1
edit
Inner Product: Difference between revisions
Jump to navigation
Jump to search
m
changed a 2 to a 4
DanielAjoy (talk | contribs) m (changed a 2 to a 4) |
|||
| (2 intermediate revisions by one other user not shown) | |||
| Line 51: | Line 51: | ||
\begin{align} | \begin{align} | ||
\text{For example, if}\\ | \text{For example, if}\\ | ||
\ | \boldsymbol{A}&=\begin{pmatrix} | ||
1&3&2&0\\ | 1&3&2&0\\ | ||
2&1&0&1\\ | 2&1&0&1\\ | ||
4&0&0&2\\ | |||
\end{pmatrix} | \end{pmatrix} | ||
\qquad\text{and}\qquad | \qquad\text{and}\qquad | ||
\ | \boldsymbol{B}=\begin{pmatrix} | ||
4&1\\ | 4&1\\ | ||
0&3\\ | 0&3\\ | ||
| Line 63: | Line 63: | ||
2&0\\ | 2&0\\ | ||
\end{pmatrix}\\ | \end{pmatrix}\\ | ||
\text{then}\qquad\ | \text{then}\qquad\boldsymbol{A}\;^+_\times\,\boldsymbol{B}&=\begin{pmatrix} | ||
4&14\\ | 4&14\\ | ||
10&5\\ | 10&5\\ | ||
20&4\\ | 20&4\\ | ||
\end{pmatrix}, | \end{pmatrix}, | ||
\quad\ | \quad\boldsymbol{A}\;^\and_=\,\boldsymbol{B}=\begin{pmatrix} | ||
0&1\\ | 0&1\\ | ||
0&0\\ | 0&0\\ | ||
1&0\\ | 1&0\\ | ||
\end{pmatrix}\text{,}\\ | \end{pmatrix}\text{,}\\ | ||
\ | \boldsymbol{A}\;^\or_\neq\;\boldsymbol{B}&=\begin{pmatrix} | ||
1&0\\ | 1&0\\ | ||
1&1\\ | 1&1\\ | ||
0&1\\ | 0&1\\ | ||
\end{pmatrix}, | \end{pmatrix}, | ||
\qquad\text{and}\qquad(\ | \qquad\text{and}\qquad(\boldsymbol{A}\neq0)\;^+_{\,/}\,\boldsymbol{B}=\begin{pmatrix} | ||
4&6\\ | 4&6\\ | ||
6&4\\ | 6&4\\ | ||
| Line 116: | Line 116: | ||
== Differences between dialects == | == Differences between dialects == | ||
Implementations differ on the exact behaviour of inner product when the right operand is not a [[scalar function]]. It follows from page 121 of the ISO/IEC 13751:2001(E) [[standard]] specifies that <source lang=apl inline>X f.g Y</source> is equivalent to <source lang=apl inline>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</source>. This is indeed what [[APL2]], [[APLX]], and [[ngn/apl]] follow, while [[Dyalog APL]] and [[GNU APL]] differ as described by [[Roger Hui]]:<ref>[[Roger Hui]]. ''inner product''. Internal Dyalog email. 24 July 2020.</ref> | Implementations differ on the exact behaviour of inner product when the right operand is not a [[scalar function]]. It follows from page 121 of the ISO/IEC 13751:2001(E) [[standard]] specifies that <source lang=apl inline>X f.g Y</source> is equivalent to <source lang=apl inline>f/¨ (⊂[⍴⍴x]x)∘.g ⊂[1]y</source>. This is indeed what [[APL2]], [[APLX]], [[APL+Win]], and [[ngn/apl]] follow, while [[Dyalog APL]], [[NARS2000]] and [[GNU APL]] differ as described by [[Roger Hui]]:<ref>[[Roger Hui]]. ''inner product''. Internal Dyalog email. 24 July 2020.</ref> | ||
<blockquote> | <blockquote> | ||
The following dop models inner product in Dyalog APL, with caveats. If you find a case where <source lang=apl inline>f.g</source> differs from <source lang=apl inline>f IP g</source>, not covered by the caveats, I'd be interested. | The following dop models inner product in Dyalog APL, with caveats. If you find a case where <source lang=apl inline>f.g</source> differs from <source lang=apl inline>f IP g</source>, not covered by the caveats, I'd be interested. | ||