Exercise 1: NumPy

1. Array creation and manipulation
   1. Create a 2D NumPy array of shape filled with random integers between 1 and 10.
   2. Extract the second row, third column element, and the diagonal elements.
   3. Reshape it into a 1D array of shape .
2. Linear algebra operations
   1. Generate two 3x3 matrices with random integers from 1 to 10 and perform element-wise and matrix-matrix multiplication.
   2. Create a 3x3 matrix with random values, compute its inverse and determinant.
3. Statistical analysis
   1. Generate a 1D NumPy array with 20 random integers between 1 and 100.
   2. Calculate the mean, median, standard deviation, and variance.

Exercise 2: SciPy (1/2)

1. Solving a linear system of equations

   1. Define a sparse tridiagonal matrix , with over the main diagonal, and over the first lower and upper diagonals.
   2. Let where
   3. Solve the linear system and compute the residual and the error in norm 1, 2 and infinity.

2. Function optimization

   1. Consider the function over the interval .
   2. Plot the function using Matplotlib to visually identify potential minima.
   3. Use scipy.optimize.minimize with different initial guesses to find these minima.

Exercise 2: SciPy (2/2)

3. Data interpolation and integration
   1. An electric vehicle charging station erogates the following series of energy measurements over time:

      time = np.arange(0, 46, 3) # Hours.
      energy = np.array([27.29, 23.20, 24.93, 28.72, 27.60, 19.06, 24.85, 21.54, 21.69, 23.23, 22.43, 26.36, 24.28, 22.36, 23.33, 23.00]) # kW.
      

   2. Use SciPy to build a cubic interpolator of these data points.
   3. Evaluate the interpolator over 1000 equispaced nodes between 0 and 45 and plot the values obtained.
   4. Integrate the interpolant over .

Exercise 3: pandas (1/2)

1. DataFrame operations and visualization

   1. Import the sales_data.csv dataset as a pandas DataFrame.
   2. Extract data from the 'South' region, sort them by descending 'Quantity' and add a new column 'Total revenue' 'Quantity' 'Price'.
   3. Visualize trends of 'Total revenue' by 'Date' (line plot) and by 'Product' (bar plot).

2. Exploratory data analysis with the iris dataset

   1. Load the iris dataset from seaborn.
   2. Group the data by 'species' and compute summary statistics for sepal_length and sepal_width.
   3. Use seaborn to plot the histogram of the sepal length distribution for each species.
   4. Use seaborn to generate a scatter plot of sepal width vs. sepal length.

Exercise 3: pandas (2/2)

3. Time series analysis with real data
   1. Import the weather_data.csv dataset.
   2. Resample the dataset to compute monthly averages.
   3. Computing a 7-day rolling mean.
   4. Visualize the original data and the rolling mean using line plots.

Exercise 4: designing a Neural Network for binary classification

1. Import the XORDataset from dataset.py.
2. Design a neural network in PyTorch that correctly classify the samples.
3. As a loss function, use nn.BCEWithLogitsLoss().

Exercise 5: code obfuscation

Without executing the program, determine the output of the code contained in wish.cpp.