Rank/Atop - Revision history

WikiSysop at 11:11, 14 October 2023

2023-10-14T11:11:07Z

← Older revision		Revision as of 07:11, 14 October 2023
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	<table border="0" cellpadding="5" cellspacing="0" summary="">		<table border="0" cellpadding="5" cellspacing="0" summary="">
	<tr>		<tr>
	<td valign="top"><apll>Z←(<i>f</i>⍤[X] Y) R</apll></td>		<td valign="top"><apll>Z←<i>f</i>⍤[X] Y R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	<table border="0" cellpadding="5" cellspacing="0" summary="">		<table border="0" cellpadding="5" cellspacing="0" summary="">
	<tr>		<tr>
	<td valign="top"><apll>Z←L (<i>f</i>⍤[X] Y) R</apll></td>		<td valign="top"><apll>Z←L <i>f</i>⍤[X] Y R</apll></td>
	<td></td>		<td></td>
	<td></td>		<td></td>
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	<apll><pre>		<apll><pre>
	#Atop←{⍺←⊢ ⋄ ⍺⍺ ⍺ ⍵⍵ ⍵}		#Atop←{⍺←⊢ ⋄ ⍺⍺ ⍺ ⍵⍵ ⍵}
			</pre></apll>

			For example,

			<apll><pre> ⌈⍤-¯1.1 ⍝ where f⍤g R ←→ f g R
			2
	</pre></apll>		</pre></apll>

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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>R</apll> ~~is an~~ arbitrary ~~array~~, <apll><i>f</i></apll> is an arbitrary monadic function, <apll><i>g</i></apll> is an arbitrary dydadic function.</td>		<td><apll>L</apll> and <apll>R</apll> are arbitrary arrays, <apll><i>f</i></apll> is an arbitrary monadic function, <apll><i>g</i></apll> is an arbitrary dydadic function.</td>
	</tr>		</tr>
	</table>		</table>
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	</pre></apll>		</pre></apll>

			For example,

			<apll><pre> 2⌈⍤-¯1.1 ⍝ where L f⍤g R ←→ f L g R
			4
			</pre></apll>

	== Acknowledgments ==		== Acknowledgments ==

	The APL functions for the Rank operator shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.		The APL functions for the Rank operator shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.

			The Atop operator was defined by the developers at Dyalog APL.

WikiSysop: WikiSysop moved page Rank to Rank/Atop: Expanded Definition

2023-10-14T10:26:09Z

WikiSysop moved page Rank to Rank/Atop: Expanded Definition

← Older revision	Revision as of 06:26, 14 October 2023
(No difference)

WikiSysop at 23:32, 13 October 2023

2023-10-13T23:32:49Z

@@ Line 1: / Line 1: @@
-==Monadic Derived Function==
+==Rank Monadic Derived Function==
 <table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
@@ Line 55: / Line 55: @@
 <br />
-==Dyadic Derived Function==
+==Rank Dyadic Derived Function==
 <table border="1" cellpadding="5" cellspacing="0" rules="none" summary="">
@@ Line 133: / Line 133: @@
   a b c d e f
 2 3 4 5 6</pre></apll>
 == Acknowledgments ==
-The APL functions shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.
+The APL functions for the Rank operator shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.

WikiSysop at 04:26, 16 April 2018

2018-04-16T04:26:13Z

← Older revision		Revision as of 00:26, 16 April 2018
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	</tr>		</tr>
	<tr>		<tr>
	<td>The result <apll>Z</apll> is the <b>conforming</b> disclose of the above ~~(see below)~~.</td>		<td>The result <apll>Z</apll> is the <b>conforming</b> disclose of the above, using <apll>[X]</apll>, if present.</td>
	</tr>		</tr>
	</table>		</table>
	<br />		<br />
	<p>The monadic derived function of this dyadic operator is ~~partially~~ implemented by calling ~~the following~~ internal magic function:</p>		<p>The monadic derived function of this dyadic operator is implemented by calling an internal magic function similar to the following:</p>

	<apll><pre>		<apll><pre>
	∇ Z←(LO #MonRank Y) R;YR		∇ Z←(LO #MonRank[X] Y) R;YR
	[1] YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R		[1] YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R
	[2] if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end		[2] if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	[3] Z←LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0		[3] Z←LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →L1
	[4] ⎕PRO:YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R		[4] ⎕PRO:YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R
	[5] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end		[5] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	[6] Z←⊃LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R		[6] Z←⊃LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R
			[7] L1::if 0=⎕NC 'X' ⋄ Z←⊃Z ⋄ :else ⋄ Z←⊃[X] Z ⋄ :end
	∇</pre></apll>		∇</pre></apll>

