Index Generator - Revision history

WikiSysop at 15:34, 26 May 2013

2013-05-26T15:34:23Z

← Older revision		Revision as of 11:34, 26 May 2013
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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>Z</apll> is an integer vector of length <apll>\|R</apll>whose values range from <apll>⎕IO+R</apll> to <apll>⎕IO-1</apll>.</td>		<td><apll>Z</apll> is an integer vector of length <apll>\|R</apll> whose values range from <apll>⎕IO+R</apll> to <apll>⎕IO-1</apll>.</td>
	</tr>		</tr>
	<tr>		<tr>
	<td>This feature extends monadic iota to negative arguments.</td>		<td>This feature extends monadic iota to negative arguments.</td>
			</tr>
			<tr>
			<td>This function is sensitive to <apll>⎕IO</apll> and <apll>⎕FEATURE</apll>. In particular, <apll>⎕FEATURE[⎕IO]</apll> must be <apll>1</apll> in order for negative values in <apll>R</apll> to be accepted; otherwise a <apll>DOMAIN ERROR</apll> is signalled.</td>
	</tr>		</tr>
	</table>		</table>
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	<tr>		<tr>
	<td>This feature extends monadic iota to multi-element vector arguments.</td>		<td>This feature extends monadic iota to multi-element vector arguments.</td>
			</tr>
			<tr>
			<td>This function is sensitive to <apll>⎕IO</apll> and <apll>⎕FEATURE</apll>. In particular, <apll>⎕FEATURE[⎕IO]</apll> must be <apll>1</apll> in order for negative values in <apll>R</apll> to be accepted; otherwise a <apll>DOMAIN ERROR</apll> is signalled.</td>
	</tr>		</tr>
	</table>		</table>

Sudleyplace at 01:21, 8 May 2008

2008-05-08T01:21:55Z

← Older revision		Revision as of 21:21, 7 May 2008
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	<table border="0" cellpadding="5" cellspacing="0" summary="">		<table border="0" cellpadding="5" cellspacing="0" summary="">
	<tr>		<tr>
	<td><apll>Z←⍳R</apll></td>		<td valign="top"><apll>Z←⍳R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	<apll>¯2 ¯1 0</apll>		<apll>¯2 ¯1 0</apll>

	<p>This function is used to create [[APA\|Arithmetic Progression Arrays (APAs)]]. For example, <apll>~~Z←2~~ 3 4⍴⍳24</apll> has a very compact storage consisting of the array shape (<apll>2 3 4</apll>), the starting offset (<apll>⎕IO</apll>) and multiplier (<apll>1</apll>), plus the normal array overhead (which includes the number of elements (<apll>24</apll>)).</p>		<p>This function is used to create [[APA\|Arithmetic Progression Arrays (APAs)]]. For example, <apll>2 3 4⍴⍳24</apll> has a very compact storage consisting of the array shape (<apll>2 3 4</apll>), the starting offset (<apll>⎕IO</apll>) and multiplier (<apll>1</apll>), plus the normal array overhead (which includes the number of elements (<apll>24</apll>)).</p>


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	<table border="0" cellpadding="5" cellspacing="0" summary="">		<table border="0" cellpadding="5" cellspacing="0" summary="">
	<tr>		<tr>
	<td><apll>Z←⍳R</apll></td>		<td valign="top"><apll>Z←⍳R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>

Sudleyplace at 21:54, 14 April 2008

2008-04-14T21:54:57Z

← Older revision		Revision as of 17:54, 14 April 2008
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	<br />		<br />

	<p>For example, taking into account both of the above extensions, <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical for ~~an arbitrary~~ array <apll>A</apll> in either origin.</p>		<p>For example, taking into account both of the above extensions, <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical for any array <apll>A</apll> in either origin.</p>

Sudleyplace at 21:53, 14 April 2008

2008-04-14T21:53:58Z

← Older revision		Revision as of 17:53, 14 April 2008
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	<apll> 2 ¯2  2 ¯1  2 0</apll>		<apll> 2 ¯2  2 ¯1  2 0</apll>

	<p>In both of the above extensions ~~it is always the case that, for an arbitrary array <apll>A</apll>~~, ~~the following arrays~~ <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical.</p>		<br />
			<br />

			<p>For example, taking into account both of the above extensions, <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical for an arbitrary array <apll>A</apll> in either origin.</p>

Sudleyplace at 21:49, 14 April 2008

2008-04-14T21:49:29Z

← Older revision		Revision as of 17:49, 14 April 2008
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	<apll> 2 ¯2  2 ¯1  2 0</apll>		<apll> 2 ¯2  2 ¯1  2 0</apll>

	<p>In both of the above extensions it is always the case that, for an arbitrary array <apll>A</apll>, the following ~~are all identical:~~ <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and ~~for that matter so is~~ <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll>.</p>		<p>In both of the above extensions it is always the case that, for an arbitrary array <apll>A</apll>, the following arrays <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and even <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll> are all identical.</p>

