tf.matrix_band_part()

tf.matrix_band_part(input, num_lower, num_upper, name=None)

Copy a tensor setting everything outside a central band in each innermost matrix

to zero.

The band part is computed as follows: Assume input has k dimensions [I, J, K, ..., M, N], then the output is a tensor with the same shape where

band[i, j, k, ..., m, n] = in_band(m, n) * input[i, j, k, ..., m, n].

The indicator function 'in_band(m, n)is one if(num_lower < 0 || (m-n) <= num_lower)) && (num_upper < 0 || (n-m) <= num_upper)`, and zero otherwise.

For example:

# if 'input' is [[ 0,  1,  2, 3]
                 [-1,  0,  1, 2]
                 [-2, -1,  0, 1]
                 [-3, -2, -1, 0]],

tf.matrix_band_part(input, 1, -1) ==> [[ 0,  1,  2, 3]
                                             [-1,  0,  1, 2]
                                             [ 0, -1,  0, 1]
                                             [ 0,  0, -1, 0]],

tf.matrix_band_part(input, 2, 1) ==> [[ 0,  1,  0, 0]
                                            [-1,  0,  1, 0]
                                            [-2, -1,  0, 1]
                                            [ 0, -2, -1, 0]]

Useful special cases:

tf.matrix_band_part(input, 0, -1) ==> Upper triangular part.
tf.matrix_band_part(input, -1, 0) ==> Lower triangular part.
tf.matrix_band_part(input, 0, 0) ==> Diagonal.

Args:

• input: A Tensor. Rank k tensor.
• num_lower: A Tensor of type int64. 0-D tensor. Number of subdiagonals to keep. If negative, keep entire lower triangle.
• num_upper: A Tensor of type int64. 0-D tensor. Number of superdiagonals to keep. If negative, keep entire upper triangle.
• name: A name for the operation (optional).

Returns:

A Tensor. Has the same type as input. Rank k tensor of the same shape as input. The extracted banded tensor.