	~~See the discussion below for details on the final processing of the result of this magic function.~~

	~~<br />~~
	<br />		<br />

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	</tr>		</tr>
	<tr>		<tr>
	<td>The result <apll>Z</apll> is the <b>conforming</b> disclose of the above ~~(see below)~~.</td>		<td>The result <apll>Z</apll> is the <b>conforming</b> disclose of the above, using <apll>[X]</apll>, if present.</td>
	</tr>		</tr>
	</table>		</table>
	<br />		<br />
	<p>The dyadic derived function of this dyadic operator is ~~partially~~ implemented by calling ~~the following~~ internal magic function:</p>		<p>The dyadic derived function of this dyadic operator is implemented by calling an internal magic function similar to the following:</p>

	<apll><pre>		<apll><pre>
	∇ Z←L (LO #DydRank Y) R;YL;YR		∇ Z←L (LO #DydRank[X] Y) R;YL;YR
	[1] (YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R		[1] (YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R
	[2] :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end		[2] :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end
	[3] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end		[3] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	[4] Z←(⊂[(-YL)↑⍳⍴⍴L] L) LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0		[4] Z←(⊂[(-YL)↑⍳⍴⍴L] L) LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →L1
	[5] ⎕PRO:(YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R		[5] ⎕PRO:(YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R
	[6] :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end		[6] :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end
	[7] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end		[7] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	[8] Z←⊃(⊂[(-YL)↑⍳⍴⍴L]¨0⍴⊂L) LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R		[8] Z←⊃(⊂[(-YL)↑⍳⍴⍴L]¨0⍴⊂L) LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R
			[9] L1::if 0=⎕NC 'X' ⋄ Z←⊃Z ⋄ :else ⋄ Z←⊃[X] Z ⋄ :end
	∇</pre></apll>		∇</pre></apll>

	If the axis operator <apll>[X]</apll> is present on the rank operator, it is used in the final stage to disclose with axis (<apll>⊃[X]</apll>) the <apll>#Conform</apll> result to produce the final result <apll>Z</apll>. If the axis operator is not present, the final result <apll>Z</apll> is the disclose without axis (<apll>⊃</apll>) of the <apll>#Conform</apll> result.

	For example, the rank operator can emulate laminate between the following two vectors to produce the first result, but not the second without help from the axis operator:		For example, the rank operator can emulate laminate between the following two vectors to produce the first result, but not the second without help from the axis operator:

Sudleyplace at 00:03, 16 April 2018

2018-04-16T00:03:26Z

← Older revision		Revision as of 20:03, 15 April 2018
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	<p>The monadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>		<p>The monadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>

	<apll>~~    ~~∇ Z←(LO #MonRank Y) R;YR~~<br />~~		<apll><pre>
	[1]~~   ~~YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R~~<br />~~		∇ Z←(LO #MonRank Y) R;YR
	[2]~~   :~~if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end~~<br />~~		[1] YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R
	[3]~~   ~~Z←LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0~~<br />~~		[2] if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	[4]~~   ~~⎕PRO:YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R~~<br />~~		[3] Z←LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0
	[5]~~   ~~:if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end~~<br />~~		[4] ⎕PRO:YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R
	[6]~~   ~~Z←⊃LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R<br />		[5] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	~~    ∇~~</apll>		[6] Z←⊃LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R
			∇</pre></apll>

	See the discussion below for details on the final processing of the result of this magic function.		See the discussion below for details on the final processing of the result of this magic function.
Line 107:		Line 108:
	<p>The dyadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>		<p>The dyadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>

