def sliced_l3(source, target, size=16, nbins=32, alpha=-1, name='idt'):
src_shape = source.get_shape().as_list()
tar_shape = target.get_shape().as_list()
sbatch = src_shape[0]
tbatch = tar_shape[0]
height = src_shape[1]
width = src_shape[2]
w0, _ = tf.qr(tf.random_normal([height, height], mean=0.0, stddev=1.0))
w1, _ = tf.qr(
tf.random_normal([width * 3, width * 3], mean=0.0, stddev=1.0))
w0_ = tf.expand_dims(w0, 0)
w1_ = tf.expand_dims(w1, 0)
w0_s = tf.tile(w0_, [sbatch, 1, 1])
w1_s = tf.tile(w1_, [sbatch, 1, 1])
src = tf.reshape(source,
[sbatch, height, width * 3]) # NOTE!!!!!!!!!!!!!!!!
src_proj = tf.matmul(tf.matmul(w0_s, src), w1_s)
w0_t = tf.tile(w0_, [tbatch, 1, 1])
w1_t = tf.tile(w1_, [tbatch, 1, 1])
tar = tf.reshape(target, [tbatch, height, width * 3])
tar_proj = tf.matmul(tf.matmul(w0_t, tar), w1_t)
source_proj = tf.reshape(src_proj, [sbatch, height * width * 3])
target_proj = tf.reshape(tar_proj, [tbatch, height * width * 3])
# src_out = optimal(source_proj, target_proj, sbatch, tbatch, height * width * 3, nbins, alpha)
return wasser_1d(source_proj, target_proj, sbatch, tbatch,
height * width * 3, nbins, alpha)
def testWrongDimensions(self):
# The input to qr should be a tensor of at least rank 2.
scalar = tf.constant(1.)
with self.assertRaisesRegexp(ValueError,
"Shape must be at least rank 2 but is rank 0"):
tf.qr(scalar)
vector = tf.constant([1., 2.])
with self.assertRaisesRegexp(ValueError,
"Shape must be at least rank 2 but is rank 1"):
tf.qr(vector)
def re_unitarize(self, W):
# TODO: check this.
#_, U, V = tf.svd(W, full_matrices=True, compute_uv=True)
# W = tf.matmul(U, tf.transpose(tf.conj(V)))
W, _ = tf.qr(W)
W = tf.Print(W, [tf.constant(0)], 'step with qr.')
return W
def __call__(self, shape, dtype=None, partition_info=None):
if dtype is None:
dtype = self.dtype
# Check the shape
if len(shape) < 3 or len(shape) > 5:
raise ValueError("The tensor to initialize must be at least "
"three-dimensional and at most five-dimensional")
if shape[-2] > shape[-1]:
raise ValueError("In_filters cannot be greater than out_filters.")
# Generate a random matrix
a = tf.random_normal([shape[-1], shape[-1]],
dtype=dtype,
seed=self.seed)
# Compute the qr factorization
q, r = tf.qr(a, full_matrices=False)
# Make Q uniform
d = tf.diag_part(r)
# ph = D / math_ops.abs(D)
q *= tf.sign(d)
q = q[:shape[-2], :]
q *= tf.sqrt(tf.cast(self.gain, dtype=dtype))
if len(shape) == 3:
weight = tf.scatter_nd([[(shape[0] - 1) // 2]],
tf.expand_dims(q, 0), shape)
elif len(shape) == 4:
weight = tf.scatter_nd([[(shape[0] - 1) // 2,
(shape[1] - 1) // 2]],
tf.expand_dims(q, 0), shape)
else:
weight = tf.scatter_nd([[(shape[0] - 1) // 2, (shape[1] - 1) // 2,
(shape[2] - 1) // 2]],
tf.expand_dims(q, 0), shape)
return weight
def sliced_l1(source, target, fz=3, nbins=32, alpha=-1, name='idt'):
f_num = fz * fz * 3
src_shape = source.get_shape().as_list()
tar_shape = target.get_shape().as_list()
sbatch = src_shape[0]
tbatch = tar_shape[0]
ndepth = np.prod(src_shape[1:])
weight, _ = tf.qr(tf.random_normal([f_num, f_num]))
weight = tf.reshape(weight, [fz, fz, 3, f_num])
src_proj = tf.nn.relu(
tf.nn.conv2d(source, weight, strides=[1, 1, 1, 1], padding='SAME'))
tar_proj = tf.nn.relu(
tf.nn.conv2d(target, weight, strides=[1, 1, 1, 1], padding='SAME'))
src = tf.nn.max_pool(src_proj,
ksize=[1, 2, 2, 1],
strides=[1, 1, 1, 1],
padding="SAME")
tar = tf.nn.max_pool(tar_proj,
ksize=[1, 2, 2, 1],
strides=[1, 1, 1, 1],
padding="SAME")
# weight1, _ = tf.qr(tf.random_normal([f_num, f_num]))
# weight1 = tf.reshape(weight1, [1, 1, f_num, f_num])
# src = tf.nn.elu(tf.nn.conv2d(src, weight1, strides=[1, 1, 1, 1], padding='SAME'))
# tar = tf.nn.elu(tf.nn.conv2d(tar, weight1, strides=[1, 1, 1, 1], padding='SAME'))
sbat = sbatch
tbat = tbatch
# ndepth = 64
# return ID_wasserstein(src_proj, tar_proj, sbat, tbat, ndepth, nbins, alpha)
# return wasser_1d(src_proj, tar_proj, sbat, tbat, ndepth, nbins, alpha)
return tf.reduce_mean(tf.abs(src - tar))
def project_l1(source, target, fz=3, nbins=32, alpha=-1, name='idt'):
f_num = fz * fz * 3
wei, _ = tf.qr(tf.random_normal([f_num, f_num]))
weight = tf.reshape(wei, [fz, fz, 3, f_num])
src_proj = tf.nn.conv2d(source,
weight,
strides=[1, fz, fz, 1],
padding='VALID')
tar_proj = tf.nn.conv2d(target,
weight,
strides=[1, fz, fz, 1],
padding='VALID')
src_shape = src_proj.get_shape().as_list()
tar_shape = tar_proj.get_shape().as_list()
sbatch = src_shape[0]
tbatch = tar_shape[0]
ndepth = np.prod(src_shape[1:])
src_new = optimal(tf.reshape(src_proj, [-1, ndepth]),
tf.reshape(tar_proj, [-1, ndepth]), sbatch, tbatch,
ndepth, nbins, alpha)
src_new = tf.reshape(src_new, src_proj.get_shape())
weight_t = tf.reshape(tf.transpose(wei), [fz, fz, 3, f_num])
src_out = tf.nn.conv2d_transpose(src_new,
tf.transpose(weight),
source.get_shape(),
strides=[1, fz, fz, 1],
padding='VALID')
return src_out
def tensor_qr(self,
legs1,
legs2,
new_legs,
restrict_mode=True,
name='tensor_qr',
*args,
**kw):
"""对node做qr分解.
