6.9 Comprehensions and Sequences

► |  | Math Library

1 | Constants and Elementary Functions
2 | Flonums
3 | Special Functions
4 | Number Theory
5 | Arbitrary-Precision Floating-Point Numbers (Bigfloats)
6 | Arrays
7 | Matrices and Linear Algebra
8 | Statistics Functions
9 | Probability Distributions
10 | Stuff That Doesn’t Belong Anywhere Else

▼ | 6 | Arrays

6.1 | Quick Start
6.2 | Definitions
6.3 | Broadcasting
6.4 | Slicing
6.5 | Nonstrict Arrays
6.6 | Types, Predicates and Accessors
6.7 | Construction
6.8 | Conversion
6.9 | Comprehensions and Sequences
6.10 | Pointwise Operations
6.11 | Indexing and Slicing
6.12 | Transformations
6.13 | Folds, Reductions and Expansions
6.14 | Other Array Operations
6.15 | Subtypes
6.16 | Strictness

On this page:

for/ array:
for*/ array:
for/ array
for*/ array
in-array
in-array-axis
in-array-indexes

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### 6.9 Comprehensions and Sequences🔗ℹ

Sometimes sequential processing is unavoidable, so math/array provides loops and sequences.

> > syntax
> > (for/array: maybe-shape maybe-fill (for:-clause ...) maybe-type-ann
> > body ...+)
> > syntax
> > (for*/array: maybe-shape maybe-fill (for:-clause ...) maybe-type-ann
> > body ...+)
> maybe-shape |  | = |  |
> |  | | |  | #:shape ds
> maybe-fill |  | = |  |
> |  | | |  | #:fill fill
> maybe-type-ann |  | = |  |
> |  | | |  | : body-type
> > | ds |  | : |  | In-Indexes
> > | fill |  | : |  | body-type

Creates arrays by generating elements in a for-loop or for*-loop. Unlike other Typed Racket loop macros, these accept a body annotation, which declares the type of elements. They do not accept an annotation for the entire type of the result.

Examples:

> > (for/array: ([x (in-range 3)] [y (in-range 3)]) : Integer
> (+ x y))
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes Integer)
> (-> Indexes Integer Void)
> (Vectorof Integer))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array #[0 2 4])
> > (for*/array: ([x (in-range 3)] [y (in-range 3)]) : Integer
> (+ x y))
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes Integer)
> (-> Indexes Integer Void)
> (Vectorof Integer))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array #[0 1 2 1 2 3 2 3 4])

The shape of the result is independent of the loop clauses: note that the last example does not have shape #(3 3), but shape #(9). To control the shape, use the #:shape keyword:

> > (for*/array: #:shape #(3 3) ([x (in-range 3)]
> [y (in-range 3)]) : Integer
> (+ x y))
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes Integer)
> (-> Indexes Integer Void)
> (Vectorof Integer))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array #[#[0 1 2] #[1 2 3] #[2 3 4]])

If the loop does not generate enough elements, the rest are filled with the first generated value:

> > (for*/array: #:shape #(4) ([x (in-range 1 3)]) x)
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes Any)
> (-> Indexes Any Void)
> (Vectorof Any))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array #[1 2 1 1])

To change this behavior, use the #:fill keyword:

> > (for*/array: #:shape #(4) #:fill -1 ([x (in-range 1 3)]) x)
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes Any)
> (-> Indexes Any Void)
> (Vectorof Any))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array #[1 2 -1 -1])

In the last two examples, the array’s type is (Mutable-Array Any) because a body annotation was not given.

> > syntax
> > (for/array maybe-shape maybe-fill (for-clause ...)
> > body ...+)
> > syntax
> > (for*/array maybe-shape maybe-fill (for-clause ...)
> > body ...+)

Untyped versions of the loop macros.

> procedure (in-array arr) → (Sequenceof A)
> arr : (Array A)

Returns a sequence of arr’s elements in row-major order.

Examples:

> > (define arr (array #[#[1 2] #[10 20]]))
> > (for/list: : (Listof Integer) ([x (in-array arr)]) x)
> - : (Listof Integer)
> '(1 2 10 20)

> procedure (in-array-axis arr [axis]) → (Sequenceof (Array A))
> arr : (Array A)
> axis : Integer = 0

Like array->array-list, but returns a sequence.

Examples:

> > (define arr (array #[#[1 2] #[10 20]]))
> > (sequence->list (in-array-axis arr))
> - : (Listof
> #(struct:Array
> (Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Byte))
> #<syntax:.../array/typed-array-struct.rkt:56:13 prop:equal+hash>
> #<syntax:.../array/typed-array-struct.rkt:55:13 prop:custom-write>
> #<syntax:.../array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>))
> (list (array #[1 2]) (array #[10 20]))
> > (sequence->list (in-array-axis arr 1))
> - : (Listof
> #(struct:Array
> (Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Positive-Byte))
> #<syntax:.../array/typed-array-struct.rkt:56:13 prop:equal+hash>
> #<syntax:.../array/typed-array-struct.rkt:55:13 prop:custom-write>
> #<syntax:.../array/typed-array-struct.rkt:54:13 prop:custom-print-quotable>))
> (list (array #[1 10]) (array #[2 20]))

> procedure (in-array-indexes ds) → (Sequenceof Indexes)
> ds : In-Indexes

Returns a sequence of indexes for shape ds, in row-major order.

Examples:

> > (for/array: #:shape #(3 3) ([js (in-array-indexes #(3 3))]) : Indexes
> js)
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes Indexes)
> (-> Indexes Indexes Void)
> (Vectorof Indexes))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array
> #[#['#(0 0) '#(0 1) '#(0 2)]
> #['#(1 0) '#(1 1) '#(1 2)]
> #['#(2 0) '#(2 1) '#(2 2)]])
> > (for*/array: #:shape #(3 3) ([j0 (in-range 3)]
> [j1 (in-range 3)]) : In-Indexes
> (vector j0 j1))
> - : #(struct:Mutable-Array
> (Indexes
> Index
> (Boxof Boolean)
> (-> Void)
> (-> Indexes In-Indexes)
> (-> Indexes In-Indexes Void)
> (Vectorof In-Indexes))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-mutable-array.rkt:14:13 prop:custom-write>)
> (mutable-array
> #[#['#(0 0) '#(0 1) '#(0 2)]
> #['#(1 0) '#(1 1) '#(1 2)]
> #['#(2 0) '#(2 1) '#(2 2)]])
> > (indexes-array #(3 3))
> - : #(struct:Array
> (Indexes Index (Boxof Boolean) (-> Void) (-> Indexes Indexes))
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-array-struct.rkt:56:13 prop:equal+hash>
> #<syntax:build/user/9.0/pkgs/math-lib/math/private/array/typed-array-struct.rkt:55:13 prop:custom-write>
> #<syntax:build/user/9.0/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)]
> #['#(2 0) '#(2 1) '#(2 2)]])

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