Delphi algorithm for solving the logic equation of 4 or 5 parameters?

Question

I am looking for an algorithm [Pascal / Delphi] that can solve the logic equation of 4 or 5 parameters. I searched the Internet for a long time and did not manage to find an algorithm that works.

For example, 4 parameters logstics;

Y = (AD) / (1+ (x / C) ^ B) + D

Given a set of coordinates (x, y), I will need to determine A, B, C, D. (A = max, B = slope, C = inflection point, D = min)

Any help in the right direction ?: (

Answer 1

You can use a non-linear curve fitting library, for example. using the Levenberg-Marquard algorithm .

I have already used this open source C library , it is very easy to interact with Delphi (after compiling with the BC ++ compiler).

This code is based on the standard lmfit known algorithm implementation and perfectly solves the 4PL or 5PL equations. I used this library in high-value biological software, including a full check, using the NIST reference material . Here I can’t include Delphi code (this is copyrighted), but the C source code is ready to download above and easy to work (only one .obj file to include - or do a clean Delphi conversion).

You have several paid libraries, but I haven’t found anything better, faster or more accurate than lmfit.