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 $x^{(N-1)}, x^{(N-2)}, ..., x^0$. If increasing is True, the order of the columns is reversed $x^0, x^1, ..., x^{(N-1)}$. 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 $(N = len(x))$.

• 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 $x^{(N-1)}$, the second $x^{(N-2)}$ and so forth. If increasing is True, the columns are $x^0, x^1, ..., x^{(N-1)}$.

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]])