Returns a batched diagonal tensor with given batched diagonal values.

tf.raw_ops.MatrixDiagV3( diagonal, k, num_rows, num_cols, padding_value, align='RIGHT_LEFT', name=None )

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] - 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. 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 tridiagonal band (per batch). 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.matrix_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]]] # LEFT_RIGHT alignment. 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.matrix_diag(diagonals, k = (-1, 1), align="LEFT_RIGHT") ==> [[[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.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` . Rank `r` , where `r >= 1` |

`k` | A `Tensor` of type `int32` . 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` | A `Tensor` of type `int32` . 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 k and the innermost dimension of `diagonal` . |

`num_cols` | A `Tensor` of type `int32` . 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 k and the innermost dimension of `diagonal` . |

`padding_value` | A `Tensor` . Must have the same type as `diagonal` . The number to fill the area outside the specified diagonal band with. Default is 0. |

`align` | An optional `string` from: `"LEFT_RIGHT", "RIGHT_LEFT", "LEFT_LEFT", "RIGHT_RIGHT"` . Defaults to `"RIGHT_LEFT"` . 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. |

`name` | A name for the operation (optional). |

Returns | |
---|---|

A `Tensor` . Has the same type as `diagonal` . |

© 2020 The TensorFlow Authors. All rights reserved.

Licensed under the Creative Commons Attribution License 3.0.

Code samples licensed under the Apache 2.0 License.

https://www.tensorflow.org/versions/r2.4/api_docs/python/tf/raw_ops/MatrixDiagV3