def test_1(self):
# dimension of the nullspace
A = sp.array([[1., 2., 3., 1.], [1., 1., 2., 1.], [1., 2., 3., 1.]])
N = nullspace(A)
dimension = rank(N)
assert dimension == 2
def test_4():
# numpy 0-D array
A = sp.array([1, 0])
assert artools.rank(A) == 1
def test_3():
# row vector
A = sp.array([[1, 0]])
assert artools.rank(A) == 1
def test_2():
# two linearly dependent rows
A = sp.array([[1, 1], [1, 1]])
assert artools.rank(A) == 1
def test_1():
# identity matrix
A = sp.array([[1, 0], [0, 1]])
assert artools.rank(A) == 2
def test_8():
# square matrix of independent vectors
A = sp.array([[1, 2], [3, 1]])
# rank(A) = number of columns
assert rank(A) == A.shape[1]
def test_1():
# identity matrix
A = sp.array([[1, 0], [0, 1]])
assert rank(A) == 2
def test_6():
# matrix and its transpose
A = sp.array([[1, 1, 1], [2, 1, 2], [3, 2, 3], [1, 1, 1]])
A_transpose = A.T
assert rank(A) == rank(A_transpose)
def test_5():
# linear combination of preceeding vectors
A = sp.array([[1, 1, 1], [2, 1, 2], [3, 2, 3], [1, 1, 1]])
assert rank(A) == 2
def test_4():
# numpy 0-D array
A = sp.array([1, 0])
assert rank(A) == 1
def test_3():
# row vector
A = sp.array([[1, 0]])
assert rank(A) == 1
def test_2():
# two linearly dependent rows
A = sp.array([[1, 1], [1, 1]])
assert rank(A) == 1
