def _matmul(self, x, adjoint=False, adjoint_arg=False): if self._assert_proper_shapes: x = linalg.adjoint(x) if adjoint_arg else x aps = linear_operator_util.assert_compatible_matrix_dimensions( self, x) x = distribution_util.with_dependencies([aps], x) if self.is_square: # Note that adjoint has no effect since this matrix is self-adjoint. if adjoint_arg: output_shape = array_ops.concat([ array_ops.shape(x)[:-2], [array_ops.shape(x)[-1], array_ops.shape(x)[-2]] ], axis=0) else: output_shape = array_ops.shape(x) return self._possibly_broadcast_batch_shape( array_ops.zeros(shape=output_shape, dtype=x.dtype)) x_shape = array_ops.shape(x) n = self._num_columns if adjoint else self._num_rows m = x_shape[-2] if adjoint_arg else x_shape[-1] output_shape = array_ops.concat([x_shape[:-2], [n, m]], axis=0) zeros = array_ops.zeros(shape=output_shape, dtype=x.dtype) return self._possibly_broadcast_batch_shape(zeros)
def _to_dense(self): product = self.operators[0].to_dense() for operator in self.operators[1:]: # Product has shape [B, R1, 1, C1, 1]. product = product[..., :, _ops.newaxis, :, _ops.newaxis] # Operator has shape [B, 1, R2, 1, C2]. op_to_mul = operator.to_dense()[..., _ops.newaxis, :, _ops.newaxis, :] # This is now [B, R1, R2, C1, C2]. product = 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)) tensorshape_util.set_shape(product, tensor_shape.TensorShape(self.shape)) return product
def _to_dense(self): num_cols = 0 rows = [] broadcasted_blocks = [ operator.to_dense() for operator in self.operators ] broadcasted_blocks = linear_operator_util.broadcast_matrix_batch_dims( broadcasted_blocks) for block in broadcasted_blocks: batch_row_shape = array_ops.shape(block)[:-1] zeros_to_pad_before_shape = array_ops.concat( [batch_row_shape, [num_cols]], axis=-1) zeros_to_pad_before = array_ops.zeros( shape=zeros_to_pad_before_shape, dtype=block.dtype) num_cols += array_ops.shape(block)[-1] zeros_to_pad_after_shape = array_ops.concat( [batch_row_shape, [self.domain_dimension_tensor() - num_cols]], axis=-1) zeros_to_pad_after = array_ops.zeros( shape=zeros_to_pad_after_shape, dtype=block.dtype) rows.append( array_ops.concat( [zeros_to_pad_before, block, zeros_to_pad_after], axis=-1)) mat = array_ops.concat(rows, axis=-2) tensorshape_util.set_shape(mat, tensor_shape.TensorShape(self.shape)) return mat
def _shape_tensor(self, row=None, col=None): row = self.row if row is None else row col = self.col if col is None else col v_shape = array_ops.broadcast_dynamic_shape(array_ops.shape(row), array_ops.shape(col)) k = v_shape[-1] return array_ops.concat((v_shape, [k]), 0)
def _to_dense(self): row = ops.convert_to_tensor(self.row) col = ops.convert_to_tensor(self.col) total_shape = array_ops.broadcast_dynamic_shape( array_ops.shape(row), array_ops.shape(col)) n = array_ops.shape(row)[-1] row = _ops.broadcast_to(row, total_shape) col = _ops.broadcast_to(col, total_shape) # We concatenate the column in reverse order to the row. # This gives us 2*n + 1 elements. elements = array_ops.concat( [array_ops.reverse(col, axis=[-1]), row[..., 1:]], axis=-1) # Given the above vector, the i-th row of the Toeplitz matrix # is the last n elements of the above vector shifted i right # (hence the first row is just the row vector provided, and # the first element of each row will belong to the column vector). # We construct these set of indices below. indices = math_ops.mod( # How much to shift right. This corresponds to `i`. math_ops.range(0, n) + # Specifies the last `n` indices. math_ops.range(n - 1, -1, -1)[..., _ops.newaxis], # Mod out by the total number of elements to ensure the index is # non-negative (for tf.gather) and < 2 * n - 1. 2 * n - 1) return array_ops.gather(elements, indices, axis=-1)
def _shape_tensor(self): batch_shape = array_ops.broadcast_dynamic_shape( self.base_operator.batch_shape_tensor(), array_ops.shape(self.u)[:-2]) batch_shape = array_ops.broadcast_dynamic_shape( batch_shape, array_ops.shape(self.v)[:-2]) return array_ops.concat( [batch_shape, self.base_operator.shape_tensor()[-2:]], axis=0)
