norm_op

→TensorImplPtr

int norm_op(const int & a, double ord, int axis, bool keepdims)

source edit

Python wrappers

pylucid.linalg.normfunction

Compute the p-norm of a float tensor over the specified axes.

Math

\|A\|_p = \Bigl(\sum_i |a_i|^p\Bigr)^{1/p}.

For $p = 2$ on a matrix this is the Frobenius norm; for $p = 1$ on a matrix this is the entrywise L1 norm (not the operator 1-norm).

Shape

a: arbitrary float shape.
Output:
- axis empty, keepdims=false $\to$ scalar (rank 0).
- axis empty, keepdims=true $\to$ all-ones shape of the same rank as a.
- Otherwise: rank of a minus the number of reduced axes (keepdims=false) or rank preserved with those axes set to 1 (keepdims=true).

See Also

SVD.h : Underpins operator norms (spectral, nuclear) once exposed.

Parameters

aTensorImplPtr

Input tensor (any float dtype, any shape).

orddouble

Norm order. 2.0 selects the Frobenius / Euclidean norm

\|A\|_F = \sqrt{\sum a_{ij}^2}

; 1.0 selects the entrywise L1 norm

\|A\|_1 = \sum |a_{ij}|

. Other values may be forwarded to the backend in the forward pass but have no registered backward.

axisstd::vector<int>

Axes to reduce. Empty means a global reduction over every element; negative indices are accepted and normalised.

keepdimsbool

If true the reduced axes are retained as size-1 stubs in the output; otherwise they are removed.

Returns

TensorImplPtr

Reduced norm tensor.

Raises

ValueError

If a is non-float.

NotImplementedError

(At backward time.) If ord is not 1.0 or 2.0 and a gradient is requested.

Notes

Operator norms (spectral, nuclear, induced 1-/inf-norm) are not yet dispatched here — they would require SVD and a separate backward. This op currently covers only the entrywise reductions.