def _unvec_by(y, num_col):
"""Unstack vector to form a matrix, with a specified amount of columns."""
return _linalg.matrix_transpose(
array_ops.reshape(
y,
array_ops.concat(
[array_ops.shape(y)[:-1], [num_col, -1]], axis=0)))
def _vectorize_then_blockify(self, matrix):
"""Shape batch matrix to batch vector, then blockify trailing dimensions."""
# Suppose
# _ops.TensorShape(matrix.shape) = [m0, m1, m2, m3],
# and matrix is a matrix because the final two dimensions are matrix dims.
# self.block_depth = 2,
# self.block_shape = [b0, b1] (note b0 * b1 = m2).
# We will reshape matrix to
# [m3, m0, m1, b0, b1].
# Vectorize: Reshape to batch vector.
# [m0, m1, m2, m3] --> [m3, m0, m1, m2]
# This is called "vectorize" because we have taken the final two matrix dims
# and turned this into a size m3 batch of vectors.
vec = distribution_util.rotate_transpose(matrix, shift=1)
# Blockify: Blockfy trailing dimensions.
# [m3, m0, m1, m2] --> [m3, m0, m1, b0, b1]
if (_ops.TensorShape(vec.shape).is_fully_defined()
and self.block_shape.is_fully_defined()):
# vec_leading_shape = [m3, m0, m1],
# the parts of vec that will not be blockified.
vec_leading_shape = _ops.TensorShape(vec.shape)[:-1]
final_shape = vec_leading_shape.concatenate(self.block_shape)
else:
vec_leading_shape = array_ops.shape(vec)[:-1]
final_shape = array_ops.concat(
(vec_leading_shape, self.block_shape_tensor()), 0)
return array_ops.reshape(vec, final_shape)
def _broadcast_batch_dims(self, x, spectrum):
"""Broadcast batch dims of batch matrix `x` and spectrum."""
# _ops.TensorShape(spectrum.shape) = batch_shape + block_shape
# First make spectrum a batch matrix with
# _ops.TensorShape(spectrum.shape) = batch_shape + [prod(block_shape), 1]
spec_mat = array_ops.reshape(
spectrum,
array_ops.concat((self.batch_shape_tensor(), [-1, 1]), axis=0))
# Second, broadcast, possibly requiring an addition of array of zeros.
x, spec_mat = linear_operator_util.broadcast_matrix_batch_dims(
(x, spec_mat))
# Third, put the block shape back into spectrum.
batch_shape = array_ops.shape(x)[:-2]
spectrum = array_ops.reshape(
spec_mat,
array_ops.concat((batch_shape, self.block_shape_tensor()), axis=0))
return x, spectrum
def reshape_inv(y):
# Expand the extra dims hanging off the end, "b_extra_sh".
# Note we use y_sh[:-1] + [b_main_sh[-1]] rather than b_main_sh, because y
# Could have different batch dims than a and b, because of broadcasting.
y_extra_shape = array_ops.concat(
(array_ops.shape(y)[:-1], [b_main_sh[-1]], b_extra_sh), 0)
y_extra_on_end = array_ops.reshape(y, y_extra_shape)
inverse_perm = np.argsort(perm)
return array_ops.transpose(y_extra_on_end, perm=inverse_perm)
def _diag_part(self):
diag_part = self.operators[0].diag_part()
for operator in self.operators[1:]:
diag_part = diag_part[..., :, array_ops.newaxis]
op_diag_part = operator.diag_part()[..., array_ops.newaxis, :]
diag_part *= op_diag_part
diag_part = array_ops.reshape(
diag_part,
shape=array_ops.concat(
[array_ops.shape(diag_part)[:-2], [-1]], axis=0))
if self.range_dimension > self.domain_dimension:
diag_dimension = self.domain_dimension
else:
diag_dimension = self.range_dimension
diag_part.set_shape(
self.batch_shape.concatenate(diag_dimension))
return diag_part
def _to_dense(self):
product = self.operators[0].to_dense()
for operator in self.operators[1:]:
# Product has shape [B, R1, 1, C1].
product = product[
..., :, array_ops.newaxis, :, array_ops.newaxis]
# Operator has shape [B, 1, R2, 1, C2].
op_to_mul = operator.to_dense()[
..., array_ops.newaxis, :, array_ops.newaxis, :]
# This is now [B, R1, R2, C1, C2].
product *= op_to_mul
# Now merge together dimensions to get [B, R1 * R2, C1 * C2].
product = array_ops.reshape(
product,
shape=array_ops.concat(
[array_ops.shape(product)[:-4],
[array_ops.shape(product)[-4] * array_ops.shape(product)[-3],
array_ops.shape(product)[-2] * array_ops.shape(product)[-1]]
], axis=0))
product.set_shape(_ops.TensorShape(self.shape))
return product
def _unblockify_then_matricize(self, vec):
"""Flatten the block dimensions then reshape to a batch matrix."""