参数依次是Q侧leg, R侧leg, 和新产生的leg名称."""
with tf.name_scope(name):
assert set(legs1) | set(legs2) >= set(self.legs) and set(
legs1) & set(legs2) == set(), 'qr legs not correct'
if restrict_mode:
assert set(legs1) | set(legs2) == set(
self.legs), 'qr legs not correct'
legs1 = [i for i in self.legs if i in legs1]
legs2 = [i for i in self.legs if i in legs2]
transposed = self.tensor_transpose([*legs1, *legs2])
size1 = np.prod(transposed.data.shape[:len(legs1)], dtype=int)
size2 = np.prod(transposed.data.shape[len(legs1):], dtype=int)
tensor1, tensor2 = tf.qr(
tf.reshape(transposed.data, [size1, size2]), *args, **kw)
assert tensor1.shape[0] == size1
assert tensor2.shape[-1] == size2
tensor1 = tf.reshape(tensor1,
[*transposed.data.shape[:len(legs1)], -1])
tensor2 = tf.reshape(tensor2,
[-1, *transposed.data.shape[len(legs1):]])
if not isinstance(new_legs, list):
new_legs = [new_legs, new_legs]
return Node(tensor1,
[*legs1, new_legs[0]]), Node(tensor2,
[new_legs[1], *legs2])
def _orthogonalize_tt_cores_right_to_left(tt):
"""Orthogonalize TT-cores of a TT-object in the right to left order.
Args:
tt: TenosorTrain or a TensorTrainBatch.
Returns:
The same type as the input `tt` (TenosorTrain or a TensorTrainBatch).
"""
# Left to right orthogonalization.
ndims = tt.ndims()
raw_shape = shapes.lazy_raw_shape(tt)
tt_ranks = shapes.lazy_tt_ranks(tt)
prev_rank = tt_ranks[ndims]
# Copy cores references so we can change the cores.
tt_cores = list(tt.tt_cores)
for core_idx in range(ndims - 1, 0, -1):
curr_core = tt_cores[core_idx]
# TT-ranks could have changed on the previous iteration, so `tt_ranks` can
# be outdated for the current TT-rank, but should be valid for the next
# TT-rank.
curr_rank = prev_rank
prev_rank = tt_ranks[core_idx]
if tt.is_tt_matrix():
curr_mode_left = raw_shape[0][core_idx]
curr_mode_right = raw_shape[1][core_idx]
curr_mode = curr_mode_left * curr_mode_right
else:
curr_mode = raw_shape[0][core_idx]
qr_shape = (prev_rank, curr_mode * curr_rank)
curr_core = tf.reshape(curr_core, qr_shape)
curr_core, triang = tf.qr(tf.transpose(curr_core))
curr_core = tf.transpose(curr_core)
triang = tf.transpose(triang)
if triang.get_shape().is_fully_defined():
triang_shape = triang.get_shape().as_list()
else:
triang_shape = tf.shape(triang)
# The TT-rank could have changed: if qr_shape is e.g. 4 x 10, than q would
# be of size 4 x 4 and r would be 4 x 10, which means that the next rank
# should be changed to 4.
prev_rank = triang_shape[1]
if tt.is_tt_matrix():
new_core_shape = (prev_rank, curr_mode_left, curr_mode_right,
curr_rank)
else:
new_core_shape = (prev_rank, curr_mode, curr_rank)
tt_cores[core_idx] = tf.reshape(curr_core, new_core_shape)
prev_core = tf.reshape(tt_cores[core_idx - 1], (-1, triang_shape[0]))
tt_cores[core_idx - 1] = tf.matmul(prev_core, triang)
if tt.is_tt_matrix():
first_core_shape = (1, raw_shape[0][0], raw_shape[1][0], prev_rank)
else:
first_core_shape = (1, raw_shape[0][0], prev_rank)
tt_cores[0] = tf.reshape(tt_cores[0], first_core_shape)
# TODO: infer the tt_ranks.
return TensorTrain(tt_cores, tt.get_raw_shape())
def get_u_init_for_g(self, g):
N_g = tf.shape(g)[0] # number of datapoints in this cluster
gt = tf.transpose(g)
q, r = tf.qr(gt, full_matrices=False)
idx = [j for j in xrange(args.rank)]
qq = tf.gather(tf.transpose(q), idx)
qq = tf.transpose(qq)
return qq
def _variable_with_orth_weight_decay(name1, shape):
s1 = tf.cast(shape[2], tf.int32)
s2 = tf.cast(shape[2]/2, tf.int32)
w0_init, _ = tf.qr(tf.random_normal([s1, s2], mean=0.0, stddev=1.0))
w0 = tf.get_variable(name1, initializer=w0_init)
tmp1 = tf.reshape(w0, (1, s1, s2))
tmp2 = tf.reshape(tf.transpose(w0), (1, s2, s1))
tmp1 = tf.tile(tmp1, [shape[0], 1, 1])
tmp2 = tf.tile(tmp2, [shape[0], 1, 1])
return tmp1, tmp2
def stiefel_update(self, param, constraints, grad, moment, lr):
"""
Override the Stiefel updates accordingly.
Parameters
----------
param
constraint
grad
Returns
-------
corresponding Stiefel updates.
