def test_creation_from_vectors(self):
vec1 = Vector(self.lsF2[:4])
vec2 = Vector.copy(vec1)
vec3 = Vector.copy(vec1)
vec4 = Vector.copy(vec1)
mat = matrix.Matrix.from_vectors([vec1, vec2, vec3, vec4])
self.is_matrix_equal(self.matF2, mat)
def test_creation_from_vectors(self):
vec1 = Vector(self.lsF2[:4])
vec2 = Vector.copy(vec1)
vec3 = Vector.copy(vec1)
vec4 = Vector.copy(vec1)
mat = matrix.Matrix.from_vectors([vec1,vec2,vec3,vec4])
self.is_matrix_equal(self.matF2, mat)
def solve_lower_triangular_system(self, b):
"""
This function is going to solve for
L*z = b
where we solve for z, b is given and L is a lower unit triangular matrix
(most likely the result of a LU operation)
:b: Vector, the vector needed to solve the system
:returns: Vector
"""
res = Vector.copy(b)
bit = res.vector_iterator()
it = self.full_iterator()
for TL, value, BL in bit:
data = it.next()
BL = BL + (-(value * data["a21"]))
bit.merge(TL, value, BL)
return res
def solve_lower_triangular_system(self, b):
"""
This function is going to solve for
L*z = b
where we solve for z, b is given and L is a lower unit triangular matrix
(most likely the result of a LU operation)
:b: Vector, the vector needed to solve the system
:returns: Vector
"""
res = Vector.copy(b)
bit = res.vector_iterator()
it = self.full_iterator()
for TL,value,BL in bit:
data = it.next()
BL = BL + (-(value * data["a21"]))
bit.merge(TL,value,BL)
return res
def solve_upper_triangular_system(self, b):
"""
This function is the complementary one for solving a liner equation system
based on LU,
with solve_lower_triangular_system we solved L* z = b
where now we can solve U* x = b where z = U*x and U is the upper triangular
matrix from the factoriazition, basically we are performing a backward sostiuition
:b: Vector, the vector needed to solve the system
:returns: Vector
"""
res = Vector.copy(b)
bit = res.vector_iterator(True)
it = self.full_iterator(True)
for TL, value, BL in bit:
data = it.next()
value -= data["at12"].dot(BL)
value /= data["a11"]
bit.merge(TL, value, BL)
return res
def solve_upper_triangular_system(self,b):
"""
This function is the complementary one for solving a liner equation system
based on LU,
with solve_lower_triangular_system we solved L* z = b
where now we can solve U* x = b where z = U*x and U is the upper triangular
matrix from the factoriazition, basically we are performing a backward sostiuition
:b: Vector, the vector needed to solve the system
:returns: Vector
"""
res = Vector.copy(b)
bit = res.vector_iterator(True)
it = self.full_iterator(True)
for TL,value,BL in bit:
data = it.next()
value -= data["at12"].dot(BL)
value /= data["a11"]
bit.merge(TL,value,BL)
return res
def copy(cls, mat):
"""
Alternative constructor to generate a matrix identical to the given one
"""
return cls(mat.columns(),
[Vector.copy(v) for v in mat.column_iterator()], False)
def copy(cls, mat):
"""
Alternative constructor to generate a matrix identical to the given one
"""
return cls(mat.columns(),[Vector.copy(v) for v in mat.column_iterator()],False)