================ numpy: Exercises ================ #. Implement a function that takes a ``d`` dimensional vector ``x`` returns their Euclidean norm. .. hint:: The Euclidean norm of a vector is the square root of its dot product with itself. #. Implement a function that takes two ``d`` dimensional vectors ``x`` and ``z`` and returns their Euclidean distance. .. hint:: Can you re-use the solution of the previous exercise? #. Implement a function that takes a matrix ``A`` and an integer ``k``, and returns ``A`` elevated to the ``k`` th power. #. Write a Python program that plots the data here:: https://drive.google.com/open?id=0B0wILN942aEVVlk4TS1WaDItVU0 Every row has an experiment ID and a value; there are 10 experiments, and 100 values (rows) per experiment. For each experiment, plot its values as a time series. The plot the average time series, i.e. the average curve, where the average is taken over all experiments. .. hint:: Use ``matplotlib.pyplot`` and the ``plot(x, y)`` function, as done in the examples above, to plot the ten curves and their mean. #. Implement the Power Iteration method for finding the largest eigenvalue and eigenvector of a matrix, as described in the first paragraph of: https://en.wikipedia.org/wiki/Power_iteration#The_method Check that it matches the results given by the ``eig()`` method of the ``linalg`` module. #. Implement the Gram-Schmidt orthogonalization routine, described here: https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process #. Given the *iris dataset*, compute the covariance matrix of the petal lenght and petal widht for the *iris setosa* rows. .. hint:: The covariance matrix is defined here: https://en.wikipedia.org/wiki/Covariance_matrix