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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

By : Ivan Idris
2 (1)
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Numpy Beginner's Guide (Update)

Numpy Beginner's Guide (Update)

2 (1)
By: Ivan Idris

Overview of this book

This book is for the scientists, engineers, programmers, or analysts looking for a high-quality, open source mathematical library. Knowledge of Python is assumed. Also, some affinity, or at least interest, in mathematics and statistics is required. However, I have provided brief explanations and pointers to learning resources.
Table of Contents (16 chapters)
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14
C. NumPy Functions' References
15
Index

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 numbers:
    n = np.arange(1, 9)
    sqrt5 = np.sqrt(5)
    phi = (1 + sqrt5)/2
    fibonacci = np.rint((phi**n - (-1/phi)**n)/sqrt5)
    print("Fibonacci", fibonacci)

    The first eight Fibonacci numbers are as follows:

    Fibonacci [...

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