Take: Difference between revisions

In the expression <code>X↑Y</code>, <code>X</code> may be any array, and <code>Y</code> is a [[Simple array|simple]] [[numeric]] [[vector]] whose length is less than or equal to the [[rank]] of <code>Y</code>. Many APLs require the length to be exactly equal; however, an extension by [[SHARP APL]] to allow a shorter left argument has been widely adopted by recent APLs. <code>X</code> may also be a scalar, in which case it is treated as a one-element vector in an instance of [[scalar rank extension]]. In some APLs, <code>Y</code> is also subject to [[scalar rank extension]]: if it is scalar then it will be extended so its rank is the length <code>≢X</code>.

Elements of <code>X</code> are matched with axes of <code>Y</code> with the same [[index]], that is, the left argument corresponds to [[Leading axis theory|leading axes]] of the right. The trailing axes of <code>Y</code> which are not matched in this way are unchanged by Take; this may also be modelled by extending <code>X</code> using the lengths of those axes.

For each modified axis the result length along that axis is equal to the corresponding element of <code>|X</code>. If the original element in <code>X</code> is positive then the result is aligned with the argument at the beginning of that axis, and if that element is negative they are aligned at the end. If it is zero then the result is empty, so both are true. Elements from the right argument are used in the result until the result is filled. If the argument axis is shorter than the result axis then [[Fill element|fills]] are used once it is exhausted. If the result is empty, its [[prototype]] is the same as the right argument's.

If the result is no larger than the right argument along each axis (equivalently, no fills are used, or <code>(|X)≤(≢X)↑⍴Y</code>), then the result is a [[subarray]] of <code>Y</code>. Not all subarrays can be produced in this way: only those which align with one boundary of the argument along each axis.

This definition could be converted to work in a [[Flat array model|flat]] APL with the [[Rank operator]] by using an [[odometer function]] like <code>⊢⊤(⍳×/)</code> in place of [[Iota]] and changing the two subsequent uses of [[Each]] to Rank 1.

In [[A Programming Language]], prefix and suffix operations were described using the syntax <code>⍺^j/x</code> to take the first <code>j</code> elements of vector <code>x</code> and <code>⍵^j/x</code> for the last <code>j</code> elements. This combined a use of the special prefix and suffix vectors <code>⍺^j(n)</code> and <code>⍵^j(n)</code> with [[Compress|compression]], with the length <code>n</code> inferred based on the length of <code>x</code>. The symbol <code>↑</code> was used for vector [[Rotate]], while <code>↓</code> rotated in the opposite direction.<ref>Iverson, K.E. (1962). A Programming Language. Wiley. ISBN 978-0-471-43014-8.</ref>

Take using the symbol <code>↑</code> was absent from the first version of [[APL\360]]<ref>Falkoff, A.D., and K.E. Iverson. [https://www.jsoftware.com/papers/APL360TerminalSystem.htm "The APL\360 Terminal System"]. Research Report RC-1922, IBM, 1967-10-16.</ref> but was introduced by 1968<ref>Falkoff, A.D., and K.E. Iverson, "[http://keiapl.org/archive/APL360_UsersMan_Aug1968.pdf APL\360 User's Manual]". IBM, August 1968.</ref>.

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