# U_model_1D_LR_LB_SF

## Description

U-model with

(1) a correction factor to L/R (LRcorrection)

(2) linear baseline correction (LB_a+x*LB_b)

(3) normalization correction (ScaleFactor)

This model fits individual linear baselines for each dataset and corrects for improper normalization due to noise. Difference from U-model is that a normalization factor, ScaleFactor, is individual for every spectral slice instead of being fit as a common multiplier for all slices originating from the same spectrum.

In this model we consider the fact that with noisy and curved baselines it is difficult to correctly normalize the spectrum (so its peak area is unity). Therefore we fit linear baseline together with real line shape and then fit adjustment factor to scale simulated intensities to the data. This leads to ugly appearance of the raw data graph. One should use special plotting function instead, where spectral trace are scaled with ScaleFactor from each dataset.

ScaleFactor may be fit individually for each dataset or globally for all sets from the titration series.

This model may be universally used in place of U-model and U-model_LRcorrection. Simply set LB_a and LB_b to 0 and make them fixed---you get U-model LRcorrection model. Fix LRcorrection at 1 and you have U-model. If ScaleFactor is not set linked between all datasets---adds correction to normalization protocol.

WARNING: Fitting normalization factor for each spectrum individually may be a dangerous proposition. Fitting the baseline though is completely legitimate operation (if line shapes tails reach near baseline).

## Parameters

'Rtotal', 'LRratio', 'K_A', 'k_2_A', 'w0_1', 'w0_2', 'FWHH_1', 'FWHH_2', 'ScaleFactor ', 'LRcorrection', 'LB_a', 'LB_b'

## Source code

U_model_1D_LR_LB_SF.m