Sudleyplace at 12:00, 13 April 2008

2008-04-13T12:00:24Z

@@ Line 1: / Line 1: @@
-<ul>
+<table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
-   <li><p>Monadic iota (<apll>⍳R</apll>) is extended to negative right arguments, returning a vector of length <apll>|R</apll> whose values complement on the left the corresponding values from <apll>⍳|R</apll>.</p>
+<tr>
+  <td>
 <p>For example, in origin-0</p>
@@ Line 16: / Line 37: @@
 <apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;⍳¯3</apll><br />
-<apll>¯2 ¯1 0</apll></li>
+<apll>¯2 ¯1 0</apll>
 <p>For example, in origin-0</p>
@@ Line 40: / Line 87: @@
 <apll>&nbsp;2 ¯2&nbsp;&nbsp;2 ¯1&nbsp;&nbsp;2 0</apll>
-<p>This extension is implemented via an internal magic function due to Carl M. Cheney:</p>
+<p>In both of the above extensions it is always the case that, for an arbitrary array <apll>A</apll>, the following are all identical:  <apll>A</apll>, <apll>A[⍳⍴A]</apll>, <apll>A[⍳-⍴A]</apll>, and for that matter so is <apll>A[⍳¯1 1[?(⍴⍴A)⍴2]×⍴A]</apll>.</p>
 <apll>&nbsp;&nbsp;&nbsp;&nbsp;∇&nbsp;Z←#MonIota V</apll><br />
 <apll>[1]&nbsp;&nbsp;&nbsp;Z←⊃∘.,/⍳¨V</apll><br />
-<apll>&nbsp;&nbsp;&nbsp;&nbsp;∇</apll></li>
+<apll>&nbsp;&nbsp;&nbsp;&nbsp;∇</apll>

Sudleyplace at 02:34, 11 April 2008

2008-04-11T02:34:40Z

← Older revision		Revision as of 22:34, 10 April 2008
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	<p>This extension is implemented via an internal magic function due to Carl M. Cheney:</p>		<p>This extension is implemented via an internal magic function due to Carl M. Cheney:</p>

	<apll>    ∇ ~~Z←F~~ V</apll><br />		<apll>    ∇ Z←#MonIota V</apll><br />
	<apll>[1]   Z←⊃∘.,/⍳¨V</apll><br />		<apll>[1]   Z←⊃∘.,/⍳¨V</apll><br />
	<apll>    ∇</apll></li>		<apll>    ∇</apll></li>
	</ul>		</ul>

Sudleyplace: New page:

Monadic iota (⍳R) is extended to negative right arguments, returning a vector of length |R whose values complement on the left the corresponding v...

2008-04-10T20:16:57Z

New page: <ul> <li>Monadic iota (<apll>⍳R</apll>) is extended to negative right arguments, returning a vector of length <apll>|R</apll> whose values complement on the left the corresponding v...

New page

<ul>
<li>Monadic iota (<apll>⍳R</apll>) is extended to negative right arguments, returning a vector of length <apll>|R</apll> whose values complement on the left the corresponding values from <apll>⍳|R</apll>.

For example, in origin-0

<apll>      ⍳3</apll> 
<apll>0 1 2</apll>

<apll>      ⍳¯3</apll> 
<apll>¯3 ¯2 ¯1</apll>

and in origin-1

<apll>      ⍳3</apll> 
<apll>1 2 3</apll>

<apll>      ⍳¯3</apll> 
<apll>¯2 ¯1 0</apll></li>

<li>Monadic iota (<apll>⍳R</apll>) is extended to length > 1 vector right arguments, returning a nested array of shape <apll>R</apll> whose items are each integer vectors of length <apll>⍴⍴R</apll>.

For example, in origin-0

<apll>      ⍳2 3</apll> 
<apll> 0 0  0 1  0 2</apll> 
<apll> 1 0  1 1  1 2</apll>

<apll>      ⍳2 ¯3</apll> 
<apll> 0 ¯3  0 ¯2  0 ¯1</apll> 
<apll> 1 ¯3  1 ¯2  1 ¯1</apll>

and in origin-1

<apll>      ⍳2 3</apll> 
<apll> 1 1  1 2  1 3</apll> 
<apll> 2 1  2 2  2 3</apll>

<apll>      ⍳2 ¯3</apll> 
<apll> 1 ¯2  1 ¯1  1 0</apll> 
<apll> 2 ¯2  2 ¯1  2 0</apll>

This extension is implemented via an internal magic function due to Carl M. Cheney:

<apll>    ∇ Z←F V</apll> 
<apll>[1]   Z←⊃∘.,/⍳¨V</apll> 
<apll>    ∇</apll></li>
</ul>