def test_transpose_is_self_inverse(expr):
expr = simplify(expr)
assert transpose(transpose(expr)) == expr
def generate_equation(n_ops):
expr_size = operand_sizes()
out = ae.Matrix("out", expr_size)
expr = simplify(generate_expression(n_ops, expr_size))
return aeq.Equations(ae.Equal(out, expr))
def test_transpose_and_invert_same_as_invert_transpose(expr):
expr = simplify(expr)
assert transpose(invert(expr)) == invert_transpose(expr)
def test_transpose_and_invert_order_does_not_matter(expr):
expr = simplify(expr)
assert invert(transpose(expr)) == transpose(invert(expr))
def test_invert_is_self_inverse(expr):
expr = simplify(expr)
assert invert(invert(expr)) == expr
def matrix_chain_generator():
while True:
# for _ in range(20):
# expression_strategy.example()
# generate_matrix_chain()
length = random.randrange(4, 10)
sizes = []
if 0.95 <= random.random():
sizes.append(1)
else:
sizes.append(matrix_size())
for i in range(length):
rand = random.random()
if 0.6 <= rand < 0.95:
# square
sizes.append(sizes[i])
elif 0.95 <= rand:
# vector
sizes.append(1)
else:
# non-square
sizes.append(matrix_size())
# print(sizes)
operands = []
restart = False
for rows, columns in window(sizes):
if rows == columns:
if rows == 1:
restart = True
break
# operands.append(None) # error
op = random.choices([ae.Identity, ae.Transpose, ae.Inverse, ae.InverseTranspose], weights=[2, 1, 1, 1])[0]
operands.append(op(generate_operand(rows, columns)))
elif rows == 1:
operands.append(ae.Transpose(generate_operand(columns, rows)))
elif columns == 1:
operands.append(generate_operand(rows, columns))
else:
op = random.choices([ae.Identity, ae.Transpose], weights=[3, 1])[0]
if op == ae.Transpose:
operands.append(op(generate_operand(columns, rows)))
else:
operands.append(op(generate_operand(rows, columns)))
if restart:
continue
# print(operands)
expr = ae.Times(*operands)
expr = simplify(expr)
# print(expr)
# print(expr.size)
# print((sizes[0], sizes[-1]))
if expr.has_property(properties.MATRIX):
lhs = ae.Matrix('X'.format(_n), size=(sizes[0], sizes[-1]))
elif expr.has_property(properties.VECTOR):
lhs = ae.Vector('x'.format(_n), size=(sizes[0], sizes[-1]))
yield Equations(ae.Equal(lhs, expr))
def test_simplify(input, expected_output):
output = simplify(input)
assert output == expected_output, "{} did not simplify to {}, but instead to {}.".format(
input, expected_output, output)