def rmul(self, vec):
'''
Returns a vector that is the product of 'vec' (taken as a row vector) and this matrix using the * operator
If the two are incompatible return None
Return vec*self
'''
# Your Code
new_list = []
list_of_vectors = []
prod = []
if(len(self) <> len(vec)):
return None
else:
lst = []
for i in range(len(self)):
for j in range(len(self[0])):
lst.append(self[j][i])
new_list.append(lst)
lst = []
for lists in new_list:
vect = make_vector(lists ,zero_test = lambda x : (x == 0))
list_of_vectors.append(vect)
new_matrix = make_matrix(list_of_vectors)
for i in range(len(new_matrix)):
prod.append(new_matrix[i]*vec)
final_vector = make_vector(prod , zero_test = lambda x : (x == 0))
return final_vector
def get_quarters(self):
'''
Get all 4 quarters of the matrix - get the left-right split
Then split each part into top and bottom
Return the 4 parts - topleft, topright, bottomleft, bottomright - in that order
'''
# Your Code
ele = [[],[],[],[]]
for i in range(len(self)/2):
ls = []
for j in range(0, int(float(len(self))/2.0 + 0.5)):
ls.append(self[i][j])
ele[0].append( make_vector(ls) )
ls = []
for j in range(int(len(self)/2), len(self[i])):
ls.append(self[i][j])
ele[1].append( make_vector(ls) )
ls = []
for j in range(0, int(float(len(self))/2.0 + 0.5)):
ls.append(self[len(self)/2 + i][j])
ele[2].append( make_vector(ls) )
ls = []
for j in range(int(len(self)/2), len(self[i])):
ls.append(self[len(self)/2 + i][j])
ele[3].append( make_vector(ls) )
ls = []
#return make_matrix(ele[0]), make_matrix(ele[1]), make_matrix(ele[2]), make_matrix(ele[3])
return Matrix(ele[0]), Matrix(ele[1]), Matrix(ele[2]), Matrix(ele[3])
def get_quarters(self):
'''
Get all 4 quarters of the matrix - get the left-right split
Then split each part into top and bottom
Return the 4 parts - topleft, topright, bottomleft, bottomright - in that order
'''
# Your Code
left_matrix , right_matrix = self.left_right_split()
topleft = []
topright = []
bottomleft = []
bottomright = []
mid = len(left_matrix) / 2
for i in range(0 , mid):
topleft.append(make_vector((left_matrix[i]) , lambda x : (x == 0)))
for i in range(mid , len(left_matrix)):
bottomleft.append(make_vector((left_matrix[i]) , lambda x : (x == 0)))
mid = len(right_matrix) / 2
for i in range(0 , mid):
topright.append(make_vector((right_matrix[i]) , lambda x : (x == 0)))
for i in range(mid , len(left_matrix)):
bottomright.append(make_vector((right_matrix[i]) , lambda x : (x == 0)))
return make_matrix(topleft) , make_matrix(topright) , make_matrix(bottomleft) , make_matrix(bottomright)
def __getitem__(self, key):
'''
Overriding the default __getitem__ method with behavior specific to sparse matrices
'''
# Your Code
if isinstance(key, int):
if key >= len(self):
return None
if len(self.indices) == 0 or len(self.vectors) == 0:
return make_vector([0] * self.ncols, lambda x: x == 0)
idx = bisect_left(self.indices, key)
return (make_vector([0] * self.ncols)
if (idx == len(self.indices) or self.indices[idx] != key)
else self.vectors[idx])
else:
if key[0] >= len(self):
return None
idx = bisect_left(self.indices, key[0])
return (0 if (idx == len(self.vectors)
or self.indices[idx] != key[0])
else self.vectors[idx][key[1]])
def pad(self):
'''
padding to incomplete matrix
'''
l_rows = len(self)
l_cols = len(self.rows[0])
i = 1
while(i<l_rows):
i *= 2
