Description
Slides template Starting from this week, it is mandatory to submit a report of the exercises in the presentation format (slides). The maximum length is six slides, including:
- First slide: heading with your name, the date, exercise number and course name and year.
- Different sections, such as (if applicable)
- Theory: Explain very briefly the theory you have based your solution on.
- Code development: Introduce strategies, tests, and report debugging problems, compilations options.
- Results: Present data and explain your results.
- Upload the slide report in Moodle under the correspondent exercise.
- File names must include your name, exercise number and codewords SLIDES, and code. Example: Ex3-Rossi-SLIDES.pdf
Exercise 1: Scaling of the matrix-matrix multiplication
Consider the program developed in Exercise 3 of Week 1 (matrix-matrix multiplication).
- Write a python script that changes N between two values Nmin and Nmax, and launches the program.
- Store the results of the time needed in different files depending on the multiplication method used.
- Fit the scaling of the time needed for different methods as a function of the input size. Considerthe biggest possible difference between Nmin and Nmax.
- Plot the results for the different multiplication methods.
Exercise 2: Eigenproblem
Consider a random Hermitian matrix A of size N.
- Diagonalize A and store the N eigenvalues λi in crescent order.
- Compute the normalized spacings between eigenvaluessi = ∆λi/∆¯λ where
∆λi = λi+1− λi,
and ∆¯λ is the average ∆λi.
Exercise 3: Random Matrix Theory
Study P(s), the distribution of the si defined in the previous exercise, accumulating values of si from different random matrices of size at least N = 1000.
- Compute P(s) for a random HERMITIAN matrix.
- Compute P(s) for a DIAGONAL matrix with random real entries.
- Fit the corresponding distributions with the function:
P(s) = asα exp(−bsβ)
and report α,β,a,b.
Hint: if necessary neglect the first matrix eigenvalue.
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