Summation using a for loop and putting data into a matrix

1. Consider the model y(t)=tan(u*0.9*pi/2) evaluated for the inputs u= linspace(0,1,N). Use the model structure: 1

y_hat = sum from i = 0 to n of theta*u^i

to describe these data. Note that this is a nonlinear model that is linear-in-the- parameters ?.

• Generate a dataset of y based on the model. N = 100.
• Create a Matlab script that solves for varying orders of the model structure (n varies from 1 to 20). Make sure to save the different parameters (n = 1 will have 2 parameters in theta, n = 2 will have 3, and so on).
• Plot the estimated output ?- for n = 1, 5, 10 and 15 as well as the true output (from the model) on a single plot.

I hope this makes sense

I am able to create the summation using a for loop, but I don't know how to put it into a matrix. My professor said something about concatinating the data so that we end up with a 100x21 matrix, with all 1's being in the first column and the calculate "u" value is going across.

[Allen]

Here a link to the MATLAB's reference page for array (aka. matrix) indexing. It explains the general concept of how to access single elements, rows, or columns of an array.

https://www.mathworks.com/help/matlab/learn_matlab/array-indexing.html

Another resource for creating and concatenating arrays.

https://www.mathworks.com/help/matlab/math/creating-and-concatenating-matrices.html

[Mohammad Sami]

A good starting point to learn Matlab is to complete Matlab Onramp course.

https://www.mathworks.com/learn/tutorials/matlab-onramp.html