►Math Library
▼6 Arrays
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array-ref
array-set!
array-indexes-ref
array-indexes-set!
array-slice-ref
array-slice-set!
Slice-Spec
Slice
:  :
slice?
slice-start
slice-end
slice-step
slice->range-values
Slice-Dots
:  :  ...
slice-dots?
Slice-New-Axis
:  :  new
slice-new-axis?
slice-new-axis-length
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6.11 Indexing and Slicing

procedure

(array-ref arr js) → A

  arr : (Array A)
  js : In-Indexes
Returns the element of arr at position js. If any index in js is negative or not less than its corresponding axis length, array-ref raises an error.

procedure

(array-set! arr js value) → Void

  arr : (Settable-Array A)
  js : In-Indexes
  value : A
Sets the element of arr at position js to value. If any index in js is negative or not less than its corresponding axis length, array-set! raises an error.

procedure

(array-indexes-ref arr idxs) → (Array A)

  arr : (Array A)
  idxs : (Array In-Indexes)
High-level explanation: Returns multiple elements from arr in a new array.

Lower-level explanation: Returns an array with same shape as idxs, whose elements are array-ref’d from arr using the indexes in idxs.

Examples:
> (define arr (array #[#[1 2] #[10 20]]))
> (define idxs (array #['#(0 0) '#(1 1)]))
> (array-indexes-ref arr idxs)

- : #(struct:Array

      (Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Byte))

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[1 20])

Implementation-level explanation: (array-indexes-ref arr idxs) is equivalent to
> (build-array (array-shape idxs)
               (λ: ([js : Indexes])
                 (array-ref arr (array-ref idxs js))))

- : #(struct:Array

      (Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Byte))

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[1 20])

but faster.

procedure

(array-indexes-set! arr idxs vals) → Void

  arr : (Settable-Array A)
  idxs : (Array In-Indexes)
  vals : (Array A)
Indexes arr in the same way that array-indexes-ref does, but mutates elements. If idxs and vals do not have the same shape, they are broadcast first.

Examples:
> (define arr (mutable-array #[#[1 2] #[10 20]]))
> (define idxs (array #['#(0 0) '#(1 1)]))
> (array-indexes-set! arr idxs (array -1))
> arr

- : #(struct:Mutable-Array

      (Indexes

       Index

       (Boxof Boolean)

       (-> Void)

       (-> Indexes Integer)

       (-> Indexes Integer Void)

       (Vectorof Integer))

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)

(mutable-array #[#[-1 2] #[10 -1]])

When two indexes in idxs are the same, the element at that index is mutated more than once in some unspecified order.

procedure

(array-slice-ref arr specs) → (Array A)

  arr : (Array A)
  specs : (Listof Slice-Spec)
Returns a transformation of arr according to the list of slice specifications specs. See Slicing for a discussion and examples.

procedure

(array-slice-set! arr specs vals) → Void

  arr : (Settable-Array A)
  specs : (Listof Slice-Spec)
  vals : (Array A)
Like array-indexes-set!, but for slice specifications. Equivalent to
(let ([idxs  (array-slice-ref (indexes-array (array-shape arr)) specs)])
  (array-indexes-set! arr idxs vals))

Examples:
> (define arr (array->mutable-array (axis-index-array #(5 5) 1)))
> (array-slice-set! arr (list (:: 1 #f 2) (::)) (array 1))
> arr

- : #(struct:Mutable-Array

      (Indexes

       Index

       (Boxof Boolean)

       (-> Void)

       (-> Indexes Integer)

       (-> Indexes Integer Void)

       (Vectorof Integer))

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)

(mutable-array

 #[#[0 1 2 3 4]

   #[1 1 1 1 1]

   #[0 1 2 3 4]

   #[1 1 1 1 1]

   #[0 1 2 3 4]])

> (array-slice-set!
   arr (list (::) (:: 1 #f 2))
   (array-scale (array-slice-ref arr (list (::) (:: 1 #f 2))) -1))
> arr

- : #(struct:Mutable-Array

      (Indexes

       Index

       (Boxof Boolean)

       (-> Void)

       (-> Indexes Integer)

       (-> Indexes Integer Void)

       (Vectorof Integer))

      #<syntax:build/user/8.5/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)

(mutable-array

 #[#[0 -1 2 -3 4]

   #[1 -1 1 -1 1]

   #[0 -1 2 -3 4]

   #[1 -1 1 -1 1]

   #[0 -1 2 -3 4]])

When a slice specification refers to an element in arr more than once, the element is mutated more than once in some unspecified order.

syntax

Slice-Spec

The type of a slice specification. Currently defined as

(U (Sequenceof Integer) Slice Slice-Dots Integer Slice-New-Axis)

A (Sequenceof Integer) slice specification causes array-slice-ref to pick rows from an axis. An Integer slice specification causes array-slice-ref to remove an axis by replacing it with one of its rows.

See Slicing for an extended example.

syntax

Slice

procedure

(:: [end]) → Slice

  end : (U #f Integer) = #f
(:: start end [step]) → Slice
  start : (U #f Integer)
  end : (U #f Integer)
  step : Integer = 1

procedure

(slice? v) → Boolean

  v : Any

procedure

(slice-start s) → (U #f Fixnum)

  s : Slice

procedure

(slice-end s) → (U #f Fixnum)

  s : Slice

procedure

(slice-step s) → Fixnum

  s : Slice
The type of in-range-like slice specifications, its constructor, predicate, and accessors.

array-slice-ref interprets a Slice like an in-range sequence object. When start or end is #f, it is interpreted as an axis-length-dependent endpoint.

procedure

(slice->range-values s dk) → (Values Fixnum Fixnum Fixnum)

  s : Slice
  dk : Index
Given a slice s and an axis length dk, returns the arguments to in-range that would produce an equivalent slice specification.

This is used internally by array-slice-ref to interpret a Slice object as a sequence of indexes.

syntax

Slice-Dots

value

::... : Slice-Dots

procedure

(slice-dots? v) → Boolean

  v : Any
The type of greedy, multiple-axis-preserving slice specifications, its singleton value, and predicate.

syntax

Slice-New-Axis

procedure

(::new [dk]) → Slice-New-Axis

  dk : Integer = 1

procedure

(slice-new-axis? v) → Boolean

  v : Any

procedure

(slice-new-axis-length s) → Index

  s : Slice-New-Axis
The type of slice specifications that indicate inserting a new axis, its constructor, predicate, and accessor. The axis length dk must be nonnegative.

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