Split into separate tables

spec/API_specification/linear_algebra_functions.md

@@ -133,23 +133,36 @@ Computes the matrix or vector norm of `a`.
 
 - **ord**: _Optional\[ int, float, Literal\[ inf, -inf, 'fro', 'nuc' ] ]_
 
- - order of the norm. The following norms must be supported:
-
- | ord | matrix | vector |
- | ------------ | ------------------------------- | -------------------------- |
- | None | 'fro' | L2-norm (Euclidean) |
- | 'fro' | 'fro' | - |
- | 'nuc' | 'nuc' | - |
- | 1 | max(sum(abs(x), axis=0)) | L1-norm |
- | -1 | min(sum(abs(x), axis=0)) | sum(1./abs(x))**(-1) |
- | 2 | largest singular value | L2-norm (Euclidean) |
- | -2 | smallest singular value | 1./sqrt(sum(1./abs(x)**2)) |
- | inf | max(sum(abs(x), axis=1)) | infinity norm |
- | -inf | min(sum(abs(x), axis=1)) | min(abs(x)) |
- | (+int,+float) | - | p-norm (for p >= 1) |
- | (-int,-float) | - | sum(abs(x)**ord)**(1./ord) |
-
- where `fro` corresponds to the **Frobenius norm**, `nuc` corresponds to the **nuclear norm**, and `-` indicates that the norm is **not** supported. For matrices,
+ - order of the norm. The following mathematical norms must be supported:
+
+ | ord | matrix | vector |
+ | ---------------- | ------------------------------- | -------------------------- |
+ | 'fro' | 'fro' | - |
+ | 'nuc' | 'nuc' | - |
+ | 1 | max(sum(abs(x), axis=0)) | L1-norm (Manhattan) |
+ | 2 | largest singular value | L2-norm (Euclidean) |
+ | inf | max(sum(abs(x), axis=1)) | infinity norm |
+ | (int,float >= 1) | - | p-norm |
+
+ The following non-mathematical "norms" must be supported:
+
+ | ord | matrix | vector |
+ | ---------------- | ------------------------------- | -------------------------- |
+ | 0 | - | sum(a != 0) |
+ | -1 | min(sum(abs(x), axis=0)) | sum(1./abs(a))**(-1) |
+ | -2 | smallest singular value | 1./sqrt(sum(1./abs(a)**2)) |
+ | -inf | min(sum(abs(x), axis=1)) | min(abs(a)) |
+ | (int,float < 1) | - | sum(abs(a)**ord)**(1./ord) |
+
+ When `ord` is `None`, the following norms must be the default norms:
+
+ | ord | matrix | vector |
+ | ---------------- | ------------------------------- | -------------------------- |
+ | None | 'fro' | L2-norm (Euclidean) |
+
+ where `fro` corresponds to the **Frobenius norm**, `nuc` corresponds to the **nuclear norm**, and `-` indicates that the norm is **not** supported.
+
+ For matrices,
 
  - if `ord=1`, the norm corresponds to the induced matrix norm where `p=1` (i.e., the maximum absolute value column sum).
  - if `ord=2`, the norm corresponds to the induced matrix norm where `p=inf` (i.e., the maximum absolute value row sum).