Coding the Matrix Week 1 The vector 作業

Coding the Matrix: Linear Algebra through
Computer Science Applications 

  這次作業難度不小，第一個作業hw1還好，第二個全部都可以使用comprehension完成，但要小心傳回值，還有深入理解本課程中的vector的概念。第三個作業難度不大，但一不小心就做錯了，一個原因是grader不夠智能，另一個原因就是細節問題了，比如某個函數的參數必須是set而不能是list。

  這次作業總共花了大約7個小時，Making me gong Nut! 不過還學到了提交作業時的一個技巧，就是：

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

  使用這個命令可以看到提交作業時何處出錯，方便檢查。

  下面是三個子作業的代碼：

#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]

  第二個：

  在這個作業中comprehension很重要

#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())

  第三個：

  使用帶lambda的max可以用到

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)