j = 1
while(j<l_cols):
j *= 2
order = max(i,j)
if((order - l_cols ) != 0):
col = make_vector(([0] * (order - l_cols )), zero_test)
cols = []
for i in range(l_rows):
cols.append(col)
colms = make_matrix(cols)
self.merge_cols(colms)
if((order - l_rows) != 0):
row = make_vector(([0] * order ),zero_test)
rws = []
for i in range((order - l_rows)):
rws.append(row)
rws1 = make_matrix(rws)
self.merge_rows(rws1)
def get_quarters(self):
'''
Get all 4 quarters of the matrix - get the left-right split
Then split each part into top and bottommake_vector
Return the 4 parts - topleft, topright, bottomleft, bottomright - in that order
'''
# Your Code
topleft = []
topright = []
bottomleft = []
bottomright = []
left, right = self.left_right_split()
for rowno in range(0, len(self)/2):
if rowno in left.indices:
topleft.append(left[rowno])
else:
topleft.append(make_vector([0]*(self.ncols/2) , lambda x : (x == 0)))
if rowno in right.indices:
topright.append(right[rowno])
else:
topright.append(make_vector([0]*(self.ncols - self.ncols/2), lambda x : (x == 0)))
for rowno in range(len(self)/2, len(self)):
if rowno in left.indices:
bottomleft.append(left[rowno])
else:
bottomleft.append(make_vector([0]* (self.ncols/2), lambda x : (x == 0)))
if rowno in right.indices:
bottomright.append(right[rowno])
else:
bottomright.append(make_vector([0]*(self.ncols - self.ncols/2), lambda x : (x == 0)))
return make_matrix(topleft), make_matrix(topright), make_matrix(bottomleft), make_matrix(bottomright)
def form_pad(self):
org_row_length = len(self[0])
org_col_length = len(self)
num_row = self.is_valid(len(self[0]))
num_col = self.is_valid(len(self))
num = num_row if (num_row > num_col) else num_col
if(num != 0):
for i in range(len(self)):
temp_list = []
for j in range(len(self[i])):
temp_list.append(self[i][j])
if not is_long_and_sparse(temp_list):
self[i].merge(make_vector([0] * (num - org_row_length)))
else:
self[i].length = self[i].length + (num - org_row_length)
temp = num - org_col_length
ls = []
while(temp > 0):
ls.append(make_vector([0]*(len(self[0]))))
temp -= 1
self = self.merge_rows(ls)
return self, num - org_row_length, num - org_col_length
def get_quarters(self):
'''
Get all 4 quarters of the matrix - get the left-right split
Then split each part into top and bottom
Return the 4 parts - topleft, topright, bottomleft, bottomright - in that order
'''
left_matrix, right_matrix = self.left_right_split()
topleft = []
topright = []
bottomleft = []
bottomright = []
mid = len(left_matrix) / 2
for i in range(0, mid):
topleft.append(make_vector((left_matrix[i]), lambda x: (x == 0)))
for i in range(mid, len(left_matrix)):
bottomleft.append(make_vector((left_matrix[i]), lambda x:
(x == 0)))
mid = len(right_matrix) / 2
for i in range(0, mid):
topright.append(make_vector((right_matrix[i]), lambda x: (x == 0)))
for i in range(mid, len(left_matrix)):
bottomright.append(
make_vector((right_matrix[i]), lambda x: (x == 0)))
return make_matrix(topleft), make_matrix(topright), make_matrix(
bottomleft), make_matrix(bottomright)
def pad(self, add_temp):
zero_add = [0]*(add_temp - self.ncols)
zero_vec = make_vector(zero_add,lambda x:x==0)
zero_mat = [0]*add_temp
mat_vec = make_vector(zero_mat,lambda x:x==0)
for i in range(0,len(self)):
self[i].merge(zero_vec)
for i in range(add_temp - self.nrows):
