Peaksigmoid: Difference between revisions

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===Synopsis===
===Synopsis===


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


===Inputs===


====Inputs====
* '''x''' = 3 element vector where
:* x(1) = coefficient
:* x(2) = offset
:* x(3) = decay constant
* '''p''' = axis 1xN  (# of independent variables)


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




====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]]
<math>\sqrt{1-e^2}</math>
 
<math>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]</math>
 
 
<math>f\left( {{a}_{i}},\mathbf{x} \right)={{x}_{1}}\left[ {}+\left( 1-{{x}_{4}} \right)\left[ \frac{x_{3}^{2}}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+x_{3}^{2}} \right] \right]</math>
 
 
* '''y(1) ''' =
 
* '''y(2)  '''  = <math>{\operatorname{d}\!y\over\operatorname{d}\!{x}_{i}}</math>
 
* ''' y(3)  '''  = <math>{\operatorname{d^2}\!y\over\operatorname{d}\!{{x}_{i}}^{2}}</math>

Latest revision as of 10:05, 23 May 2023

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) = where z = , 1xN
  • y(2) = , 3xN
  • y(3) = , 3x3xN

See Also

peakfunction, peakexponential, peakgaussian, peaklorentzian, peakpvoigt1, peakpvoigt2

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