Magnitude

Magnitude (|), or Absolute Value, is a monadic scalar function which gives the absolute value of a real or complex number. Magnitude shares the glyph <syntaxhighlight lang=apl inline>|</source> with the dyadic arithmetic function Residue.

Examples

     |0 1 2 ¯1 ¯2

0 1 2 1 2

     |0J2 ¯3J¯4

2 5 </source>

Properties

The magnitude of any number is a non-negative real number.

For real numbers, the magnitude equals the original number times (or divided by, for non-zero numbers) its sign.

     v←0 1E¯100 20 1E300 ¯1E¯100 ¯20 ¯1E300
     (|v)≡v××v

1

     (|v)=v÷×v

0 1 1 1 1 1 1 </source>

For complex numbers, the magnitude is defined as the Euclidean distance from the number 0 on the complex plane.

     Dist←{0.5*⍨+.×⍨9 11○⍵} ⍝ Square root of square sum of real and imaginary parts
     Dist¨ 0 1J2 ¯3J4

0 2.236067977 5

     |0 1J2 ¯3J4

0 2.236067977 5

</source>

Works in: Dyalog APL

Any real or complex number is equal to the product of its signum and magnitude.

     (⊢ ≡ ××|) 0 1 1E¯300 ¯2.5 0J3.5 ¯3J¯4

1

</source>

Works in: Dyalog APL

External links

Documentation

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
		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
Operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

Magnitude

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Examples

Properties

See also

External links

Documentation

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Magnitude

Examples

Properties

See also

External links

Documentation

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