Coding the matrix week 1 the vector job

Coding the matrix: Linear Algebra through
Computer Science Applications

This assignment is not difficult. The first job hw1 is fine, and the second job can all be completed using comprehension. However, be careful about the returned values and have a deep understanding of the concept of Vector in this course. The third task is not difficult, but it is wrong when you are not careful. One reason is that grader is not smart enough, and the other reason is that the details are incorrect, for example, the parameter of a function must be set rather than list.

It took about 7 hours for this assignment, making me gong nut! However, I also learned the following skills when submitting a job:

C:\Python33\python C:\Python33\submit_politics_lab.py --verbose

You can use this command to see where an error occurred when submitting a job.

The code for the three sub-jobs is as follows:

#hw1# Please fill out this stencil and submit using the provided submission script.from GF2 import one## Problem 1p1_u = [ 0, 4]p1_v = [-1, 3]p1_v_plus_u = [-1,7]p1_v_minus_u = [-1,-1]p1_three_v_minus_two_u = [-3,1]## Problem 2p2_u = [-1,  1, 1]p2_v = [ 2, -1, 5]p2_v_plus_u = [1,0,6]p2_v_minus_u = [3,-2,4]p2_two_v_minus_u = [5,-3,9]p2_v_plus_two_u = [0,1,7]## Problem 3# Write your answer using GF2's one instead of the number 1p3_vector_sum_1 = [one,0,0]p3_vector_sum_2 = [0,one,one]## Problem 4# Please express your solution as a set of the letters corresponding to the solutions.# For example, {'a','b','c'} is the subset consisting of:#   a (1100000), b (0110000), and c (0011000).# Leave an empty set if it cannot be expressed in terms of the other vectors.u_0010010 = {'c','d','e'}u_0100010 = {'b','c','d','e'}## Problem 5# Use the same format as the previous problemv_0010010 = {'c','d'}v_0100010 = set()## Problem 6uv_a = sum([5,0])uv_b = sum([x*y for x,y in zip([0,1],[12345,6])])uv_c = sum([x*y for x,y in zip([-1,3],[5,7])])uv_d =sum([-1/2,-1/2])## Problem 7# use 'one' instead of '1'x_gf2 = [one,0,0,0]## Problem 8v1 = [2,3,-4,1]v2 = [1,-5,2,0]v3 = [4,1,-1,-1]

Second:

Comprehension is very important in this job.

#vec.pydef getitem(v,d):    "Returns the value of entry d in v"    assert d in v.D    return v.f[d] if d in v.f else 0def setitem(v,d,val):    "Set the element of v with label d to be val"    assert d in v.D    v.f[d]=valdef equal(u,v):    "Returns true iff u is equal to v"    assert u.D == v.D    return {getitem(u,x)==getitem(v,x) for x in v.D}=={True}def add(u,v):    "Returns the sum of the two vectors"    assert u.D == v.D    return Vec(u.D,{x:getitem(u,x)+getitem(v,x) for x in v.D})def dot(u,v):    "Returns the dot product of the two vectors"    assert u.D == v.D    return sum([getitem(u,x)*getitem(v,x) for x in v.D])def scalar_mul(v, alpha):    "Returns the scalar-vector product alpha times v"    return Vec(v.D,{x:alpha*v.f[x] for x in v.f.keys()})def neg(v):    "Returns the negation of a vector"    return Vec(v.D,{x:-y for x,y in v.f.items()})##### NO NEED TO MODIFY BELOW HERE #####class Vec:    """    A vector has two fields:    D - the domain (a set)    f - a dictionary mapping (some) domain elements to field elements        elements of D not appearing in f are implicitly mapped to zero    """    def __init__(self, labels, function):        self.D = labels        self.f = function    __getitem__ = getitem    __setitem__ = setitem    __neg__ = neg    __rmul__ = scalar_mul #if left arg of * is primitive, assume it's a scalar    def __mul__(self,other):        #If other is a vector, returns the dot product of self and other        if isinstance(other, Vec):            return dot(self,other)        else:            return NotImplemented  #  Will cause other.__rmul__(self) to be invoked    def __truediv__(self,other):  # Scalar division        return (1/other)*self    __add__ = add    def __radd__(self, other):        "Hack to allow sum(...) to work with vectors"        if other == 0:            return self        def __sub__(a,b):         "Returns a vector which is the difference of a and b."         return a+(-b)    __eq__ = equal    def __str__(v):        "pretty-printing"        try:            D_list = sorted(v.D)        except TypeError:            D_list = sorted(v.D, key=hash)        numdec = 3        wd = dict([(k,(1+max(len(str(k)), len('{0:.{1}G}'.format(v[k], numdec))))) if isinstance(v[k], int) or isinstance(v[k], float) else (k,(1+max(len(str(k)), len(str(v[k]))))) for k in D_list])        # w = 1+max([len(str(k)) for k in D_list]+[len('{0:.{1}G}'.format(value,numdec)) for value in v.f.values()])        s1 = ''.join(['{0:>{1}}'.format(k,wd[k]) for k in D_list])        s2 = ''.join(['{0:>{1}.{2}G}'.format(v[k],wd[k],numdec) if isinstance(v[k], int) or isinstance(v[k], float) else '{0:>{1}}'.format(v[k], wd[k]) for k in D_list])        return "\n" + s1 + "\n" + '-'*sum(wd.values()) +"\n" + s2    def __repr__(self):        return "Vec(" + str(self.D) + "," + str(self.f) + ")"    def copy(self):        "Don't make a new copy of the domain D"        return Vec(self.D, self.f.copy())

