|---| | [ View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.21.0/tensorflow/python/ops/array_ops.py#L2076-L2242) | Returns a batched diagonal tensor with given batched diagonal values. #### View aliases **Compat aliases for migration** See [Migration guide](https://www.tensorflow.org/guide/migrate) for more details. [`tf.compat.v1.matrix_diag`](https://www.tensorflow.org/api_docs/python/tf/linalg/diag)
tf.linalg.diag( diagonal, name='diag', k=0, num_rows=-1, num_cols=-1, padding_value=0, align='RIGHT_LEFT' ) ### Used in the notebooks | Used in the guide | Used in the tutorials | |---|---| | - [Matrix approximation with Core APIs](https://www.tensorflow.org/guide/core/matrix_core) | - [Quantum data](https://www.tensorflow.org/quantum/tutorials/quantum_data) | 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) + 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. diagonal = np.array([[1, 2, 3, 4], # Input shape: (2, 4) [5, 6, 7, 8]]) tf.linalg.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.linalg.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 tridiagonal band (per batch). diagonals = np.array([[[8, 9, 0], # Input shape: (2, 2, 3) [1, 2, 3], [0, 4, 5]], [[2, 3, 0], [6, 7, 9], [0, 9, 1]]]) tf.linalg.diag(diagonals, k = (-1, 1)) ==> [[[1, 8, 0], # Output shape: (2, 3, 3) [4, 2, 9], [0, 5, 3]], [[6, 2, 0], [9, 7, 3], [0, 1, 9]]] # RIGHT_LEFT alignment. diagonals = np.array([[[0, 8, 9], # Input shape: (2, 2, 3) [1, 2, 3], [4, 5, 0]], [[0, 2, 3], [6, 7, 9], [9, 1, 0]]]) tf.linalg.diag(diagonals, k = (-1, 1), align="RIGHT_LEFT") ==> [[[1, 8, 0], # Output shape: (2, 3, 3) [4, 2, 9], [0, 5, 3]], [[6, 2, 0], [9, 7, 3], [0, 1, 9]]] # Rectangular matrix. diagonal = np.array([1, 2]) # Input shape: (2) tf.linalg.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.linalg.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. | | `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. |



| ## Returns || |---|---| | A Tensor. Has the same type as `diagonal`. ||