def test_get_item():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
assert A[5] == 6
assert A[-1] == 9
assert A[2, 2] == 9
assert A[-2, 2] == 6
assert A[1:2, 0] == DenseMatrix(1, 1, [4])
assert A[1:3, 0] == DenseMatrix(2, 1, [4, 7])
assert A[1:3, 0] == DenseMatrix(2, 1, [4, 7])
assert A[1:3, 1:] == DenseMatrix(2, 2, [5, 6, 8, 9])
assert A[1:3, :1] == DenseMatrix(2, 1, [4, 7])
assert A[0, 0:] == DenseMatrix(1, 3, [1, 2, 3])
assert A[2, :] == DenseMatrix(1, 3, [7, 8, 9])
assert A[:2, -2:] == DenseMatrix(2, 2, [2, 3, 5, 6])
assert A[1:, :3] == DenseMatrix(2, 3, [4, 5, 6, 7, 8, 9])
assert A[1:] == [2, 3, 4, 5, 6, 7, 8, 9]
assert A[-2:] == [8, 9]
raises(IndexError, lambda: A[-10])
raises(IndexError, lambda: A[9])
raises(IndexError, lambda: A[1:3, 3])
raises(IndexError, lambda: A[1:3, -4])
def test_LDL():
A = DenseMatrix(3, 3, [4, 12, -16, 12, 37, -43, -16, -43, 98])
L, D = A.LDL()
assert L == DenseMatrix(3, 3, [1, 0, 0, 3, 1, 0, -4, 5, 1])
assert D == DenseMatrix(3, 3, [4, 0, 0, 0, 1, 0, 0, 0, 9])
def test_is_real_matrix():
A = DenseMatrix(2, 2, [1, 2, 3, I])
assert not A.is_real_matrix
B = DenseMatrix(1, 1, [Symbol('x')])
assert B.is_real_matrix is None
C = DenseMatrix(3, 3, [0, 0, 0, 0, 0, 0, 0, 0, 0])
assert C.is_real_matrix
def test_submatrix():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
assert A.submatrix(0, 0, 0, 2) == DenseMatrix(1, 3, [1, 2, 3])
assert A.submatrix(2, 2, 0, 2) == DenseMatrix(1, 3, [7, 8, 9])
assert A.submatrix(0, 1, 1, 2) == DenseMatrix(2, 2, [2, 3, 5, 6])
assert A.submatrix(1, 2, 0, 2) == DenseMatrix(2, 3, [4, 5, 6, 7, 8, 9])
def test_is_diagonal():
A = DenseMatrix(2, 2, [1, 0, 0, I])
assert A.is_diagonal
B = DenseMatrix(1, 1, [Symbol('x')])
assert B.is_diagonal
C = DenseMatrix(3, 3, [0, 0, 0, 0, 0, 0, 0, 2, 0])
assert not C.is_diagonal
def test_is_hermitian():
A = DenseMatrix(2, 2, [1, 3, 2, I])
assert not A.is_hermitian
B = DenseMatrix(1, 1, [Symbol('x')])
assert B.is_hermitian is None
C = DenseMatrix(3, 3, [0, I, 0, 0, 0, 0, 0, 2, 0])
assert not C.is_hermitian
def test_is_symmetric():
A = DenseMatrix(2, 2, [1, 3, 2, I])
assert not A.is_symmetric
B = DenseMatrix(1, 1, [Symbol('x')])
assert B.is_symmetric
C = DenseMatrix(3, 3, [0, 0, 0, 0, 0, 0, 0, 2, 0])
assert not C.is_symmetric
def test_mul_scalar():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
a = Symbol("a")
assert A.mul_scalar(a) == DenseMatrix(2, 2, [a, 2*a, 3*a, 4*a])
i5 = Integer(5)
assert A.mul_scalar(i5) == DenseMatrix(2, 2, [5, 10, 15, 20])
def test_DenseMatrix_symbols():
x, y, z = symbols("x y z")
D = DenseMatrix(4, 4,
[1, 0, 1, 0,
0, z, y, 0,
z, 1, x, 1,
1, 1, 0, 0])
assert D.get(1, 2) == y
def test_dump_complex():
if not HAVE_NUMPY: # nosetests work-around
return
ref = [1j, 2j, 3j, 4j]
A = DenseMatrix(2, 2, ref)
out = np.empty(4, dtype=np.complex128)
A.dump_complex(out)
assert np.allclose(out, ref)
def test_add_scalar():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
a = Symbol("a")
assert A.add_scalar(a) == DenseMatrix(2, 2, [1 + a, 2 + a, 3 + a, 4 + a])
i5 = Integer(5)
assert A.add_scalar(i5) == DenseMatrix(2, 2, [6, 7, 8, 9])
def test_dump_real():