self.vectors.append(mat_vec)
def __getitem__(self, key, ):
'''
Overriding the default __getitem__ method with behavior specific to sparse matrices
'''
# Your Code
if key in self.indices:
return self.vectors[self.indices.index(key)]
elif self.vectors != []:
return make_vector([0]*len(self.vectors[0]))
else:
return make_vector([0]*len(self))
def __add__(self, mat):
'''
Return the sum of this matrix with 'mat' - (allows use of + operator between matrices)
Return None if the number of rows do not match
'''
if len(self) != len(mat):
return None
s_matrix = []
for i in range(len(self)):
s_matrix.append(make_vector(self[i], zero_test = lambda x : (x == 0))+make_vector(mat[i],zero_test = lambda x : (x == 0) ))
sum_mat = make_matrix(s_matrix)
return sum_mat
def __sub__(self, mat):
'''
Return the difference between this matrix and 'mat' - (allows use of - operator between matrices)
Return None if the number of rows do not match
'''
if len(self) != len(mat):
return None
sub_mat = []
for i in range(len(self)):
sub_mat.append(make_vector(self[i],zero_test = lambda x : (x == 0)) - make_vector(mat[i], zero_test = lambda x : (x == 0)))
sub_matrix = make_matrix(sub_mat)
return sub_matrix
def __rmul__(self, vec):
'''
Returns a vector that is the product of 'vec' (taken as a row vector) and this matrix using the * operator
If the two are incompatible return None
Return vec*self
'''
if(len(vec) == self.nrows):
transposed_matrix = make_matrix([make_vector(list(column), vec.zero_test)
for column in itertools.izip(*self.components())])
return make_vector([(vec * row) for row in transposed_matrix.components()], vec.zero_test)
else:
return None
def __sub__(self, mat):
'''
Return the difference between this matrix and 'mat' - (allows use of - operator between matrices)
Return None if the number of rows do not match
'''
matrix_diff = []
if len(self) != len(mat):
return None
for i in range(0, len(self)):
v1 = make_vector(self[i], lambda x: (x == 0))
v2 = make_vector(mat[i], lambda x: (x == 0))
matrix_diff.append(v1 - v2)
return make_matrix(matrix_diff)
def __iadd__(self, mat):
'''
Implements the += operator with another matrix 'mat'
Assumes that the elements of the matrices have a + operator defined between them (if they are not numbers)
Add corresponding elements upto the min of the number of rows in each (in case the matrices
have different numbers of rows)
'''
lst_iadd = []
for i in range(0 , min(len(self) , len(mat))):
v1 = make_vector(self[i] , lambda x : (x == 0))
v2 = make_vector(mat[i] , lambda x : (x == 0))
v1 += v2
lst_iadd.append(v1)
return make_matrix(lst_iadd)
def make_matrix(vector_list):
'''
Make a matrix out of a list of vectors 'vector_list'
Just like make_vector in the vector module, this decides whether to instantiate the FullMatrix or SparseMatrix class
by using the is_zero method of the Vector class
'''
# Your Code
matrix_vec_val = []
sparse_val = []
sparse_ind = []
for idx , i in enumerate(vector_list):
matrix_val = []
for j in range(0 , len(i)):
columns = len(i)
matrix_val.append(i[j])
if(i.is_zero() == False):
sparse_val.append(i)
sparse_ind.append(idx)
matrix_vec_val.append(make_vector(matrix_val , lambda x : (x == 0)))
if float(len(sparse_val))/float(len(vector_list)) < DENSITY_THRESHOLD and float(len(vector_list) * columns) > SIZE_THRESHOLD:
obj = SparseMatrix(sparse_val , sparse_ind , len(vector_list),columns)
else :
obj = FullMatrix(matrix_vec_val)
return obj
def __mul__(self, mat):
'''
Multiplication of two matrices using Strassen's algorithm
If either this matrix or mat is a 'small' matrix then do regular multiplication
Else use recursive Strassen's algorithm
'''
matrix = []
if (self.is_small() or mat.is_small == True):
for i in range(len(self)):
rows = []
for j in range(len(mat[0])):
val = 0
for k in range(len(mat[0])):
val += self[i][k] * mat[k][j]
rows.append(val)
matrix.append(make_vector((rows) , zero_test=lambda x : (x == 0)))
return make_matrix(matrix)
else:
topleft , topright , bottomleft , bottomright = self.get_quarters()
top_left , top_right , bottom_left , bottom_right = mat.get_quarters()
val1 = topleft * (top_right - bottom_right)
val2 = (topleft + topright) * bottom_right
val3 = (bottomleft + bottomright) * top_left
val4 = bottomright * (bottom_left - top_left)
val5 = (topleft + bottomright) * (top_left + bottom_right)
val6 = (topright - bottomright) * (bottom_left + bottom_right)
val7 = (topleft - bottomleft) * ( top_left + top_right)
row1 = val4+val5+val6-val2
row2 = val1+val2
row3 = val3+val4
row4 = val1-val3+val5-val7
col1 = row1.merge_cols(row2)
col2 = row3.merge_cols(row4)
mat = col1.merge_rows(col2)
return mat
def pad_row(self):
'''
Pad the rows of this matrix to the nearest power of 2
'''
pad = 2
while pad < self.nrows:
pad = pad << 1
pad -= self.nrows
if var_globals.FLAG_ROW == 0:
var_globals.FLAG_ROW += 1
var_globals.ROW_LENGTH = self.nrows
if pad != 0:
if var_globals.ROW_PAD == 0:
var_globals.ROW_PAD = pad
pad_vector = [make_vector([0] * self.ncols)
for _ in range(pad)]
new_mat = self.merge_rows(make_matrix(pad_vector))
t_list = [new_mat[i] for i in range(len(new_mat))]
return make_matrix(t_list)
else:
return self
def __isub__(self, mat):
'''
Implements the -= operator with another matrix 'mat'
Assumes that the elements of the matrices have a - operator defined between them (if they are not numbers)
Subtract corresponding elements upto the min of the number of rows in each (in case the matrices
have different numbers of rows)
'''
lst_isub = []
for i in range(0, min(len(self), len(mat))):
v1 = make_vector(self[i], lambda x: (x == 0))
v2 = make_vector(mat[i], lambda x: (x == 0))
v1 -= v2
lst_isub.append(v1)
return make_matrix(lst_isub)
def make_matrix(vector_list):
'''
Make a matrix out of a list of vectors 'vector_list'
Just like make_vector in the vector module, this decides whether to instantiate the FullMatrix or SparseMatrix class
by using the is_zero method of the Vector class
'''
# Your Code
count = 0
matrix = []
vect_matrix = []
for vect in vector_list:
vect_matrix.append(make_vector(vect, zero_test = lambda x : (x == 0)))
count = 0
if len(vect_matrix) > 2:
for vect in vect_matrix:
if vect.is_zero():
count += 1
if count/len(vect_matrix) <= DENSITY_THRESHOLD:
vect_list = []
indices = []
for ind in range(len(vect_matrix)):
if vect_matrix[ind].is_zero() == False:
vect_list.append(vect_matrix[ind])
indices.append(ind)
matrix = SparseMatrix(vect_list, indices, len(vect_matrix))
return matrix
matrix = FullMatrix(vect_matrix)
return matrix
def make_matrix(vector_list):
'''
Make a matrix out of a list of vectors 'vector_list'
Just like make_vector in the vector module, this decides whether to instantiate the FullMatrix or SparseMatrix class
