Peaksigmoid

Purpose

Outputs a sigmoid function.

Synopsis

[y,y1,y2] = peaksigmoid(x,ax)

Inputs

• x = 3 element vector where

• x(1) = coefficient
• x(2) = offset
• x(3) = decay constant

• ax = axis 1 x N (independent variable)

Outputs

• y(1) = ${{x}_{1}}\left({\frac {1-{{\operatorname {e} }^{-z}}}{{1}+{{\operatorname {e} }^{-z}}}}\right)$

where z = ${x}_{3}\left(ax-{x}_{2}\right)$

• y(2) = ${\operatorname {d} \!y \over \operatorname {d} \!{x}_{i}}$

• y(3) = ${\operatorname {d^{2}} \!y \over \operatorname {d} \!{{x}_{i}}^{2}}$