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fit_equations [Mon Oct 25 23:12:15 2010] Alexander |
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====== Predefined Fit Curves Equations ====== | ====== Predefined Fit Curves Equations ====== | ||
- | This is the table of predefined Fit Curves. | + | All predefined Fit Curves |
- | ^ Name ^ Formula ^ Additional Properties ^ | + | ^ Name ^ Formula |
- | | Line | <m>y = a x + b</m> | | | + | | Line | <m>y = a x + b</ |
- | | Parabola | <m>y = a x^2 + b x + c</m> | Vertex: \\ < | + | | Parabola | <m>y = a x^2 + b x + c</m>| //a// --- quadratic \\ //b// --- linear \\ //c// --- constant |
- | | Gaussian | <m>y = a exp(− ln(2) ({x−x_0}/ | + | | Spline | Natural cubic spline, \\ on each //i//-th piece: \\ < |
- | | Gaussian-A \\ (normalized) | <m>y = sqrt{{ln {2}} / pi} ~ a / dx exp(− ln(2) ({x−x_0}/ | + | | Gaussian | <m>y = a exp(− ln(2) ({x−x_0}/ |
- | | Lorentzian | <m>y = a 1 / {1 + ({x−x_0} / dx)^2}</ | + | | Gaussian-A \\ (area-normalized) | <m>y = sqrt{{ln {2}} / pi} ~ a / dx exp(− ln(2) ({x−x_0}/ |
- | | Lorentzian-A \\ (normalized) | <m>y = a / {pi dx} 1 / {1 + ({x−x_0} / dx)^2}</ | + | | Lorentzian | <m>y = a 1 / {1 + ({x−x_0} / dx)^2}</ |
- | | Gauss Derivative | <m>y = − 2 ln(2) ~ {a (x−x_0)} / {dx^2} exp(− ln(2) ({x−x_0}/ | + | | Lorentzian-A \\ (area-normalized) | <m>y = a / {pi dx} 1 / {1 + ({x−x_0} / dx)^2}</ |
- | | Lorentz Derivative | < | + | | Gauss Derivative | <m>y = − 2 ln(2) ~ {a (x−x_0)} / {dx^2} exp(− ln(2) ({x−x_0}/ |
+ | | Lorentz Derivative | < | ||
+ | |||
+ | ===== See Also ===== | ||
+ | * [[fitting]] | ||
+ | * [[spline]] | ||
+ | * [[guess_peaks]] |