# Sample Code
## This file implements common matrix operations

`# Packages
import numpy as np
import random`

def NMatrix(N):
    """
    This functions generates an N*N size matrix with randome numbers
    """
    
    Parameters
    ----------
    N
        dimension of the matrix to create
    
    Returns
    -------
    2D array of the N * N matrix
    """
    # Elements in the matrix are normally distributed with mean 0 
    #  and standard deviation 1
    matrix = [[random.normalvariate(0, 1) for _ in range(N)] 
              for _ in range(N)]
    print(matrix)
    return matrix

def NMatrix(N):
    """
    This functions uses numpy to generate an N*N size matrix with 
    randome numbers
    
    Parameters
    ----------
    N
        dimension of the matrix to create
    
    Returns
    -------
    2D array of the N * N matrix
    """
    # Elements in the matrix are normally distributed with mean 0 
    #  and standard deviation 1
    matrix = np.random.normal(0, 1, size = (N, N))
    matrix = matrix.tolist()
    print(matrix)
    return matrix

def addMatricesNP(A, B):
    """
    This function performs 2 matrices addition
    Passed in matrices are all valid matrices
    
    Parameters
    ----------
    A
        The first matrix
    B
        The second matrix
    
    Returns
    -------
    Sum Matrix when two matrices have compatible size
    -1 otherwise
    """
    
    # Check whether 2 matrices have same size
    if len(A) != len(B):
        return -1
    
    if len(A) and len(A[0]) != len(B[0]):
        return -1
    
    rowNum = len(A)
    colNum = len(A[0])
    
    res = [[0 for _ in range(colNum)] for _ in range(rowNum)]
    
    for i in range(rowNum):
        for j in range(colNum):
            res[i][j] = A[i][j] + B[i][j]
    
    return res

def addMatricesNP(A, B):
    """
    This function performs 2 matrices addition with numPy
    Passed in matrices are all valid matrices
    
    Parameters
    ----------
    A
        The first matrix
    B
        The second matrix
    
    Returns
    -------
    Sum Matrix when two matrices have compatible size
    -1 otherwise
    """
    # Convert to numPy array
    A = np.array(A)
    B = np.array(B)
    
    # Check whether size compatibility
    if A.shape != B.shape:
        return -1
    res = (A + B).tolist()
    
    return res

def dotProduct(A, B):
    """
    Calculate dot product of two vectors
    
    Parameters
    ----------
    A
        The first vector
    B
        The second vector
    
    Returns
    -------
    Dot product when two vectors have the same size
    -1 otherwise
    """
    
    if len(A) != len(B):
        return -1
    
    dotProduct = 0
    for i in range(len(A)):
        dotProduct += A[i] * B[i]
        
    return dotProduct

def dotProductNP(A, B):
    """
    Calculate dot product of two vectors using NumPy
    
    Parameters
    ----------
    A
        The first vector
    B
        The second vector
    
    Returns
    -------
    Dot product when two vectors have the same size
    -1 otherwise
    """
    A = np.array(A)
    B = np.array(B)
    if A.shape != B.shape:
        return -1
    
    dotProduct = np.dot(A, B).tolist()
        
    return dotProduct

def matrixProduct(A, B):
    """
    Calculate matrix vector product of two matrices
    
    Parameters
    ----------
    A
        The first matrix
    B
        The second matrix
    
    Returns
    -------
    Matrix vector product when the column number 
    of A equals row number of B
    otherwise -1
    """
        
    rowA, colA = len(A), len(A[0])
    rowB, colB = len(B), len(B[0])
    
    if colA != rowB:
        return -1
    
    res = [[0 for _ in range(colB)] for _ in range(rowA)]
    
    for i in range(rowA):
        for j in range(colB):
            for k in range(colA):
                res[i][j] += A[i][k] * B[k][j]

    return res

def matrixProductNP(A, B):
    """
    Calculate matrix vector product of two matrices 
    with NumPy
    
    Parameters
    ----------
    A
        The first matrix
    B
        The second matrix
    
    Returns
    -------
    Matrix vector product when the column number 
    of A equals row number of B
    otherwise -1
    """
    A = np.array(A)
    B = np.array(B)
    
    if A.shape[1] != B.shape[0]:
        return -1
    
    res = np.dot(A, B).tolist()
    return res

def transpose(matrix):
    """
    Obtain the transpose of the given matrix
    
    Parameters
    ----------
    matrix
        Input matrix to be transposed
    
    Returns
    -------
    The transposed matrix
    """
    res = [[matrix[j][i] for j in range(len(matrix))] 
           for i in range(len(matrix[0]))]
    return res

def transposeNP(matrix):
    """
    Obtain the transpose of the given matrix with NumPy
    
    Parameters
    ----------
    matrix
        Input matrix to be transposed
    
    Returns
    -------
    The transposed matrix
    """
    res = np.array(matrix).T.tolist()
    return res