"""
p = param
m = moment
g = grad
new_g = g - K.dot(p, matrix_sym_op(K.dot(K.transpose(p), g)))
v = self.momentum * m - lr * new_g # velocity
# v.name = p.name + '_v'
# m.name = p.name + '_m'
self.updates.append(K.update(m, v))
# if self.nesterov:
# new_p = p + self.momentum * v - lr * new_g
# else:
new_p = p + v
p_shape = new_p.get_shape()
if p_shape[0]._value > p_shape[1]._value:
new_p, _ = tf.qr(new_p, full_matrices=False)
else:
new_p, _ = tf.qr(tf.transpose(new_p), full_matrices=False)
new_p = tf.transpose(new_p)
# apply constraints
if p in constraints:
c = constraints[p]
new_p = c(new_p)
self.updates.append(K.update(p, new_p))
def matrix_qr():
"""
qr分解
:return:
"""
isses = tf.InteractiveSession()
A = tf.Variable(tf.random_normal(shape=(4, 4)))
A.initializer.run()
logger.info("A\n%s" % A.eval())
logger.info("tf.qr(A)\n {0}".format(tf.qr(A)))
isses.close()
def row_dets(mat):
(n, np1) = mat.shape
q, r = tf.qr(mat)
dets = np.zeros(np1)
dets[np1-1] = 1.0
for lw in range(2, np1+1):
i = np1 - lw
ik = i + 1
dets[i] = -np.dot(qr[i, ik:np1], dets[ik:np1])/qr[i, i]
dets *= np.sign(np.prod(np.diag(qr))) # just for the sign
#dets *= np.prod(np.diag(qr)) # to get the scale exactly
return dets
def row_dets(mat):
(n, np1) = mat.shape
q, r = tf.qr(mat)
dets = np.zeros(np1)
dets[np1-1] = 1.0
for lw in range(2, np1+1):
i = np1 - lw
ik = i + 1
dets[i] = -np.dot(qr[i, ik:np1], dets[ik:np1])/qr[i, i]
dets *= np.sign(np.prod(np.diag(qr))) # just for the sign
#dets *= np.prod(np.diag(qr)) # to get the scale exactly
return dets
def sliced_l2(source, target, size=16, nbins=32, alpha=-1, name='idt'):
# target = tf.image.resize_nearest_neighbor(target, size=(size, size))
# source = tf.image.resize_nearest_neighbor(source, size=(size, size))
src_shape = source.get_shape().as_list()
tar_shape = target.get_shape().as_list()
sbatch = src_shape[0]
tbatch = tar_shape[0]
ndepth = np.prod(src_shape[1:])
weight, _ = tf.qr(tf.random_normal([ndepth, ndepth]))
src_proj = tf.matmul(tf.reshape(source, [-1, ndepth]), weight)
tar_proj = tf.matmul(tf.reshape(target, [-1, ndepth]), weight)
return wasser_1d(src_proj, tar_proj, sbatch, tbatch, ndepth, nbins, alpha)
def _orthogonal_matrix(n):
"""Construct an n x n orthogonal matrix.
Args:
n: Dimension.
Returns:
A n x n orthogonal matrix.
"""
seed = None
a = tf.random_normal([n, n], dtype=dtype, seed=seed)
if seed:
seed += 1
q, r = tf.qr(a)
d = tf.diag_part(r)
# make q uniform
q *= tf.sign(d)
return q
def idt_vec(source, target, nbins=32, alpha=-1, name='idt'):
src_shape = source.get_shape().as_list()
tar_shape = target.get_shape().as_list()
sbatch = src_shape[0]
tbatch = tar_shape[0]
ndepth = np.prod(src_shape[1:])
initializer, _ = tf.qr(tf.random_normal([ndepth, ndepth]))
with tf.variable_scope(name):
weight = tf.get_variable('w_proj', initializer=initializer)
src_proj = tf.matmul(source, weight)
tar_proj = tf.matmul(target, weight)
src_new = optimal(src_proj, tar_proj, sbatch, tbatch, ndepth, nbins,
alpha)
src_out = tf.matmul(src_new, tf.transpose(weight))
return src_out
def get_ortho_weights(var, gain):
''' compute the orthogonal initialization, this is only an approximate '''
num_rows = 1
for dim in var.shape[:-1]:
num_rows *= dim
num_cols = var.shape[-1]
flat_shape = (num_cols, num_rows) if num_rows < num_cols else (num_rows,
num_cols)
a = tf.reshape(tf.nn.l2_normalize(var), flat_shape)
# using svd would be better approximation but tf.qr seems faster
q, r = tf.qr(a, full_matrices=False)
d = tf.diag_part(r)
q *= tf.sign(d)
if num_rows < num_cols:
q = tf.matrix_transpose(q)
# gain is used to scale the new weights, needed for deeper networks
return tf.reshape(gain * q, var.shape)
def retract(X, G):
# retract tangent vector U on X to tangent space of Stiefel
# first dim of X,G are number of stiefels (product space)
#k = X.shape[0]
#assert(k == G.shape[0])
#if k == 1:
# Calculate 'thin' qr decomposition of X + G
Q, R = tf.qr(X + G)
# Unflip any flipped signs
XNew = tf.matmul(Q, tf.diag(tf.sign(tf.sign(tf.diag_part(R)) + .5)))
#else:
# XNew = X + G
# for i in xrange(k):
# q, r = tf.qr(XNew[i,:,:])
# XNew[i,:,:] = tf.dot(q, tf.diag(tf.sign(tf.sign(tf.diag(r))+.5)))
return XNew
def orthogonal_matrix_chunk(cols, dtype):
use_numpy = False
if use_numpy:
unstructured_block = tf.random_normal((cols, cols), dtype=tf.float32)
# with tf.GradientTape() as tape:
# tape.watch(unstructured_block)
q, _ = tf.py_function(func=my_eig, inp=[unstructured_block], Tout=[tf.float32, tf.float32])
q.set_shape(unstructured_block.get_shape())
q = tf.saturate_cast(q, dtype=dtype)
# print(q.shape)
else:
# unstructured_block = tf.stop_gradient(tf.random_normal((cols, cols), dtype=dtype))
# q, r = tf.qr(unstructured_block, full_matrices=False)
# q, r = tf.stop_gradient(q), tf.stop_gradient(r)
# q, r = qr_wo_grad(unstructured_block)
unstructured_block = tf.random_normal((cols, cols), dtype=tf.float32)
q, r = tf.qr(unstructured_block, full_matrices=False)
return tf.transpose(q)
def qr(A):
Q, R = tf.qr(A)
#m, n = A.shape.as_list()
#norm = lambda v, u: tf.reduce_sum(v*u)
#qi = tf.reshape(A[:,0], (m,1))
#ri = norm(qi, qi)
#q = [qi/ri]
#R = [tf.sparse_to_dense([0], (n,), [ri])]
#for i in range(1, n):
# qi = tf.reshape(A[:,i], (m, 1))
# r = []
# for j in range(0, i):
# ri = norm(qi, q[j])
# qi -= ri*q[j]
# r.append(ri)
# r.append(norm(qi, qi)**0.5)
# q.append(qi/r[-1])
# R.append(tf.sparse_to_dense(np.arange(0, i+1), (n,), ri))
#Q = tf.concat(q, axis=1)
