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 and x(3) is equal to the decay constant

Outputs

${\sqrt {1-e^{2}}}$

$f\left({{a}_{i}},\mathbf {x} \right)={{x}_{1}}\left[{{x}_{4}}{{\operatorname {e} }^{\frac {-4\ln \left(2\right){{\left({{a}_{i}}-{{x}_{2}}\right)}^{2}}}{x_{3}^{2}}}}+\left(1-{{x}_{4}}\right)\left[{\frac {x_{3}^{2}}{{{\left({{a}_{i}}-{{x}_{2}}\right)}^{2}}+x_{3}^{2}}}\right]\right]$

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

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

• ${\operatorname {d} \!y \over \operatorname {d} \!{x}_{i}}$

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left( 1-{{x}_{4}} \right)\left[ \frac{x_{3}^{2}}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+x_{3}^{2}} \right] \right] }