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]])