#R = tf.transpose(tf.concat([tf.reshape(r, (n, 1)) for r in R], axis=1))
return Q, R
def Test(self):
np.random.seed(1)
x_np = np.random.uniform(
low=-1.0, high=1.0, size=np.prod(shape_)).reshape(shape_).astype(dtype_)
if is_complex:
x_np += 1j * np.random.uniform(
low=-1.0, high=1.0,
size=np.prod(shape_)).reshape(shape_).astype(dtype_)
for full_matrices in False, True:
with self.test_session() as sess:
if use_static_shape_:
x_tf = tf.constant(x_np)
else:
x_tf = tf.placeholder(dtype_)
q_tf, r_tf = tf.qr(x_tf, full_matrices=full_matrices)
if use_static_shape_:
q_tf_val, r_tf_val = sess.run([q_tf, r_tf])
else:
q_tf_val, r_tf_val = sess.run([q_tf, r_tf], feed_dict={x_tf: x_np})
q_dims = q_tf_val.shape
np_q = np.ndarray(q_dims, dtype_)
np_q_reshape = np.reshape(np_q, (-1, q_dims[-2], q_dims[-1]))
new_first_dim = np_q_reshape.shape[0]
x_reshape = np.reshape(x_np, (-1, x_np.shape[-2], x_np.shape[-1]))
for i in range(new_first_dim):
if full_matrices:
np_q_reshape[i,:,:], _ = \
np.linalg.qr(x_reshape[i,:,:], mode="complete")
else:
np_q_reshape[i,:,:], _ = \
np.linalg.qr(x_reshape[i,:,:], mode="reduced")
np_q = np.reshape(np_q_reshape, q_dims)
CompareOrthogonal(self, np_q, q_tf_val, min(shape_[-2:]))
CheckApproximation(self, x_np, q_tf_val, r_tf_val)
CheckUnitary(self, q_tf_val)
def svd_initialization(self, z, y):
group_index = [tf.where(tf.equal(y, k)) for k in xrange(self.n_class)
] # indices of datapoints in k-th cluster
groups = [tf.gather(z, group_index[k])
for k in xrange(self.n_class)] # datapoints in k-th cluster
# remove extra dimension
groups = [tf.squeeze(g, axis=1) for g in groups]
# subtract mean
if self.args.submean:
groups = [g - tf.reduce_mean(g, 0, keep_dims=True) for g in groups]
dim1 = tf.shape(z)[1]
u_prime = []
for i, g in enumerate(groups):
N_g = tf.shape(g)[0] # number of datapoints in this cluster
gt = tf.transpose(g)
q, r = tf.qr(gt, full_matrices=False)
idx = [j for j in xrange(args.rank)]
qq = tf.gather(tf.transpose(q), idx)
qq = tf.transpose(qq)
u_prime.append(qq)
return u_prime
def _orthogonalize_batch_tt_cores_left_to_right(tt):
"""Orthogonalize TT-cores of a batch TT-object in the left to right order.
Args:
tt: TensorTrainBatch.
Returns:
TensorTrainBatch
"""
# Left to right orthogonalization.
ndims = tt.ndims()
raw_shape = shapes.lazy_raw_shape(tt)
tt_ranks = shapes.lazy_tt_ranks(tt)
next_rank = tt_ranks[0]
batch_size = shapes.lazy_batch_size(tt)
# Copy cores references so we can change the cores.
tt_cores = list(tt.tt_cores)
for core_idx in range(ndims - 1):
curr_core = tt_cores[core_idx]
# TT-ranks could have changed on the previous iteration, so `tt_ranks` can
# be outdated for the current TT-rank, but should be valid for the next
# TT-rank.
curr_rank = next_rank
next_rank = tt_ranks[core_idx + 1]
if tt.is_tt_matrix():
curr_mode_left = raw_shape[0][core_idx]
curr_mode_right = raw_shape[1][core_idx]
curr_mode = curr_mode_left * curr_mode_right
else:
curr_mode = raw_shape[0][core_idx]
qr_shape = (batch_size, curr_rank * curr_mode, next_rank)
curr_core = tf.reshape(curr_core, qr_shape)
curr_core, triang = tf.qr(curr_core)
if triang.get_shape().is_fully_defined():
triang_shape = triang.get_shape().as_list()
else:
triang_shape = tf.shape(triang)
# The TT-rank could have changed: if qr_shape is e.g. 4 x 10, than q would
# be of size 4 x 4 and r would be 4 x 10, which means that the next rank
# should be changed to 4.
next_rank = triang_shape[1]
if tt.is_tt_matrix():
new_core_shape = (batch_size, curr_rank, curr_mode_left,
curr_mode_right, next_rank)
else:
new_core_shape = (batch_size, curr_rank, curr_mode, next_rank)
tt_cores[core_idx] = tf.reshape(curr_core, new_core_shape)
next_core = tf.reshape(tt_cores[core_idx + 1],
(batch_size, triang_shape[2], -1))
tt_cores[core_idx + 1] = tf.matmul(triang, next_core)
if tt.is_tt_matrix():
last_core_shape = (batch_size, next_rank, raw_shape[0][-1],
raw_shape[1][-1], 1)
else:
last_core_shape = (batch_size, next_rank, raw_shape[0][-1], 1)
tt_cores[-1] = tf.reshape(tt_cores[-1], last_core_shape)
# TODO: infer the tt_ranks.
return TensorTrainBatch(tt_cores,
tt.get_raw_shape(),
batch_size=batch_size)
def trainspd(total_loss,
global_step,
optimizer,
learning_rate,
moving_average_decay,
update_gradient_vars,
log_histograms=True):
# Generate moving averages of all losses and associated summaries.
loss_averages_op = _add_loss_summaries(total_loss)
# Compute gradients.
with tf.control_dependencies([loss_averages_op]):
if optimizer == 'ADAGRAD':
opt = tf.train.AdagradOptimizer(learning_rate)
elif optimizer == 'ADADELTA':
opt = tf.train.AdadeltaOptimizer(learning_rate,
rho=0.9,
epsilon=1e-6)
elif optimizer == 'ADAM':
opt = tf.train.AdamOptimizer(learning_rate,
beta1=0.9,
beta2=0.999,
epsilon=0.1)
elif optimizer == 'RMSPROP':
opt = tf.train.RMSPropOptimizer(learning_rate,
decay=0.9,
momentum=0.9,
epsilon=1.0)
elif optimizer == 'MOM':
opt = tf.train.MomentumOptimizer(learning_rate,
0.9,
use_nesterov=True)
else:
raise ValueError('Invalid optimization algorithm')
grads = opt.compute_gradients(total_loss, update_gradient_vars)
for idx, (egrad, var) in enumerate(grads):
if 'orth' in var.name:
tmp1 = tf.matmul(tf.transpose(var), egrad)
tmp2 = 0.5 * (tmp1 + tf.transpose(tmp1))
rgrad = egrad - tf.matmul(var, tmp2)
grads[idx] = (rgrad, var)
# Apply gradients.
apply_gradient_op = opt.apply_gradients(grads, global_step=global_step)
redun = 0.
