Parabolic fit features

[matwey]

Hi,

It would be great to have features extracted from parabolic (quadratic) fit similar to what we have from linear fit:

1. Fit residual aka $\chi^2$
2. Curve value in maximum (minimum) $m_0$
3. Maximum (minimum) time moment $t_0$
4. Acceleration $g$

The model is $m_i = m_0 + g \left( t_i - t_0 \right)^2$

Equations:

$$ \begin{bmatrix} \sum_i t^4_i & \sum_i t^3_i & \sum_i t^2_i \\ \sum_i t^3_i & \sum_i t^2_i & \sum_i t_i \\ \sum_i t^2_i & \sum_i t_i & N \end{bmatrix} \begin{bmatrix} a \ b \ c \end{bmatrix} = \begin{bmatrix} \sum_i t^2_i m_i \ \sum_i t_i m_i \ \sum_i m_i \end{bmatrix} $$

$g = a$
$t_0 = -\frac{b}{2a}$
$m_0 = c - \frac{b^2}{4a}$