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matrix.py
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matrix.py
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from random import randint
class Matrix:
def __init__(self,*args) -> None:
if len(args) == 1 and type(args[0]) in (list,tuple) and len(args[0]) > 0 and type(args[0][0]) in (list,tuple): # Matrix from matrix
# If :
# There is only one argument
# The argument is a list or tuple
# This list isn't empty
# This list contains lists or tuple
dim_x = len(args[0][0])
equal_rows = True
for row in args[0]:
if len(row) != dim_x:
equal_rows = False
if equal_rows:
self.val = args[0][:]
self.dim_x = dim_x
self.dim_y = len(args[0])
return
if len(args) == 1 and isinstance(args[0],Graph) and len(args[0]) > 0: # Matrix from Graph
# If :
# There is only one argument
# The argument is a Graph
# This Graph isn't empty
self = args[0].matrix.copy
return
if len(args) == 1 and isinstance(args[0],Matrix) and len(args[0]) > 0: # Matrix from Matrix
self.dim_y = args[0].dim_y
self.dim_x = args[0].dim_x
self.val = []
for i in range(self.dim_y):
self.val.append([])
for j in range(self.dim_x):
self.val[i].append(args[0][i,j])
return
if len(args) >= 1 and isinstance(args[0],int): # Matrix creation
if len(args) == 1:
dim_y, dim_x, value = args[0], args[0], 0
value = 0
elif len(args) == 2:
dim_y, dim_x, value = args[0], args[1], 0
else:
dim_y, dim_x, value = args[0], args[1], args[2]
if dim_x > 0 and dim_y > 0:
val = []
for i in range(dim_y):
val.append([])
for j in range(dim_x):
val[i].append(value)
self.val = val
self.dim_x = dim_x
self.dim_y = dim_y
return
self.val = []
self.dim_x = 0
self.dim_y = 0
def __str__(self) -> str:
if self.dim_y == 0:
return "┌ ┐\n└ ┘"
max = []
for i in self.val[0]:
max.append(0)
for i in self.val:
for j in range(0,len(i)):
if max[j] < len(str(i[j])):
max[j] = len(str(i[j]))
S = ""
raw_size = 0
for i in range(0,len(self.val)):
for j in range(0,len(self.val[i])):
element = str(self.val[i][j])
S += element
S += ' '*(max[j]-len(element)+1)
if i==0:
raw_size = len(S)+1
S += "│\n│ "
return "┌" + " "*raw_size + "┐\n│ " + S[:-2] + "└" + " "*raw_size + "┘"
def __repr__(self) -> str:
if self.val == []:
return "Matrix()"
return "Matrix(" + self.val.__repr__() + ")"
def get_raw(self,n) -> list:
return self.val[n]
def get_column(self,n) -> list:
s = []
for i in self.val:
s.append(i[n])
return s
def insert_raw(self,n:int,content:list) -> None:
self.val = self.val[0:n] + [content] + self.val[n:]
self.dim_x += 1
def insert_column(self,n:int,content:list) -> None:
for i in range(0,len(self.val)):
self.val[i] = self.val[i][0:n] + [content[i]] + self.val[i][n:]
self.dim_y += 1
def remove_raw(self,n) -> None:
del self.val[n]
self.dim_y -= 1
def remove_column(self,n) -> None:
for i in range(self.dim_y):
del self.val[i][n]
self.dim_x -= 1
def __getitem__(self, position:tuple[int,int]):
return self.val[position[0]][position[1]]
def __setitem__(self, position:tuple[int,int], value):
self.val[position[0]][position[1]] = value
def __add__(self,other):
K = self.copy
K += other
return K
def __iadd__(self,other):
for i in range(self.dim_y):
for j in range(self.dim_x):
self[i,j] += other[i,j]
return self
def __mul__(self,other):
K = self.copy
K *= other
return K
def __imul__(self,other):
if isinstance(other, Matrix):
self = Matrix([[sum(self[i,k]*other[k,j] for k in range(self.dim_x)) for j in range(other.dim_x)] for i in range(self.dim_y)])
else:
for i in range(self.dim_y):
for j in range(self.dim_x):
self[i,j] *= other
return self
def __rmul__(self,other):
return self*other
def __neg__(self):
K = self.copy
K *= -1
return K
def __sub__(self,other):
return self + (-other)
def __list__(self) -> list:
return self.val
def __len__(self) -> int:
return self.dim_y
def __invert__(self):
return (1/self.det)*self.comatrix.T
def __pow__(self,other:int):
if other == 0: return id_mat(self.dim_y)
if other == 2: return self*self
if other < 0: return ~(self**-other)
return (self**(other//2)).square*(self if other%2==1 else 1)
def __eq__(self, other) -> bool:
return isinstance(other, Matrix) and self.val == other.val
def __neq__(self, other) -> bool:
return not self == other
def column_shear(self,i,j,value):
self.val = (self*shear_mat(self.dim_x, j, i, value)).val
return self
def column_expand(self,i,value):
self.val = (self*expansion_mat(self.dim_x, i, value)).val
return self
def column_permutate(self,i,j):
self.val = (self*permutation_mat(self.dim_x, i, j)).val
return self
def raw_shear(self,i,j,value):
self.val = (shear_mat(self.dim_y, i, j, value)*self).val
return self
def raw_expand(self,i,value):