by using the is_zero method of the Vector class
'''
# Your Code
matrix2 = []
count = 0
for i in range(len(vector_list)):
ls = []
for j in range(len(vector_list[i])):
ls.append( vector_list[i][j] )
if (isinstance(ls, list)):
ls = make_vector(ls)
if(ls.is_zero()):
count += 1
matrix2.append(ls)
if float(count) / float(len(vector_list)) >= DENSITY_THRESHOLD:
indices = []
val_vectors = []
for i in range(len(matrix2)):
if(matrix2[i].is_zero() == False):
val_vectors.append(matrix2[i])
indices.append(i)
mat = SparseMatrix(val_vectors, indices, len(matrix2))
else:
mat = FullMatrix(matrix2)
return mat
def __add__(self, mat):
'''
Return the sum of this matrix with 'mat' - (allows use of + operator between matrices)
Return None if the number of rows do not match
'''
matrix_sum = []
if len(self) != len(mat):
return None
for i in range(0, len(self)):
v1 = make_vector(self[i], lambda x: (x == 0))
v2 = make_vector(mat[i], lambda x: (x == 0))
matrix_sum.append(v1 + v2)
return make_matrix(matrix_sum)
def make_matrix(vector_list):
'''
Make a matrix out of a list of vectors 'vector_list'
Just like make_vector in the vector module, this decides whether to instantiate the FullMatrix or SparseMatrix class
by using the is_zero method of the Vector class
'''
matrix_vec_val = []
sparse_val = []
sparse_ind = []
for idx, i in enumerate(vector_list):
matrix_val = []
for j in range(0, len(i)):
columns = len(i)
matrix_val.append(i[j])
if (i.is_zero() == False):
sparse_val.append(i)
sparse_ind.append(idx)
matrix_vec_val.append(make_vector(matrix_val, lambda x: (x == 0)))
if float(len(sparse_val)) / float(
len(vector_list)) < DENSITY_THRESHOLD and float(
len(vector_list) * columns) > SIZE_THRESHOLD:
obj = SparseMatrix(sparse_val, sparse_ind, len(vector_list), columns)
else:
obj = FullMatrix(matrix_vec_val)
return obj
def pad_col(self):
'''
Pad the columns of this matrix to the nearest power of 2
'''
pad = 2
while pad < self.ncols:
pad = pad << 1
pad -= self.ncols
if var_globals.FLAG_COL == 1:
var_globals.COL_LENGTH = self.ncols
var_globals.FLAG_COL += 1
if pad != 0:
var_globals.COL_PAD = pad
pad_vector = [make_vector([0] * pad)
for _ in range(self.nrows)]
new_mat = self.merge_cols(make_matrix(pad_vector))
t_list = [new_mat[i] for i in range(len(new_mat))]
return make_matrix(t_list)
else:
return self
def pad_matrix(vector_list):
'''
To pad the matrix
'''
nrow_pad = int(pow(2, ceil(log(len(vector_list), 2))))
ncol_pad = int(pow(2, ceil(log(len(vector_list[0]), 2))))
zero_append.append(len(vector_list))
zero_append.append(len(vector_list[0]))
if nrow_pad == len(vector_list) and ncol_pad == len(vector_list[0]):
return vector_list
new_list = [[0]*ncol_pad]*len(vector_list)
for i in range(len(vector_list)):
for j in range(len(vector_list[0])):
new_list[i][j] = vector_list[i][j]
i = 0
while( i < nrow_pad-len(vector_list)):
new_list.append([0]*len(new_list[0]))
i += 1
vect_list = []
for i in new_list:
vect_list.append(make_vector(i, zero_test = lambda x : (x == 0)))
return vect_list
def merge_rows(self, mat):
'''
Return the matrix with rows of mat appended to the rows of this matrix
'''
# Your Code
final_list = []
for i in range(0, len(self)):
vec = make_vector(self[i], lambda x: (x == 0))
final_list.append(vec)
for i in range(0, len(mat)):