Third:

Maxcompute with Lambda can be used.

voting_data = list(open("voting_record_dump109.txt"))## Task 1def create_voting_dict():    """    Input: None (use voting_data above)    Output: A dictionary that maps the last name of a senator            to a list of numbers representing the senator's voting            record.    Example:         >>> create_voting_dict()['Clinton']        [-1, 1, 1, 1, 0, 0, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1]    This procedure should return a dictionary that maps the last name    of a senator to a list of numbers representing that senator's    voting record, using the list of strings from the dump file (strlist). You    will need to use the built-in procedure int() to convert a string    representation of an integer (e.g. '1') to the actual integer    (e.g. 1).    You can use the split() procedure to split each line of the    strlist into a list; the first element of the list will be the senator's    name, the second will be his/her party affiliation (R or D), the    third will be his/her home state, and the remaining elements of    the list will be that senator's voting record on a collection of bills.    A "1" represents a 'yea' vote, a "-1" a 'nay', and a "0" an abstention.    The lists for each senator should preserve the order listed in voting data.     """    return {x.split()[0]:[int(y) for y in x.split()[3:]] for x in voting_data}     ## Task 2def policy_compare(sen_a, sen_b, voting_dict):    """    Input: last names of sen_a and sen_b, and a voting dictionary mapping senator           names to lists representing their voting records.    Output: the dot-product (as a number) representing the degree of similarity            between two senators' voting policies    Example:        >>> voting_dict = {'Fox-Epstein':[-1,-1,-1,1],'Ravella':[1,1,1,1]}        >>> policy_compare('Fox-Epstein','Ravella', voting_dict)        -2    """    return sum([x*y for (x,y) in zip(voting_dict[sen_a],voting_dict[sen_b])])## Task 3def most_similar(sen, voting_dict):    """    Input: the last name of a senator, and a dictionary mapping senator names           to lists representing their voting records.    Output: the last name of the senator whose political mindset is most            like the input senator (excluding, of course, the input senator            him/herself). Resolve ties arbitrarily.    Example:        >>> vd = {'Klein': [1,1,1], 'Fox-Epstein': [1,-1,0], 'Ravella': [-1,0,0]}        >>> most_similar('Klein', vd)        'Fox-Epstein'    Note that you can (and are encouraged to) re-use you policy_compare procedure.    """        max_sen=sen    max_sim=-len(voting_dict[sen])    for x in voting_dict.keys():        if not x==sen:            sim_x=policy_compare(sen, x, voting_dict)        if sim_x>max_sim:            max_sim=sim_x            max_sen=x    return max_sen    ## Task 4def least_similar(sen, voting_dict):    """    Input: the last name of a senator, and a dictionary mapping senator names           to lists representing their voting records.    Output: the last name of the senator whose political mindset is least like the input            senator.    Example:        >>> vd = {'Klein': [1,1,1], 'Fox-Epstein': [1,-1,0], 'Ravella': [-1,0,0]}        >>> least_similar('Klein', vd)        'Ravella'    """    min_sen=sen    sim_x=0    min_sim=len(voting_dict[sen])    for x in voting_dict.keys():        if not x==sen:            sim_x=policy_compare(sen, x, voting_dict)        if sim_x<min_sim:            min_sim=sim_x            min_sen=x    return min_sen        ## Task 5most_like_chafee    = 'Jeffords'least_like_santorum = 'Feingold' # Task 6def find_average_similarity(sen, sen_set, voting_dict):    """    Input: the name of a senator, a set of senator names, and a voting dictionary.    