self.val = (expansion_mat(self.dim_y, i, value)*self).val
return self
def raw_permutate(self,i,j):
self.val = (permutation_mat(self.dim_y, i, j) * self).val
return self
def get_copy(self):
copy = Matrix(self.dim_y,self.dim_x)
for i in range(self.dim_y):
for j in range(self.dim_x):
copy[i,j] = self[i,j]
return copy
def get_dims(self):
return (self.dim_x, self.dim_y)
def get_square(self):
return self*self
def get_transpo(self):
return Matrix([[self[j,i] for j in range(self.dim_y)] for i in range(self.dim_x)])
def get_det(self):
if self.dim_y == 2:
return self[0,0]*self[1,1]-self[0,1]*self[1,0]
S = 0
for k in range(self.dim_y):
sub = Matrix([[self[i,j-(j-1<k)] for j in range(1,self.dim_y)] for i in range(1,self.dim_y)])
S += self[0,k] * sub.get_det() * (-1)**k
return S
def get_comatrix(self):
return Matrix([[self[1,1],-self[1,0]],[-self[0,1],self[0,0]]]) if len(self)==2 else Matrix([[(-1)**(i+j)*Matrix([[self[ii+(ii>=i),jj+(jj>=j)] for jj in range(self.dim_x-1)] for ii in range(self.dim_y-1)]).det for j in range(self.dim_x)] for i in range(self.dim_y)])
copy = property(get_copy)
dims = property(get_dims)
det = property(get_det)
square = property(get_square)
transpo = property(get_transpo)
T = property(get_transpo)
comatrix = property(get_comatrix)
class Graph:
"Mathematicl Graph"
def __init__(self, verteces:list = [], matrix:Matrix|None = None) -> None:
self.verteces = verteces
if matrix is None or matrix.dim_y != len(verteces) or matrix.dim_x != len(verteces):
self.matrix = Matrix(len(verteces))
else:
self.matrix = matrix
def __len__(self):
return len(self.verteces)
def __repr__(self) -> str:
if len(self) == 0:
return "Graph()"
s = "Graph ("
for vertex in self.verteces:
s += repr(vertex) + ", "
return s[:-2] + ')'
def __getitem__(self, index):
return self.verteces[index]
def __setitem__(self, index, vertex):
self.verteces[index] = vertex
def append(self, vertex):
self.verteces.append(vertex)
def edge(self, vertex1, vertex2, weight=1, directed=False):
self.matrix[self.verteces.index(vertex1),self.verteces.index(vertex2)] += weight
if not directed:
self.matrix[self.verteces.index(vertex2),self.verteces.index(vertex1)] += weight
def id_mat(n:int) -> Matrix:
"""Return the identity matrix n-sized"""
m = Matrix(n)
for i in range(n):
m[i,i] = 1
return m
def elem_mat(n:int, i:int, j:int) -> Matrix:
"""Return the Elementary matrix (i,j) with a size of n
The Elementary matrix (i,j) is the matrix filled with 0 with only a 1 at position (i,j)"""
m = Matrix(n)
m[i,j] = 1
return m
def diag_mat(*args) -> Matrix:
"""Return the diagonal matrix with given values"""
m = Matrix(len(args))
for i in range(len(args)):
m[i,i] = args[i]
return m
def raw_mat(*args) -> Matrix:
"""Return the Raw matrix with given values"""
return Matrix([list(args)])
def column_mat(*args) -> Matrix:
"""Return the Column matrix with given values"""
m = Matrix(len(args),1)
for i in range(len(args)):
m[i,0] = args[i]
return m
def scalar_mat(n:int, value) -> Matrix:
"""Return the diagonal matrix n-sized filled with the given value"""
m = Matrix(n)
for i in range(n):
m[i,i] = value
return m
def shear_mat(n:int,i:int,j:int,value) -> Matrix:
"""Return the Matrix of the transvection Lᵢ ← Lᵢ + value*Lⱼ"""
m = id_mat(n)
m[i,j] = value
return m
def expansion_mat(n:int,i:int,value) -> Matrix:
"""Return the Matrix of the expansion Lᵢ ← value*Lᵢ"""
m = id_mat(n)
m[i,i] = value
return m
def permutation_mat(n:int, i:int, j:int) -> Matrix:
"""Return the Matrix of the permutation Lᵢ ←→ Lⱼ"""
m = id_mat(n)
m[i,j] = 1
m[j,i] = 1
m[i,i] = 0
m[j,j] = 0
return m
def rand_mat(n:int,p:int,min=0,max=9) -> Matrix:
"""Return a random matrix of size n,p filled with random integers between min and max (including both)"""
return Matrix([[randint(min,max) for j in range(p)] for i in range(n)])
def print_mat(mat:Matrix,start="Matrix",end='\n',start_raw='',raw_prefix=False,dimensions=True,printed=True) -> str:
# affiche une matrice
if mat.val == []:
S = "Empty Matrix" + end
if printed: print(S)
return S
S = ""
if dimensions:
start += (" "*(start!=''))+str(mat.dim_y)+"*"+str(mat.dim_x)
if start != '':
S += start + '\n'
max = []
for i in mat.val[0]:
max.append(0)
for i in mat.val:
for j in range(0,len(i)):
if max[j] < len(str(i[j])):
max[j] = len(str(i[j]))
for i in range(0,len(mat.val)):
if raw_prefix:
S += str(i)
S += start_raw
for j in range(0,len(mat.val[i])):
element = str(mat.val[i][j])
S += element
S += ' '*(max[j]-len(element)+1)
S += '\n'
S = S[:-1] + end
if printed: print(S)
return S
def minor(mat:Matrix, i:int, j:int):
return Matrix([[mat[ii-(ii-1<i),jj-(jj-1<j)] for jj in range(1,mat.dim_x)] for ii in range(1,mat.dim_y)]).det