vec = make_vector(mat[i], lambda x: (x == 0))
final_list.append(vec)
return make_matrix(final_list)
def left_right_split(self):
'''
Split the matrix into two halves - left and right - and return the two matrices
Split each row (use the split method of Vector) and put them together into the
left and right matrices
Use the make_matrix method for forming the new matrices
'''
# Your Code
splt_left = []
splt_right = []
for lst_vector in len(self):
splt_left.append(lst_vector.splt(lst_vector))
splt_right.append(lst_vector.splt(lst_vector))
mat_left=make_vector(splt_left)
mat_right=make_vector(splt_right)
return mat_left,mat_right
def merge_rows(self, mat):
'''
Overriding the merge rows method of the parent Matrix class
'''
# Your Code
mat_list = []
for nrow in range(0, len(self)):
if nrow in self.indices:
mat_list.append(self[nrow])
else:
mat_list.append(make_vector([0]*self.ncols, lambda x : (x == 0)))
for nrow in range(0, len(mat)):
if nrow in mat.indices:
mat_list.append(mat[nrow])
else:
mat_list.append(make_vector([0]*self.ncols, lambda x : (x == 0)))
return make_matrix(mat_list)
def pad(self, add_temp):
'''
to add 0's to the matrices to make them 2^n x 2^n matrices
'''
zero_mat = []
temp_mat = []
for pos in range(add_temp - self.ncols):
zero_mat.append(0)
if(add_temp != self.ncols):
zero_mat_obj = make_vector(zero_mat, zero_test)
for pos in range(len(self)):
temp_mat.append(self[pos].merge(zero_mat_obj))
row = [0]*(add_temp)
for elem in range(add_temp - self.nrows):
temp_mat.append(make_vector(row, zero_test))
return make_matrix(temp_mat)
def __add__(self, mat):
'''
Return the sum of this matrix with 'mat' - (allows use of + operator between matrices)
Return None if the number of rows do not match
'''
matrix_sum = []
if len(self) != len(mat) :
return None
for i in range(0 , len(self)):
v1 = make_vector(self[i] , lambda x : (x == 0))
v2 = make_vector(mat[i] , lambda x : (x == 0))
matrix_sum.append(v1 + v2)
return make_matrix(matrix_sum)
def __sub__(self, mat):
'''
Return the difference between this matrix and 'mat' - (allows use of - operator between matrices)
Return None if the number of rows do not match
'''
matrix_diff = []
if len(self) != len(mat) :
return None
for i in range(0 , len(self)):
v1 = make_vector(self[i] , lambda x : (x == 0))
v2 = make_vector(mat[i] , lambda x : (x == 0))
matrix_diff.append(v1 - v2)
return make_matrix(matrix_diff)
def merge_rows(self, mat):
'''
Return the matrix with rows of mat appended to the rows of this matrix
'''
# Your Code
final_list = []
for i in range(0 , len(self)):
vec = make_vector(self[i] , lambda x : (x == 0))
final_list.append(vec)
for i in range(0 , len(mat)):
vec = make_vector(mat[i] , lambda x : (x == 0))
final_list.append(vec)
return make_matrix(final_list)
def __add__(self, mat):
'''
Return the sum of this matrix with 'mat' - (allows use of + operator between matrices)
Return None if the number of rows do not match
'''
sum_mat = []
if len(self) == len(mat):
for i in range(len(self)):
if self[i]!= None and mat[i]!= None:
vector1 = make_vector(self[i], None)
vector2 = make_vector(mat[i], None)
vector = (vector1 + vector2)
sum_mat.append(vector.data)
mat = make_matrix(sum_mat)
return mat
return None
def pad(self, mat):
'''
Pad two matrices with zero_vectors as rows and columns to nearest multiple of 2.
