TensorFlow 1 version | View source on GitHub |
Returns a batched diagonal tensor with given batched diagonal values.
tf.linalg.diag(
diagonal, name='diag', k=0, num_rows=-1, num_cols=-1, padding_value=0
)
Returns a tensor with the contents in diagonal
as k[0]
-th to k[1]
-th
diagonals of a matrix, with everything else padded with padding
. num_rows
and num_cols
specify the dimension of the innermost matrix of the output. If
both are not specified, the op assumes the innermost matrix is square and
infers its size from k
and the innermost dimension of diagonal
. If only
one of them is specified, the op assumes the unspecified value is the smallest
possible based on other criteria.
Let diagonal
have r
dimensions [I, J, ..., L, M, N]
. The output tensor
has rank r+1
with shape [I, J, ..., L, M, num_rows, num_cols]
when only
one diagonal is given (k
is an integer or k[0] == k[1]
). Otherwise, it has
rank r
with shape [I, J, ..., L, num_rows, num_cols]
.
The second innermost dimension of diagonal
has double meaning. When k
is
scalar or k[0] == k[1]
, M
is part of the batch size [I, J, ..., M], and
the output tensor is:
output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, n-max(d_upper, 0)] ; if n - m == d_upper
padding_value ; otherwise
Otherwise, M
is treated as the number of diagonals for the matrix in the
same batch (M = k[1]-k[0]+1
), and the output tensor is:
output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, diag_index, index_in_diag] ; if k[0] <= d <= k[1]
padding_value ; otherwise
where d = n - m
, diag_index = k[1] - d
, and
index_in_diag = n - max(d, 0)
.
For example:
# The main diagonal.
diagonal = np.array([[1, 2, 3, 4], # Input shape: (2, 4)
[5, 6, 7, 8]])
tf.matrix_diag(diagonal) ==> [[[1, 0, 0, 0], # Output shape: (2, 4, 4)
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]],
[[5, 0, 0, 0],
[0, 6, 0, 0],
[0, 0, 7, 0],
[0, 0, 0, 8]]]
# A superdiagonal (per batch).
diagonal = np.array([[1, 2, 3], # Input shape: (2, 3)
[4, 5, 6]])
tf.matrix_diag(diagonal, k = 1)
==> [[[0, 1, 0, 0], # Output shape: (2, 4, 4)
[0, 0, 2, 0],
[0, 0, 0, 3],
[0, 0, 0, 0]],
[[0, 4, 0, 0],
[0, 0, 5, 0],
[0, 0, 0, 6],
[0, 0, 0, 0]]]
# A band of diagonals.
diagonals = np.array([[[1, 2, 3], # Input shape: (2, 2, 3)
[4, 5, 0]],
[[6, 7, 9],
[9, 1, 0]]])
tf.matrix_diag(diagonals, k = (-1, 0))
==> [[[1, 0, 0], # Output shape: (2, 3, 3)
[4, 2, 0],
[0, 5, 3]],
[[6, 0, 0],
[9, 7, 0],
[0, 1, 9]]]
# Rectangular matrix.
diagonal = np.array([1, 2]) # Input shape: (2)
tf.matrix_diag(diagonal, k = -1, num_rows = 3, num_cols = 4)
==> [[0, 0, 0, 0], # Output shape: (3, 4)
[1, 0, 0, 0],
[0, 2, 0, 0]]
# Rectangular matrix with inferred num_cols and padding_value = 9.
tf.matrix_diag(diagonal, k = -1, num_rows = 3, padding_value = 9)
==> [[9, 9], # Output shape: (3, 2)
[1, 9],
[9, 2]]
Args | |
---|---|
diagonal
|
A Tensor with rank k >= 1 .
|
name
|
A name for the operation (optional). |
k
|
Diagonal offset(s). Positive value means superdiagonal, 0 refers to the
main diagonal, and negative value means subdiagonals. k can be a single
integer (for a single diagonal) or a pair of integers specifying the low
and high ends of a matrix band. k[0] must not be larger than k[1] .
|
num_rows
|
The number of rows of the output matrix. If it is not provided,
the op assumes the output matrix is a square matrix and infers the matrix
size from d_lower , d_upper , and the innermost dimension of diagonal .
|
num_cols
|
The number of columns of the output matrix. If it is not provided,
the op assumes the output matrix is a square matrix and infers the matrix
size from d_lower , d_upper , and the innermost dimension of diagonal .
|
padding_value
|
The value to fill the area outside the specified diagonal band with. Default is 0. |
Returns | |
---|---|
A Tensor. Has the same type as diagonal .
|