model peak center

use the derivative of the parabolic equation to find the peak center, and then put the center into the equation to find the intensity at that point.

Usage

model_peak_center_intensity(x, coefficients)

Arguments

x

the x-values to use (non-centered)

coefficients

the model coefficients generated from centered model

Value

numeric

Details

The coefficients are generated using the linear model: $$y = a + bx + cx^2$$.

The derivative of this is: $$y = b + 2cx$$

The peak of a parabola is defined where y is zero for the derivative.

$$x = -b / 2c$$

We can use this to derive where the center of the peak is, and then put the center value back into the equation to get the intensity.