tensorflow:: ops:: MatrixDiagV3
#include <array_ops.h>
Returns a batched diagonal tensor with given batched diagonal values.
Summary
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 ; otherwisewhere
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 ; otherwisewhere
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]]
Args:
- scope: A Scope object
- diagonal: Rank
r
, wherer >= 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 thank[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 k 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 k and the innermost dimension of
diagonal
. - padding_value: The number to fill the area outside the specified diagonal band with. Default is 0.
Optional attributes (see Attrs
):
- 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:
Output
: Has rankr+1
whenk
is an integer ork[0] == k[1]
, rankr
otherwise.
Constructors and Destructors |
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MatrixDiagV3(const ::tensorflow::Scope & scope, ::tensorflow::Input diagonal, ::tensorflow::Input k, ::tensorflow::Input num_rows, ::tensorflow::Input num_cols, ::tensorflow::Input padding_value)
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MatrixDiagV3(const ::tensorflow::Scope & scope, ::tensorflow::Input diagonal, ::tensorflow::Input k, ::tensorflow::Input num_rows, ::tensorflow::Input num_cols, ::tensorflow::Input padding_value, const MatrixDiagV3::Attrs & attrs)
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Public attributes |
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operation
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output
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Public functions |
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node() const
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::tensorflow::Node *
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operator::tensorflow::Input() const
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operator::tensorflow::Output() const
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Public static functions |
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Align(StringPiece x)
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Structs |
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tensorflow:: |
Optional attribute setters for MatrixDiagV3. |
Public attributes
operation
Operation operation
output
::tensorflow::Output output
Public functions
MatrixDiagV3
MatrixDiagV3( const ::tensorflow::Scope & scope, ::tensorflow::Input diagonal, ::tensorflow::Input k, ::tensorflow::Input num_rows, ::tensorflow::Input num_cols, ::tensorflow::Input padding_value )
MatrixDiagV3
MatrixDiagV3( const ::tensorflow::Scope & scope, ::tensorflow::Input diagonal, ::tensorflow::Input k, ::tensorflow::Input num_rows, ::tensorflow::Input num_cols, ::tensorflow::Input padding_value, const MatrixDiagV3::Attrs & attrs )
node
::tensorflow::Node * node() const
operator::tensorflow::Input
operator::tensorflow::Input() const
operator::tensorflow::Output
operator::tensorflow::Output() const
Public static functions
Align
Attrs Align( StringPiece x )