6.12 Transformations

> (define arr(array #[#[01]#[2'three]]))
> (array-transform arr#(33)(λ: ([js: Indexes ])#(11)))

- : #(struct:Array

(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes (U 'three Byte)))

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array

#[#['three 'three 'three]

#['three 'three 'three]

#['three 'three 'three]])

Doubling an array in every dimension by duplicating elements:

> (define arr(index-array #(33)))
> arr

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 1 2] #[3 4 5] #[6 7 8]])

> (array-transform
arr
(vector-map (λ: ([d: Index ])(* d2))(array-shape arr))
(λ: ([js: Indexes ])
(vector-map (λ: ([j: Index ])(quotient j2))js)))

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array

#[#[0 0 1 1 2 2]

#[0 0 1 1 2 2]

#[3 3 4 4 5 5]

#[3 3 4 4 5 5]

#[6 6 7 7 8 8]

#[6 6 7 7 8 8]])

When array-strictness is #f, the above result takes little more space than the original array.

Almost all array transformations, including Slicing, are implemented using array-transform or its unsafe counterpart.

procedure
( array-append* arrs[k])→(Array A)
arrs:(Listof (Array A))
k:Integer =0

Appends the arrays in arrs along axis k. If the arrays’ shapes are not the same, they are broadcast first.

Examples:

> (define arr(array #[#[01]#[23]]))
> (define brr(array #[#['a'b]#['c'd]]))
> (array-append* (list arrbrr))

- : #(struct:Array

(Indexes

Index

(Boxof Boolean)

(-> Void)

(-> Indexes (U 'a 'b 'c 'd Byte)))

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 1] #[2 3] #['a 'b] #['c 'd]])
> (array-append* (list arrbrr)1)

- : #(struct:Array

(Indexes

Index

(Boxof Boolean)

(-> Void)

(-> Indexes (U 'a 'b 'c 'd Byte)))

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 1 'a 'b] #[2 3 'c 'd]])
> (array-append* (list arr(array 'x)))

- : #(struct:Array

(Indexes Index (Boxof Boolean) (-> Void) (-> Indexes (U 'x Byte)))

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 1] #[2 3] #['x 'x]])

For an append-like operation that increases the dimension of the broadcast arrays, see array-list->array .

procedure
( array-axis-insert arrk[dk])→(Array A)
arr:(Array A)
k:Integer
dk:Integer =1

Inserts an axis of length dk before axis number k, which must be no greater than the dimension of arr.

Examples:

> (define arr(array #[#[01]#[23]]))
> (array-axis-insert arr0)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[#[0 1] #[2 3]]])
> (array-axis-insert arr1)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[#[0 1]] #[#[2 3]]])
> (array-axis-insert arr2)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[#[0] #[1]] #[#[2] #[3]]])
> (array-axis-insert arr12)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[#[0 1] #[0 1]] #[#[2 3] #[2 3]]])

procedure
( array-axis-ref arrkjk)→(Array A)
arr:(Array A)
k:Integer
jk:Integer

Removes an axis from arr by keeping only row jk in axis k, which must be less than the dimension of arr.

Examples:

> (define arr(array #[#[01]#[23]]))
> (array-axis-ref arr00)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[0 1])
> (array-axis-ref arr01)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[2 3])
> (array-axis-ref arr10)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[0 2])

procedure
( array-axis-swap arrk0k1)→(Array A)
arr:(Array A)
k0:Integer
k1:Integer

Returns an array like arr, but with axes k0 and k1 swapped. In two dimensions, this is called a transpose.

Examples:

> (array-axis-swap (array #[#[01]#[23]])01)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 2] #[1 3]])
> (define arr(indexes-array #(222)))
> arr

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array

#[#[#['#(0 0 0) '#(0 0 1)]

#['#(0 1 0) '#(0 1 1)]]

#[#['#(1 0 0) '#(1 0 1)]

#['#(1 1 0) '#(1 1 1)]]])
> (array-axis-swap arr01)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array

#[#[#['#(0 0 0) '#(0 0 1)]

#['#(1 0 0) '#(1 0 1)]]

#[#['#(0 1 0) '#(0 1 1)]

#['#(1 1 0) '#(1 1 1)]]])
> (array-axis-swap arr12)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array

#[#[#['#(0 0 0) '#(0 1 0)]

#['#(0 0 1) '#(0 1 1)]]

#[#['#(1 0 0) '#(1 1 0)]

#['#(1 0 1) '#(1 1 1)]]])

procedure
( array-axis-permute arrperm)→(Array A)
arr:(Array A)
perm:(Listof Integer )

Returns an array like arr, but with axes permuted according to perm.

The list perm represents a mapping from source axis numbers to destination axis numbers: the source is the list position, the destination is the list element. For example, the permutation '(012) is the identity permutation for three-dimensional arrays, '(10) swaps axes 0 and 1, and '(3120) swaps axes 0 and 3.

The permutation must contain each integer from 0 to (- (array-dims arr)1) exactly once.

Examples:

> (array-axis-swap (array #[#[01]#[23]])01)

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 2] #[1 3]])
> (array-axis-permute (array #[#[01]#[23]])'(10))

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#[0 2] #[1 3]])

procedure
( array-reshape arrds)→(Array A)
arr:(Array A)
ds:In-Indexes

Returns an array with elements in the same row-major order as arr, but with shape ds. The product of the indexes in ds must be (array-size arr).

Examples:

> (define arr(indexes-array #(23)))
> arr

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#['#(0 0) '#(0 1) '#(0 2)] #['#(1 0) '#(1 1) '#(1 2)]])
> (array-reshape arr#(32))

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[#['#(0 0) '#(0 1)] #['#(0 2) '#(1 0)] #['#(1 1) '#(1 2)]])
> (array-reshape (index-array #(33))#(9))

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[0 1 2 3 4 5 6 7 8])

procedure
( array-flatten arr)→(Array A)
arr:(Array A)

Returns an array with shape (vector (array-size arr)), with the elements of arr in row-major order.

Examples:

> (array-flatten (array 10))

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[10])
> (array-flatten (array #[#[01]#[23]]))

- : #(struct:Array

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

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>

#<syntax:build/user/8.18/pkgs/math-lib/math/private/array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>)

(array #[0 1 2 3])

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