if not HAVE_NUMPY: # nosetests work-around
return
ref = [1, 2, 3, 4]
A = DenseMatrix(2, 2, ref)
out = np.empty(4)
A.dump_real(out)
assert np.allclose(out, ref)
def test_jacobian():
x, y, z, t = symbols("x y z t")
J_correct = DenseMatrix(4, 4,
[1, 0, 1, 0, 0, z, y, 0, z, 1, x, 1, 1, 1, 0, 0])
D = DenseMatrix(4, 1, [x + z, y * z, z * x + y + t, x + y])
x = DenseMatrix(4, 1, [x, y, z, t])
J = D.jacobian(x)
assert J == J_correct
def test_LUdecomp():
testmat = DenseMatrix([[0, 2, 5, 3], [3, 3, 7, 4], [8, 4, 0, 2],
[-2, 6, 3, 4]])
L, U, p = testmat.LUdecomposition()
res = L * U
for orig, new in p:
res.row_swap(orig, new)
assert res - testmat == zeros(4)
def test_dump_real():
if not HAVE_NUMPY: # nosetests work-around
return
ref = [1, 2, 3, 4]
A = DenseMatrix(2, 2, ref)
out = np.empty(4)
A.dump_real(out)
assert np.allclose(out, ref)
def test_transpose():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
assert A.transpose() == DenseMatrix(3, 3, [1, 4, 7, 2, 5, 8, 3, 6, 9])
A = DenseMatrix(2, 2, [1, 2, 2, 1])
assert A.transpose() == A
def test_FFLU():
A = DenseMatrix(4, 4, [1, 2, 3, 4, 2, 2, 3, 4, 3, 3, 3, 4, 9, 8, 7, 6])
L, U = A.FFLU()
assert L == DenseMatrix(
4, 4, [1, 0, 0, 0, 2, -2, 0, -0, 3, -3, 3, 0, 9, -10, 10, -10])
assert U == DenseMatrix(
4, 4, [1, 2, 3, 4, 0, -2, -3, -4, 0, 0, 3, 4, 0, 0, 0, -10])
def test_DenseMatrix_symbols():
x, y, z = symbols("x y z")
D = DenseMatrix(4, 4,
[1, 0, 1, 0,
0, z, y, 0,
z, 1, x, 1,
1, 1, 0, 0])
assert D.get(1, 2) == y
def test_dump_complex():
if not HAVE_NUMPY: # nosetests work-around
return
ref = [1j, 2j, 3j, 4j]
A = DenseMatrix(2, 2, ref)
out = np.empty(4, dtype=np.complex128)
A.dump_complex(out)
assert np.allclose(out, ref)
def test_sub():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [0, -1, -2, -3])
a = Symbol("a")
assert A - B == DenseMatrix(2, 2, [1, 3, 5, 7])
C = DenseMatrix(2, 1, [1, 2])
raises(ShapeError, lambda: A - C)
raises(TypeError, lambda: A - 5)
raises(TypeError, lambda: 5 - A)
def test_set_item():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
A[2] = 7
A[2, 2] = 8
A[-2] = 3
A[-2, -1] = 1
B = DenseMatrix(3, 3, [1, 2, 7, 4, 5, 1, 7, 3, 8])
assert A == B
def test_jacobian():
x, y, z, t = symbols("x y z t")
J_correct = DenseMatrix(4, 4,
[1, 0, 1, 0,
0, z, y, 0,
z, 1, x, 1,
1, 1, 0, 0])
D = DenseMatrix(4, 1, [x+z, y*z, z*x+y+t, x+y])
x = DenseMatrix(4, 1, [x, y, z, t])
J = D.jacobian(x)
assert J == J_correct
def test_div():
w, x, y, z = symbols("w, x, y, z")
A = DenseMatrix([[w, x], [y, z]])
B = DenseMatrix([[1, 1], [1, 0]])
C = DenseMatrix([[x, w - x], [z, y - z]])
assert A / 2 == DenseMatrix([[w / 2, x / 2], [y / 2, z / 2]])
assert C * B == A
assert A / B == C
raises(TypeError, lambda: 2 / A)
def test_add_scalar():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
a = Symbol("a")
assert A.add_scalar(a) == DenseMatrix(2, 2, [1 + a, 2 + a, 3 + a, 4 + a])
i5 = Integer(5)
assert A.add_scalar(i5) == DenseMatrix(2, 2, [6, 7, 8, 9])
raises(TypeError, lambda: A + 5)
raises(TypeError, lambda: 5 + A)
def test_solve():
A = DenseMatrix(4, 4, [1, 2, 3, 4, 2, 2, 3, 4, 3, 3, 3, 4, 9, 8, 7, 6])
