Peaksigmoid

Purpose

Outputs a sigmoid function.

Synopsis

[i0,iw] = peakfind(x,width,tolfac,w,options)

[i0,iw] = peakfind(x,width,options)

Inputs

• x = 3 element vector where x(1) = coefficient, x(2) = offset and x(3) is equal to the decay constant

Outputs

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

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

• ${\operatorname {d^{2}} \!y \over \operatorname {d} \!{{x}_{i}}^{2}}$

• Failed to parse (syntax error): {\displaystyle 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}}}}}
• ${\operatorname {d} \!y \over \operatorname {d} \!{x}_{i}}$