6.10 Pointwise Operations
Most of the operations documented in this section are simple macros that apply array-map to a function and their array arguments.
procedure
f : (-> R) (array-map f arr0) → (Array R) f : (A -> R) arr0 : (Array A) (array-map f arr0 arr1 arrs ...) → (Array R) f : (A B Ts ... -> R) arr0 : (Array A) arr1 : (Array B) arrs : (Array Ts)
> (array-map (λ: ([x : String]) (string-append x "!")) (array #[#["Hello" "I"] #["Am" "Shouting"]]))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes String))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[#["Hello!" "I!"] #["Am!" "Shouting!"]])
> (array-map string-append (array #[#["Hello" "I"] #["Am" "Shouting"]]) (array "!"))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes String))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[#["Hello!" "I!"] #["Am!" "Shouting!"]])
> (array-map + (index-array #(3 3 3)) (array 2))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Fixnum))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array
#[#[#[2 3 4]
#[5 6 7]
#[8 9 10]]
#[#[11 12 13]
#[14 15 16]
#[17 18 19]]
#[#[20 21 22]
#[23 24 25]
#[26 27 28]]])
> (array-map + (index-array #(2 2)) (index-array #(3 3))) array-shape-broadcast: incompatible array shapes
(array-broadcasting #t): '#(2 2), '#(3 3)
> (array-map * (array #[-4.3 -1.2 -0.2]) (array -2.81))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Nonnegative-Flonum))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[12.083 3.372 0.562])
> (array-map (λ () "Whoa, Nelly!"))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes String))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array "Whoa, Nelly!")
> (array-map + (array #[1 2 3]) (array-map (λ () -10)))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Fixnum))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[-9 -8 -7])
When explicitly instantiating array-map’s types using inst, instantiate R (the return type’s element type) first, then the arguments’ element types in order.
syntax
(inline-array-map f arrs ...)
syntax
(array+ arrs ...)
syntax
(array* arrs ...)
syntax
(array- arr0 arrs ...)
syntax
(array/ arr0 arrs ...)
syntax
(array-min arr0 arrs ...)
syntax
(array-max arr0 arrs ...)
> (array+ (array #[#[0.0 1.0] #[2.0 3.0]]) (array 200))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Flonum))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[#[200.0 201.0] #[202.0 203.0]])
> (array+)
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Zero))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array 0)
> (array*)
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes One))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array 1)
> (array/ (array #[2 1/2]))
- : #(struct:Array
(Indexes
Index
(Boxof Boolean)
(-> Void)
(-> Indexes Positive-Exact-Rational))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[1/2 2])
syntax
(array-scale arr x)
syntax
(array-abs arr)
syntax
(array-sqr arr)
syntax
(array-sqrt arr)
syntax
(array-conjugate arr)
syntax
(array-real-part arr)
syntax
(array-imag-part arr)
syntax
(array-make-rectangular arr0 arr1)
syntax
(array-magnitude arr)
syntax
(array-angle arr)
syntax
(array-make-polar arr0 arr1)
syntax
(array< arr0 arr1 arrs ...)
syntax
(array<= arr0 arr1 arrs ...)
syntax
(array> arr0 arr1 arrs ...)
syntax
(array>= arr0 arr1 arrs ...)
syntax
(array= arr0 arr1 arrs ...)
syntax
(array-not arr)
syntax
(array-and arr ...)
syntax
(array-or arr ...)
syntax
(array-if cond-arr true-arr false-err)
(: array-factorial ((Array Integer) -> (Array Integer))) (define (array-factorial arr) (array-if (array<= arr (array 0)) (array 1) (array* arr (array-factorial (array- arr (array 1))))))
6.10.1 Broadcasting
parameter
(array-broadcasting) → (U Boolean 'permissive)
(array-broadcasting broadcasting) → void? broadcasting : (U Boolean 'permissive)
procedure
(array-shape-broadcast dss [broadcasting]) → Indexes
dss : (Listof Indexes) broadcasting : (U Boolean 'permissive) = (array-broadcasting)
> (array-shape-broadcast '()) - : Indexes
'#()
> (array-shape-broadcast (list (vector) ((inst vector Index) 10))) - : Indexes
'#(10)
> (array-shape-broadcast (list ((inst vector Index) 2) ((inst vector Index) 10))) array-shape-broadcast: incompatible array shapes
(array-broadcasting #t): '#(2), '#(10)
> (array-shape-broadcast (list ((inst vector Index) 2) ((inst vector Index) 10)) 'permissive) - : Indexes
'#(10)
procedure
(array-broadcast arr ds) → (Array A)
arr : (Array A) ds : Indexes
> (array-broadcast (array 10) ((inst vector Index) 10))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Byte))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[10 10 10 10 10 10 10 10 10 10])
> (array-broadcast (array #[0 1]) #()) array-broadcast: cannot broadcast to a lower-dimensional
shape; given (array #[0 1]) and '#()
> (array-broadcast (array #[0 1]) ((inst vector Index) 5))
- : #(struct:Array
(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes (U One Zero)))
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
#<syntax:build/user/8.13.0.7/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)
(array #[0 1 0 1 0])
When array-strictness is #f, array-broadcast always returns a nonstrict array.
When array-strictness is #t, array-broadcast returns a strict array when arr is nonstrict and the result has more elements than arr.