def testConsistent(self):
nums, divs = self.intTestData()
with self.test_session():
tf_result = (
math_ops.floor_div(nums, divs) * divs + math_ops.floor_mod(nums, divs)
).eval()
tf_nums = array_ops.constant(nums)
tf_divs = array_ops.constant(divs)
tf2_result = (tf_nums // tf_divs * tf_divs + tf_nums % tf_divs).eval()
np_result = (nums // divs) * divs + (nums % divs)
# consistentcy with numpy
self.assertAllEqual(tf_result, np_result)
# consistentcy with two forms of divide
self.assertAllEqual(tf_result, tf2_result)
# consistency for truncation form
tf3_result = (
math_ops.truncatediv(nums, divs) * divs
+ math_ops.truncatemod(nums, divs)
).eval()
expanded_nums = np.reshape(np.tile(nums, divs.shape[1]),
(nums.shape[0], divs.shape[1]))
# Consistent with desire to get numerator
self.assertAllEqual(tf3_result, expanded_nums)
# Consistent with desire to get numerator
self.assertAllEqual(tf_result, expanded_nums)
def testConsistent(self):
nums, divs = self.intTestData()
with self.test_session():
tf_result = (
math_ops.floor_div(nums, divs) * divs + math_ops.floormod(nums, divs)
).eval()
tf_nums = array_ops.constant(nums)
tf_divs = array_ops.constant(divs)
tf2_result = (tf_nums // tf_divs * tf_divs + tf_nums % tf_divs).eval()
np_result = (nums // divs) * divs + (nums % divs)
# consistentcy with numpy
self.assertAllEqual(tf_result, np_result)
# consistentcy with two forms of divide
self.assertAllEqual(tf_result, tf2_result)
# consistency for truncation form
tf3_result = (
math_ops.truncatediv(nums, divs) * divs
+ math_ops.truncatemod(nums, divs)
).eval()
expanded_nums = np.reshape(np.tile(nums, divs.shape[1]),
(nums.shape[0], divs.shape[1]))
# Consistent with desire to get numerator
self.assertAllEqual(tf3_result, expanded_nums)
# Consistent with desire to get numerator
self.assertAllEqual(tf_result, expanded_nums)
def testFloorDivideInt(self): nums, divs = self.intTestData() tf_result = math_ops.floor_div(nums, divs) np_result = self.numpySafeFloorDivInt(nums, divs) self.assertAllEqual(tf_result, np_result) tf2_result = (array_ops.constant(nums) // array_ops.constant(divs)) self.assertAllEqual(tf2_result, tf_result)
def update_state(self, labels, predictions, weights=None):
"""
Arg:
labels: shape of (#batch, #num_joint, 3) : num_joint=18
predictions: shape of (#batch, #height, #width, #num_joint) : num_joint=18
weights: shape of (#batch, #height*output_stride, #width*output_stride)
"""
b, h, w, c = predictions.get_shape()
euclid_dists = []
masks = []
predictions = array_ops.reshape(
array_ops.transpose(predictions, (0, 3, 1, 2)), (-1, h * w))
# weights = image.resize(weights, (h, w), align_corners=True,
# method=image.ResizeMethod.NEAREST_NEIGHBOR)
a_ = []
labels = array_ops.reshape(labels, (-1, 3))
if weights is None:
weights = array_ops.ones_like(predictions)
else:
weights = array_ops.tile(array_ops.expand_dims(weights, axis=-1),
[1, 1, 1, c])
weights = array_ops.reshape(
array_ops.transpose(weights, (0, 3, 1, 2)), (-1, h * w))
for prediction, label, weight in zip(array_ops.unstack(predictions),
array_ops.unstack(labels),
