Theories common to all applications¶
Polynomial¶
Summary¶
Fit a polynomial of degree \(n\) to the data
- Function
- \[y(x) = \sum_{i=0}^n A_i x^i\]
- Parameters
\(n\): degree of the polynomial function.
\(A_i\): polynomial coefficeints.
Power Law¶
Summary¶
Fit a power law to the data
- Function
- \[y(x) = a x^b\]
- Parameters
\(a\): prefactor.
\(b\): exponent.
Exponential¶
Summary¶
Fit a single exponential decay to the data
- Function
- \[y(x) = a \exp(-x/T)\]
- Parameters
\(a\): prefactor.
\(T\): exponential “time” constant.
Double Exponential¶
Summary¶
Fit two single exponential decay to the data
- Function
- \[y(x) = a_1 \exp(x/T_1) + a_2 \exp(-x/T_2)\]
- Parameters
\(a_1\), \(a_2\): prefactors.
\(T_1\), \(T_2\): exponential “time” constants.
Algebraic Expression¶
Summary¶
Fit a user algebraic expression with \(n\) parameters.
The expression can contain any of the following mathematical functions: sin, cos, tan, arccos, arcsin, arctan, arctan2, deg2rad, rad2deg, sinh, cosh, tanh, arcsinh, arccosh, arctanh, around, round, rint, floor, ceil,trunc, exp, log, log10, fabs, mod, e, pi, power, sqrt
It is the responsability of the user to input functions that make mathematical sense.
- Function
- \[y(x) = f({A_i}, x, F_{params})\]
- Parameters
\(n\): number of parameters.
\(A_i\): coefficeints of the algebraic expression
