def Test(self):
with self.test_session():
np.random.seed(1)
m = np.random.uniform(
low=1.0, high=100.0,
size=np.prod(shape_)).reshape(shape_).astype(dtype_)
a = tf.constant(m)
epsilon = np.finfo(dtype_).eps
# Optimal stepsize for central difference is O(epsilon^{1/3}).
delta = epsilon**(1.0 / 3.0)
# tolerance obtained by looking at actual differences using
# np.linalg.norm(theoretical-numerical, np.inf) on -mavx build
tol = 1e-3
if len(shape_) == 2:
c = tf.matrix_determinant(a)
else:
c = tf.batch_matrix_determinant(a)
out_shape = shape_[:-2] # last two dimensions hold matrices
theoretical, numerical = tf.test.compute_gradient(a,
shape_,
c,
out_shape,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
def Test(self):
with self.test_session():
np.random.seed(1)
m = np.random.uniform(low=1.0,
high=100.0,
size=np.prod(shape_)).reshape(shape_).astype(dtype_)
a = tf.constant(m)
epsilon = np.finfo(dtype_).eps
# Optimal stepsize for central difference is O(epsilon^{1/3}).
delta = epsilon**(1.0 / 3.0)
# tolerance obtained by looking at actual differences using
# np.linalg.norm(theoretical-numerical, np.inf) on -mavx build
tol = 1e-3
if len(shape_) == 2:
c = tf.matrix_determinant(a)
else:
c = tf.batch_matrix_determinant(a)
out_shape = shape_[:-2] # last two dimensions hold matrices
theoretical, numerical = tf.test.compute_gradient(a,
shape_,
c,
out_shape,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
def _compareDeterminant(self, matrix_x):
with self.test_session():
# Check the batch version, which should work for ndim >= 2
self._compareDeterminantBase(
matrix_x, tf.batch_matrix_determinant(matrix_x))
if matrix_x.ndim == 2:
# Check the simple version
self._compareDeterminantBase(matrix_x, tf.matrix_determinant(matrix_x))
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef*tf.rsqrt(tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1,k]), [n,1]) # [n,k]
diff = tf.sub(tf.tile(points, [k,1,1]), tf.tile(mu, [n,1,1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n,1,1]) # [n*k,p,p]
exp = tf.exp(-0.5*tf.batch_matmul( tf.transpose(diff,perm=[0,2,1]), tf.batch_matmul(tf.batch_matrix_inverse(sigma), diff) )) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n,k])
return tf.mul(div, exp)
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef*tf.rsqrt(tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1,k]), [n,1]) # [n,k]
diff = tf.sub(tf.tile(points, [k,1,1]), tf.tile(mu, [n,1,1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n,1,1]) # [n*k,p,p]
exp = tf.exp(-0.5*tf.batch_matmul( tf.transpose(diff,perm=[0,2,1]), tf.batch_matmul(tf.batch_matrix_inverse(sigma), diff) )) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n,k])
return tf.mul(div, exp) # Multivariate normal distribution evaluated for each vector, for each cluster parameter. Hence the [n,k] shape.
def _compareDeterminant(self, matrix_x):
with self.test_session():
# Check the batch version, which should work for ndim >= 2
self._compareDeterminantBase(matrix_x,
tf.batch_matrix_determinant(matrix_x))
if matrix_x.ndim == 2:
# Check the simple version
self._compareDeterminantBase(matrix_x,
tf.matrix_determinant(matrix_x))
def test_determinants(self):
with self.test_session():
for batch_shape in [(), (2, 3,)]:
for k in [1, 4]:
operator, mat = self._build_operator_and_mat(batch_shape, k)
expected_det = tf.batch_matrix_determinant(mat).eval()
self._compare_results(expected_det, operator.det())
self._compare_results(np.log(expected_det), operator.log_det())
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef * tf.rsqrt(tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1, k]), [n, 1]) # [n,k]
diff = tf.sub(tf.tile(points, [k, 1, 1]), tf.tile(mu, [n, 1, 1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n, 1, 1]) # [n*k,p,p]
exp = tf.exp(
-0.5
