MATLAB and R Programming (ME-705) - Important Questions

Write an M-file that reads an $n \times n$ matrix, extracts its main diagonal and returns the sum of diagonal elements (handle complex entries).

Write an M-file that takes a character vector (string) of ASCII characters, converts each character to its ASCII code, shifts each code by 3 (Caesar cipher), handles wrap-around for letters, and returns the encoded string.

Using MATLAB, demonstrate creation of matrices using the colon operator, linspace, zeros, ones, and eye. Perform matrix addition, element-wise multiplication, matrix multiplication, compute inverse and determinant for a square matrix, and explain the difference between element-wise and matrix operations. Provide short code examples for each operation.

In MATLAB, plot the parametric curve $x=\cos(t)$, $y=\sin(2t)$ for $t\in\left[0,2\pi\right]$. Label the axes, add a title and legend, and set an appropriate line style and marker.

In MATLAB, generate a random complex vector $z$ of length 100, compute the sum $\sum z$, compute the mean and standard deviation of real and imaginary parts, and plot $\operatorname{real}(z)$ versus $\operatorname{imag}(z)$. Provide the script and explain each step.

Explain the basic MATLAB environment and commonly used commands: help, doc, who, whos, clear, clc, and workspace operations. Demonstrate with a short script that creates variables, lists them, clears one variable, and saves the workspace to a .mat file.

Explain differences between MATLAB matrices and R data frames. Provide short examples in MATLAB and in R showing the creation of a numeric matrix in MATLAB and an equivalent data frame in R, and state scenarios where each structure is preferable.

Using R, create a data frame with one numeric column and one factor column. Show R code to append a new row and subset the data frame to include only rows where the factor has a specified level. Explain issues that may arise with factor levels when appending rows.

Write a MATLAB script to generate a 3-D surface plot of $z=\sin\left(\sqrt{x^2 + y^2}\right)$ over $x,y\in\left[-6,6\right]$ using meshgrid and surf. Include axis labels and a colorbar.