NumPy : Beginner's Guide - Third Edition

Time for action – computing Fibonacci numbers

A matrix can represent the Fibonacci recurrence relation. We can express the calculation of Fibonacci numbers as a repeated matrix multiplication:

1. Create the Fibonacci matrix as follows:

   F = np.matrix([[1, 1], [1, 0]])
   print("F", F)

   The Fibonacci matrix appears as follows:

   F [[1 1]
     [1 0]]
   

2. Calculate the 8th Fibonacci number (ignoring 0), by subtracting 1 from 8 and taking the power of the matrix. The Fibonacci number then appears on the diagonal:

   print("8th Fibonacci", (F ** 7)[0, 0])

   The Fibonacci number is as follows:

   8th Fibonacci 21
   

3. The golden ratio formula, better known as Binet's formula, allows us to calculate Fibonacci numbers with a rounding step at the end. Calculate the first eight Fibonacci ...