'''
pow_2 = self.get_pow_2(mat)
pad_info = [(pow_2 - dim) for dim in [self.nrows, self.ncols, mat.nrows, mat.ncols]]
self = (self.merge_rows(make_matrix([make_vector([0] * self.ncols, self[0].zero_test)
for _ in xrange(pad_info[0])])) if(pad_info[0] != 0) else self)
self = (self.merge_cols(make_matrix([make_vector([0] * pad_info[1]) for _ in xrange(self.nrows)]))
if(pad_info[1] != 0) else self)
mat = (mat.merge_rows(make_matrix([make_vector([0] * mat.ncols, mat[0].zero_test)
for _ in xrange(pad_info[2])])) if(pad_info[2] != 0) else mat)
mat = (mat.merge_cols(make_matrix([make_vector([0] * pad_info[3]) for _ in xrange(mat.nrows)]))
if(pad_info[3] != 0) else mat)
return self, mat, pad_info
def rmul(self, vec):
'''
Returns a vector that is the product of 'vec' (taken as a row vector) and this matrix using the * operator
If the two are incompatible return None
Return vec*self
'''
# Your Code
if len(vec) == len(self):
vec_list = []
for cols in range(0, self.ncols):
vec_element = []
for rows in range(0, len(self)):
vec_element.append(self[rows][cols])
vector = make_vector(vec_element, lambda x : (x == 0))
vec_list.append(vec * vector)
return make_vector(vec_list, lambda x : (x == 0))
else :
return None
def merge_rows(self, mat):
'''
Overriding the merge rows method of the parent Matrix class
'''
if len(self) != len(mat):
return None
merged_list = []
for i in range(0, len(self)):
vec = make_vector(self[i], lambda x: (x == 0))
merged_list.append(vec)
for i in range(0, len(mat)):
vec = make_vector(mat[i], lambda x: (x == 0))
merged_list.append(vec)
return make_matrix(merged_list)
def __sub__(self, mat):
'''
Return the difference between this matrix and 'mat' - (allows use of - operator between matrices)
Return None if the number of rows do not match
'''
sub_mat = []
if len(self) == len(mat):
for i in range(len(self)):
if self[i]!=None and mat[i]!=None:
vector1 = make_vector(self[i], None)
vector2 = make_vector(mat[i], None)
vector = (vector2 - vector1)
sub_mat.append(vector.data)
mat = make_matrix(sub_mat)
return mat
return None
def unpadding(self):
global org_rows, org_column
unpadded_list = []
for i in range(0, org_rows):
lst = []
for j in range(0, org_column):
lst.append(self[i][j])
vec = make_vector(lst, lambda x: (x == 0))
unpadded_list.append(vec)
return make_matrix(unpadded_list)
def padding(self):
list_vectors = []
global org_rows, org_column
org_rows = len(self)
org_column = len(self[0])
pad_zeros_rows = pad_zeros(len(self[0]))
pad_zeros_column = pad_zeros(len(self))
dimen = max(
int(pad_zeros_rows) + len(self[0]),
int(pad_zeros_column) + len(self))
for i in range(0, len(self)):
padded_row = self[i] + [0] * (dimen - len(self[i]))
vec = make_vector(padded_row, lambda x: (x == 0))
list_vectors.append(vec)
lst = [0] * (dimen)
for i in range(0, (dimen - len(self))):
vec = make_vector(lst, lambda x: (x == 0))
list_vectors.append(vec)
return make_matrix(list_vectors)
def rmul(self, vec):
'''
Returns a vector that is the product of 'vec' (taken as a row vector) and this matrix using the * operator
If the two are incompatible return None
Return vec*self
'''
rmul_vector = []
for i in range(0, len(self)):
Sum = 0
for j in range(0, len(vec)):
Sum = Sum + vec[j] * self[j][i]
rmul_vector.append(Sum)
return make_vector(rmul_vector, lambda x: (x == 0))
def merge_cols(self, mat):
'''
Return the matrix whose rows are rows of this merged with the corresponding rows of mat (columnwise merge)
'''
if (len(self) != len(mat)):
return None
merged_list = []