array_ops.unstack(weights)):
prediction = array_ops.where(
math_ops.equal(weight, 1), prediction,
array_ops.ones_like(prediction) *
array_ops.constant(np.nan, dtype=dtypes.float32))
arg_index = math_ops.arg_max(prediction, 0)
masks.append(
clip_ops.clip_by_value(label[2], 0., 1.) *
array_ops.gather(weight, arg_index))
col, row = arg_index % w, math_ops.floor_div(arg_index, w)
arg_coord = math_ops.cast(array_ops.stack([col, row]),
dtype=dtypes.float32)
# arg_coord = (self.output_stride / 2 - 0.5) + self.output_stride * arg_coord
a_.append(arg_coord)
euclid_dists.append(math_ops.reduce_sum(
(arg_coord - label[:2])**2))
masks = array_ops.reshape(array_ops.stack(masks), (b, c))
euclid_dists = array_ops.reshape(array_ops.stack(euclid_dists), (b, c))
self.a = array_ops.reshape(array_ops.stack(a_), (b, c, 2))
with fops.control_dependencies([self.count]):
self.update_ops.append(
state_ops.assign_add(self.count,
math_ops.reduce_sum(masks, axis=0)))
add_value = operator(euclid_dists) * masks
with fops.control_dependencies([self.total_value]):
self.update_ops.append(
state_ops.assign_add(self.total_value,
math_ops.reduce_sum(add_value, axis=0)))
def testFloorDivModIntEdges(self):
for dtype in [np.int32, np.int64]:
x, y = self.intEdgeTestData(dtype)
tf_floor_div = math_ops.floor_div(x, y)
np_floor_div = self.numpySafeFloorDivInt(x, y)
self.assertAllEqual(tf_floor_div, np_floor_div)
tf_floor_mod = math_ops.floormod(x, y)
np_floor_mod = self.numpySafeFloorModInt(x, y)
self.assertAllEqual(tf_floor_mod, np_floor_mod)
z = math_ops.add(math_ops.multiply(tf_floor_div, y), tf_floor_mod)
# x = floor_div(x, y) * y + floor_mod(x, y)
self.assertAllEqual(z, np.broadcast_to(x, z.shape))
def testConsistent(self):
nums, divs = self.intTestData()
with self.test_session():
tf_result = (
math_ops.floor_div(nums, divs) * divs + math_ops.floor_mod(nums, divs)
).eval()
tf_nums = array_ops.constant(nums)
tf_divs = array_ops.constant(divs)
tf2_result = (tf_nums // tf_divs * tf_divs + tf_nums % tf_divs).eval()
np_result = (nums // divs) * divs + (nums % divs)
self.assertAllEqual(tf_result, np_result)
self.assertAllEqual(tf_result, tf2_result)
def testConsistent(self):
nums, divs = self.intTestData()
with self.test_session():
tf_result = (
math_ops.floor_div(nums, divs) * divs + math_ops.floor_mod(nums, divs)
).eval()
tf_nums = array_ops.constant(nums)
tf_divs = array_ops.constant(divs)
tf2_result = (tf_nums // tf_divs * tf_divs + tf_nums % tf_divs).eval()
np_result = (nums // divs) * divs + (nums % divs)
self.assertAllEqual(tf_result, np_result)
self.assertAllEqual(tf_result, tf2_result)
def _FloorModGrad(op, grad):
"""Returns grad * (1, -floor(x/y))."""
x = math_ops.conj(op.inputs[0])
y = math_ops.conj(op.inputs[1])
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
floor_xy = math_ops.floor_div(x, y)
gx = array_ops.reshape(math_ops.reduce_sum(grad, rx), sx)
gy = array_ops.reshape(
math_ops.reduce_sum(grad * math_ops.negative(floor_xy), ry), sy)
return gx, gy
def _FloorModGrad(op, grad):
"""Returns grad * (1, -floor(x/y))."""
x = math_ops.conj(op.inputs[0])
y = math_ops.conj(op.inputs[1])
sx = array_ops.shape(x)
sy = array_ops.shape(y)
rx, ry = gen_array_ops.broadcast_gradient_args(sx, sy)
floor_xy = math_ops.floor_div(x, y)
gx = array_ops.reshape(math_ops.reduce_sum(grad, rx), sx)
gy = array_ops.reshape(
math_ops.reduce_sum(grad * math_ops.negative(floor_xy), ry), sy)
return gx, gy
def testDivideInt(self):
nums, divs = self.intTestData()
with self.test_session():
tf_result = math_ops.floor_div(nums, divs).eval()
np_result = nums // divs
self.assertAllEqual(tf_result, np_result)
def testDivideInt(self):
nums, divs = self.intTestData()
with self.cached_session():
tf_result = math_ops.floor_div(nums, divs).eval()
np_result = nums // divs
self.assertAllEqual(tf_result, np_result)
def testDivideInt(self):
nums, divs = self.intTestData()
tf_result = math_ops.floor_div(nums, divs)
np_result = nums // divs
self.assertAllEqual(tf_result, np_result)
def sample(dim, num_samples=None, sample_indices=None, dtype=None, name=None):
r"""Returns a sample from the `m` dimensional Halton sequence.
Warning: The sequence elements take values only between 0 and 1. Care must be
taken to appropriately transform the domain of a function if it differs from
the unit cube before evaluating integrals using Halton samples. It is also
important to remember that quasi-random numbers are not a replacement for
pseudo-random numbers in every context. Quasi random numbers are completely
deterministic and typically have significant negative autocorrelation (unless
randomized).
Computes the members of the low discrepancy Halton sequence in dimension
`dim`. The d-dimensional sequence takes values in the unit hypercube in d
dimensions. Currently, only dimensions up to 1000 are supported. The prime
base for the `k`-th axes is the k-th prime starting from 2. For example,
if dim = 3, then the bases will be [2, 3, 5] respectively and the first
element of the sequence will be: [0.5, 0.333, 0.2]. For a more complete
description of the Halton sequences see:
https://en.wikipedia.org/wiki/Halton_sequence. For low discrepancy sequences
and their applications see:
https://en.wikipedia.org/wiki/Low-discrepancy_sequence.
The user must supply either `num_samples` or `sample_indices` but not both.
The former is the number of samples to produce starting from the first
element. If `sample_indices` is given instead, the specified elements of
the sequence are generated. For example, sample_indices=tf.range(10) is
equivalent to specifying n=10.
Example Use:
```python
bf = tf.contrib.bayesflow
# Produce the first 1000 members of the Halton sequence in 3 dimensions.
num_samples = 1000
dim = 3
sample = bf.halton_sequence.sample(dim, num_samples=num_samples)
# Evaluate the integral of x_1 * x_2^2 * x_3^3 over the three dimensional
# hypercube.
powers = tf.range(1.0, limit=dim + 1)
integral = tf.reduce_mean(tf.reduce_prod(sample ** powers, axis=-1))
true_value = 1.0 / tf.reduce_prod(powers + 1.0)
with tf.Session() as session:
values = session.run((integral, true_value))
# Produces a relative absolute error of 1.7%.
print ("Estimated: %f, True Value: %f" % values)
# Now skip the first 1000 samples and recompute the integral with the next
# thousand samples. The sample_indices argument can be used to do this.
sample_indices = tf.range(start=1000, limit=1000 + num_samples,
dtype=tf.int32)
sample_leaped = halton.sample(dim, sample_indices=sample_indices)
integral_leaped = tf.reduce_mean(tf.reduce_prod(sample_leaped ** powers,
axis=-1))
with tf.Session() as session:
values = session.run((integral_leaped, true_value))
# Now produces a relative absolute error of 0.05%.
print ("Leaped Estimated: %f, True Value: %f" % values)
```
Args:
dim: Positive Python `int` representing each sample's `event_size.` Must
not be greater than 1000.
num_samples: (Optional) positive Python `int`. The number of samples to
generate. Either this parameter or sample_indices must be specified but
not both. If this parameter is None, then the behaviour is determined by
the `sample_indices`.
sample_indices: (Optional) `Tensor` of dtype int32 and rank 1. The elements
of the sequence to compute specified by their position in the sequence.
The entries index into the Halton sequence starting with 0 and hence,
must be whole numbers. For example, sample_indices=[0, 5, 6] will produce
the first, sixth and seventh elements of the sequence. If this parameter
is None, then the `num_samples` parameter must be specified which gives
the number of desired samples starting from the first sample.
dtype: (Optional) The dtype of the sample. One of `float32` or `float64`.
Default is `float32`.
name: (Optional) Python `str` describing ops managed by this function. If
not supplied the name of this function is used.
Returns:
halton_elements: Elements of the Halton sequence. `Tensor` of supplied dtype
and `shape` `[num_samples, dim]` if `num_samples` was specified or shape
`[s, dim]` where s is the size of `sample_indices` if `sample_indices`
were specified.
Raises:
ValueError: if both `sample_indices` and `num_samples` were specified or
if dimension `dim` is less than 1 or greater than 1000.
"""
if dim < 1 or dim > _MAX_DIMENSION:
raise ValueError(
'Dimension must be between 1 and {}. Supplied {}'.format(_MAX_DIMENSION,
dim))
if (num_samples is None) == (sample_indices is None):
raise ValueError('Either `num_samples` or `sample_indices` must be'
' specified but not both.')
dtype = dtype or dtypes.float32
if not dtype.is_floating:
raise ValueError('dtype must be of `float`-type')
with ops.name_scope(name, 'sample', values=[sample_indices]):
# Here and in the following, the shape layout is as follows:
# [sample dimension, event dimension, coefficient dimension].
# The coefficient dimension is an intermediate axes which will hold the
# weights of the starting integer when expressed in the (prime) base for
# an event dimension.
indices = _get_indices(num_samples, sample_indices, dtype)
radixes = array_ops.constant(_PRIMES[0:dim], dtype=dtype, shape=[dim, 1])
max_sizes_by_axes = _base_expansion_size(math_ops.reduce_max(indices),
radixes)
max_size = math_ops.reduce_max(max_sizes_by_axes)
# The powers of the radixes that we will need. Note that there is a bit
# of an excess here. Suppose we need the place value coefficients of 7
# in base 2 and 3. For 2, we will have 3 digits but we only need 2 digits
# for base 3. However, we can only create rectangular tensors so we
# store both expansions in a [2, 3] tensor. This leads to the problem that
# we might end up attempting to raise large numbers to large powers. For
# example, base 2 expansion of 1024 has 10 digits. If we were in 10
# dimensions, then the 10th prime (29) we will end up computing 29^10 even
# though we don't need it. We avoid this by setting the exponents for each
# axes to 0 beyond the maximum value needed for that dimension.
exponents_by_axes = array_ops.tile([math_ops.range(max_size)], [dim, 1])
weight_mask = exponents_by_axes > max_sizes_by_axes
capped_exponents = array_ops.where(
weight_mask, array_ops.zeros_like(exponents_by_axes), exponents_by_axes)
weights = radixes ** capped_exponents
coeffs = math_ops.floor_div(indices, weights)
coeffs *= 1 - math_ops.cast(weight_mask, dtype)
coeffs = (coeffs % radixes) / radixes
return math_ops.reduce_sum(coeffs / weights, axis=-1)
def sample(dim,
num_results=None,
sequence_indices=None,
dtype=None,
randomized=True,
seed=None,
name=None):
r"""Returns a sample from the `dim` dimensional Halton sequence.
Warning: The sequence elements take values only between 0 and 1. Care must be
taken to appropriately transform the domain of a function if it differs from
the unit cube before evaluating integrals using Halton samples. It is also
important to remember that quasi-random numbers without randomization are not
a replacement for pseudo-random numbers in every context. Quasi random numbers
are completely deterministic and typically have significant negative
autocorrelation unless randomization is used.