b = DenseMatrix(4, 1, [10, 11, 13, 30])
y = DenseMatrix(4, 1, [1, 1, 1, 1]);
x = A.solve(b, 'LU')
assert x == y
x = A.solve(b, 'FFLU')
assert x == y
x = A.solve(b, 'FFGJ')
assert x == y
def test_inv():
A = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.inv() == A
A = DenseMatrix(2, 2, [1, 2, 2, 3])
B = DenseMatrix(2, 2, [-3, 2, 2, -1])
assert A.inv('LU') == B
assert A.inv('FFLU') == B
assert A.inv('GJ') == B
def test_add_matrix():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.add_matrix(B) == DenseMatrix(2, 2, [2, 2, 3, 5])
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a + b, a - b, a, b])
B = DenseMatrix(2, 2, [a - b, a + b, -a, b])
assert A.add_matrix(B) == DenseMatrix(2, 2, [2*a, 2*a, 0, 2*b])
def test_submatrix():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
assert A.submatrix(0, 0, 0, 2) == DenseMatrix(1, 3, [1, 2, 3])
assert A.submatrix(2, 2, 0, 2) == DenseMatrix(1, 3, [7, 8, 9])
assert A.submatrix(0, 1, 1, 2) == DenseMatrix(2, 2, [2, 3, 5, 6])
assert A.submatrix(1, 2, 0, 2) == DenseMatrix(2, 3, [4, 5, 6, 7, 8, 9])
def test_mul_matrix():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.mul_matrix(B) == A
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
B = DenseMatrix(2, 2, [1, 0, 1, 0])
assert A.mul_matrix(B) == DenseMatrix(2, 2, [a + b, 0, c + d, 0])
def test_mul_scalar():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
a = Symbol("a")
assert A.mul_scalar(a) == DenseMatrix(2, 2, [a, 2 * a, 3 * a, 4 * a])
i5 = Integer(5)
assert A.mul_scalar(i5) == DenseMatrix(2, 2, [5, 10, 15, 20])
assert A * 5 == DenseMatrix(2, 2, [5, 10, 15, 20])
assert 5 * A == DenseMatrix(2, 2, [5, 10, 15, 20])
assert a * A == DenseMatrix(2, 2, [a, 2 * a, 3 * a, 4 * a])
def test_add_scalar():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
a = Symbol("a")
assert A.add_scalar(a) == DenseMatrix(2, 2, [1 + a, 2 + a, 3 + a, 4 + a])
i5 = Integer(5)
assert A.add_scalar(i5) == DenseMatrix(2, 2, [6, 7, 8, 9])
assert A + 5 == DenseMatrix(2, 2, [6, 7, 8, 9])
assert 5 + A == DenseMatrix(2, 2, [6, 7, 8, 9])
assert a + A == DenseMatrix(2, 2, [a + 1, a + 2, a + 3, a + 4])
def test_row_insert():
M = zeros(3)
V = ones(1, 3)
assert M.row_insert(1, V) == DenseMatrix([[0, 0, 0],
[1, 1, 1],
[0, 0, 0],
[0, 0, 0]])
def test_QR():
A = DenseMatrix(3, 3, [12, -51, 4, 6, 167, -68, -4, 24, -41])
Q, R = A.QR()
assert Q == DenseMatrix(3, 3, [
Rational(6, 7),
Rational(-69, 175),
Rational(-58, 175),
Rational(3, 7),
Rational(158, 175),
Rational(6, 175),
Rational(-2, 7),
Rational(6, 35),
Rational(-33, 35)
])
assert R == DenseMatrix(3, 3, [14, 21, -14, 0, 175, -70, 0, 0, 35])
def test_det():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
assert A.det() == -2
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
assert A.det() == a * d - b * c
A = DenseMatrix(3, 2, [1, 2, 3, 4, 5, 6])
raises(NonSquareMatrixError, lambda: A.det())
def test_set_item():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
A[2] = 7
A[2, 2] = 8
A[-2] = 3
A[-2, -1] = 1
assert A == DenseMatrix(3, 3, [1, 2, 7, 4, 5, 1, 7, 3, 8])
A[0, :] = [10, 11, 12]
assert A == DenseMatrix(3, 3, [10, 11, 12, 4, 5, 1, 7, 3, 8])