for grad, var in grads:
if 'orth' in var.name:
o_n, _ = tf.qr(var)
redun = redun + tf.reduce_sum(var.assign(o_n), [0, 1])
# Add histograms for trainable variables.
if log_histograms:
for var in tf.trainable_variables():
tf.summary.histogram(var.op.name, var)
# Add histograms for gradients.
if log_histograms:
for grad, var in grads:
if grad is not None:
tf.summary.histogram(var.op.name + '/gradients', grad)
# Track the moving averages of all trainable variables.
variable_averages = tf.train.ExponentialMovingAverage(
moving_average_decay, global_step)
variables_averages_op = variable_averages.apply(tf.trainable_variables())
with tf.control_dependencies([apply_gradient_op, variables_averages_op]):
train_op = tf.no_op(name='train')
return train_op, redun
def train_model():
with tf.Session(config=tf.ConfigProto(
allow_soft_placement=True)) as session:
all_real_data_conv = tf.placeholder(tf.int32,
shape=[BATCH_SIZE, 3, DIM, DIM])
split_real_data_conv = tf.split(all_real_data_conv, len(DEVICES))
gen_costs, disc_costs, recon_costs = [], [], []
for device_index, (device, real_data_conv) in enumerate(
zip(DEVICES, split_real_data_conv)):
with tf.device(device):
real_data = tf.reshape(
2 * ((tf.cast(real_data_conv, tf.float32) / 255.) - .5),
[BATCH_SIZE // len(DEVICES), OUTPUT_DIM])
fake_z = BEGANEncoder(real_data)
fake_data = BEGANGenerator(BATCH_SIZE // len(DEVICES),
noise=fake_z,
bn=BN_G)
if MODE == 'swae':
recon_cost = tf.reduce_mean(
tf.reduce_mean(
tf.squared_difference(real_data, fake_data)))
else:
raise Exception()
recon_costs.append(recon_cost)
recon_cost = tf.add_n(recon_costs) / len(DEVICES)
if MODE == 'swae':
optimizer = tf.train.AdamOptimizer(learning_rate=D_LR,
beta1=BETA1_D,
beta2=0.9)
grads_and_vars = optimizer.compute_gradients(
recon_cost,
var_list=lib.params_with_name1('Encoder', 'Generator'))
for idx, (egrad, var) in enumerate(grads_and_vars):
# print var.name
if 'swd_proj' in var.name:
# print var.name
tmp1 = tf.matmul(tf.transpose(var), egrad)
tmp2 = 0.5 * (tmp1 + tf.transpose(tmp1))
rgrad = egrad - tf.matmul(var, tmp2)
grads_and_vars[idx] = (rgrad, var)
recon_train_op = optimizer.apply_gradients(grads_and_vars)
# stiefel update
stiefel_up = tf.random_normal([FEATURE_DIM, FEATURE_DIM])
for var in lib.params_with_name('Encoder.swd'):
# print var.name
if 'swd_proj' in var.name:
print(var.name)
o_n, _ = tf.qr(var)
stiefel_up = stiefel_up + tf.reduce_sum(
var.assign(o_n), [0, 1])
tf.summary.scalar("recon_cost", recon_cost)
summary_op = tf.summary.merge_all()
else:
raise Exception()
# For generating samples
fixed_noise = tf.constant(
np.random.normal(size=(BATCH_SIZE, FEATURE_DIM)).astype('float32'))
all_fixed_noise_samples = []
for device_index, device in enumerate(DEVICES):
n_samples = BATCH_SIZE // len(DEVICES)
all_fixed_noise_samples.append(BEGANGenerator(n_samples))
if tf.__version__.startswith('1.'):
all_fixed_noise_samples = tf.concat(all_fixed_noise_samples,
axis=0)
else:
all_fixed_noise_samples = tf.concat(0, all_fixed_noise_samples)
def generate_image(iteration):
samples = session.run(all_fixed_noise_samples)
samples = ((samples + 1.) * 127.5).astype('int32')
tflib.save_images.save_images(
samples.reshape((BATCH_SIZE, 3, DIM, DIM)),
'%s/samples_%d.png' % (SAMPLES_DIR, iteration))
writer = tf.summary.FileWriter(TBOARD_DIR, session.graph)
# Dataset iterator
train_gen, dev_gen = tflib.data_loader.load(BATCH_SIZE, DATA_DIR,
DATASET)
def inf_train_gen():
while True:
for (images, ) in train_gen():
yield images
# Save a batch of ground-truth samples
_x = inf_train_gen().__next__()
_x_r = session.run(
real_data, feed_dict={real_data_conv: _x[:BATCH_SIZE // N_GPUS]})
_x_r = ((_x_r + 0.5) * 255).astype('int32')
tflib.save_images.save_images(
_x_r.reshape((BATCH_SIZE // N_GPUS, 3, DIM, DIM)),
'%s/samples_groundtruth.png' % SAMPLES_DIR)
session.run(tf.global_variables_initializer())
# Checkpoint saver
ckpt_saver = tf.train.Saver(max_to_keep=int(ITERS / CHECKPOINT_STEP))
if LOAD_CHECKPOINT:
is_check, ITER_START = load_checkpoint(session, ckpt_saver,
CHECKPOINT_DIR)
if is_check:
print(" [*] Load SUCCESS")
else:
print(" [!] Load failed...")
