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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
Step1:  1. Write a function that returns the Pythagorean triplet (a, b, c) given any two of the arguments a, b or c.
For example, triplet(a=3, c=5) will return (3, 4, 5).
Step3:  2. The $n^\text{th}$ Catalan number is given by 
$$
C_n = \prod_{k=2}^n  \frac{n+k}{k}
$$
for $n \ge 0$. 
Write a function to calculate the $n^\text{th}$ Catalan number - it should take a single argument $n$ and return $C_n$. Use this function to generate a list of the first 10 odd Catalan numbers (i.e., n = 1, 3, 5, ...).
Step4:  3. Rewrite the above function as a lambda function. This is tricky but introduces you to the functional  style that is very useful in advanced programming. Some imports are done for you as a hint.
Step6:  4.  Write a class called Matrix that can be initialized with an iterable of numbers, together with the number of rows r and the number of columns c. That is, you should be able to create a matrix M by calling M =  Matrix([1,2,3,4], 2, 2) (assume the matrix is row ordered). The Matrix class will have a single additional method called at that takes a tuple (r, c) and returns the value at row r and column c. For example, M.at(0,1) will return 2. Internally, the data should be stored as a list and the at method will use indexing to find the right value to return.
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Python Code:
import numpy as np
def triplet(a=None, b=None, c=None):
    Returns the Pythagoraen tripler (a, b, c) given any two arguments.
    
    Assumes but does not check that two named argumets are called.
    Retruns None if no triplet possible with given arguments.
    
    
    if a is None:
        q, r = divmod(np.sqrt(c**2 - b**2), 1)
        if r == 0:
            return int(q), b, c
    elif b is None:
        q, r = divmod(np.sqrt(c**2 - a**2), 1)
        if r == 0:
            return a, int(q), c
    else:
        q, r= divmod(np.sqrt(a**2 + b**2), 1)
        if r == 0:
            return a, b, int(q)
triplet(a=3, c=5)
triplet(a=3, b=5)
Explanation: 1. Write a function that returns the Pythagorean triplet (a, b, c) given any two of the arguments a, b or c.
For example, triplet(a=3, c=5) will return (3, 4, 5).
End of explanation
def catalan(n):
    Returns the nth Catalan number.
    
    ans = 1
    for k in range(2, n+1):
        ans *= (n+k)/k
    return ans
[catalan(n) for n in range(1, 10, 2)]
Explanation: 2. The $n^\text{th}$ Catalan number is given by 
$$
C_n = \prod_{k=2}^n  \frac{n+k}{k}
$$
for $n \ge 0$. 
Write a function to calculate the $n^\text{th}$ Catalan number - it should take a single argument $n$ and return $C_n$. Use this function to generate a list of the first 10 odd Catalan numbers (i.e., n = 1, 3, 5, ...).
End of explanation
from functools import reduce
from operator import mul
catalan_L = lambda n: reduce(mul, ((n+k)/k for k in range(2, n+1)), 1)
[catalan_L(n) for n in range(1, 10, 2)]
Explanation: 3. Rewrite the above function as a lambda function. This is tricky but introduces you to the functional  style that is very useful in advanced programming. Some imports are done for you as a hint.
End of explanation
class Matrix:
    Simple class to represent a matrix.
    
    def __init__(self, xs, rows, cols):
        self.xs = list(xs)
        self.rows = rows
        self.cols = cols  
            
    def at(self, i, j):
        idx = i*self.cols + j
        return self.xs[idx]
M =  Matrix([1,2,3,4], 2, 2)
M.at(0,1)
Explanation: 4.  Write a class called Matrix that can be initialized with an iterable of numbers, together with the number of rows r and the number of columns c. That is, you should be able to create a matrix M by calling M =  Matrix([1,2,3,4], 2, 2) (assume the matrix is row ordered). The Matrix class will have a single additional method called at that takes a tuple (r, c) and returns the value at row r and column c. For example, M.at(0,1) will return 2. Internally, the data should be stored as a list and the at method will use indexing to find the right value to return.
End of explanation
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