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

@@ Line 5: / Line 5: @@
 ===Synopsis===
-:[y,y1,y2] = peaksigmoid(x,ax)
+:[y,y1,y2] = peaksigmoid(x,p)
 ===Inputs===
@@ Line 14: / Line 13: @@
 :* 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
-<math>\sqrt{1-e^2}</math>
+===See Also===
-<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{1-x_{3}^{2}}{{{\left( \right)}+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>
+[[peakfunction]], [[peakexponential]], [[peakgaussian]], [[peaklorentzian]], [[peakpvoigt1]], [[peakpvoigt2]]