Linear_Algebra_with_numpy.py

'''In the upcoming weeks you will have to implement different assignments in Python. For linear algebra calculations 
in Python you can use NumPy. We provide a subset of the NumPy functionality, which is sufficient to solve the 
different tasks. A complete list of the supported functions can be found in the wiki. If you find errors in the 
behavior of our NumPy implementation feel free to post them in the forum.

In the code editor below you find a couple of examples demonstrating basic linear algebra calculations in NumPy.'''


import numpy as np

def run():
    # create a column vector
    col_vec = np.array([[1], [2]])
    print "column vector"
    print col_vec
    
    # create a row vector
    row_vec = np.array([[1, 2]])
    print "row vector"
    print row_vec
    
    # create a matrix
    mat = np.array([[1, 2], [3, 4]])
    print "matrix"
    print mat
    
    # inspect dimensions
    print "row vector dimensions", row_vec.ndim
    shape = row_vec.shape
    print "row vector rows", shape[0], "columns", shape[1]
    
    print "matrix dimensions", mat.ndim
    shape = mat.shape
    print "matrix rows", shape[0], "columns", shape[1]
    
    # transpose
    vec_t = row_vec.transpose() # or row_vec.T
    print "transposed vector"
    print vec_t
    
    mat_t = mat.transpose() # or mat.T
    print "transposed matrix"
    print mat_t
    
    a = np.array([[2], [-4], [1]])
    b = np.array([[2], [1], [-2]])
    
    # addition 
    print "a + b"
    print a + b
    
    # subtraction
    print "a - b"
    print a - b
    
    # scalar multiplication
    print "1.2 * a"
    print 1.2 * a
    
    # element wise multiplication
    print "a * b"
    print a * b    
    
    # vector scalar product
    print "a . b"
    print np.dot(a.transpose(), b)
    
    # vector cross product
    print "a x b"
    print np.cross(a, b, axis=0) # or np.cross(a.T, b.T).T
    
    identity = np.array([[1, 0], [0, 1]])
    
    # matrix vector product
    print "identity . col_vec"
    print np.dot(identity, col_vec)
    
    # matrix product
    print "identity . mat"
    print np.dot(identity, mat)