Peakdoublesigmoid

Purpose

Outputs a double sigmoid function.

Synopsis

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

Inputs

• x = 5 element vector where

• x(1) = coefficient,
• x(2) = offset (left),
• x(3) = decay constant (left),
• x(4) = offset (right),
• x(5) = decay constant (right).

Note: if length(x)==4 then x(5)=x(3) providing a symmetric double sigmoid.

• p = axis 1xN (# of independent variables)

Outputs

• y(1) = ${{x}_{1}}\left({\frac {1-{{\operatorname {e} }^{{-z}_{1}}}}{{1}+{{\operatorname {e} }^{{-z}_{1}}}}}+{\frac {1-{{\operatorname {e} }^{{-z}_{2}}}}{{1}+{{\operatorname {e} }^{{-z}_{2}}}}}\right)$ where ${{z}_{1}}={x}_{3}\left(p-{x}_{2}\right)$ and ${{z}_{2}}={x}_{4}\left(p-{x}_{5}\right)$, 1xN
• y(2) = ${\operatorname {d} \!y \over \operatorname {d} \!{x}_{i}}$ , 3xN

• y(3) = ${\operatorname {d^{2}} \!y \over \operatorname {d} \!{{x}_{i}}^{2}}$ , 3x3xN

See Also

peakfunction, peakexponential, peakgaussian, peaklorentzian, peaksigmoid, peakpvoigt1, peakpvoigt2