gen = inf_train_gen()
for it in range(ITERS):
iteration = it + ITER_START
start_time = time.time()
_data = gen.__next__()
_recon_cost, _, _, _summary_op = session.run(
[recon_cost, recon_train_op, stiefel_up, summary_op],
feed_dict={all_real_data_conv: _data})
writer.add_summary(_summary_op, iteration)
if iteration % SAVE_SAMPLES_STEP == SAVE_SAMPLES_STEP - 1:
generate_image(iteration)
print("Time: %g/itr, Itr: %d, reconstruction loss: %g" %
(time.time() - start_time, iteration, _recon_cost))
# Save checkpoint
if (iteration != 0) and (iteration % CHECKPOINT_STEP
== CHECKPOINT_STEP - 1):
if iteration == CHECKPOINT_STEP - 1:
ckpt_saver.save(session,
os.path.join(CHECKPOINT_DIR, "SWAE.model"),
iteration,
write_meta_graph=True)
else:
ckpt_saver.save(session,
os.path.join(CHECKPOINT_DIR, "SWAE.model"),
iteration,
write_meta_graph=False)
def CameraIteration3(self, conv1, conv2, intrinsics, p, D, R, T, level, fx,
fy, ox, oy):
conv1_shape = conv1.get_shape()
nbatch = int(conv1_shape[0])
npixels = int(conv1_shape[1])
nchannels1 = int(conv1_shape[2])
nchannels2 = int(2 * nchannels1)
nchannels3 = nchannels1 + nchannels2
with tf.name_scope("jacobian_and_projection"):
P = tf.multiply(p, tf.tile(tf.transpose(D, [0, 2, 1]), [1, 3, 1]))
P = tf.transpose(P, [0, 2, 1])
#jacobianMatrixGeometry,projection=jacobian_construction(P,intrinsics,tf.transpose(R,[0,2,1]),T)
#print "jacobian_test_ok"
#print jacobianMatrixGeometry.get_shape()
jacobianMatrixGeometry, grad, diff, valid = equation_construction_prepare(
P, intrinsics, tf.transpose(R, [0, 2, 1]), T, conv1,
conv2[:, :, :, 0:nchannels1], conv2[:, :, :,
nchannels1:nchannels2],
conv2[:, :, :, nchannels2:nchannels3])
# print "prepare_test_ok"
# print jacobianMatrixGeometry.get_shape()
#print grad_.get_shape(),diff_.get_shape(),valid_.get_shape()
_, gra, dif, _ = equation_construction_fused(
P, intrinsics, tf.transpose(R, [0, 2, 1]), T, conv1,
conv2[:, :, :, 0:nchannels1], conv2[:, :, :,
nchannels1:nchannels2],
conv2[:, :, :, nchannels2:nchannels3])
with tf.name_scope("weighting"):
# _conv2,_mask,index00,i00=utils.interpolate2d3(conv2,projection[:,:,0],projection[:,:,1])
# num_valid= npixels/tf.reduce_sum(_mask,axis=1,keepdims=True)
# mask = tf.expand_dims(_mask,axis=-1)
# _diff = tf.expand_dims(_conv2[:,:,0:nchannels1]-conv1,-1)
# _gradx = tf.expand_dims(_conv2[:,:,nchannels1:nchannels2],-1)
# _grady = tf.expand_dims(_conv2[:,:,nchannels2:nchannels3],-1)
# diff = tf.matmul(_diff,mask)
# grad = tf.concat([tf.matmul(_gradx,mask),tf.matmul(_grady,mask)],-1)
num_valid = npixels / tf.reduce_sum(valid, axis=1, keepdims=True)
# assert_op = tf.Assert(False,[num_valid,num_valid2,projection,index00,tf.abs(tf.squeeze(grad)-tf.squeeze(grad_))],summarize=10000)
# with tf.control_dependencies([assert_op]):
# diff=tf.identity(diff)
# _,gra,dif,vali=equation_construction_fused(P,intrinsics,tf.transpose(R,[0,2,1]),T,conv1,conv2[:,:,:,0:nchannels1],conv2[:,:,:,nchannels1:nchannels2],conv2[:,:,:,nchannels2:nchannels3])
# assert_op = tf.Assert(False,[gra,tf.matmul(grad,grad,transpose_a=True)],summarize=10000)
# with tf.control_dependencies([assert_op]):
# diff=tf.identity(diff)
with tf.name_scope("lambda_prediction"):
avg_residual = num_valid * tf.reduce_mean(
tf.abs(tf.squeeze(diff, axis=-1)), axis=1, keep_dims=True)
lambda_conv1 = self.conv1d(avg_residual,
2 * nchannels1,
name="lambda_" + level + "_1",
activation=tf.nn.selu)
lambda_conv2 = self.conv1d(lambda_conv1,
4 * nchannels1,
name="lambda_" + level + "_2",
activation=tf.nn.selu)
lambda_conv3 = self.conv1d(lambda_conv2,
2 * nchannels1,
name="lambda_" + level + "_3",
activation=tf.nn.selu)
lambda_conv4 = self.conv1d(lambda_conv3,
nchannels1,
name="lambda_" + level + "_4",
activation=tf.nn.selu)
lambda_conv5 = self.conv1d(lambda_conv4,
1,
name="lambda_" + level + "_5",
activation=tf.nn.tanh)
lambda_prediction = tf.pow(
tf.norm(avg_residual, axis=-1, keepdims=True),
1.0 + lambda_conv5)
avg_residual = tf.reduce_mean(avg_residual)
with tf.name_scope("FirstEstimation"):
with tf.name_scope("Solve"):
#AtA,Atb=equation_construction(jacobian=jacobianMatrixGeometry,gradient=grad,difference=diff)
AtA = tf.reduce_sum(tf.matmul(jacobianMatrixGeometry,
tf.matmul(
gra, jacobianMatrixGeometry),
transpose_a=True),
axis=1)
Atb = tf.reduce_sum(tf.matmul(jacobianMatrixGeometry,
dif,
transpose_a=True),
axis=1)
diag = tf.matrix_diag_part(AtA)
AtA = AtA + tf.matrix_diag(
tf.squeeze(tf.matmul(
tf.expand_dims(diag, axis=-1) + 1e-5,
lambda_prediction),
axis=-1))
if not qr:
motion = tf.matmul(tf.matrix_inverse(AtA), Atb)
else:
q_full, r_full = tf.qr(AtA, full_matrices=True)
motion = tf.linalg.solve(
r_full, tf.matmul(q_full, Atb, transpose_a=True))
assert_op = tf.Assert(tf.reduce_all(tf.is_finite(motion)),
[gra, diff],
summarize=10000)
with tf.control_dependencies([assert_op]):
motion = tf.identity(motion)
