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 <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>

Works in: Dyalog APL

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>

Works in: Dyalog APL

External links

Documentation

References

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector