def test_matrix_vector_multiplication():
result = []
for i in range(rownum):
result.append(Vector(A[i]).dot(x))
y = Vector(result)
assert A * x == y
assert x * A == y
# multiply column by column
result = Vector.zero(size=rownum)
AT = tuple(A.transpose().vectorize_rows())
for i in range(rownum):
result = result + AT[i] * x.components[i]
assert result == A * x
# multiply column by column (using axpy)
result = Vector.zero(size=rownum)
AT = tuple(A.transpose().vectorize_rows())
for i in range(rownum):
result = axpy(AT[i], x.components[i], result)
assert result == A * x
def test_zero_creation():
assert Vector.zero(2) == Vector(0, 0)
assert Vector.zero(5) == Vector(0, 0, 0, 0, 0)
def test_vector_splitting_to_basis_products():
product_vector = Vector.zero(len(a))
for i, component in enumerate(a):
product_vector += Vector.basis(i, len(a)) * component
assert product_vector == a
def zero(cls, m: int, n: int) -> 'Matrix':
"""
Returns the zero matrix of given dimensions
"""
return cls(rows=(Vector.zero(n) for _ in range(m)))