A[:, 1] = [13, 14, 15]
assert A == DenseMatrix(3, 3, [10, 13, 12, 4, 14, 1, 7, 15, 8])
A[0::2, :] = [[1, 2, 3], [4, 5, 6]]
assert A == DenseMatrix(3, 3, [1, 2, 3, 4, 14, 1, 4, 5, 6])
def test_add_matrix():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.add_matrix(B) == DenseMatrix(2, 2, [2, 2, 3, 5])
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a + b, a - b, a, b])
B = DenseMatrix(2, 2, [a - b, a + b, -a, b])
assert A.add_matrix(B) == DenseMatrix(2, 2, [2*a, 2*a, 0, 2*b])
assert A + B == DenseMatrix(2, 2, [2*a, 2*a, 0, 2*b])
C = DenseMatrix(1, 2, [a, b])
raises(ShapeError, lambda: A + C)
def test_transpose():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
assert A.transpose() == DenseMatrix(3, 3, [1, 4, 7, 2, 5, 8, 3, 6, 9])
A = DenseMatrix(2, 2, [1, 2, 2, 1])
assert A.transpose() == A
def test_FFLDU():
A = DenseMatrix(3, 3, [1, 2, 3, 5, -3, 2, 6, 2, 1])
L, D, U = A.FFLDU()
assert L == DenseMatrix(3, 3, [1, 0, 0, 5, -13, 0, 6, -10, 1])
assert D == DenseMatrix(3, 3, [1, 0, 0, 0, -13, 0, 0, 0, -13])
assert U == DenseMatrix(3, 3, [1, 2, 3, 0, -13, -13, 0, 0, 91])
def test_solve():
A = DenseMatrix(4, 4, [1, 2, 3, 4, 2, 2, 3, 4, 3, 3, 3, 4, 9, 8, 7, 6])
b = DenseMatrix(4, 1, [10, 11, 13, 30])
y = DenseMatrix(4, 1, [1, 1, 1, 1])
x = A.solve(b, 'LU')
assert x == y
x = A.solve(b, 'FFLU')
assert x == y
x = A.solve(b, 'FFGJ')
assert x == y
def test_get():
A = DenseMatrix([[1, 2], [3, 4]])
assert A.get(0, 0) == 1
assert A.get(0, 1) == 2
assert A.get(1, 1) == 4
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
assert A.get(0, 0) == a
assert A.get(1, 0) == c
assert A.get(1, 1) == d
assert A.get(-1, 0) == c
assert A.get(-1, -1) == d
raises(IndexError, lambda: A.get(2, 0))
raises(IndexError, lambda: A.get(0, 2))
raises(IndexError, lambda: A.get(-3, 0))
def test_sub():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [0, -1, -2, -3])
a = Symbol("a")
assert A - 5 == DenseMatrix(2, 2, [-4, -3, -2, -1])
assert a - A == DenseMatrix(2, 2, [a - 1, a - 2, a - 3, a - 4])
assert A - B == DenseMatrix(2, 2, [1, 3, 5, 7])
C = DenseMatrix(2, 1, [1, 2])
raises(ShapeError, lambda: A - C)
def test_add_scalar():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
a = Symbol("a")
assert A.add_scalar(a) == DenseMatrix(2, 2, [1 + a, 2 + a, 3 + a, 4 + a])
i5 = Integer(5)
assert A.add_scalar(i5) == DenseMatrix(2, 2, [6, 7, 8, 9])
raises(TypeError, lambda: A + 5)
raises(TypeError, lambda: 5 + A)
def test_inv():
A = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.inv() == A
A = DenseMatrix(2, 2, [1, 2, 2, 3])
B = DenseMatrix(2, 2, [-3, 2, 2, -1])
assert A.inv('LU') == B
assert A.inv('FFLU') == B
assert A.inv('GJ') == B
def test_det():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
assert A.det() == -2
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
assert A.det() == a*d - b*c
A = DenseMatrix(3, 2, [1, 2, 3, 4, 5, 6])
raises(NonSquareMatrixError, lambda: A.det())
def test_get():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
assert A.get(0, 0) == 1
assert A.get(0, 1) == 2
assert A.get(1, 1) == 4
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