Computes the members of the low discrepancy Halton sequence in dimension
`dim`. The `dim`-dimensional sequence takes values in the unit hypercube in
`dim` dimensions. Currently, only dimensions up to 1000 are supported. The
prime base for the k-th axes is the k-th prime starting from 2. For example,
if `dim` = 3, then the bases will be [2, 3, 5] respectively and the first
element of the non-randomized sequence will be: [0.5, 0.333, 0.2]. For a more
complete description of the Halton sequences see:
https://en.wikipedia.org/wiki/Halton_sequence. For low discrepancy sequences
and their applications see:
https://en.wikipedia.org/wiki/Low-discrepancy_sequence.
If `randomized` is true, this function produces a scrambled version of the
Halton sequence introduced by Owen in arXiv:1706.02808. For the advantages of
randomization of low discrepancy sequences see:
https://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method#Randomization_of_quasi-Monte_Carlo
The number of samples produced is controlled by the `num_results` and
`sequence_indices` parameters. The user must supply either `num_results` or
`sequence_indices` but not both.
The former is the number of samples to produce starting from the first
element. If `sequence_indices` is given instead, the specified elements of
the sequence are generated. For example, sequence_indices=tf.range(10) is
equivalent to specifying n=10.
Example Use:
```python
bf = tf.contrib.bayesflow
# Produce the first 1000 members of the Halton sequence in 3 dimensions.
num_results = 1000
dim = 3
sample = bf.halton_sequence.sample(dim, num_results=num_results, seed=127)
# Evaluate the integral of x_1 * x_2^2 * x_3^3 over the three dimensional
# hypercube.
powers = tf.range(1.0, limit=dim + 1)
integral = tf.reduce_mean(tf.reduce_prod(sample ** powers, axis=-1))
true_value = 1.0 / tf.reduce_prod(powers + 1.0)
with tf.Session() as session:
values = session.run((integral, true_value))
# Produces a relative absolute error of 1.7%.
print ("Estimated: %f, True Value: %f" % values)
# Now skip the first 1000 samples and recompute the integral with the next
# thousand samples. The sequence_indices argument can be used to do this.
sequence_indices = tf.range(start=1000, limit=1000 + num_results,
dtype=tf.int32)
sample_leaped = halton.sample(dim, sequence_indices=sequence_indices,
seed=111217)
integral_leaped = tf.reduce_mean(tf.reduce_prod(sample_leaped ** powers,
axis=-1))
with tf.Session() as session:
values = session.run((integral_leaped, true_value))
# Now produces a relative absolute error of 0.05%.
print ("Leaped Estimated: %f, True Value: %f" % values)
```
Args:
dim: Positive Python `int` representing each sample's `event_size.` Must
not be greater than 1000.
num_results: (Optional) positive Python `int`. The number of samples to
generate. Either this parameter or sequence_indices must be specified but
not both. If this parameter is None, then the behaviour is determined by
the `sequence_indices`.
sequence_indices: (Optional) `Tensor` of dtype int32 and rank 1. The
elements of the sequence to compute specified by their position in the
sequence. The entries index into the Halton sequence starting with 0 and
hence, must be whole numbers. For example, sequence_indices=[0, 5, 6] will
produce the first, sixth and seventh elements of the sequence. If this
parameter is None, then the `num_results` parameter must be specified
which gives the number of desired samples starting from the first sample.
dtype: (Optional) The dtype of the sample. One of `float32` or `float64`.
Default is `float32`.
randomized: (Optional) bool indicating whether to produce a randomized
Halton sequence. If True, applies the randomization described in
Owen (2017) [arXiv:1706.02808].
seed: (Optional) Python integer to seed the random number generator. Only
used if `randomized` is True. If not supplied and `randomized` is True,
no seed is set.
name: (Optional) Python `str` describing ops managed by this function. If
not supplied the name of this function is used.
Returns:
halton_elements: Elements of the Halton sequence. `Tensor` of supplied dtype
and `shape` `[num_results, dim]` if `num_results` was specified or shape
`[s, dim]` where s is the size of `sequence_indices` if `sequence_indices`
were specified.