Output: the average dot-product between sen and those in sen_set.    Example:        >>> vd = {'Klein': [1,1,1], 'Fox-Epstein': [1,-1,0], 'Ravella': [-1,0,0]}        >>> find_average_similarity('Klein', {'Fox-Epstein','Ravella'}, vd)        -0.5    """    sum=0    for x in sen_set:        sum+=policy_compare(sen, x, voting_dict)    return sum/len(sen_set)most_average_Democrat = 'Smith' # give the last name (or code that computes the last name)# Task 7def find_average_record(sen_set, voting_dict):    """    Input: a set of last names, a voting dictionary    Output: a vector containing the average components of the voting records            of the senators in the input set    Example:         >>> voting_dict = {'Klein': [-1,0,1], 'Fox-Epstein': [-1,-1,-1], 'Ravella': [0,0,1]}        >>> find_average_record({'Fox-Epstein','Ravella'}, voting_dict)        [-0.5, -0.5, 0.0]    """    t=[]    tmp=sen_set.pop()    sen_set=sen_set|{tmp}    for x in range(len(voting_dict[tmp])):        t.append(sum([voting_dict[y][x]for y in sen_set])/len(sen_set))    return t#voting_dict=create_voting_dict()#democrats=[x.split()[0] for x in voting_data if x.split()[1]=='D']#average_Democrat_record = set(find_average_record(democrats, voting_dict))average_Democrat_record = [-0.16279069767441862, -0.23255813953488372, 1.0, 0.8372093023255814, 0.9767441860465116, -0.13953488372093023, -0.9534883720930233, 0.813953488372093, 0.9767441860465116, 0.9767441860465116, 0.9069767441860465, 0.7674418604651163, 0.6744186046511628, 0.9767441860465116, -0.5116279069767442, 0.9302325581395349, 0.9534883720930233, 0.9767441860465116, -0.3953488372093023, 0.9767441860465116, 1.0, 1.0, 1.0, 0.9534883720930233, -0.4883720930232558, 1.0, -0.32558139534883723, -0.06976744186046512, 0.9767441860465116, 0.8604651162790697, 0.9767441860465116, 0.9767441860465116, 1.0, 1.0, 0.9767441860465116, -0.3488372093023256, 0.9767441860465116, -0.4883720930232558, 0.23255813953488372, 0.8837209302325582, 0.4418604651162791, 0.9069767441860465, -0.9069767441860465, 1.0, 0.9069767441860465, -0.3023255813953488] # (give the vector)# average_Democrat_record = [-0.162791, -0.232558, 1.000000, 0.837209, 0.976744, -0.139535, -0.953488, 0.813953, 0.976744, 0.976744, 0.906977, 0.767442, 0.674419, 0.976744, -0.511628, 0.930233, 0.953488, 0.976744, -0.395349, 0.976744, 1.000000, 1.000000, 1.000000, 0.953488, -0.488372, 1.000000, -0.325581, -0.069767, 0.976744, 0.860465, 0.976744, 0.976744, 1.000000, 1.000000, 0.976744, -0.348837, 0.976744, -0.488372, 0.232558, 0.883721, 0.441860, 0.906977, -0.906977, 1.000000, 0.906977, -0.302326]# Task 8def bitter_rivals(voting_dict):    """    Input: a dictionary mapping senator names to lists representing           their voting records    Output: a tuple containing the two senators who most strongly            disagree with one another.    Example:         >>> voting_dict = {'Klein': [-1,0,1], 'Fox-Epstein': [-1,-1,-1], 'Ravella': [0,0,1]}        >>> bitter_rivals(voting_dict)        ('Fox-Epstein', 'Ravella')    """    tx=0    ty=0    sums=len(voting_dict[list(voting_dict.keys())[0]])    for x in voting_dict.keys():        y=least_similar(x, voting_dict)        min_s=policy_compare(x, y, voting_dict)        if min_s<sums:            sums=min_s            tx=x            ty=y    return (tx, ty)