	<apll>~~    ~~∇ Z←L (LO #DydRank Y) R;YL;YR~~<br />~~		<apll><pre>
	[1]~~   ~~(YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R~~<br />~~		∇ Z←L (LO #DydRank Y) R;YL;YR
	[2]~~   ~~:if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end~~<br />~~		[1] (YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R
	[3]~~   ~~:if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end~~<br />~~		[2] :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end
	[4]~~   ~~Z←(⊂[(-YL)↑⍳⍴⍴L] L) LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0~~<br />~~		[3] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	[5]~~   ~~⎕PRO:(YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R~~<br />~~		[4] Z←(⊂[(-YL)↑⍳⍴⍴L] L) LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0
	[6]~~   ~~:if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end~~<br />~~		[5] ⎕PRO:(YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R
	[7]~~   ~~:if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end~~<br />~~		[6] :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end
	[8]~~   ~~Z←⊃(⊂[(-YL)↑⍳⍴⍴L]¨0⍴⊂L) LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R~~<br />~~		[7] :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end
	~~    ∇</apll>~~		[8] Z←⊃(⊂[(-YL)↑⍳⍴⍴L]¨0⍴⊂L) LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R
			∇</pre></apll>
	~~== Conforming Disclose ==~~

	Both of the above magic functions implement their respective derived function except for some final processing which is essentially a disclose but one which allows for mismatched ranks. That part is implemented by the following function where <apll>L</apll> has already been calculated as the maximum rank across all items:

	~~<apll>    ~~∇ ~~Z←L #Conform R</apll><br />~~
	<~~apll>[1]   Z←(((L-∊⍴∘⍴¨R)⍴¨1),¨⍴¨R)⍴¨R</apll><br~~ />
	~~<apll>    ∇~~</apll>

	If the axis operator <apll>[X]</apll> is present on the rank operator, it is used in the final stage to disclose with axis (<apll>⊃[X]</apll>) the <apll>#Conform</apll> result to produce the final result <apll>Z</apll>. If the axis operator is not present, the final result <apll>Z</apll> is the disclose without axis (<apll>⊃</apll>) of the <apll>#Conform</apll> result.		If the axis operator <apll>[X]</apll> is present on the rank operator, it is used in the final stage to disclose with axis (<apll>⊃[X]</apll>) the <apll>#Conform</apll> result to produce the final result <apll>Z</apll>. If the axis operator is not present, the final result <apll>Z</apll> is the disclose without axis (<apll>⊃</apll>) of the <apll>#Conform</apll> result.
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	For example, the rank operator can emulate laminate between the following two vectors to produce the first result, but not the second without help from the axis operator:		For example, the rank operator can emulate laminate between the following two vectors to produce the first result, but not the second without help from the axis operator:

	<apll>~~      ~~L←'abcdef' {diamond} R←⍳⍴L~~</apll><br />~~		<apll><pre>
	~~<apll>      ~~L ,⍤0 R~~</apll>                             ~~a.k.a. ~~<apll>~~L,[1.5] R~~</apll><br />~~		L←'abcdef' {diamond} R←⍳⍴L
	~~<apll> ~~a 1~~</apll><br />~~		L ,⍤0 R a.k.a. L,[1.5] R
	~~<apll> ~~b 2~~</apll><br />~~		a 1
	~~<apll> ~~c 3~~</apll><br />~~		b 2
	~~<apll> ~~d 4~~</apll><br />~~		c 3
	~~<apll> ~~e 5~~</apll><br />~~		d 4
	~~<apll> ~~f 6~~</apll><br />~~		e 5
	~~<apll>      ~~L ,⍤[1] 0 R~~</apll>                   ~~a.k.a. ~~<apll>~~L,[0.5] R~~</apll><br />~~		f 6
	~~<apll> ~~a b c d e f~~</apll><br />~~		L ,⍤[1] 0 R a.k.a. L,[0.5] R
	~~<apll> ~~1 2 3 4 5 6</~~apll~~><br />		a b c d e f
			1 2 3 4 5 6</pre></apll>

	== Acknowledgments ==		== Acknowledgments ==

	The APL functions shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.		The APL functions shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.

