Natural Logarithm: Difference between revisions

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:''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>⍟</source> with the dyadic arithmetic function [[Logarithm]]. The [[glyph]], a composition of the glyphs for [[Circular]] (<source lang=apl inline>○</source>) and [[Exponential]] (<source lang=apl inline>*</source>) to indicate its close mathematical ties with these two functions, is a stylised tree log.
{{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>⍟</source> with the dyadic arithmetic function [[Logarithm]]. The [[glyph]], a composition of the glyphs for [[Circular]] (<source lang=apl inline>○</source>) and [[Exponential]] (<source lang=apl inline>*</source>) 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>○</source>]. [[APL Quote-Quad]], Volume 8, Number 2, 1977-12.</ref>


== Examples ==
== Examples ==
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* [http://microapl.com/apl_help/ch_020_020_210.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_210.htm APLX]
* J [https://www.jsoftware.com/help/dictionary/d201.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/hatdot NuVoc]
* J [https://www.jsoftware.com/help/dictionary/d201.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/hatdot NuVoc]
== References ==
<references/>
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]

Revision as of 19:27, 22 October 2020

A natural log
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 ⍟ with the dyadic arithmetic function Logarithm. The glyph, a composition of the glyphs for Circular (○) and Exponential (*) to indicate its close mathematical ties with these two functions, is a stylised tree log.[1]

Examples

      ⍟1 2 (*1) (*10)
0 0.6931471806 1 10

Properties

Natural logarithm is a special case of Logarithm with the default left argument of e (*1). 

      ((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1
1
Works in: Dyalog APL

Natural logarithm and exponential * are inverses of each other, except where the natural log is undefined. 

      (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1
1
      (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined
1
Works in: Dyalog APL

External links

Documentation

References

  1. ↑ McDonnell, E. E.. Recreational APL: The Story of ○. APL Quote-Quad, Volume 8, Number 2, 1977-12.
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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