with tf.name_scope("Update"):
wx, wy, wz, tx, ty, tz = tf.unstack(motion, num=6, axis=1)
dr = self.AngleaAxisRotation(wx, wy, wz)
dv = self.VMatrix(wx, wy, wz)
dt = tf.stack([tx, ty, tz], axis=1)
updatedR = tf.matmul(dr, R)
updatedT = tf.add(tf.matmul(dv, dt), tf.matmul(dr, T))
#with tf.name_scope("CheckUpdate"):
# Rp = tf.matmul(updatedR,p)
# RP = tf.multiply(Rp,tf.tile(tf.transpose(D,[0,2,1]),[1,3,1]))
# RPT= tf.add(RP,tf.tile(updatedT,[1,1,npixels]))
# Z = RPT[:,2,:]
# X = RPT[:,0,:]
# Y = RPT[:,1,:]
# x = tf.div(X,Z)
# y = tf.div(Y,Z)
# px=fx*x+ox
# py=fy*y+oy
# _conv2,_mask =utils.interpolate2d(conv2,px,py)
# _num_valid =npixels/tf.reduce_sum(_mask,axis=1,keepdims=True)
# #_num_valid =tf.constant(1.0)
# _diff =_mask*(_conv2[:,:,0:nchannels1]-conv1)
# _avg_residual=_num_valid*tf.reduce_mean(tf.abs(_diff),axis=1,keep_dims=True)
# _avg_residual=tf.reduce_mean(_avg_residual)
# motion=tf.squeeze(motion)
# return tf.cond(tf.less(_avg_residual,residual_ratio*avg_residual),
# lambda:(updatedR,updatedT,tf.norm(motion[:3]),tf.norm(motion[3:]),tf.squeeze(_num_valid)),
# lambda:(R,T,tf.to_float(0.0),tf.to_float(0.0),tf.squeeze(num_valid)))
return updatedR, updatedT, tf.norm(motion[:3]), tf.norm(
motion[3:]), tf.squeeze(num_valid)
def CameraIteration2(self, conv1, conv2, fx, fy, ox, oy, p, D, R, T,
level):
with tf.name_scope("initialization"):
conv1_shape = conv1.get_shape()
nbatch = int(conv1_shape[0])
npixels = int(conv1_shape[1])
nchannels1 = int(conv1_shape[2])
nchannels2 = int(2 * nchannels1)
nchannels3 = nchannels1 + nchannels2
with tf.name_scope("warp_compute"):
Rp = tf.matmul(R, p)
RP = tf.multiply(Rp, tf.tile(tf.transpose(D, [0, 2, 1]),
[1, 3, 1]))
RPT = tf.add(RP, tf.tile(T, [1, 1, npixels]))
Z = RPT[:, 2, :]
X = RPT[:, 0, :]
Y = RPT[:, 1, :]
x = tf.div(X, Z)
y = tf.div(Y, Z)
px = fx * x + ox
py = fy * y + oy
with tf.name_scope("warp_conv"):
with tf.name_scope("weighting"):
_conv2, _mask = utils.interpolate2d(conv2, px, py)
num_valid = npixels / tf.reduce_sum(
_mask, axis=1, keepdims=True)
mask = tf.expand_dims(_mask, axis=-1)
_diff = tf.expand_dims(_conv2[:, :, 0:nchannels1] - conv1, -1)
_gradx = tf.expand_dims(_conv2[:, :, nchannels1:nchannels2],
-1)
_grady = tf.expand_dims(_conv2[:, :, nchannels2:nchannels3],
-1)
diff = tf.matmul(_diff, mask)
grad = tf.concat(
[tf.matmul(_gradx, mask),
tf.matmul(_grady, mask)], -1)
with tf.name_scope("lambda_prediction"):
avg_residual = num_valid * tf.reduce_mean(
tf.abs(tf.squeeze(diff, axis=-1)), axis=1, keep_dims=True)
lambda_conv1 = self.conv1d(avg_residual,
2 * nchannels1,
name="lambda_" + level + "_1",
activation=tf.nn.selu)
lambda_conv2 = self.conv1d(lambda_conv1,
4 * nchannels1,
name="lambda_" + level + "_2",
activation=tf.nn.selu)
lambda_conv3 = self.conv1d(lambda_conv2,
2 * nchannels1,
name="lambda_" + level + "_3",
activation=tf.nn.selu)
lambda_conv4 = self.conv1d(lambda_conv3,
nchannels1,
name="lambda_" + level + "_4",
activation=tf.nn.selu)
lambda_conv5 = self.conv1d(lambda_conv4,
1,
name="lambda_" + level + "_5",
activation=tf.nn.tanh)
lambda_prediction = tf.pow(
tf.norm(avg_residual, axis=-1, keepdims=True),
1.0 + lambda_conv5)
avg_residual = tf.reduce_mean(avg_residual)
with tf.name_scope("FirstEstimation"):
with tf.name_scope("Solve"):
jacobianMatrixGeometry = self.CameraJacobianMatrix(
x, y, Z, fx, fy)
AtA = tf.reduce_sum(tf.matmul(jacobianMatrixGeometry,
tf.matmul(
tf.matmul(grad,
grad,
transpose_a=True),
jacobianMatrixGeometry),
transpose_a=True),
axis=1)
Atb = tf.reduce_sum(tf.matmul(jacobianMatrixGeometry,
tf.matmul(grad,
diff,
transpose_a=True),
transpose_a=True),
axis=1)
diag = tf.matrix_diag_part(AtA)
AtA = AtA + tf.matrix_diag(
tf.squeeze(tf.matmul(
tf.expand_dims(diag, axis=-1) + 1e-5,
lambda_prediction),
axis=-1))
#motion = tf.matmul(tf.matrix_inverse(AtA),Atb)
if not qr:
motion = tf.matmul(tf.matrix_inverse(AtA), Atb)
else:
q_full, r_full = tf.qr(AtA, full_matrices=True)
motion = tf.linalg.solve(
r_full, tf.matmul(q_full, Atb, transpose_a=True))
with tf.name_scope("Update"):
wx, wy, wz, tx, ty, tz = tf.unstack(motion, num=6, axis=1)
dr = self.AngleaAxisRotation(wx, wy, wz)
dv = self.VMatrix(wx, wy, wz)
dt = tf.stack([tx, ty, tz], axis=1)
updatedR = tf.matmul(dr, R)
updatedT = tf.add(tf.matmul(dv, dt), tf.matmul(dr, T))
with tf.name_scope("CheckUpdate"):
Rp = tf.matmul(updatedR, p)
RP = tf.multiply(
Rp, tf.tile(tf.transpose(D, [0, 2, 1]), [1, 3, 1]))
RPT = tf.add(RP, tf.tile(updatedT, [1, 1, npixels]))
Z = RPT[:, 2, :]
X = RPT[:, 0, :]
Y = RPT[:, 1, :]
x = tf.div(X, Z)
y = tf.div(Y, Z)
px = fx * x + ox
py = fy * y + oy
_conv2, _mask = utils.interpolate2d(conv2, px, py)
_num_valid = npixels / tf.reduce_sum(
_mask, axis=1, keepdims=True)
_diff = _mask * (_conv2[:, :, 0:nchannels1] - conv1)
_avg_residual = _num_valid * tf.reduce_mean(
tf.abs(_diff), axis=1, keep_dims=True)
