MagicPlot Manual

Plotting and nonlinear fitting software

User Tools

Site Tools


fit_equations

Table of Contents

Predefined Fit Curves Equations

All predefined Fit Curves are listed in this table. You also can specify custom fit equation. Unlike custom fit equations these curves can be adjusted with mouse on Fit Plot.

Name Formula Parameters Meaning Additional Properties
Line y = a x + b a — linear
b — constant
Parabola y = a x^2 + b x + c a — quadratic
b — linear
c — constant
Vertex:
x_0 = − b / {2 a}
y_0 = c − {b^2} / {4 a}
Spline Natural cubic spline,
on each i-th piece:
y_i = a_i + b_i x + c_i x^2 + d_i  x^3
xN — anchor point x-coordinates
yN — anchor point y-coordinates
Gaussian y = a exp(− ln(2) ({x−x_0}/dx)^2) a — amplitude
dx — half width at half
maximum (HWHM)
x0 — maximum position
Area (integral):
S = sqrt{pi / {ln {2}}} ~ a dx
Standard deviation:
sigma = dx / sqrt{2 ln 2}
Gaussian-A
(area-normalized)
y = sqrt{{ln {2}} / pi} ~ a / dx exp(− ln(2) ({x−x_0}/dx)^2) a — area (integral)
dx — half width at half
maximum (HWHM)
x0 — maximum position
Amplitude:
A = sqrt{{ln 2} / pi} ~ a/dx
Standard deviation:
sigma = dx / sqrt{2 ln 2}
Lorentzian y = a 1 / {1 + ({x−x_0} / dx)^2} a — amplitude
dx — half width at half
maximum (HWHM)
x0 — maximum position
Area (integral):
S = pi a dx
Lorentzian-A
(area-normalized)
y = a / {pi dx} 1 / {1 + ({x−x_0} / dx)^2} a — area (integral)
dx — half width at half
maximum (HWHM)
x0 — maximum position
Amplitude:
A = a / {pi dx}
Gauss Derivative y = − 2 ln(2) ~ {a (x−x_0)} / {dx^2} exp(− ln(2) ({x−x_0}/dx)^2) 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):
S = sqrt{pi / {ln {2}}} ~ a dx
Standard deviation:
sigma = dx / sqrt{2 ln 2}
Peak-to-peak horizontal:
p_x = sqrt{2/{ln {2}}} ~ dx
Peak-to-peak vertical:
p_y = 2 sqrt{{2 ln {2}} / e} ~ a / dx
Lorentz Derivative y=−2 a {x−x_0}/{dx^2} {(1 + ({x−x_0} / dx)^2)^{−2}} 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):
S = pi a dx
Peak-to-peak horizontal:
p_x = 2/{sqrt {3}} ~ dx
Peak-to-peak vertical:
p_y = {3 sqrt {3}} / 4 ~ a / dx

See Also

fit_equations.txt · Last modified: Sun Nov 8 12:21:24 2015 (external edit)