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# torch.vander

torch.vander(x, N=None, increasing=False) → Tensor

  Generates a Vandermonde matrix.

  The columns of the output matrix are elementwise powers of the input vector x(N−1),x(N−2),...,x 0 x^{(N-1)}, x^{(N-2)}, ..., x^0 x(N−1),x(N−2),...,x 0. If increasing is True, the order of the columns is reversed x 0,x 1,...,x(N−1)x^0, x^1, ..., x^{(N-1)}x 0,x 1,...,x(N−1). Such a matrix with a geometric progression in each row is named for Alexandre-Theophile Vandermonde.

  Parameters:

    - x (Tensor) – 1-D input tensor.

    - N (int, optional) – Number of columns in the output. If N is not specified, a square array is returned (N=l e n(x))(N = len(x))(N=l e n(x)).

    - increasing (bool, optional) – Order of the powers of the columns. If True, the powers increase from left to right, if False (the default) they are reversed.

  Returns:

    Vandermonde matrix. If increasing is False, the first column is x(N−1)x^{(N-1)}x(N−1), the second x(N−2)x^{(N-2)}x(N−2) and so forth. If increasing is True, the columns are x 0,x 1,...,x(N−1)x^0, x^1, ..., x^{(N-1)}x 0,x 1,...,x(N−1).

  Return type:

    Tensor

  Example:

      >>> x = torch.tensor([1, 2, 3, 5])
      >>> torch.vander(x)
      tensor([[  1,   1,   1,   1],
              [  8,   4,   2,   1],
              [ 27,   9,   3,   1],
              [125,  25,   5,   1]])
      >>> torch.vander(x, N=3)
      tensor([[ 1,  1,  1],
              [ 4,  2,  1],
              [ 9,  3,  1],
              [25,  5,  1]])
      >>> torch.vander(x, N=3, increasing=True)
      tensor([[ 1,  1,  1],
              [ 1,  2,  4],
              [ 1,  3,  9],
              [ 1,  5, 25]])

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