def fn(data, weight1, weight2, bias1, bias2):
l1 = weight1.dot(data)
l1 = Matrix(l1) + b1.T
e1 = l1.applyfunc(sigmoid)
l2 = weight2.dot(e1)
l2 = Matrix(l2) + b2.T
e2 = l2.applyfunc(sigmoid)
return e2[0] - e2[1]
def test_bidiagonalize():
M = Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
assert M.bidiagonalize() == M
assert M.bidiagonalize(upper=False) == M
assert M.bidiagonalize() == M
assert M.bidiagonal_decomposition() == (M, M, M)
assert M.bidiagonal_decomposition(upper=False) == (M, M, M)
assert M.bidiagonalize() == M
import random
#Real Tests
for real_test in range(2):
test_values = []
row = 2
col = 2
for _ in range(row * col):
value = random.randint(-1000000000, 1000000000)
test_values = test_values + [value]
# L -> Lower Bidiagonalization
# M -> Mutable Matrix
# N -> Immutable Matrix
# 0 -> Bidiagonalized form
# 1,2,3 -> Bidiagonal_decomposition matrices
# 4 -> Product of 1 2 3
M = Matrix(row, col, test_values)
N = ImmutableMatrix(M)
N1, N2, N3 = N.bidiagonal_decomposition()
M1, M2, M3 = M.bidiagonal_decomposition()
M0 = M.bidiagonalize()
N0 = N.bidiagonalize()
N4 = N1 * N2 * N3
M4 = M1 * M2 * M3
N2.simplify()
N4.simplify()
N0.simplify()
M0.simplify()
M2.simplify()
M4.simplify()
LM0 = M.bidiagonalize(upper=False)
LM1, LM2, LM3 = M.bidiagonal_decomposition(upper=False)
LN0 = N.bidiagonalize(upper=False)
LN1, LN2, LN3 = N.bidiagonal_decomposition(upper=False)
LN4 = LN1 * LN2 * LN3
LM4 = LM1 * LM2 * LM3
LN2.simplify()
LN4.simplify()
LN0.simplify()
LM0.simplify()
LM2.simplify()
LM4.simplify()
assert M == M4
assert M2 == M0
assert N == N4
assert N2 == N0
assert M == LM4
assert LM2 == LM0
assert N == LN4
assert LN2 == LN0
#Complex Tests
for complex_test in range(2):
test_values = []
size = 2
for _ in range(size * size):
real = random.randint(-1000000000, 1000000000)
comp = random.randint(-1000000000, 1000000000)
value = real + comp * I
test_values = test_values + [value]
M = Matrix(size, size, test_values)
N = ImmutableMatrix(M)
# L -> Lower Bidiagonalization
# M -> Mutable Matrix
# N -> Immutable Matrix
# 0 -> Bidiagonalized form
# 1,2,3 -> Bidiagonal_decomposition matrices
# 4 -> Product of 1 2 3
N1, N2, N3 = N.bidiagonal_decomposition()
M1, M2, M3 = M.bidiagonal_decomposition()
M0 = M.bidiagonalize()
N0 = N.bidiagonalize()
N4 = N1 * N2 * N3
M4 = M1 * M2 * M3
N2.simplify()
N4.simplify()
N0.simplify()
M0.simplify()
M2.simplify()
M4.simplify()
LM0 = M.bidiagonalize(upper=False)
LM1, LM2, LM3 = M.bidiagonal_decomposition(upper=False)
LN0 = N.bidiagonalize(upper=False)
LN1, LN2, LN3 = N.bidiagonal_decomposition(upper=False)
LN4 = LN1 * LN2 * LN3
LM4 = LM1 * LM2 * LM3
LN2.simplify()
LN4.simplify()
LN0.simplify()
LM0.simplify()
LM2.simplify()
LM4.simplify()
assert M == M4
assert M2 == M0
assert N == N4
assert N2 == N0
assert M == LM4
assert LM2 == LM0
assert N == LN4
assert LN2 == LN0
M = Matrix(18, 8, range(1, 145))
M = M.applyfunc(lambda i: Float(i))
assert M.bidiagonal_decomposition()[1] == M.bidiagonalize()
assert M.bidiagonal_decomposition(upper=False)[1] == M.bidiagonalize(
upper=False)
a, b, c = M.bidiagonal_decomposition()
diff = a * b * c - M
assert abs(max(diff)) < 10**-12