WikiSysop at 13:23, 18 October 2013

2013-10-18T13:23:50Z

← Older revision		Revision as of 09:23, 18 October 2013
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	<p>The monadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>		<p>The monadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>

	<apll>    ∇ Z←(LO #MonRank Y) R;~~O;⎕FEATURE</apll>~~<br />		<apll>    ∇ Z←(LO #MonRank Y) R;YR<br />
	~~<apll>~~[1]   ~~⎕FEATURE[⎕IO]←1</apll>~~<br />		[1]   YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R<br />
	~~<apll>~~[2]   ~~Y←1↑⌽3⍴⌽Y</apll~~><br />		[2]   :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end<br />
	~~<apll>~~[3]   ~~O←⍴⍴R</apll><br />~~		[3]   Z←LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0<br />
	~~<apll>~~[~~4]   Y←~~(-O)~~⌈O⌊Y</apll><br />~~		[4]   ⎕PRO:YR←(1↑⌽3⍴⌽Y)⌊⍴⍴R<br />
	~~<apll>[5]   Z←LO¨⊂[⍳-Y~~]R ⋄ →0~~</apll>~~<br />		[5]   :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end<br />
	~~<apll>~~[6]   ⎕PRO:~~Y←1↑⌽3⍴⌽Y</apll>~~<br />		[6]   Z←⊃LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R<br />
	~~<apll>~~[7]   ~~O←⍴⍴R</apll~~><br />		∇</apll>
	~~<apll>~~[8]   Y←(-O)~~⌈O⌊Y</apll><br />~~
	~~<apll>[9]   Z←⊃LO¨¨⊂[⍳-Y~~]¨0⍴⊂R~~</apll>~~<br />
	~~<apll>~~    ∇</apll>

	See the discussion below for details on the final processing of the result of this magic function.		See the discussion below for details on the final processing of the result of this magic function.
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	<p>The dyadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>		<p>The dyadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>

	<apll>    ∇ Z←L (LO #DydRank Y) R;O;~~⎕FEATURE</apll>~~<br />		<apll>    ∇ Z←L (LO #DydRank Y) R;YL;YR<br />
	~~<apll>~~[1]   ~~⎕FEATURE[⎕IO]←1</apll>~~<br />		[1]   (YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R<br />
	~~<apll>~~[2]   ~~Y←1↓⌽3⍴⌽Y</apll~~><br />		[2]   :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end<br />
	~~<apll>~~[3]   ~~O←(⍴⍴L),~~⍴⍴R~~</apll>~~<br />		[3]   :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end<br />
	~~<apll>~~[4~~]   Y←(-O)⌈O⌊Y</apll><br />~~		[4]   Z←(⊂[(-YL)↑⍳⍴⍴L] L) LO¨⊂[(-YR)↑⍳⍴⍴R] R ⋄ →0<br />
	~~<apll>[5~~]   Z←(⊂[⍳-~~1↑Y~~]L)LO¨⊂[⍳-~~1↓Y~~]R ⋄ →0~~</apll>~~<br />		[5]   ⎕PRO:(YL YR)←(1↓⌽3⍴⌽Y)⌊(⍴⍴L),⍴⍴R<br />
	~~<apll>~~[6]   ⎕PRO:~~Y←1↓⌽3⍴⌽Y</apll>~~<br />		[6]   :if 0>YL ⋄ YL←0⌈YL+⍴⍴L ⋄ :end<br />
	~~<apll>~~[7]   ~~O←(~~⍴⍴L~~),⍴⍴R</apll>~~<br />		[7]   :if 0>YR ⋄ YR←0⌈YR+⍴⍴R ⋄ :end<br />
	~~<apll>~~[8]   ~~Y←(-O)⌈O⌊Y</apll~~><br />		[8]   Z←⊃(⊂[(-YL)↑⍳⍴⍴L]¨0⍴⊂L) LO¨¨⊂[(-YR)↑⍳⍴⍴R]¨0⍴⊂R<br />
	~~<apll>~~[9]   Z←⊃(⊂[⍳-~~1↑Y~~]¨0⍴⊂L)LO¨¨⊂[⍳-~~1↓Y~~]¨0⍴⊂R~~</apll>~~<br />		∇</apll>
	~~<apll>~~    ∇</apll>

	== Conforming Disclose ==		== Conforming Disclose ==
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	== Acknowledgments ==		== Acknowledgments ==

	The APL functions shown above were based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431\| Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991.		The APL functions shown above were originally based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431 Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991, but later was modified to reflect the definition of the Rank operator in the ISO-IEC 13751 Extended APL Standard.

