Scan

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\ ⍀

Scan (\, ⍀) is a primitive monadic operator which takes a dyadic function operand and produces a monadic function which is equivalent to the reductions of the prefixes of the arguments. This operation is known as also known as cumulative reduction.

Explanation

Scan is similar to Reduce, however all the intermediate results will be retained. That being said, unlike Reduce, Scan does not reduce the rank of its argument, i.e. performing a scan over an N-dimensional array will produce an N-dimensional array.

Examples

      +\⍳5 ⍝ plus-scan over range of integers from 1 to 5
1 3 6 10 15

Applications

Removing disconnected trailing 1s from a boolean mask: 

      mask←1 1 1 1 0 1 1 0 0 1
      mask
1 1 1 1 0 1 1 0 0 1
      ∧\mask ⍝ and-scan mask
1 1 1 1 0 0 0 0 0 0

External links

Lessons

Documentation


APL built-ins [edit]
Primitive 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 ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Primitive operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut (J)
Quad names
Arrays Index origin ∙ Migration level ∙ Atomic vector
Functions Name class ∙ Case convert ∙ Unicode convert
Operators Search ∙ Replace
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