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# torch.tril

torch.tril(input, diagonal=0, *, out=None) → Tensor

  Returns the lower triangular part of the matrix (2-D tensor) or batch of matrices `input`, the other elements of the result tensor `out` are set to 0.

  The lower triangular part of the matrix is defined as the elements on and below the diagonal.

  The argument `diagonal` controls which diagonal to consider. If `diagonal` = 0, all elements on and below the main diagonal are retained. A positive value includes just as many diagonals above the main diagonal, and similarly a negative value excludes just as many diagonals below the main diagonal. The main diagonal are the set of indices {(i,i)}\lbrace (i, i) \rbrace{(i,i)} for i∈[0,min⁡{d 1,d 2}−1]i \in [0, \min\{d_{1}, d_{2}\} - 1]i∈[0,min{d 1​,d 2​}−1] where d 1,d 2 d_{1}, d_{2}d 1​,d 2​ are the dimensions of the matrix.

  Parameters:

    - input (Tensor) – the input tensor.

    - diagonal (int, optional) – the diagonal to consider

  Keyword Arguments:

    out (Tensor, optional) – the output tensor.

  Example:

      >>> a = torch.randn(3, 3)
      >>> a
      tensor([[-1.0813, -0.8619,  0.7105],
              [ 0.0935,  0.1380,  2.2112],
              [-0.3409, -0.9828,  0.0289]])
      >>> torch.tril(a)
      tensor([[-1.0813,  0.0000,  0.0000],
              [ 0.0935,  0.1380,  0.0000],
              [-0.3409, -0.9828,  0.0289]])

      >>> b = torch.randn(4, 6)
      >>> b
      tensor([[ 1.2219,  0.5653, -0.2521, -0.2345,  1.2544,  0.3461],
              [ 0.4785, -0.4477,  0.6049,  0.6368,  0.8775,  0.7145],
              [ 1.1502,  3.2716, -1.1243, -0.5413,  0.3615,  0.6864],
              [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024,  0.0978]])
      >>> torch.tril(b, diagonal=1)
      tensor([[ 1.2219,  0.5653,  0.0000,  0.0000,  0.0000,  0.0000],
              [ 0.4785, -0.4477,  0.6049,  0.0000,  0.0000,  0.0000],
              [ 1.1502,  3.2716, -1.1243, -0.5413,  0.0000,  0.0000],
              [-0.0614, -0.7344, -1.3164, -0.7648, -1.4024,  0.0000]])
      >>> torch.tril(b, diagonal=-1)
      tensor([[ 0.0000,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
              [ 0.4785,  0.0000,  0.0000,  0.0000,  0.0000,  0.0000],
              [ 1.1502,  3.2716,  0.0000,  0.0000,  0.0000,  0.0000],
              [-0.0614, -0.7344, -1.3164,  0.0000,  0.0000,  0.0000]])

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