Natural Logarithm: Difference between revisions
No edit summary |
m (Text replacement - "</source>" to "</syntaxhighlight>") |
||
| Line 2: | Line 2: | ||
:''This page describes the monadic arithmetic function. For the dyadic logarithm function, see [[Logarithm]].'' | :''This page describes the monadic arithmetic function. For the dyadic logarithm function, see [[Logarithm]].'' | ||
{{Built-in|Natural Logarithm|⍟}}, or '''Natural Log''', is a [[monadic]] [[scalar function]] which computes the [[wikipedia:natural logarithm|natural logarithm]] of the [[argument]]. Logarithm shares the [[glyph]] <source lang=apl inline>⍟</ | {{Built-in|Natural Logarithm|⍟}}, or '''Natural Log''', is a [[monadic]] [[scalar function]] which computes the [[wikipedia:natural logarithm|natural logarithm]] of the [[argument]]. Logarithm shares the [[glyph]] <source lang=apl inline>⍟</syntaxhighlight> with the dyadic arithmetic function [[Logarithm]]. The [[glyph]], a composition of the glyphs for [[Circular]] (<source lang=apl inline>○</syntaxhighlight>) and [[Exponential]] (<source lang=apl inline>*</syntaxhighlight>) to indicate its close mathematical ties with these two functions, is a stylised tree log.<ref>[[E. E. McDonnell|McDonnell, E. E.]]. [https://www.jsoftware.com/papers/eem/storyofo.htm Recreational APL: The Story of <source lang=apl inline>○</syntaxhighlight>]. [[APL Quote-Quad]], Volume 8, Number 2, 1977-12.</ref> | ||
== Examples == | == Examples == | ||
| Line 9: | Line 9: | ||
⍟1 2 (*1) (*10) | ⍟1 2 (*1) (*10) | ||
0 0.6931471806 1 10 | 0 0.6931471806 1 10 | ||
</ | </syntaxhighlight> | ||
== Properties == | == Properties == | ||
Natural logarithm is a special case of [[Logarithm]] with the default left argument of e (<source lang=apl inline>*1</ | Natural logarithm is a special case of [[Logarithm]] with the default left argument of e (<source lang=apl inline>*1</syntaxhighlight>). | ||
<source lang=apl> | <source lang=apl> | ||
((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1 | ((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1 | ||
1 | 1 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
Natural logarithm and [[exponential]] <source lang=apl inline>*</ | Natural logarithm and [[exponential]] <source lang=apl inline>*</syntaxhighlight> are inverses of each other, except where the natural log is undefined. | ||
<source lang=apl> | <source lang=apl> | ||
| Line 27: | Line 27: | ||
(⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined | (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined | ||
1 | 1 | ||
</ | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
== External links == | == External links == | ||
Revision as of 20:58, 10 September 2022
- This page describes the monadic arithmetic function. For the dyadic logarithm function, see Logarithm.
⍟
|
Natural Logarithm (⍟), or Natural Log, is a monadic scalar function which computes the natural logarithm of the argument. Logarithm shares the glyph <source lang=apl inline>⍟</syntaxhighlight> with the dyadic arithmetic function Logarithm. The glyph, a composition of the glyphs for Circular (<source lang=apl inline>○</syntaxhighlight>) and Exponential (<source lang=apl inline>*</syntaxhighlight>) to indicate its close mathematical ties with these two functions, is a stylised tree log.[1]
Examples
<source lang=apl>
⍟1 2 (*1) (*10)
0 0.6931471806 1 10 </syntaxhighlight>
Properties
Natural logarithm is a special case of Logarithm with the default left argument of e (<source lang=apl inline>*1</syntaxhighlight>).
<source lang=apl>
((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1
1
</syntaxhighlight>
Natural logarithm and exponential <source lang=apl inline>*</syntaxhighlight> are inverses of each other, except where the natural log is undefined.
<source lang=apl>
(⊢ ≡ ⍟∘*) 0 1 ¯1 0J1
1
(⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined
1
</syntaxhighlight>
External links
Documentation
References
- ↑ McDonnell, E. E.. Recreational APL: The Story of <source lang=apl inline>○</syntaxhighlight>. APL Quote-Quad, Volume 8, Number 2, 1977-12.