Dynamic Correction Factor Adjustment in Matlab to Match Slope (Power) in Log-Log Plot

Hello everyone,

I am working on a data analysis task where I need to dynamically adjust a correction factor for a dataset to match a specific slope in a log-log plot. The dataset consists of two main columns: Time (s) and Corrected Data (Factor 0.98578). My objective is to apply a rolling correction factor to the Corrected Data (Factor 0.98578) such that its slope in a log-log plot matches the slope of a reference dataset (which I have as Corrected Data (Factor 0.98578)).

• Dynamic Adjustment: The correction factor should start with a 0.98578 and decrease dynamically over time to ensure the slope of the corrected Corrected Data (Factor 0.98578) aligns with the target slope (not necessarly).

I am seeking advice or suggestions on how to implement this in Matlab. Any guidance on formulas, functions, or scripting approaches that could effectively handle this task would be greatly appreciated.

Thank you in advance for your help!

Answer 1

[Suraj Kumar]

Hi Trung,

To dynamically adjust a correction factor and match a specific slope in a log-log plot, you can follow these steps and the attached code snippets:

1. Load the data using the “readtable” function and compute the initial slope. The initial slope is computed using “polyfit” function which performs a linear fit and returns the slope.

data = readtable('Data.xlsx'); 
log_time = log10(time); 
log_corrected_data = log10(corrected_data); 
initial_slope = polyfit(log_time, log_corrected_data, 1); 

2. Define the target slope, initial factor and parameters for iterative adjustment process.

target_slope = -1;  
correction_factor = initial_factor; 
num_iterations = 1000; 
step_size = 0.0001; 

3. Iterate through and scale the correction factor in each iteration and recalculate the slope till it matches the target slope.

for i = 1:num_iterations 
    adjusted_data = corrected_data * correction_factor; 
    log_adjusted_data = log10(adjusted_data); 
    current_slope = polyfit(log_time, log_adjusted_data, 1); 
    if abs(current_slope(1) - target_slope) < 1e-5 
        break; 
    end 
    if current_slope(1) > target_slope 
        correction_factor = correction_factor - step_size; 
    else 
        correction_factor = correction_factor + step_size; 
    end 
end 

4. Plot the original and the adjusted data on a “log-log” scale to visualize the effect of correction factor adjustment.

figure; 
loglog(time, corrected_data, 'b', 'DisplayName', 'Original    Data'); 
hold on; 
loglog(time, adjusted_data, 'r', 'DisplayName', 'Adjusted  Data'); 

Refer to the attached plot for a clear understanding:

For more details on the “polyfit” function or the “log-log” plot, please refer to the documentation linked below:

• https://www.mathworks.com/help/matlab/ref/polyfit.html
• https://www.mathworks.com/help/matlab/ref/loglog.html

Happy Coding!