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Magnitude: Difference between revisions
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{{Built-in|Magnitude|<nowiki>|</nowiki>}}, or '''Absolute Value''', is a [[monadic]] [[scalar function]] which gives the [[wikipedia:Absolute value|absolute value]] of a real or [[complex]] number. Magnitude shares the [[glyph]] < | {{Built-in|Magnitude|<nowiki>|</nowiki>}}, or '''Absolute Value''', is a [[monadic]] [[scalar function]] which gives the [[wikipedia:Absolute value|absolute value]] of a real or [[complex]] number. Magnitude shares the [[glyph]] <syntaxhighlight lang=apl inline>|</syntaxhighlight> with the dyadic arithmetic function [[Residue]]. | ||
== Examples == | == Examples == | ||
< | <syntaxhighlight lang=apl> | ||
|0 1 2 ¯1 ¯2 | |0 1 2 ¯1 ¯2 | ||
0 1 2 1 2 | 0 1 2 1 2 | ||
| Line 8: | Line 8: | ||
|0J2 ¯3J¯4 | |0J2 ¯3J¯4 | ||
2 5 | 2 5 | ||
</ | </syntaxhighlight> | ||
== Properties == | == Properties == | ||
| Line 16: | Line 16: | ||
For real numbers, the magnitude equals the original number [[times]] (or [[Divide|divided]] by, for non-zero numbers) its [[Signum|sign]]. | For real numbers, the magnitude equals the original number [[times]] (or [[Divide|divided]] by, for non-zero numbers) its [[Signum|sign]]. | ||
< | <syntaxhighlight lang=apl> | ||
v←0 1E¯100 20 1E300 ¯1E¯100 ¯20 ¯1E300 | v←0 1E¯100 20 1E300 ¯1E¯100 ¯20 ¯1E300 | ||
(|v)≡v××v | (|v)≡v××v | ||
| Line 22: | Line 22: | ||
(|v)=v÷×v | (|v)=v÷×v | ||
0 1 1 1 1 1 1 | 0 1 1 1 1 1 1 | ||
</ | </syntaxhighlight> | ||
For complex numbers, the magnitude is defined as the Euclidean distance from the number 0 on the [[wikipedia:Complex plane|complex plane]]. | For complex numbers, the magnitude is defined as the Euclidean distance from the number 0 on the [[wikipedia:Complex plane|complex plane]]. | ||
< | <syntaxhighlight lang=apl> | ||
Dist←{0.5*⍨+.×⍨9 11○⍵} ⍝ Square root of square sum of real and imaginary parts | Dist←{0.5*⍨+.×⍨9 11○⍵} ⍝ Square root of square sum of real and imaginary parts | ||
Dist¨ 0 1J2 ¯3J4 | Dist¨ 0 1J2 ¯3J4 | ||
| Line 32: | Line 32: | ||
|0 1J2 ¯3J4 | |0 1J2 ¯3J4 | ||
0 2.236067977 5 | 0 2.236067977 5 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
Any real or complex number is equal to the [[Times|product]] of its [[signum]] and magnitude. | Any real or complex number is equal to the [[Times|product]] of its [[signum]] and magnitude. | ||
< | <syntaxhighlight lang=apl> | ||
(⊢ ≡ ××|) 0 1 1E¯300 ¯2.5 0J3.5 ¯3J¯4 | (⊢ ≡ ××|) 0 1 1E¯300 ¯2.5 0J3.5 ¯3J¯4 | ||
1 | 1 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
== See also == | == See also == | ||