WikiSysop: /* Monadic Derived Function */

2013-05-25T17:54:32Z

Monadic Derived Function

← Older revision		Revision as of 13:54, 25 May 2013
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	</tr>		</tr>
	<tr>		<tr>
	<td><apll>Y</apll> is a scalar or one-, two-, or three-element integer vector that describes the cell size of the arguments. When it is a three-element vector, the first element specifies the cell size of the right argument when the derived function is called monadically; the second and third elements specify the left and right argument cell sizes when the derived function is called dyadically. When it is a two-element vector, the two values are used for the left and right arguments cell sizes when the derived function is called dyadically; if the derived function is called monadically, the cell size is the second value of the two. When it is a scalar or one-element vector, the single value is used for all three cell sizes. Moreover, the value of <apll>Y</apll> for the monadic derived function case may be positive or negative with an absolute value no larger than <apll>⍴⍴R</apll>. In this case (first element only), the above rules may be summarized by setting <apll>Y</apll> to <apll>(-⍴⍴R)⌈(⍴⍴R)⌊1↑⌽3⍴⌽Y</apll>.</td>		<td><apll>Y</apll> is a scalar or one-, two-, or three-element integer vector that describes the cell size of the arguments. When it is a three-element vector, the first element specifies the cell size of the right argument when the derived function is called monadically; the second and third elements specify the left and right argument cell sizes when the derived function is called dyadically. When it is a two-element vector, the two values are used for the left and right arguments cell sizes when the derived function is called dyadically; if the derived function is called monadically, the cell size is the second value of the two. When it is a scalar or one-element vector, the single value is used for all three cell sizes. Moreover, the value of <apll>Y</apll> for the monadic derived function case may be positive or negative with an absolute value no larger than <apll>⍴⍴R</apll>. In this case (first element only), the above rules may be summarized by setting <apll>Y</apll> to the one-element integer vector <apll>(-⍴⍴R)⌈(⍴⍴R)⌊1↑⌽3⍴⌽Y</apll>.</td>
	</tr>		</tr>
	<tr>		<tr>

WikiSysop: /* Dyadic Derived Function */

2013-05-25T17:52:26Z

Dyadic Derived Function

← Older revision		Revision as of 13:52, 25 May 2013
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	<td><apll>Y</apll> is a scalar or one-, two-, or three-element integer vector that describes the cell size of the arguments. When it is a three-element vector, the first element specifies the cell size of the right argument when the derived function is called monadically; the second and third elements specify the left and right argument cell sizes when the derived function is called dyadically. When it is a two-element vector, the two values are used for the left and right arguments cell sizes when the derived function is called dyadically; if the derived function is called monadically, the cell size is the second value of the two. When it is a scalar or one-element vector, the single value is used for all three cell sizes.		<td><apll>Y</apll> is a scalar or one-, two-, or three-element integer vector that describes the cell size of the arguments. When it is a three-element vector, the first element specifies the cell size of the right argument when the derived function is called monadically; the second and third elements specify the left and right argument cell sizes when the derived function is called dyadically. When it is a two-element vector, the two values are used for the left and right arguments cell sizes when the derived function is called dyadically; if the derived function is called monadically, the cell size is the second value of the two. When it is a scalar or one-element vector, the single value is used for all three cell sizes.

	Moreover, the values of <apll>Y</apll> for the dyadic derived function case may be positive or negative with an absolute value no larger than <apll>(⍴⍴L),⍴⍴R</apll>. In this case (second and third elements only), the above rules may be summarized by setting <apll>Y</apll> to <apll>(-(⍴⍴L),⍴⍴R)⌈((⍴⍴L),⍴⍴R)⌊1↓⌽3⍴⌽Y</apll>.</td>		Moreover, the values of <apll>Y</apll> for the dyadic derived function case may be positive or negative with an absolute value no larger than <apll>(⍴⍴L),⍴⍴R</apll>. In this case (second and third elements only), the above rules may be summarized by setting <apll>Y</apll> to the two-element integer vector <apll>(-(⍴⍴L),⍴⍴R)⌈((⍴⍴L),⍴⍴R)⌊1↓⌽3⍴⌽Y</apll>.</td>
	</tr>		</tr>
	<tr>		<tr>
	<td>The cells from <apll>L</apll> are of rank <apll>\|~~Y[⎕IO]~~</apll>; the cells from <apll>R</apll> are of rank <apll>\|~~Y[⎕IO+1]~~</apll>.</td>		<td>The cells from <apll>L</apll> are of rank <apll>\|1↑Y</apll>; the cells from <apll>R</apll> are of rank <apll>\|1↓Y</apll>.</td>
	</tr>		</tr>
	<tr>		<tr>

