NON-LINEAR CURVE FITTING

Description

This program uses the Levenberg–Marquardt algorithm to perform a non-linear parmateric fit to two-column x-y data. Click on the function type, write initial guesses for the parameters, and paste data below (no commas).

Function Library

function	description	Initial parameters
$y=\sum a_n x^n$	polynomial	$a_0, a_1,..., a_N$ for Nth degree
$y=a_0 e^{a_1 x} + a_2$	exponential + const.	$a_0, a_1, a_2$
$y=a_0 (1-e^{-a_1 x})e^{-a_2 x}$	rising and falling exponential	$a_0, a_1, a_2$
$y=a_0 (1-e^{-a_1 x})e^{-a_2 x}+a_3$	rising and falling exponential + const.	$a_0, a_1, a_2, a_3$
$y=\sum a_{0n} e^{-\left({\frac{x-a_{1n}}{a_{2n}}}\right)^2}$	sum of Gaussians	$a_0, a_1, a_2 ... a_n, a_{n+1}, a_{n+2}$
$y=\sum a_{0n} e^{-\left({\frac{x-a_{1n}}{a_{2n}}}\right)^2 }+c$	sum of Gaussians+ const.	$a_0, a_1, a_2 ... a_n, a_{n+1}, a_{n+2},c$

Paste x-y data (sample shown)
0 0.0061071 0.1 0.0974315 0.2 0.178104 0.3 0.247211 0.4 0.31143 0.5 0.365493 0.6 0.407943 0.7 0.442791 0.8 0.475864 0.9 0.504899 1 0.521929 1.1 0.54396 1.2 0.55397 1.3 0.567109 1.4 0.578643 1.5 0.580848 1.6 0.586075 1.7 0.582739 1.8 0.585795 1.9 0.582474 2 0.583493 2.1 0.583514 2.2 0.579135 2.3 0.568846 2.4 0.567289 2.5 0.564783 2.6 0.558876 2.7 0.546676 2.8 0.540344 2.9 0.537786 3 0.525729 3.1 0.522059 3.2 0.507708 3.3 0.500653 3.4 0.4922 3.5 0.482807 3.6 0.483311 3.7 0.471046 3.8 0.457922 3.9 0.450707 4 0.448465 4.1 0.437385 4.2 0.433595 4.3 0.425815 4.4 0.41681 4.5 0.403344 4.6 0.397023 4.7 0.38756 4.8 0.380681 4.9 0.378826 5 0.37023 5.1 0.365646 5.2 0.35534 5.3 0.351415 5.4 0.345437 5.5 0.334046 5.6 0.325221 5.7 0.319373 5.8 0.320632 5.9 0.313672 6 0.30655 6.1 0.299604 6.2 0.297408 6.3 0.283512 6.4 0.286522 6.5 0.273612 6.6 0.270164 6.7 0.271494 6.8 0.259982 6.9 0.256454 7 0.25475 7.1 0.242192 7.2 0.242125 7.3 0.239629 7.4 0.236114 7.5 0.232139 7.6 0.226742 7.7 0.221432 7.8 0.215861 7.9 0.211891 8 0.202777 8.1 0.199863 8.2 0.196657 8.3 0.195474 8.4 0.195239 8.5 0.188425 8.6 0.180326 8.7 0.185277 8.8 0.177305 8.9 0.176724 9 0.171161 9.1 0.171738 9.2 0.160988 9.3 0.157137 9.4 0.159585 9.5 0.152591 9.6 0.147552 9.7 0.150888 9.8 0.144111 9.9 0.144232 10 0.139673
Calculate Fit