TensorFlow 1 version
|
View source on GitHub
|
Returns a batched matrix tensor with new batched diagonal values.
tf.linalg.set_diag(
input, diagonal, name='set_diag', k=0, align='RIGHT_LEFT'
)
Given input and diagonal, this operation returns a tensor with the
same shape and values as input, except for the specified diagonals of the
innermost matrices. These will be overwritten by the values in diagonal.
input has r+1 dimensions [I, J, ..., L, M, N]. When k is scalar or
k[0] == k[1], diagonal has r dimensions [I, J, ..., L, max_diag_len].
Otherwise, it has r+1 dimensions [I, J, ..., L, num_diags, max_diag_len].
num_diags is the number of diagonals, num_diags = k[1] - k[0] + 1.
max_diag_len is the longest diagonal in the range [k[0], k[1]],
max_diag_len = min(M + min(k[1], 0), N + min(-k[0], 0))
The output is a tensor of rank k+1 with dimensions [I, J, ..., L, M, N].
If k is scalar or k[0] == k[1]:
output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, n-max(k[1], 0)] ; if n - m == k[1]
input[i, j, ..., l, m, n] ; otherwise
Otherwise,
output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, diag_index, index_in_diag] ; if k[0] <= d <= k[1]
input[i, j, ..., l, m, n] ; otherwise
where d = n - m, diag_index = k[1] - d, and
index_in_diag = n - max(d, 0) + offset.
offset is zero except when the alignment of the diagonal is to the right.
offset = max_diag_len - diag_len(d) ; if (`align` in {RIGHT_LEFT, RIGHT_RIGHT}
and `d >= 0`) or
(`align` in {LEFT_RIGHT, RIGHT_RIGHT}
and `d <= 0`)
0 ; otherwise
where diag_len(d) = min(cols - max(d, 0), rows + min(d, 0)).
For example:
# The main diagonal.
input = np.array([[[7, 7, 7, 7], # Input shape: (2, 3, 4)
[7, 7, 7, 7],
[7, 7, 7, 7]],
[[7, 7, 7, 7],
[7, 7, 7, 7],
[7, 7, 7, 7]]])
diagonal = np.array([[1, 2, 3], # Diagonal shape: (2, 3)
[4, 5, 6]])
tf.matrix_set_diag(input, diagonal)
==> [[[1, 7, 7, 7], # Output shape: (2, 3, 4)
[7, 2, 7, 7],
[7, 7, 3, 7]],
[[4, 7, 7, 7],
[7, 5, 7, 7],
[7, 7, 6, 7]]]
# A superdiagonal (per batch).
tf.matrix_set_diag(input, diagonal, k = 1)
==> [[[7, 1, 7, 7], # Output shape: (2, 3, 4)
[7, 7, 2, 7],
[7, 7, 7, 3]],
[[7, 4, 7, 7],
[7, 7, 5, 7],
[7, 7, 7, 6]]]
# A band of diagonals.
diagonals = np.array([[[9, 1, 0], # Diagonal shape: (2, 4, 3)
[6, 5, 8],
[1, 2, 3],
[0, 4, 5]],
[[1, 2, 0],
[5, 6, 4],
[6, 1, 2],
[0, 3, 4]]])
tf.matrix_set_diag(input, diagonals, k = (-1, 2))
==> [[[1, 6, 9, 7], # Output shape: (2, 3, 4)
[4, 2, 5, 1],
[7, 5, 3, 8]],
[[6, 5, 1, 7],
[3, 1, 6, 2],
[7, 4, 2, 4]]]
# RIGHT_LEFT alignment.
diagonals = np.array([[[0, 9, 1], # Diagonal shape: (2, 4, 3)
[6, 5, 8],
[1, 2, 3],
[4, 5, 0]],
[[0, 1, 2],
[5, 6, 4],
[6, 1, 2],
[3, 4, 0]]])
tf.matrix_set_diag(input, diagonals, k = (-1, 2), align="RIGHT_LEFT")
==> [[[1, 6, 9, 7], # Output shape: (2, 3, 4)
[4, 2, 5, 1],
[7, 5, 3, 8]],
[[6, 5, 1, 7],
[3, 1, 6, 2],
[7, 4, 2, 4]]]
Args | |
|---|---|
input
|
A Tensor with rank k + 1, where k >= 1.
|
diagonal
|
A Tensor with rank k, when d_lower == d_upper, or k + 1,
otherwise. 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].
|
align
|
Some diagonals are shorter than max_diag_len and need to be padded.
align is a string specifying how superdiagonals and subdiagonals should
be aligned, respectively. There are four possible alignments: "RIGHT_LEFT"
(default), "LEFT_RIGHT", "LEFT_LEFT", and "RIGHT_RIGHT". "RIGHT_LEFT"
aligns superdiagonals to the right (left-pads the row) and subdiagonals to
the left (right-pads the row). It is the packing format LAPACK uses.
cuSPARSE uses "LEFT_RIGHT", which is the opposite alignment.
|