Coding the Matrix Week 3 The Matrix 矩阵
本周共有三次作业。所花费的时间为一天左右，还算可以，需要注意的是考虑一些特殊情况，写出能够通用的程序，这就行了。
体会
set()和{}结果相同，可以通用，可以采取后者。
[python]
>>> type({})
<class 'dict'>
>>> type(set())
<class 'set'>
>>> type(dict())
<class 'dict'>
>>> {}==set()
False
>>> {}==dict()
True
>>> type({})
<class 'dict'>
>>> type(set())
<class 'set'>
>>> type(dict())
<class 'dict'>
>>> {}==set()
False
>>> {}==dict()
True 作业1 hw3
这一节讲的是矩阵的运算。值得注意的是左乘和右乘稀疏矩阵的意义，和矩阵求逆的方法和线性方程组的通解。
左乘矩阵，对于这个稀疏矩阵的任意点（i,j），相当于把矩阵第j行加到结果的i行。右乘矩阵，对于点（i,j），相当于把矩阵第i列加到结果的j列。用来计算包含稀疏矩阵的乘法十分方便。
代码如下
[python]
# version code 893
# Please fill out this stencil and submit using the provided submission script.
from mat import Mat
from vec import Vec
from matutil import *
## Problem 1
# Please represent your solutions as lists.
vector_matrix_product_1 = [1,0]
vector_matrix_product_2 = [0,4.44]
vector_matrix_product_3 = [14,20,26]
## Problem 2
# Represent your solution as a list of rows.
# For example, the identity matrix would be [[1,0],[0,1]].
M_swap_two_vector = [[0,1],[1,0]]
## Problem 3
three_by_three_matrix = [[1,0,1],[0,1,0],[1,0,0]] # Represent with a list of rows lists.
## Problem 4
multiplied_matrix = [[2,0,0],[0,4,0],[0,0,3]] # Represent with a list of row lists.
## Problem 5
# Please enter a boolean representing if the multiplication is valid.
# If it is not valid, please enter None for the dimensions.
part_1_valid = False # True or False
part_1_number_rows = None # Integer or None
part_1_number_cols = None # Integer or None
part_2_valid = False
part_2_number_rows = None
part_2_number_cols = None
part_3_valid = True
part_3_number_rows = 1
part_3_number_cols = 2
part_4_valid = True
part_4_number_rows = 2
part_4_number_cols = 1
part_5_valid = False
part_5_number_rows = None
part_5_number_cols = None
part_6_valid = True
part_6_number_rows = 1
part_6_number_cols = 1
part_7_valid = True
part_7_number_rows = 3
part_7_number_cols = 3
## Problem 6
# Please represent your answer as a list of row lists.
small_mat_mult_1 = [[8,13],[8,14]]
small_mat_mult_2 = [[24,11,4],[1,3,0]]
small_mat_mult_3 = [[3,13]]
small_mat_mult_4 = [[14]]
small_mat_mult_5 = [[1,2,3],[2,4,6],[3,6,9]]
small_mat_mult_6 = [[-2,4],[1,1],[1,-3]]
## Problem 7
# Please represent your solution as a list of row lists.
part_1_AB = [[5,2,0,1],[2,1,-4,6],[2,3,0,-4],[-2,3,4,0]]
part_1_BA = [[1,-4,6,2],[3,0,-4,2],[3,4,0,-2],[2,0,1,5]]
part_2_AB = [[5,1,0,2],[2,6,-4,1],[2,-4,0,3],[-2,0,4,3]]
part_2_BA = [[3,4,0,-2],[3,0,-4,2],[1,-4,6,2],[2,0,1,5]]
part_3_AB = [[1,0,5,2],[6,-4,2,1],[-4,0,2,3],[0,4,-2,3]]
part_3_BA = [[3,4,0,-2],[1,-4,6,2],[2,0,1,5],[3,0,-4,2]]
## Problem 8
# Please represent your answer as a list of row lists.
# Please represent the variables a and b as strings.
# Represent multiplication of the variables, make them one string.
# For example, the sum of 'a' and 'b' would be 'a+b'.
matrix_matrix_mult_1 = [[1,'a+b'],[0,1]]
matrix_matrix_mult_2_A2 = [[1,2],[0,1]]
matrix_matrix_mult_2_A3 = [[1,3],[0,1]]
# Use the string 'n' to represent variable the n in A^n.
matrix_matrix_mult_2_An = [[1,'n'],[0,1]]
## Problem 9
# Please represent your answer as a list of row lists.
your_answer_a_AB = [[0,0,2,0],[0,0,5,0],[0,0,4,0],[0,0,6,0]]
your_answer_a_BA = [[0,0,0,0],[4,4,4,0],[0,0,0,0],[0,0,0,0]]
your_answer_b_AB = [[0,2,-1,0],[0,5,3,0],[0,4,0,0],[0,6,-5,0]]
your_answer_b_BA = [[0,0,0,0],[1,5,-2,3],[0,0,0,0],[4,4,4,0]]
your_answer_c_AB = [[6,0,0,0],[6,0,0,0],[8,0,0,0],[5,0,0,0]]
your_answer_c_BA = [[4,2,1,-1],[4,2,1,-1],[0,0,0,0],[0,0,0,0]]
your_answer_d_AB = [[0,3,0,4],[0,4,0,1],[0,4,0,4],[0,-6,0,-1]]
your_answer_d_BA = [[0,11,0,-2],[0,0,0,0],[0,0,0,0],[1,5,-2,3]]
your_answer_e_AB = [[0,3,0,8],[0,-9,0,2],[0,0,0,8],[0,15,0,-2]]
your_answer_e_BA = [[-2,12,4,-10],[0,0,0,0],[0,0,0,0],[-3,-15,6,-9]]
your_answer_f_AB = [[-4,4,2,-3],[-1,10,-4,9],[-4,8,8,0],[1,12,4,-15]]
your_answer_f_BA = [[-4,-2,-1,1],[2,10,-4,6],[8,8,8,0],[-3,18,6,-15]]
## Problem 10
column_row_vector_multiplication1 = Vec({0, 1}, {0:13,1:20})
column_row_vector_multiplication2 = Vec({0, 1, 2}, {0:24,1:11,2:4})
column_row_vector_multiplication3 = Vec({0, 1, 2, 3}, {0:4,1:8,2:11,3:3})
column_row_vector_multiplication4 = Vec({0,1}, {0:30,1:16})
column_row_vector_multiplication5 = Vec({0, 1, 2}, {0:-3,1:1,2:9})
## Problem 11
def lin_comb_mat_vec_mult(M, v):
assert(M.D[1] == v.D)
nm=mat2coldict(M)
return sum([v[x]*nm[x] for x in M.D[1]])
## Problem 12
def lin_comb_vec_mat_mult(v, M):
assert(v.D == M.D[0])
nm=mat2rowdict(M)
return sum([v[x]*nm[x] for x in M.D[0]])
## Problem 13
def dot_product_mat_vec_mult(M, v):
assert(M.D[1] == v.D)
nm=mat2rowdict(M)
return Vec(M.D[0],{x:v*nm[x] for x in M.D[0]})
## Problem 14
def dot_product_vec_mat_mult(v, M):
assert(v.D == M.D[0])
nm=mat2coldict(M)&n
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