assert A.get(0, 0) == a
assert A.get(1, 0) == c
assert A.get(1, 1) == d
def test_mul_matrix():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.mul_matrix(B) == A
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
B = DenseMatrix(2, 2, [1, 0, 1, 0])
assert A.mul_matrix(B) == DenseMatrix(2, 2, [a + b, 0, c + d, 0])
assert A * B == DenseMatrix(2, 2, [a + b, 0, c + d, 0])
A = DenseMatrix(2, 3, [1, 2, 3, 2, 3, 4])
B = DenseMatrix(3, 2, [3, 4, 4, 5, 5, 6])
assert A.mul_matrix(B) == DenseMatrix(2, 2, [26, 32, 38, 47])
def test_mul_matrix():
A = DenseMatrix(2, 2, [1, 2, 3, 4])
B = DenseMatrix(2, 2, [1, 0, 0, 1])
assert A.mul_matrix(B) == A
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
d = Symbol("d")
A = DenseMatrix(2, 2, [a, b, c, d])
B = DenseMatrix(2, 2, [1, 0, 1, 0])
assert A.mul_matrix(B) == DenseMatrix(2, 2, [a + b, 0, c + d, 0])
assert A * B == DenseMatrix(2, 2, [a + b, 0, c + d, 0])
C = DenseMatrix(2, 3, [1, 2, 3, 2, 3, 4])
D = DenseMatrix(3, 2, [3, 4, 4, 5, 5, 6])
assert C.mul_matrix(D) == DenseMatrix(2, 2, [26, 32, 38, 47])
raises(ShapeError, lambda: A*D)
def test_set():
i7 = Integer(7)
y = Symbol("y")
g = function_symbol("g", y)
c = 2*I + 3
A = DenseMatrix(2, 2,
[Integer(5), Symbol("x"), function_symbol("f", Symbol("x")), 1 + I])
A.set(0, 0, i7)
assert A.get(0, 0) == i7
A.set(0, 1, y)
assert A.get(0, 1) == y
A.set(1, 0, g)
assert A.get(1, 0) == g
A.set(1, 1, c)
assert A.get(1, 1) == c
def test_repr_latex():
testmat = DenseMatrix([[0, 2]])
init_printing(True)
latex_string = testmat._repr_latex_()
assert isinstance(latex_string, str)
init_printing(False)
def test_set_item():
A = DenseMatrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
A[2] = 7
A[2, 2] = 8
A[-2] = 3
A[-2, -1] = 1
assert A == DenseMatrix(3, 3, [1, 2, 7, 4, 5, 1, 7, 3, 8])
A[0, :] = [10, 11, 12]
assert A == DenseMatrix(3, 3, [10, 11, 12, 4, 5, 1, 7, 3, 8])
A[:, 1] = [13, 14, 15]
assert A == DenseMatrix(3, 3, [10, 13, 12, 4, 14, 1, 7, 15, 8])
A[0::2, :] = [[1, 2, 3], [4, 5, 6]]
assert A == DenseMatrix(3, 3, [1, 2, 3, 4, 14, 1, 4, 5, 6])
B = DenseMatrix(A)
B[[0, 2], 0] = -1
assert B == DenseMatrix(3, 3, [-1, 2, 3, 4, 14, 1, -1, 5, 6])
B = DenseMatrix(A)
B[[0, 2], 0] = [-1, -2]
assert B == DenseMatrix(3, 3, [-1, 2, 3, 4, 14, 1, -2, 5, 6])
B = DenseMatrix(A)
B[[0, 2], 0] = [[-1], [-2]]
assert B == DenseMatrix(3, 3, [-1, 2, 3, 4, 14, 1, -2, 5, 6])
B = DenseMatrix(A)
B[[0, 2], [0]] = [-1, -2]
assert B == DenseMatrix(3, 3, [-1, 2, 3, 4, 14, 1, -2, 5, 6])
B = DenseMatrix(A)
B[[0, 2], [0]] = [[-1], [-2]]
assert B == DenseMatrix(3, 3, [-1, 2, 3, 4, 14, 1, -2, 5, 6])
B = DenseMatrix(A)
B[0, [0, 2]] = [-1, -2]
assert B == DenseMatrix(3, 3, [-1, 2, -2, 4, 14, 1, 4, 5, 6])
B = DenseMatrix(A)
B[0, [0, 2]] = -1
assert B == DenseMatrix(3, 3, [-1, 2, -1, 4, 14, 1, 4, 5, 6])
B = DenseMatrix(A)
B[:, [0, 2]] = -1
assert B == DenseMatrix(3, 3, [-1, 2, -1, -1, 14, -1, -1, 5, -1])
B = DenseMatrix(A)
B[[0, 1], [0, 2]] = -1
assert B == DenseMatrix(3, 3, [-1, 2, -1, -1, 14, -1, 4, 5, 6])
A = zeros(3, 4)
B = ones(1, 4)
A[0, :] = B
assert A[0, :] == B
A = zeros(3, 4)
B = ones(3, 1)
A[:, 0] = B
assert A[:, 0] == B