def _vectorize_then_blockify(self, matrix): """Shape batch matrix to batch vector, then blockify trailing dimensions.""" # Suppose # tensor_shape.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 (tensor_shape.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 = tensor_shape.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 _unblockify_then_matricize(self, vec): """Flatten the block dimensions then reshape to a batch matrix.""" # Suppose # tensor_shape.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 tensor_shape.TensorShape(vec.shape).is_fully_defined(): # vec_shape = [v0, v1, v2, v3] vec_shape = tensor_shape.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 assert_compatible_matrix_dimensions(operator, x): """Assert that an argument to solve/matmul has proper domain dimension. If `tensor_shape.TensorShape(operator.shape)[-2:] = [M, N]`, and `tensor_shape.TensorShape(x.shape)[-2:] = [Q, R]`, then `operator.matmul(x)` is defined only if `N = Q`. This `Op` returns an `Assert` that "fires" if this is not the case. Static checks are already done by the base class `LinearOperator`. Args: operator: `LinearOperator`. x: `Tensor`. Returns: `Assert` `Op`. """ # Static checks are done in the base class. Only tensor asserts here. assert_same_dd = check_ops.assert_equal( array_ops.shape(x)[-2], operator.domain_dimension_tensor(), # This error message made to look similar to error raised by static check # in the base class. message=("Dimensions are not compatible. " "shape[-2] of argument to be the same as this operator")) return assert_same_dd
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 _block_shape_tensor(self, spectrum_shape=None): if self.block_shape.is_fully_defined(): return linear_operator_util.shape_tensor( self.block_shape.as_list(), name="block_shape") spectrum_shape = (array_ops.shape(self.spectrum) if spectrum_shape is None else spectrum_shape) return spectrum_shape[-self.block_depth:]
def _shape_tensor(self): # See _ops.TensorShape(self.shape) for explanation of steps s_shape = array_ops.shape(self._spectrum) batch_shape = s_shape[:-self.block_depth] trailing_dims = s_shape[-self.block_depth:] n = math_ops.reduce_prod(trailing_dims) n_x_n = [n, n] return array_ops.concat((batch_shape, n_x_n), 0)
def _shape_tensor(self, spectrum=None): spectrum = self.spectrum if spectrum is None else spectrum # See tensor_shape.TensorShape(self.shape) for explanation of steps s_shape = array_ops.shape(spectrum) batch_shape = s_shape[:-self.block_depth] trailing_dims = s_shape[-self.block_depth:] n = math_ops.reduce_prod(trailing_dims) n_x_n = [n, n] return array_ops.concat((batch_shape, n_x_n), 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)
def _eigvals(self): # We have (n - 1) +1 eigenvalues and a single -1 eigenvalue. result_shape = array_ops.shape(self.reflection_axis) n = result_shape[-1] ones_shape = array_ops.concat([result_shape[:-1], [n - 1]], axis=-1) neg_shape = array_ops.concat([result_shape[:-1], [1]], axis=-1) eigvals = array_ops.ones(shape=ones_shape, dtype=self.dtype) eigvals = array_ops.concat( [-array_ops.ones(shape=neg_shape, dtype=self.dtype), eigvals], axis=-1) return eigvals
def _set_diag_operators(self, diag_update, is_diag_update_positive): """Set attributes self._diag_update and self._diag_operator.""" if diag_update is not None: self._diag_operator = linear_operator_diag.LinearOperatorDiag( self._diag_update, is_positive_definite=is_diag_update_positive) else: if tensor_shape.dimension_value(tensor_shape.TensorShape(self.u.shape)[-1]) is not None: r = tensor_shape.dimension_value(tensor_shape.TensorShape(self.u.shape)[-1]) else: r = array_ops.shape(self.u)[-1] self._diag_operator = linear_operator_identity.LinearOperatorIdentity( num_rows=r, dtype=self.dtype)
def _to_dense(self): num_cols = 0 dense_rows = [] flat_broadcast_operators = linear_operator_util.broadcast_matrix_batch_dims( [op.to_dense() for row in self.operators for op in row]) # pylint: disable=g-complex-comprehension broadcast_operators = [ flat_broadcast_operators[i * (i + 1) // 2:(i + 1) * (i + 2) // 2] for i in range(len(self.operators))] for row_blocks in broadcast_operators: batch_row_shape = array_ops.shape(row_blocks[0])[:-1] num_cols += array_ops.shape(row_blocks[-1])[-1] zeros_to_pad_after_shape = array_ops.concat( [batch_row_shape, [self.domain_dimension_tensor() - num_cols]], axis=-1) zeros_to_pad_after = array_ops.zeros( shape=zeros_to_pad_after_shape, dtype=self.dtype) row_blocks.append(zeros_to_pad_after) dense_rows.append(array_ops.concat(row_blocks, axis=-1)) mat = array_ops.concat(dense_rows, axis=-2) tensorshape_util.set_shape(mat, tensor_shape.TensorShape(self.shape)) return mat
