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$x^{(N-1)},x^{(N-2)},\mathrm{.}\mathrm{.}\mathrm{.},x^0$x(N−1),x(N−2),...,x0.If increasing is True, the order of the columns is reversed$x^0,x^1,\mathrm{.}\mathrm{.}\mathrm{.},x^{(N-1)}$x0,x1,...,x(N−1). Such amatrix 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$(N=len(x))$(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$x^{(N-1)}$x(N−1),the second$x^{(N-2)}$x(N−2) and so forth. If increasing is True, the columnsare$x^0,x^1,\mathrm{.}\mathrm{.}\mathrm{.},x^{(N-1)}$x0,x1,...,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]])