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MatrixDiagV3

public final class MatrixDiagV3

Returns a batched diagonal tensor with given batched diagonal values.

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))`.

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 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]]
 
 

Nested Classes

class MatrixDiagV3.Options Optional attributes for MatrixDiagV3  

Public Methods

static MatrixDiagV3.Options
align(String align)
Output<T>
asOutput()
Returns the symbolic handle of a tensor.
static <T> MatrixDiagV3<T>
create(Scope scope, Operand<T> diagonal, Operand<Integer> k, Operand<Integer> numRows, Operand<Integer> numCols, Operand<T> paddingValue, Options... options)
Factory method to create a class wrapping a new MatrixDiagV3 operation.
Output<T>
output()
Has rank `r+1` when `k` is an integer or `k[0] == k[1]`, rank `r` otherwise.

Inherited Methods

Public Methods

public static MatrixDiagV3.Options align (String align)

Parameters
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.

public Output<T> asOutput ()

Returns the symbolic handle of a tensor.

Inputs to TensorFlow operations are outputs of another TensorFlow operation. This method is used to obtain a symbolic handle that represents the computation of the input.

public static MatrixDiagV3<T> create (Scope scope, Operand<T> diagonal, Operand<Integer> k, Operand<Integer> numRows, Operand<Integer> numCols, Operand<T> paddingValue, Options... options)

Factory method to create a class wrapping a new MatrixDiagV3 operation.

Parameters
scope current scope
diagonal Rank `r`, where `r >= 1`
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]`.
numRows 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`.
numCols 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`.
paddingValue The number to fill the area outside the specified diagonal band with. Default is 0.
options carries optional attributes values
Returns
  • a new instance of MatrixDiagV3

public Output<T> output ()

Has rank `r+1` when `k` is an integer or `k[0] == k[1]`, rank `r` otherwise.