def test_block_diag1():
x, y, z = symbols("x y z")
a = Matrix([[1, 2], [2, 3]])
b = Matrix([[3, x], [y, 3]])
c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
assert block_diag([a, b, b]) == Matrix([
[1, 2, 0, 0, 0, 0],
[2, 3, 0, 0, 0, 0],
[0, 0, 3, x, 0, 0],
[0, 0, y, 3, 0, 0],
[0, 0, 0, 0, 3, x],
[0, 0, 0, 0, y, 3],
])
assert block_diag([a, b, c]) == Matrix([
[1, 2, 0, 0, 0, 0, 0],
[2, 3, 0, 0, 0, 0, 0],
[0, 0, 3, x, 0, 0, 0],
[0, 0, y, 3, 0, 0, 0],
[0, 0, 0, 0, 3, x, 3],
[0, 0, 0, 0, y, 3, z],
[0, 0, 0, 0, x, y, z],
])
assert block_diag([a, c, b]) == Matrix([
[1, 2, 0, 0, 0, 0, 0],
[2, 3, 0, 0, 0, 0, 0],
[0, 0, 3, x, 3, 0, 0],
[0, 0, y, 3, z, 0, 0],
[0, 0, x, y, z, 0, 0],
[0, 0, 0, 0, 0, 3, x],
[0, 0, 0, 0, 0, y, 3],
])
def test_block_diag1():
x, y, z = symbols("x y z")
a = Matrix([[1, 2], [2, 3]])
b = Matrix([[3, x], [y, 3]])
c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
assert block_diag([a, b, b]) == Matrix([
[1, 2, 0, 0, 0, 0],
[2, 3, 0, 0, 0, 0],
[0, 0, 3, x, 0, 0],
[0, 0, y, 3, 0, 0],
[0, 0, 0, 0, 3, x],
[0, 0, 0, 0, y, 3],
])
assert block_diag([a, b, c]) == Matrix([
[1, 2, 0, 0, 0, 0, 0],
[2, 3, 0, 0, 0, 0, 0],
[0, 0, 3, x, 0, 0, 0],
[0, 0, y, 3, 0, 0, 0],
[0, 0, 0, 0, 3, x, 3],
[0, 0, 0, 0, y, 3, z],
[0, 0, 0, 0, x, y, z],
])
assert block_diag([a, c, b]) == Matrix([
[1, 2, 0, 0, 0, 0, 0],
[2, 3, 0, 0, 0, 0, 0],
[0, 0, 3, x, 3, 0, 0],
[0, 0, y, 3, z, 0, 0],
[0, 0, x, y, z, 0, 0],
[0, 0, 0, 0, 0, 3, x],
[0, 0, 0, 0, 0, y, 3],
])
def test_get_diag_blocks2():
x, y, z = symbols("x y z")
a = Matrix([[1, 2], [2, 3]])
b = Matrix([[3, x], [y, 3]])
c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
assert block_diag([a, b, b]).get_diag_blocks() == [a, b, b]
assert block_diag([a, b, c]).get_diag_blocks() == [a, b, c]
assert block_diag([a, c, b]).get_diag_blocks() == [a, c, b]
assert block_diag([c, c, b]).get_diag_blocks() == [c, c, b]
def test_get_diag_blocks2():
x, y, z = symbols("x y z")
a = Matrix([[1, 2], [2, 3]])
b = Matrix([[3, x], [y, 3]])
c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
assert block_diag([a, b, b]).get_diag_blocks() == [a, b, b]
assert block_diag([a, b, c]).get_diag_blocks() == [a, b, c]
assert block_diag([a, c, b]).get_diag_blocks() == [a, c, b]
assert block_diag([c, c, b]).get_diag_blocks() == [c, c, b]
def test_inv_block():
x, y, z = symbols("x y z")
a = Matrix([[1, 2], [2, 3]])
b = Matrix([[3, x], [y, 3]])
c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
A = block_diag([a, b, b])
assert A.inv(try_block_diag=True) == block_diag([a.inv(), b.inv(), b.inv()])
A = block_diag([a, b, c])
assert A.inv(try_block_diag=True) == block_diag([a.inv(), b.inv(), c.inv()])
A = block_diag([a, c, b])
assert A.inv(try_block_diag=True) == block_diag([a.inv(), c.inv(), b.inv()])
A = block_diag([a, a, b, a, c, a])
assert A.inv(try_block_diag=True) == block_diag([
a.inv(), a.inv(), b.inv(), a.inv(), c.inv(), a.inv()])
assert A.inv(try_block_diag=True, method="ADJ") == block_diag([
a.inv(method="ADJ"), a.inv(method="ADJ"), b.inv(method="ADJ"),
a.inv(method="ADJ"), c.inv(method="ADJ"), a.inv(method="ADJ")])
def test_inv_block():
x, y, z = symbols("x y z")
a = Matrix([[1, 2], [2, 3]])
b = Matrix([[3, x], [y, 3]])
c = Matrix([[3, x, 3], [y, 3, z], [x, y, z]])
A = block_diag([a, b, b])
assert A.inv(try_block_diag=True) == block_diag([a.inv(), b.inv(), b.inv()])
A = block_diag([a, b, c])
assert A.inv(try_block_diag=True) == block_diag([a.inv(), b.inv(), c.inv()])
A = block_diag([a, c, b])
assert A.inv(try_block_diag=True) == block_diag([a.inv(), c.inv(), b.inv()])
A = block_diag([a, a, b, a, c, a])
assert A.inv(try_block_diag=True) == block_diag([
a.inv(), a.inv(), b.inv(), a.inv(), c.inv(), a.inv()])
assert A.inv(try_block_diag=True, method="ADJ") == block_diag([
a.inv(method="ADJ"), a.inv(method="ADJ"), b.inv(method="ADJ"),
a.inv(method="ADJ"), c.inv(method="ADJ"), a.inv(method="ADJ")])