Peaksigmoid: Difference between revisions

Latest revision as of 10:05, 23 May 2023

Outputs a sigmoid function.

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

y(1) = ${{x}_{1}}\left({\frac {1-{{\operatorname {e} }^{-z}}}{{1}+{{\operatorname {e} }^{-z}}}}\right)$ where z = ${x}_{3}\left(p-{x}_{2}\right)$ , 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

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 ===Purpose===
 Outputs a sigmoid function.
+===Synopsis===
+:[y,y1,y2] = peaksigmoid(x,p)
+===Inputs===
+* '''x''' =  3 element vector where
+:* x(1) = coefficient
+:* x(2) = offset
+:* x(3) = decay constant
+* '''p''' = axis 1xN  (# of independent variables)
+===Outputs===
+* '''y(1) ''' = <math> {{x}_{1}} \left( \frac{1-{{\operatorname{e}}^{-z}}}{{ 1 }+{{\operatorname{e}}^{-z}}} \right)</math> where z = <math> {x}_{3}\left(p -{x}_{2} \right)</math>, 1xN
+* '''y(2)  '''  = <math>{\operatorname{d}\!y\over\operatorname{d}\!{x}_{i}}</math> , 3xN
+* ''' y(3)  '''  = <math>{\operatorname{d^2}\!y\over\operatorname{d}\!{{x}_{i}}^{2}}</math> , 3x3xN
+===See Also===
+[[peakfunction]], [[peakexponential]], [[peakgaussian]], [[peaklorentzian]], [[peakpvoigt1]], [[peakpvoigt2]]