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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))
.
# 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. |
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Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/versions/r2.3/api_docs/python/tf/linalg/set_diag