def _broadcast_batch_dims(self, x, spectrum): """Broadcast batch dims of batch matrix `x` and spectrum.""" spectrum = ops.convert_to_tensor(spectrum, name="spectrum") # tensor_shape.TensorShape(spectrum.shape) = batch_shape + block_shape # First make spectrum a batch matrix with # tensor_shape.TensorShape(spectrum.shape) = batch_shape + [prod(block_shape), 1] batch_shape = self._batch_shape_tensor(shape=self._shape_tensor( spectrum=spectrum)) spec_mat = array_ops.reshape( spectrum, array_ops.concat((batch_shape, [-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. x_batch_shape = array_ops.shape(x)[:-2] spectrum_shape = array_ops.shape(spectrum) spectrum = array_ops.reshape( spec_mat, array_ops.concat( (x_batch_shape, self._block_shape_tensor(spectrum_shape=spectrum_shape)), axis=0)) return x, spectrum
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 _shape_tensor(self): # Avoid messy broadcasting if possible. if tensor_shape.TensorShape(self.shape).is_fully_defined(): return ops.convert_to_tensor( tensor_shape.TensorShape(self.shape).as_list(), dtype=dtypes.int32, name="shape") domain_dimension = sum(self._block_domain_dimension_tensors()) range_dimension = sum(self._block_range_dimension_tensors()) matrix_shape = array_ops.stack([domain_dimension, range_dimension]) # Dummy Tensor of zeros. Will never be materialized. zeros = array_ops.zeros(shape=self.operators[0].batch_shape_tensor()) for operator in self.operators[1:]: zeros = zeros + array_ops.zeros(shape=operator.batch_shape_tensor()) batch_shape = array_ops.shape(zeros) return array_ops.concat((batch_shape, matrix_shape), 0)
def _eigvals(self): # This will be the kronecker product of all the eigenvalues. # Note: It doesn't matter which kronecker product it is, since every # kronecker product of the same matrices are similar. eigvals = [operator.eigvals() for operator in self.operators] # Now compute the kronecker product product = eigvals[0] for eigval in eigvals[1:]: # Product has shape [B, R1, 1]. product = product[..., _ops.newaxis] # Eigval has shape [B, 1, R2]. Produces shape [B, R1, R2]. product *= eigval[..., _ops.newaxis, :] # Reshape to [B, R1 * R2] product = array_ops.reshape( product, shape=array_ops.concat([array_ops.shape(product)[:-2], [-1]], axis=0)) tensorshape_util.set_shape(product, tensor_shape.TensorShape(self.shape)[:-1]) return product
def _shape_tensor(self): # Avoid messy broadcasting if possible. if tensor_shape.TensorShape(self.shape).is_fully_defined(): return ops.convert_to_tensor( tensor_shape.TensorShape(self.shape).as_list(), dtype=dtypes.int32, name="shape") # Don't check the matrix dimensions. That would add unnecessary Asserts to # the graph. Things will fail at runtime naturally if shapes are # incompatible. matrix_shape = array_ops.stack([ self.operators[0].range_dimension_tensor(), self.operators[-1].domain_dimension_tensor() ]) # Dummy Tensor of zeros. Will never be materialized. zeros = array_ops.zeros(shape=self.operators[0].batch_shape_tensor()) for operator in self.operators[1:]: zeros += array_ops.zeros(shape=operator.batch_shape_tensor()) batch_shape = array_ops.shape(zeros) return array_ops.concat((batch_shape, matrix_shape), 0)
def broadcast_matrix_batch_dims(batch_matrices, name=None): """Broadcast leading dimensions of zero or more [batch] matrices. Example broadcasting one batch dim of two simple matrices. ```python x = [[1, 2], [3, 4]] # Shape [2, 2], no batch dims y = [[[1]]] # Shape [1, 1, 1], 1 batch dim of shape [1] x_bc, y_bc = broadcast_matrix_batch_dims([x, y]) x_bc ==> [[[1, 2], [3, 4]]] # Shape [1, 2, 2], 1 batch dim of shape [1]. y_bc ==> same as y ``` Example broadcasting many batch dims ```python x = tf.random.normal(shape=(2, 3, 1, 4, 4)) y = tf.random.normal(shape=(1, 3, 2, 5, 5)) x_bc, y_bc = broadcast_matrix_batch_dims([x, y]) tensor_shape.TensorShape(x_bc.shape) ==> (2, 3, 2, 4, 4) tensor_shape.TensorShape(y_bc.shape) ==> (2, 3, 2, 5, 