for i in range(0, len(self)):
vec = make_vector(self[i], lambda x: (x == 0))
vec.merge(mat[i])
merged_list.append(vec)
return make_matrix(merged_list)
def left_right_split(self):
'''
Split the matrix into two halves - left and right - and return the two matrices
Split each row (use the split method of Vector) and put them together into the
left and right matrices
Use the make_matrix method for forming the new matrices
'''
left_matrix = []
right_matrix = []
for i in range(0, len(self)):
vec = make_vector(self[i], lambda x: (x == 0))
left_vector, right_vector = vec.split()
left_matrix.append(left_vector)
right_matrix.append(right_vector)
return make_matrix(left_matrix), make_matrix(right_matrix)
for i in range(mid, len(left_matrix)):
bottomleft.append(make_vector((left_matrix[i]), lambda x:
(x == 0)))
mid = len(right_matrix) / 2
for i in range(0, mid):
topright.append(make_vector((right_matrix[i]), lambda x: (x == 0)))
for i in range(mid, len(left_matrix)):
bottomright.append(
make_vector((right_matrix[i]), lambda x: (x == 0)))
return make_matrix(topleft), make_matrix(topright), make_matrix(
bottomleft), make_matrix(bottomright)
v1 = make_vector([1, 2, 1, 1, 3, 4, 1, 1], lambda x: (x == 0))
v2 = make_vector([1, 1, 1, 1, 1, 1], lambda x: (x == 0))
v3 = make_vector([1, 2, 3, 4, 5], lambda x: (x == 0))
v4 = make_vector([1, 0, 0, 0, 0, 0, 2, 0, 3, 4, 5, 6], lambda x: (x == 0))
v5 = make_vector([0, 0, 1, 0, 1, 0, 0, 0, 3, 6, 5, 1], lambda x: (x == 0))
v6 = make_vector([0, 0, 1, 0, 0, 0, 1, 0, 3, 4, 1, 6], lambda x: (x == 0))
v7 = make_vector([1, 0, 2, 0], lambda x: (x == 0))
v8 = make_vector([0, 0, 0, 0], lambda x: (x == 0))
m1 = make_matrix([v7, v8, v8, v8, v8, v8, v8, v8])
m2 = make_matrix([v8, v8, v8, v8])
print("m1")
for i in range(0, len(m1)):
for j in range(0, len(m1[i])):
print(m1[i][j], )
print()
def __mul__(self, mat):
'''
Multiplication of two matrices using Strassen's algorithm
If either this matrix or mat is a 'small' matrix then do regular multiplication
Else use recursive Strassen's algorithm
'''
if (len(self[0]) != len(mat)):
print("INCOMPATIBLE MULTIPLICATION")
return
else:
if (self.is_small() == True or mat.is_small() == True):
lst_mul = []
for i in range(0, len(self)):
vec = make_vector(self[i], lambda x: (x == 0))
vec_mul = mat.rmul(vec)
lst_mul.append(vec_mul)
return make_matrix(lst_mul)
global flag
if (flag == 0):
global rows, columns
flag = 1
self = padding(self)
mat = padding(mat)
if (len(self) != len(mat)):
minimum = min(len(self), len(mat))
if (minimum == len(self)):
matrix = self
else:
matrix = mat
lst_vec = []
pad = abs(len(self) - len(mat))
for i in range(0, len(matrix)):
pad_row = matrix[i] + [0] * pad
vec = make_vector(pad_row, lambda x: (x == 0))
lst_vec.append(vec)
for i in range(0, pad):
pad_row = [0] * len(mat)
vec = make_vector(pad_row, lambda x: (x == 0))
lst_vec.append(vec)
matrix = make_matrix(lst_vec)
if (minimum == len(self)):
self = matrix
else:
mat = matrix
rows = len(self)
columns = len(self[0])
A, B, C, D = self.get_quarters()
E, F, G, H = mat.get_quarters()
P1 = (A + D) * (E + H)
P2 = (C + D) * E
P3 = A * (F - H)
P4 = D * (G - E)
P5 = (A + B) * H
P6 = (C - A) * (E + F)
P7 = (B - D) * (G + H)
top_left = P1 + P4 - P5 + P7
top_right = P3 + P5
bottom_left = P2 + P4
bottom_right = P1 - P2 + P3 + P6
x = top_left.merge_cols(top_right)
y = bottom_left.merge_cols(bottom_right)
final_mat = x.merge_rows(y)
if (len(final_mat) == rows and len(final_mat[0]) == columns):
final_mat = unpadding(final_mat)
return final_mat