Peaksigmoid: Difference between revisions
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<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[ {{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> | ||
* '''y(1) ''' = | |||
* '''y(2) ''' = <math>{\operatorname{d}\!y\over\operatorname{d}\!{x}_{i}}</math> | * '''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> | * ''' y(3) ''' = <math>{\operatorname{d^2}\!y\over\operatorname{d}\!{{x}_{i}}^{2}}</math> | ||
Revision as of 13:50, 1 August 2016
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
![{\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}}}}+\left(1-{{x}_{4}}\right)\left[{\frac {x_{3}^{2}}{{{\left({{a}_{i}}-{{x}_{2}}\right)}^{2}}+x_{3}^{2}}}\right]\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/965a5fa73fcc814b61ed64985798616e4e0a5843)
- y(1) =
- y(2) =
- y(3) =