_avg_residual = tf.reduce_mean(_avg_residual)
motion = tf.squeeze(motion)
# assert_op = tf.Assert(False,[motion[3:]],summarize=10000)
# with tf.control_dependencies([assert_op]):
# motion=tf.identity(motion)
# def return_origin():
# return R,T,tf.to_float(0.0),tf.to_float(0.0),tf.squeeze(num_valid)
# def return_update():
# global motion
# assert_op = tf.Assert(False,[tf.norm(motion[:3]),tf.norm(motion[3:])],summarize=10000)
# with tf.control_dependencies([assert_op]):
# motion=tf.identity(motion)
# return updatedR,updatedT,tf.norm(motion[:3]),tf.norm(motion[3:]),tf.squeeze(num_valid)
return tf.cond(
tf.less(_avg_residual, residual_ratio * avg_residual), lambda:
(updatedR, updatedT, tf.norm(motion[:3]), tf.norm(motion[3:]),
tf.squeeze(num_valid)), lambda:
(R, T, tf.to_float(0.0), tf.to_float(0.0), tf.squeeze(num_valid)))
def CameraIteration(self, conv1, conv2, fx, fy, ox, oy, p, D, R, T):
with tf.name_scope("initialization"):
conv1_shape = conv1.get_shape()
nbatch = int(conv1_shape[0])
npixels = int(conv1_shape[1])
nchannels1 = int(conv1_shape[2])
nchannels2 = int(2 * nchannels1)
nchannels3 = nchannels1 + nchannels2
with tf.name_scope("warp_compute"):
Rp = tf.matmul(R, p)
RP = tf.multiply(Rp, tf.tile(tf.transpose(D, [0, 2, 1]),
[1, 3, 1]))
RPT = tf.add(RP, tf.tile(T, [1, 1, npixels]))
Z = RPT[:, 2, :]
X = RPT[:, 0, :]
Y = RPT[:, 1, :]
x = tf.div(X, Z)
y = tf.div(Y, Z)
px = fx * x + ox
py = fy * y + oy
with tf.name_scope("warp_conv"):
with tf.name_scope("weighting"):
_conv2, _mask = utils.interpolate2d(conv2, px, py)
mask = tf.expand_dims(_mask, axis=-1)
_diff = tf.expand_dims(_conv2[:, :, 0:nchannels1] - conv1, -1)
_gradx = tf.expand_dims(_conv2[:, :, nchannels1:nchannels2],
-1)
_grady = tf.expand_dims(_conv2[:, :, nchannels2:nchannels3],
-1)
diff = tf.matmul(_diff, mask)
grad = tf.concat(
[tf.matmul(_gradx, mask),
tf.matmul(_grady, mask)], -1)
with tf.name_scope("lambda_prediction"):
avg_residual = tf.reduce_mean(tf.abs(tf.squeeze(diff, axis=-1)),
axis=1,
keep_dims=True)
lambda_prediction = tf.pow(
tf.norm(avg_residual, axis=-1, keepdims=True), 2.0)
with tf.name_scope("FirstEstimation"):
with tf.name_scope("Solve"):
jacobianMatrixGeometry = self.CameraJacobianMatrix(
x, y, Z, fx, fy)
AtA = tf.reduce_sum(tf.matmul(jacobianMatrixGeometry,
tf.matmul(
tf.matmul(grad,
grad,
transpose_a=True),
jacobianMatrixGeometry),
transpose_a=True),
axis=1)
Atb = tf.reduce_sum(tf.matmul(jacobianMatrixGeometry,
tf.matmul(grad,
diff,
transpose_a=True),
transpose_a=True),
axis=1)
diag = tf.matrix_diag_part(AtA)
AtA = AtA + tf.matrix_diag(
tf.squeeze(tf.matmul(
tf.expand_dims(diag, axis=-1) + 1e-5,
lambda_prediction),
axis=-1))
if not qr:
motion = tf.matmul(tf.matrix_inverse(AtA), Atb)
else:
q_full, r_full = tf.qr(AtA, full_matrices=True)
motion = tf.linalg.solve(
r_full, tf.matmul(q_full, Atb, transpose_a=True))
with tf.name_scope("Update"):
wx, wy, wz, tx, ty, tz = tf.unstack(motion, num=6, axis=1)
dr = self.AngleaAxisRotation(wx, wy, wz)
dt = tf.stack([tx, ty, tz], axis=1)
updatedR = tf.matmul(dr, R)
updatedT = tf.add(dt, tf.matmul(dr, T))
return updatedR, updatedT, tf.reduce_sum(mask) / npixels
import tensorflow as tf """tf.qr(input, full_matrices=None, name=None) 功能：对矩阵进行qr分解。 输入：。""" a = tf.constant([1, 2, 2, 1, 0, 2, 0, 1, 1], shape=[3, 3], dtype=tf.float64) q, r = tf.qr(a) sess = tf.Session() print(sess.run(tf.qr(a))) sess.close() # q==>[[-0.70710678 0.57735027 -0.40824829] # [-0.70710678 -0.57735027 0.40824829] # [0. 0.57735027 0.81649658 ]] # r==>[[-1.41421356 -1.41421356 -2.82842712] # [0. 1.73205081 0.57735027] # [0. 0. 0.81649658]] # Qr(q=array([[-0.70710678, 0.57735027, -0.40824829], # [-0.70710678, -0.57735027, 0.40824829], # [ 0. , 0.57735027, 0.81649658]]), r=array([[-1.41421356, -1.41421356, -2.82842712], # [ 0. , 1.73205081, 0.57735027], # [ 0. , 0. , 0.81649658]]))
# 转置，可以通过指定 perm=[1, 0] 来进行轴变换
tf.transpose(a, perm=None, name='transpose')
# 在张量 a 的最后两个维度上进行转置
tf.matrix_transpose(a, name='matrix_transpose')
# Matrix with two batch dimensions, x.shape is [1, 2, 3, 4]
# tf.matrix_transpose(x) is shape [1, 2, 4, 3]
# 求矩阵的迹
tf.trace(x, name=None)
# 计算方阵行列式的值
tf.matrix_determinant(input, name=None)
# 求解可逆方阵的逆，input 必须为浮点型或复数
tf.matrix_inverse(input, adjoint=None, name=None)
# 奇异值分解
tf.svd(tensor, full_matrices=False, compute_uv=True, name=None)
# QR 分解
tf.qr(input, full_matrices=None, name=None)
# 求张量的范数(默认2)
tf.norm(tensor, ord='euclidean', axis=None, keep_dims=False, name=None)
# 构建一个单位矩阵, 或者 batch 个矩阵，batch_shape 以 list 的形式传入
tf.eye(num_rows, num_columns=None, batch_shape=None, dtype=tf.float32, name=None)
# Construct one identity matrix.
tf.eye(2)
"""
==> [[1., 0.],
[0., 1.]]
"""
# Construct a batch of 3 identity matricies, each 2 x 2.
# batch_identity[i, :, :] is a 2 x 2 identity matrix, i = 0, 1, 2.
batch_identity = tf.eye(2, batch_shape=[3])
