From Eigenvector Research Documentation Wiki
Jump to navigation
Jump to search
imported>Mathias |
imported>Mathias |
| Line 18: |
Line 18: |
|
| |
|
|
| |
|
| | | * '''y(1) ''' = <math> {{x}_{1}} \left( \frac{1-{{\operatorname{e}}^{-z}}}{{ 1 }+{{\operatorname{e}}^{-z}}} \right)</math> |
| | |
| <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[ {{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{1-x_{3}^{2}}{{{\left( {1}+{{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}}+1} \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{{{\operatorname{e}}^{-z}}}}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+{{\operatorname{e}}^{-z}}} \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{1}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+{{\operatorname{e}}^{-z}}} \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{{{\operatorname{e}}^{-z}}}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+{{\operatorname{e}}^{-z}}} \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 11:57, 4 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
- x(3) = decay constant
Outputs
- y(1) =
- y(2) =
- y(3) =
