Natural Logarithm

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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
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
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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
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Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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