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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