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Plotting and nonlinear fitting software

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fit_equations [Mon Oct 15 19:02:50 2012]
Alexander
fit_equations [Sun Nov 8 12:21:24 2015]
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-====== Predefined Fit Curves Equations ====== 
-All predefined Fit Curves are listed in this table. You also can specify [[custom_fit_equation|custom fit equation]]. Unlike custom fit equations these curves can be adjusted with mouse on Fit Plot. 
  
-^ Name  ^ Formula ^ Parameters meaning ^ Additional Properties ^  
-| Line | <m>y = a x + b</m> | //a// -- linear \\ //b// -- constant  | | 
-| Parabola | <m>y = a x^2 + b x + c</m>| //a// --- quadratic \\ //b// --- linear \\ //c// --- constant  | Vertex: \\ <m>x_0 = − b / {2 a}</m> \\ <m>y_0 = c − {b^2} / {4 a}</m> | 
-| Spline | Natural cubic spline, \\ on each //i//-th piece: \\ <m>y_i = a_i + b_i x + c_i x^2 + d_i  x^3</m> | //xN// --- anchor point x-coordinates \\ //yN// --- anchor point y-coordinates| |  
-| Gaussian | <m>y = a exp(− ln(2) ({x−x_0}/dx)^2)</m> | //a// --- amplitude \\ //dx// --- half width at half \\ maximum (HWHM) \\ //x0// --- maximum position | Area (integral): \\ <m>S = sqrt{pi / {ln {2}}} ~ a dx</m> \\ Standard deviation: \\ <m>sigma = dx / sqrt{2 ln 2}</m> | 
-| Gaussian-A \\ (area-normalized) | <m>y = sqrt{{ln {2}} / pi} ~ a / dx exp(− ln(2) ({x−x_0}/dx)^2)</m> | //a// --- area (integral) \\ //dx// --- half width at half \\ maximum (HWHM) \\ //x0// --- maximum position | Amplitude: \\ <m>A = sqrt{{ln 2} / pi} ~ a/dx</m> \\ Standard deviation: \\ <m>sigma = dx / sqrt{2 ln 2}</m> | 
-| Lorentzian | <m>y = a 1 / {1 + ({x−x_0} / dx)^2}</m> | //a// --- amplitude \\ //dx// --- half width at half \\ maximum (HWHM) \\ //x0// --- maximum position | Area (integral): \\ <m>S = pi a dx</m> | 
-| Lorentzian-A \\ (area-normalized) | <m>y = a / {pi dx} 1 / {1 + ({x−x_0} / dx)^2}</m> | //a// --- area (integral) \\ //dx// --- half width at half \\ maximum (HWHM) \\ //x0// --- maximum position | Amplitude: \\ <m>A = a / {pi dx}</m> | 
-| Gauss Derivative | <m>y = − 2 ln(2) ~ {a (x−x_0)} / {dx^2} exp(− ln(2) ({x−x_0}/dx)^2)</m> | Parameters are the same \\ as for original Gaussian: \\ \\ //a// --- amplitude \\ //dx// --- half width at half \\ maximum (HWHM) \\ //x0// --- center position | Area of original Gaussian \\ (second integral): \\ <m>S = sqrt{pi / {ln {2}}} ~ a dx</m> \\ Standard deviation: \\ <m>sigma = dx / sqrt{2 ln 2}</m> \\ Peak-to-peak horizontal: \\ <m>p_x = sqrt{2/{ln {2}}} ~ dx</m> \\ Peak-to-peak vertical: \\ <m>p_y = 2 sqrt{{2 ln {2}} / e} ~ a / dx</m> | 
-| Lorentz Derivative | <m>y=−2 a {x−x_0}/{dx^2} {(1 + ({x−x_0} / dx)^2)^{−2}}</m> | Parameters are the same \\ as for original Lorentzian: \\ \\ //a// --- amplitude \\ //dx// --- half width at half \\ maximum (HWHM) \\ //x0// --- center position | Area of original Lorentzian \\ (second integral): \\ <m>S = pi a dx</m> \\ Peak-to-peak horizontal: \\ <m>p_x = 2/{sqrt {3}} ~ dx</m> \\ Peak-to-peak vertical: \\ <m>p_y = {3 sqrt {3}} / 4 ~ a / dx</m> | 
- 
-===== See Also ===== 
-  * [[fitting]] 
-  * [[spline]] 
-  * [[guess_peaks]] 
fit_equations.txt · Last modified: Sun Nov 8 12:21:24 2015 (external edit)