WikiSysop at 20:45, 24 May 2013

2013-05-24T20:45:32Z

← Older revision		Revision as of 16:45, 24 May 2013
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	<p>The monadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>		<p>The monadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>

	<apll>    ∇ Z←(LO #MonRank Y) R;O</apll><br />		<apll>    ∇ Z←(LO #MonRank Y) R;O;⎕FEATURE</apll><br />
	<apll>[1]   Y←1↑⌽3⍴⌽Y</apll><br />		<apll>[1]   ⎕FEATURE[⎕IO]←1</apll><br />
	<apll>[2]   O←⍴⍴R</apll><br />		<apll>[2]   Y←1↑⌽3⍴⌽Y</apll><br />
	<apll>[3]   Y←(-O)⌈O⌊Y</apll><br />		<apll>[3]   O←⍴⍴R</apll><br />
	<apll>[4]   Z←LO¨⊂[⍳-Y]~~R⋄→0~~</apll><br />		<apll>[4]   Y←(-O)⌈O⌊Y</apll><br />
	<apll>[5]   ⎕PRO:Z←⊃LO¨¨⊂[⍳-Y]¨0⍴⊂R</apll><br />		<apll>[5]   Z←LO¨⊂[⍳-Y]R ⋄ →0</apll><br />
			<apll>[6]   ⎕PRO:Y←1↑⌽3⍴⌽Y</apll><br />
			<apll>[7]   O←⍴⍴R</apll><br />
			<apll>[8]   Y←(-O)⌈O⌊Y</apll><br />
			<apll>[9]   Z←⊃LO¨¨⊂[⍳-Y]¨0⍴⊂R</apll><br />
	<apll>    ∇</apll>		<apll>    ∇</apll>

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	<p>The dyadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>		<p>The dyadic derived function of this dyadic operator is partially implemented by calling the following internal magic function:</p>

	<apll>    ∇ Z←L (LO #DydRank Y) R;O</apll><br />		<apll>    ∇ Z←L (LO #DydRank Y) R;O;⎕FEATURE</apll><br />
	<apll>[1]   Y←1↓⌽3⍴⌽Y</apll><br />		<apll>[1]   ⎕FEATURE[⎕IO]←1</apll><br />
	<apll>[2]   O←(⍴⍴L),⍴⍴R</apll><br />		<apll>[2]   Y←1↓⌽3⍴⌽Y</apll><br />
	<apll>[3]   Y←(-O)⌈O⌊Y</apll><br />		<apll>[3]   O←(⍴⍴L),⍴⍴R</apll><br />
	<apll>[4]   Z←(⊂[⍳-1↑Y]L)LO¨⊂[⍳-1↓Y]~~R⋄→0~~</apll><br />		<apll>[4]   Y←(-O)⌈O⌊Y</apll><br />
	<apll>[5]   ⎕PRO:Z←⊃(⊂[⍳-1↑Y]¨0⍴⊂L)LO¨¨⊂[⍳-1↓Y]¨0⍴⊂R</apll><br />		<apll>[5]   Z←(⊂[⍳-1↑Y]L)LO¨⊂[⍳-1↓Y]R ⋄ →0</apll><br />
			<apll>[6]   ⎕PRO:Y←1↓⌽3⍴⌽Y</apll><br />
			<apll>[7]   O←(⍴⍴L),⍴⍴R</apll><br />
			<apll>[8]   Y←(-O)⌈O⌊Y</apll><br />
			<apll>[9]   Z←⊃(⊂[⍳-1↑Y]¨0⍴⊂L)LO¨¨⊂[⍳-1↓Y]¨0⍴⊂R</apll><br />
	<apll>    ∇</apll>		<apll>    ∇</apll>

WikiSysop: /* Acknowledgments */

2010-08-17T00:12:49Z

Acknowledgments

← Older revision		Revision as of 20:12, 16 August 2010
Line 140:		Line 140:
	== Acknowledgments ==		== Acknowledgments ==

	The APL functions shown above were based upon those found in the paper J. ~~Phillip~~ Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431\| Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991.		The APL functions shown above were based upon those found in the paper J. Philip Benkhard, "[http://portal.acm.org/citation.cfm?id=114058&dl=GUIDE&coll=GUIDE&CFID=98347615&CFTOKEN=27795431\| Extending structure, type, and expression in APL2]", ACM SIGAPL APL Quote Quad, v.21 n.4, p.20-38, Aug. 1991.