def mult_vec_lower_symmetric_by_axpy(self, vec):
"""
This function implements a matrix vector mult based on AXPY using an upper simmetrix matric
:vec: Vector, the vector to work on
:returns: Vector
"""
result = Vector([0] * self.rows())
it = self.full_iterator()
vit = result.vector_iterator()
for i, data in enumerate(it):
#slicing the vector
tl, value, bl = vit.next()
#computing the diagonal value
value = data["a11"] * vec[i] + value
tl = data["at10"].axpy(tl, vec[i])
bl = data["a21"].axpy(bl, vec[i])
#merging the result back in
vit.merge(tl, value, bl)
return result
def mult_vec_lower_triangular_by_axpy(self, vec):
"""
This function implements a lower triangular matrix vector mult based on AXPY
:vec: Vector, the vector to work on
:returns: Vector
"""
result = Vector([0] * self.rows())
it = self.full_iterator()
vit = result.vector_iterator()
for i, data in enumerate(it):
#slicing the vector
tl, value, bl = vit.next()
#computing the diagonal value
value = data["a11"] * vec[i] + value
#computing the upper diagonal value, using an axpy
#and accumulating in the up vector
bl = data["a21"].axpy(bl, vec[i])
#merging the result back in
vit.merge(tl, value, bl)
return result
def mult_vec_upper_symmetric_by_axpy(self, vec):
"""
This function implements a matrix vector mult based on AXPY using an upper simmetrix matric
:vec: Vector, the vector to work on
:returns: Vector
"""
result = Vector([0] * self.rows())
it = self.full_iterator()
vit = result.vector_iterator()
for i, data in enumerate(it):
#slicing the vector
tl, value, bl = vit.next()
#computing the diagonal value
value = data["a11"] * vec[i] + value
#we perform two different axpy and we make up for the missing part
#by using the equivalent transposed of the column below the diagonal
#aka the row after the diagonal
tl = data["a01"].axpy(tl, vec[i])
bl = data["at12"].axpy(bl, vec[i])
#merging the result back in
vit.merge(tl, value, bl)
return result
def mult_vec_lower_symmetric_by_axpy(self, vec):
"""
This function implements a matrix vector mult based on AXPY using an upper simmetrix matric
:vec: Vector, the vector to work on
:returns: Vector
"""
result = Vector([0]* self.rows())
it = self.full_iterator()
vit = result.vector_iterator()
for i,data in enumerate(it):
#slicing the vector
tl, value, bl = vit.next()
#computing the diagonal value
value = data["a11"] * vec[i] + value
tl = data["at10"].axpy(tl,vec[i])
bl = data["a21"].axpy(bl,vec[i])
#merging the result back in
vit.merge(tl,value,bl)
return result
def mult_vec_upper_symmetric_by_axpy(self, vec):
"""
This function implements a matrix vector mult based on AXPY using an upper simmetrix matric
:vec: Vector, the vector to work on
:returns: Vector
"""
result = Vector([0]* self.rows())
it = self.full_iterator()
vit = result.vector_iterator()
for i,data in enumerate(it):
#slicing the vector
tl, value, bl = vit.next()
#computing the diagonal value
value = data["a11"] * vec[i] + value
#we perform two different axpy and we make up for the missing part
#by using the equivalent transposed of the column below the diagonal
#aka the row after the diagonal
tl = data["a01"].axpy(tl,vec[i])
bl = data["at12"].axpy(bl,vec[i])
#merging the result back in
vit.merge(tl,value,bl)
return result
def mult_vec_lower_triangular_by_axpy(self, vec):
"""
This function implements a lower triangular matrix vector mult based on AXPY
:vec: Vector, the vector to work on
:returns: Vector
"""
result = Vector([0]* self.rows())
it = self.full_iterator()
vit = result.vector_iterator()
for i,data in enumerate(it):
#slicing the vector
tl, value, bl = vit.next()
#computing the diagonal value
value = data["a11"] * vec[i] + value
#computing the upper diagonal value, using an axpy
#and accumulating in the up vector
bl = data["a21"].axpy(bl,vec[i])
#merging the result back in
vit.merge(tl,value,bl)
return result
def test_solve_upper_triangular_system(self):
mat = SquareMatrix.from_list(3, [-2, 0, 0, -1, -3, 0, 1, -2, 1])
vec = Vector([6, 9, 3])
it = vec.vector_iterator(True)
res = mat.solve_upper_triangular_system(vec)
self.is_vector_equal_to_list(res, [1, -5, 3])
def test_solve_upper_triangular_system(self):
mat = SquareMatrix.from_list(3, [-2,0,0,-1,-3,0,1,-2,1])
vec = Vector([6,9,3])
it = vec.vector_iterator(True)
res = mat.solve_upper_triangular_system(vec)
self.is_vector_equal_to_list(res,[1,-5,3])