ord defines the norm that is computed. The following norms are supported:
+------------------------+---------------------------+---------------------------------+
| ord | norm for matrices | norm for vectors |
+========================+===========================+=================================+
| NULL (default) | Frobenius norm | 2-norm (see below) |
+------------------------+---------------------------+---------------------------------+
| "fro" | Frobenius norm | -- not supported -- |
+------------------------+---------------------------+---------------------------------+
| "nuc" | nuclear norm | -- not supported -- |
+------------------------+---------------------------+---------------------------------+
| Inf | max(sum(abs(x), dim=2)) | max(abs(x)) |
+------------------------+---------------------------+---------------------------------+
| -Inf | min(sum(abs(x), dim=2)) | min(abs(x)) |
+------------------------+---------------------------+---------------------------------+
| 0 | -- not supported -- | sum(x != 0) |
+------------------------+---------------------------+---------------------------------+
| 1 | max(sum(abs(x), dim=1)) | as below |
+------------------------+---------------------------+---------------------------------+
| -1 | min(sum(abs(x), dim=1)) | as below |
+------------------------+---------------------------+---------------------------------+
| 2 | largest singular value | as below |
+------------------------+---------------------------+---------------------------------+
| -2 | smallest singular value | as below |
+------------------------+---------------------------+---------------------------------+
| other int or float | -- not supported -- | sum(abs(x)^{ord})^{(1 / ord)} |
+------------------------+---------------------------+---------------------------------+
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