Raises:
ValueError: if both `sequence_indices` and `num_results` were specified or
if dimension `dim` is less than 1 or greater than 1000.
"""
if dim < 1 or dim > _MAX_DIMENSION:
raise ValueError(
'Dimension must be between 1 and {}. Supplied {}'.format(_MAX_DIMENSION,
dim))
if (num_results is None) == (sequence_indices is None):
raise ValueError('Either `num_results` or `sequence_indices` must be'
' specified but not both.')
dtype = dtype or dtypes.float32
if not dtype.is_floating:
raise ValueError('dtype must be of `float`-type')
with ops.name_scope(name, 'sample', values=[sequence_indices]):
# Here and in the following, the shape layout is as follows:
# [sample dimension, event dimension, coefficient dimension].
# The coefficient dimension is an intermediate axes which will hold the
# weights of the starting integer when expressed in the (prime) base for
# an event dimension.
indices = _get_indices(num_results, sequence_indices, dtype)
radixes = array_ops.constant(_PRIMES[0:dim], dtype=dtype, shape=[dim, 1])
max_sizes_by_axes = _base_expansion_size(math_ops.reduce_max(indices),
radixes)
max_size = math_ops.reduce_max(max_sizes_by_axes)
# The powers of the radixes that we will need. Note that there is a bit
# of an excess here. Suppose we need the place value coefficients of 7
# in base 2 and 3. For 2, we will have 3 digits but we only need 2 digits
# for base 3. However, we can only create rectangular tensors so we
# store both expansions in a [2, 3] tensor. This leads to the problem that
# we might end up attempting to raise large numbers to large powers. For
# example, base 2 expansion of 1024 has 10 digits. If we were in 10
# dimensions, then the 10th prime (29) we will end up computing 29^10 even
# though we don't need it. We avoid this by setting the exponents for each
# axes to 0 beyond the maximum value needed for that dimension.
exponents_by_axes = array_ops.tile([math_ops.range(max_size)], [dim, 1])
# The mask is true for those coefficients that are irrelevant.
weight_mask = exponents_by_axes >= max_sizes_by_axes
capped_exponents = array_ops.where(
weight_mask, array_ops.zeros_like(exponents_by_axes), exponents_by_axes)
weights = radixes ** capped_exponents
# The following computes the base b expansion of the indices. Suppose,
# x = a0 + a1*b + a2*b^2 + ... Then, performing a floor div of x with
# the vector (1, b, b^2, b^3, ...) will produce
# (a0 + s1 * b, a1 + s2 * b, ...) where s_i are coefficients we don't care
# about. Noting that all a_i < b by definition of place value expansion,
# we see that taking the elements mod b of the above vector produces the
# place value expansion coefficients.
coeffs = math_ops.floor_div(indices, weights)
coeffs *= 1 - math_ops.cast(weight_mask, dtype)
coeffs %= radixes
if not randomized:
coeffs /= radixes
return math_ops.reduce_sum(coeffs / weights, axis=-1)
coeffs = _randomize(coeffs, radixes, seed=seed)
# Remove the contribution from randomizing the trailing zero for the
# axes where max_size_by_axes < max_size. This will be accounted
# for separately below (using zero_correction).
coeffs *= 1 - math_ops.cast(weight_mask, dtype)
coeffs /= radixes
base_values = math_ops.reduce_sum(coeffs / weights, axis=-1)
# The randomization used in Owen (2017) does not leave 0 invariant. While
# we have accounted for the randomization of the first `max_size_by_axes`
# coefficients, we still need to correct for the trailing zeros. Luckily,
# this is equivalent to adding a uniform random value scaled so the first
# `max_size_by_axes` coefficients are zero. The following statements perform
# this correction.
zero_correction = random_ops.random_uniform([dim, 1], seed=seed,
dtype=dtype)
zero_correction /= (radixes ** max_sizes_by_axes)
return base_values + array_ops.reshape(zero_correction, [-1])
