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If A is complex valued, it computes the norm of A$abs() Supports input of float, double, cfloat and cdouble dtypes. This function does not necessarily treat multidimensonal A as a batch of vectors, instead:


linalg_vector_norm(A, ord = 2, dim = NULL, keepdim = FALSE, dtype = NULL)



(Tensor): tensor, flattened by default, but this behavior can be controlled using dim.


(int, float, inf, -inf, 'fro', 'nuc', optional): order of norm. Default: 2


(int, Tupleint, optional): dimensions over which to compute the vector or matrix norm. See above for the behavior when dim=NULL. Default: NULL


(bool, optional): If set to TRUE, the reduced dimensions are retained in the result as dimensions with size one. Default: FALSE


dtype (torch_dtype, optional): If specified, the input tensor is cast to dtype before performing the operation, and the returned tensor's type will be dtype. Default: NULL


  • If dim=NULL, A will be flattened before the norm is computed.

  • If dim is an int or a tuple, the norm will be computed over these dimensions and the other dimensions will be treated as batch dimensions.

This behavior is for consistency with linalg_norm().

ord defines the norm that is computed. The following norms are supported:

ordnorm for matricesnorm for vectors
NULL (default)Frobenius norm2-norm (see below)
"fro"Frobenius norm– not supported –
"nuc"nuclear norm– not supported –
Infmax(sum(abs(x), dim=2))max(abs(x))
-Infmin(sum(abs(x), dim=2))min(abs(x))
0– not supported –sum(x != 0)
1max(sum(abs(x), dim=1))as below
-1min(sum(abs(x), dim=1))as below
2largest singular valueas below
-2smallest singular valueas below
other int or float– not supported –sum(abs(x)^{ord})^{(1 / ord)}


if (torch_is_installed()) {
a <- torch_arange(0, 8, dtype = torch_float()) - 4
b <- a$reshape(c(3, 3))

linalg_vector_norm(a, ord = 3.5)
linalg_vector_norm(b, ord = 3.5)
#> torch_tensor
#> 5.43449
#> [ CPUFloatType{} ]