* tf.batch_matmul(tf.transpose(diff, perm=[0, 2, 1]), tf.batch_matmul(tf.batch_matrix_inverse(sigma), diff))
) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n, k])
return tf.mul(div, exp)
def testBatchGradientUnknownSize(self):
with self.test_session():
batch_size = tf.constant(3)
matrix_size = tf.constant(4)
batch_identity = tf.tile(
tf.expand_dims(tf.diag(tf.ones([matrix_size])), 0),
[batch_size, 1, 1])
determinants = tf.batch_matrix_determinant(batch_identity)
reduced = tf.reduce_sum(determinants)
sum_grad = tf.gradients(reduced, batch_identity)[0]
self.assertAllClose(batch_identity.eval(), sum_grad.eval())
def testBatchGradientUnknownSize(self):
with self.test_session():
batch_size = tf.constant(3)
matrix_size = tf.constant(4)
batch_identity = tf.tile(
tf.expand_dims(
tf.diag(tf.ones([matrix_size])), 0), [batch_size, 1, 1])
determinants = tf.batch_matrix_determinant(batch_identity)
reduced = tf.reduce_sum(determinants)
sum_grad = tf.gradients(reduced, batch_identity)[0]
self.assertAllClose(batch_identity.eval(), sum_grad.eval())
def _compareDeterminant(self, matrix_x):
with self.test_session():
if matrix_x.ndim == 2:
tf_ans = tf.matrix_determinant(matrix_x)
else:
tf_ans = tf.batch_matrix_determinant(matrix_x)
out = tf_ans.eval()
shape = matrix_x.shape
if shape[-1] == 0 and shape[-2] == 0:
np_ans = np.ones(shape[:-2]).astype(matrix_x.dtype)
else:
np_ans = np.array(np.linalg.det(matrix_x)).astype(matrix_x.dtype)
self.assertAllClose(np_ans, out)
self.assertShapeEqual(np_ans, tf_ans)
def _compareDeterminant(self, matrix_x):
with self.test_session():
if matrix_x.ndim == 2:
tf_ans = tf.matrix_determinant(matrix_x)
else:
tf_ans = tf.batch_matrix_determinant(matrix_x)
out = tf_ans.eval()
shape = matrix_x.shape
if shape[-1] == 0 and shape[-2] == 0:
np_ans = np.ones(shape[:-2]).astype(matrix_x.dtype)
else:
np_ans = np.array(np.linalg.det(matrix_x)).astype(matrix_x.dtype)
self.assertAllClose(np_ans, out)
self.assertShapeEqual(np_ans, tf_ans)
def test_determinants(self):
with self.test_session():
for batch_shape in [(), (
2,
3,
)]:
for k in [1, 4]:
operator, mat = self._build_operator_and_mat(
batch_shape, k)
expected_det = tf.batch_matrix_determinant(mat).eval()
self._compare_results(expected_det, operator.det())
self._compare_results(np.log(expected_det),
operator.log_det())
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef * tf.rsqrt(
tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1, k]), [n, 1]) # [n,k]
diff = tf.sub(tf.tile(points, [k, 1, 1]),
tf.tile(mu, [n, 1, 1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n, 1, 1]) # [n*k,p,p]
exp = tf.exp(-0.5 * tf.batch_matmul(
tf.transpose(diff, perm=[0, 2, 1]),
tf.batch_matmul(tf.batch_matrix_inverse(sigma),
diff))) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n, k])
return tf.mul(
div, exp
) # Multivariate normal distribution evaluated for each vector, for each cluster parameter. Hence the [n,k] shape.
x = np.random.rand(2, 3) y = np.random.rand(3, 2) z_matmul = tf.matmul(x, y) # tf.batch_matmul x = np.random.rand(10, 2, 3) y = np.random.rand(10, 3, 2) z_batch_matmul = tf.batch_matmul(x, y) # tf.matrix_determinant x = np.random.rand(5, 5) z_matrix_determinant = tf.matrix_determinant(x) # tf.batch_matrix_determinant batch_x = np.random.rand(10, 5, 5) z_batch_matrix_determinant = tf.batch_matrix_determinant(batch_x) # tf.matrix_inverse x = np.random.rand(10, 10) z_matrix_inverse = tf.matrix_inverse(x) # tf.batch_matrix_inverse batch_x = np.random.rand(10, 5, 5) z_batch_matrix_inverse = tf.batch_matrix_inverse(batch_x) # tf.cholesky x = np.random.rand(10, 10) z_cholesky = tf.cholesky(x) # tf.batch_cholesky batch_x = np.random.rand(10, 5, 5)
def test_BatchMatrixDeterminant(self):
t = tf.batch_matrix_determinant(self.random(2, 3, 4, 3, 3))
self.check(t)
