assignment three cs | Python Fiddle

#Problem 1:

#part a
def scale(s, v):
    sub = []
    for i in range(0, len(v)):
        sub.append(v[i])
        
    
    for element in range(0, len(sub)):
        sub[element] = sub[element] * s
    return sub

#part b

def norm(v):
    norm = 0
    for i in v:
        norm += i**2
    norm = norm**0.5
    return norm

#part c

def dot(v, w):
    dot = 0
    if len(v) != len(w):
        return "None"
    for i in range(len(v)):
        dot+= v[i] * w[i]
    return dot
#For dot((1,2), (3,4)), this program performs 2 multiplication operations and 2 addition operations.
#For dot((5,1,0), (1,1,2)), this program performs 3 multiplication operations and 3 addition operations.
#For dot((5,1,0,4), (1,2), this program performs 0 multiplication operations and 0 addition operations.

#part d

def orthagonal(v, w):
    
    if dot(v, w) == 0:
        return True
    elif dot(v, w) == "None":
    	return "None"
    else:
        return False

#part e
#A projection is (v * u/norm(u)) * u/norm(u)

def proj(u, v):
    return scale((1/(norm(v)**2)) * dot(u, v), v)

#Problem 2

#part a

def multTest(u, v):
    w = [((u[0][0]*v[0][0]+u[0][1]*v[1][0]), (u[0][0]*v[0][1]+ u[0][1]*v[1][1])) , ((u[1][0]*v[0][0]+u[1][1]*v[1][0]), (u[1][0]*v[0][1]+u[1][1]*v[1][1]))]
    return w

def tupleToMatrix(u):
    final = []
    for i in range(len(u)):
    	final.append(u[i])
    return final

def tupleOfTuplesToMatrix(u):
    final = []
    for i in range(len(u)):
        final.append(tupleToMatrix(u[i]))
    return final
def mult(u, v):
    x =  tupleOfTuplesToMatrix(u)
    y = tupleOfTuplesToMatrix(v)
    final = [[0 for i in range(len(x))] for j in range(len(y[0]))]
    
    for i in range(len(final)):
        for j in range(len(final[i])):
            
            yCol = [0 for i in range(len(final[i]))]
            
            for k in range(len(y)):
                print yCol
                yCol[k] = y[k][j]
            
            final[i][j] = dot(x[i], yCol)
            
			
#part b

mult(((1,2),(3,4)), ((-5,-6),(7,8)))

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