5) ``` Args: batch_matrices: Iterable of `Tensor`s, each having two or more dimensions. name: A string name to prepend to created ops. Returns: bcast_matrices: List of `Tensor`s, with `bcast_matrices[i]` containing the values from `batch_matrices[i]`, with possibly broadcast batch dims. Raises: ValueError: If any input `Tensor` is statically determined to have less than two dimensions. """ with ops.name_scope( name or "broadcast_matrix_batch_dims", values=batch_matrices): check_ops.assert_proper_iterable(batch_matrices) batch_matrices = list(batch_matrices) for i, mat in enumerate(batch_matrices): batch_matrices[i] = ops.convert_to_tensor(mat) assert_is_batch_matrix(batch_matrices[i]) if len(batch_matrices) < 2: return batch_matrices # Try static broadcasting. # bcast_batch_shape is the broadcast batch shape of ALL matrices. # E.g. if batch_matrices = [x, y], with # tensor_shape.TensorShape(x.shape) = [2, j, k] (batch shape = [2]) # tensor_shape.TensorShape(y.shape) = [3, 1, l, m] (batch shape = [3, 1]) # ==> bcast_batch_shape = [3, 2] bcast_batch_shape = tensor_shape.TensorShape(batch_matrices[0].shape)[:-2] for mat in batch_matrices[1:]: bcast_batch_shape = _ops.broadcast_static_shape( bcast_batch_shape, tensor_shape.TensorShape(mat.shape)[:-2]) if bcast_batch_shape.is_fully_defined(): for i, mat in enumerate(batch_matrices): if tensor_shape.TensorShape(mat.shape)[:-2] != bcast_batch_shape: bcast_shape = array_ops.concat( [bcast_batch_shape.as_list(), array_ops.shape(mat)[-2:]], axis=0) batch_matrices[i] = _ops.broadcast_to(mat, bcast_shape) return batch_matrices # Since static didn't work, do dynamic, which always copies data. bcast_batch_shape = array_ops.shape(batch_matrices[0])[:-2] for mat in batch_matrices[1:]: bcast_batch_shape = array_ops.broadcast_dynamic_shape( bcast_batch_shape, array_ops.shape(mat)[:-2]) for i, mat in enumerate(batch_matrices): batch_matrices[i] = _ops.broadcast_to( mat, array_ops.concat( [bcast_batch_shape, array_ops.shape(mat)[-2:]], axis=0)) return batch_matrices
def _shape_tensor(self): return array_ops.shape(self._matrix)
def _shape_tensor(self): v_shape = array_ops.broadcast_dynamic_shape(array_ops.shape(self.row), array_ops.shape(self.col)) k = v_shape[-1] return array_ops.concat((v_shape, [k]), 0)
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))
def _shape_tensor(self): d_shape = array_ops.shape(self._reflection_axis) k = d_shape[-1] return array_ops.concat((d_shape, [k]), 0)
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 tensor_shape.TensorShape(a.shape).ndims is None or tensor_shape.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 tensor_shape.TensorShape(a.shape).ndims >= tensor_shape.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: # tensor_shape.TensorShape(a.shape) = C + [m, n], tensor_shape.TensorShape(b.shape) = # tensor_shape.TensorShape(b.shape) = S + C + [n, r] b_extra_ndims = tensor_shape.TensorShape(b.shape).ndims - tensor_shape.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 + tensor_shape.TensorShape(a.shape), # which could use extra memory. But in all cases, the final output has shape # b_extra_sh + tensor_shape.TensorShape(a.shape)[:-1] + tensor_shape.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_ = tensor_shape.TensorShape(a.shape)[-2 if adjoint_a or transpose_a else -1] b_eq_sz_ = tensor_shape.TensorShape(b.shape)[-2 if adjoint_b or transpose_b else -1] b_extra_sz_ = ( np.prod(tensor_shape.TensorShape(b.shape)[:b_extra_ndims].as_list()) if tensor_shape.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.matrix_transpose(a, conjugate=True) elif transpose_a: a = _linalg.matrix_transpose(a, conjugate=False) if adjoint_b: b = _linalg.matrix_transpose(b, conjugate=True) elif transpose_a: b = _linalg.matrix_transpose(b, conjugate=False) 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, tensor_shape.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 _shape_tensor(self): d_shape = array_ops.shape(self._diag) k = d_shape[-1] return array_ops.concat((d_shape, [k]), 0)
def _shape_tensor(self): matrix_shape = array_ops.stack((self._num_rows, self._num_rows), axis=0) batch_shape = array_ops.shape(self.multiplier) return array_ops.concat((batch_shape, matrix_shape), 0)