# Suppose
# _ops.TensorShape(vec.shape) = [v0, v1, v2, v3],
# self.block_depth = 2.
# Then
# leading shape = [v0, v1]
# block shape = [v2, v3].
# We will reshape vec to
# [v1, v2*v3, v0].
# Un-blockify: Flatten block dimensions. Reshape
# [v0, v1, v2, v3] --> [v0, v1, v2*v3].
if _ops.TensorShape(vec.shape).is_fully_defined():
# vec_shape = [v0, v1, v2, v3]
vec_shape = _ops.TensorShape(vec.shape).as_list()
# vec_leading_shape = [v0, v1]
vec_leading_shape = vec_shape[:-self.block_depth]
# vec_block_shape = [v2, v3]
vec_block_shape = vec_shape[-self.block_depth:]
# flat_shape = [v0, v1, v2*v3]
flat_shape = vec_leading_shape + [np.prod(vec_block_shape)]
else:
vec_shape = array_ops.shape(vec)
vec_leading_shape = vec_shape[:-self.block_depth]
vec_block_shape = vec_shape[-self.block_depth:]
flat_shape = array_ops.concat(
(vec_leading_shape, [math_ops.reduce_prod(vec_block_shape)]),
0)
vec_flat = array_ops.reshape(vec, flat_shape)
# Matricize: Reshape to batch matrix.
# [v0, v1, v2*v3] --> [v1, v2*v3, v0],
# representing a shape [v1] batch of [v2*v3, v0] matrices.
matrix = distribution_util.rotate_transpose(vec_flat, shift=-1)
return matrix
def _reshape_for_efficiency(a,
b,
transpose_a=False,
transpose_b=False,
adjoint_a=False,
adjoint_b=False):
"""Maybe reshape a, b, and return an inverse map. For matmul/solve."""
def identity(x):
return x
# At this point, we have not taken transpose/adjoint of a/b.
still_need_to_transpose = True
if _ops.TensorShape(a.shape).ndims is None or _ops.TensorShape(
b.shape).ndims is None:
return a, b, identity, still_need_to_transpose
# This could be handled in the future, but seems less common.
if _ops.TensorShape(a.shape).ndims >= _ops.TensorShape(b.shape).ndims:
return a, b, identity, still_need_to_transpose
# From now on, we might modify b, but will not modify a.
# Suppose:
# _ops.TensorShape(a.shape) = C + [m, n], _ops.TensorShape(b.shape) =
# _ops.TensorShape(b.shape) = S + C + [n, r]
b_extra_ndims = _ops.TensorShape(b.shape).ndims - _ops.TensorShape(
a.shape).ndims
# b_extra_sh = S, b_main_sh = C + [n, r]
b_extra_sh = array_ops.shape(b)[:b_extra_ndims]
b_main_sh = array_ops.shape(b)[b_extra_ndims:]
# No reason to flip unless the extra dims of b are big enough. Why?
# Assume adjoint/transpose = False. Then...
# By not flipping, we have to replicate a to shape
# b_extra_sh + _ops.TensorShape(a.shape),
# which could use extra memory. But in all cases, the final output has shape
# b_extra_sh + _ops.TensorShape(a.shape)[:-1] + _ops.TensorShape([b.shape)[-1]]
# So we only end up creating a larger object if the end dim of b is smaller
# than the end dim of a. This often happens, e.g. if b was a vector that was
# expanded to a matrix (by appending a singleton).
# Since adjoint/transpose may not be False, we must make adjustments here.
# The dim of b that holds the multiple equations.
a_domain_sz_ = _ops.TensorShape(
a.shape)[-2 if adjoint_a or transpose_a else -1]
b_eq_sz_ = _ops.TensorShape(
b.shape)[-2 if adjoint_b or transpose_b else -1]
b_extra_sz_ = (
np.prod(_ops.TensorShape(b.shape)[:b_extra_ndims].as_list()) if
_ops.TensorShape(b.shape)[:b_extra_ndims].is_fully_defined() else None)
if (a_domain_sz_ is not None and b_eq_sz_ is not None
and b_extra_sz_ is not None):
if b_extra_sz_ < 2 or a_domain_sz_ <= b_eq_sz_:
return a, b, identity, still_need_to_transpose
# At this point, we're flipping for sure!
# Any transposes/adjoints will happen here explicitly, rather than in calling
# code. Why? To avoid having to write separate complex code for each case.
if adjoint_a:
a = linalg.adjoint(a)
elif transpose_a:
a = linalg.transpose(a)
if adjoint_b:
b = linalg.adjoint(b)
elif transpose_b:
b = linalg.transpose(b)
still_need_to_transpose = False
# Recompute shapes, since the transpose/adjoint may have changed them.
b_extra_sh = array_ops.shape(b)[:b_extra_ndims]
b_main_sh = array_ops.shape(b)[b_extra_ndims:]
# Permutation to put the extra dims at the end.
perm = (np.concatenate(
(np.arange(b_extra_ndims,
_ops.TensorShape(b.shape).ndims), np.arange(
0, b_extra_ndims)), 0))
b_extra_on_end = array_ops.transpose(b, perm=perm)
# Now squash this end into one long dim.
b_squashed_end = array_ops.reshape(
b_extra_on_end, array_ops.concat((b_main_sh[:-1], [-1]), 0))
def reshape_inv(y):
# Expand the extra dims hanging off the end, "b_extra_sh".
# Note we use y_sh[:-1] + [b_main_sh[-1]] rather than b_main_sh, because y
# Could have different batch dims than a and b, because of broadcasting.
y_extra_shape = array_ops.concat(
(array_ops.shape(y)[:-1], [b_main_sh[-1]], b_extra_sh), 0)
y_extra_on_end = array_ops.reshape(y, y_extra_shape)
inverse_perm = np.argsort(perm)
return array_ops.transpose(y_extra_on_end, perm=inverse_perm)
return a, b_squashed_end, reshape_inv, still_need_to_transpose
def _vec(x):
"""Stacks column of matrix to form a single column."""
return array_ops.reshape(
_linalg.matrix_transpose(x),
array_ops.concat(
[array_ops.shape(x)[:-2], [-1]], axis=0))