Int32): = 0: Normal return = -1: The argument f is invalid Parameters [in] a Left endpoint of initial interval. [in] b Right endpoint of initial interval. [in] f User supplied function, which evaluates f(x) defined as follows: _CODE function f(x) returns computed function value f(x). end _ENDCODE [in] tol (Optional) Desired length of the interval of uncertainty of the final result. (tol >= 0) (default = 1.0e-10) Reference D. Kahaner, C. Moler, S. Nash, "Numerical Methods and Software", Prentice-Hall (1989) Example Program Find the minimum point of the following function in the interval [0, 2]. f(x) = x^3 - 2x - 5 function TestDfmin() f(x) = x^3 - 2*x - 5 a = 0.0 b = 2.0 x = dfmin(a, b, f) println(x) end Example Results > TestDfmin() 0.8164965876303981