► |  | 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:

array
mutable-array
make-array
build-array
array->mutable-array
mutable-array-copy
indexes-array
index-array
axis-index-array
diagonal-array

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#### 6.7`` Construction

> syntax (array #[#[...] ...] maybe-type-ann)
> maybe-type-ann |  | = |  |
> |  | | |  | : type

Creates an Array from nested rows of expressions.

The vector syntax #[...] delimits rows. These may be nested to any depth, and must have a rectangular shape. Using square parentheses is not required, but is encouraged to help visually distinguish array contents from array indexes and other vectors. (See the examples for indexes-array for an illustration.)

Examples:

> > (array 0)
> - : (Array Zero)
> (array 0)
> > (array #[0 1 2 3])
> - : (Array Byte)
> (array #[0 1 2 3])
> > (array #[#[1 2 3] #[4 5 6]])
> - : (Array Positive-Byte)
> (array #[#[1 2 3] #[4 5 6]])
> > (array #[#[1 2 3] #[4 5]])
> eval:121:0: array: expected rectangular data
> at: #(#(1 2 3) #(4 5))
> in: (array/syntax array list unsafe-list->array #(#(1 2 3)
> #(4 5)))

As with the list constructor, the type chosen for the array is the narrowest type all the elements can have. Unlike list, because array is syntax, instantiating array with the desired element type is a syntax error:

> > (list 1 2 3)
> - : (Listof Positive-Byte) [more precisely: (List One Positive-Byte Positive-Byte)]
> '(1 2 3)
> > (array #[1 2 3])
> - : (Array Positive-Byte)
> (array #[1 2 3])
> > ((inst list Real) 1 2 3)
> - : (Listof Real)
> '(1 2 3)
> > ((inst array Real) #[1 2 3])
> eval:125:0: array: not allowed as an expression
> in: array

There are two easy ways to annotate the element type:

> > (array #[1 2 3] : Real)
> - : (Array Real)
> (array #[1 2 3])
> > (ann (array #[1 2 3]) (Array Real))
> - : (Array Real)
> (array #[1 2 3])

Annotating should rarely be necessary because the Array type is covariant.

Normally, the datums within literal vectors are implicitly quoted. However, when used within the array form, the datums must be explicitly quoted.

> > #(this is okay)
> - : (U (Immutable-Vector 'this 'is 'okay) (Mutable-Vector 'this 'is 'okay)) [more precisely: (Immutable-Vector 'this 'is 'okay)]
> '#(this is okay)
> > (array #[not okay])
> eval:129:0: Type Checker: missing type for top-level
> identifier;
> either undefined or missing a type annotation
> identifier: okay
> in: #(not okay)
> > (array #['this 'is 'okay])
> - : (Array (U 'is 'okay 'this))
> (array #['this 'is 'okay])
> > (array #['#(an) '#(array) '#(of) '#(vectors)])
> - : (Array
> (U (Immutable-Vector 'an)
> (Immutable-Vector 'array)
> (Immutable-Vector 'of)
> (Immutable-Vector 'vectors)))
> (array #['#(an) '#(array) '#(of) '#(vectors)])

Arrays returned by array are strict. Another way to create immutable, strict arrays from literal data is to use list->array.

> syntax (mutable-array #[#[...] ...] maybe-type-ann)
> maybe-type-ann |  | = |  |
> |  | | |  | : type

Creates a Mutable-Array from nested rows of expressions.

The semantics are almost identical to array’s, except the result is mutable:

> > (define arr (mutable-array #[0 1 2 3]))
> > arr
> - : (Mutable-Array Integer)
> (mutable-array #[0 1 2 3])
> > (array-set! arr #(0) 10)
> > arr
> - : (Mutable-Array Integer)
> (mutable-array #[10 1 2 3])

Because mutable arrays are invariant, this form additionally accepts a type annotation for the array’s elements:

> > (define arr (mutable-array #[0 1 2 3] : Real))
> > arr
> - : (Mutable-Array Real)
> (mutable-array #[0 1 2 3])
> > (array-set! arr #(0) 10.0)
> > arr
> - : (Mutable-Array Real)
> (mutable-array #[10.0 1 2 3])

Another way to create mutable arrays from literal data is to use vector->array.

> procedure (make-array ds value) → (Array A)
> ds : In-Indexes
> value : A

Returns an array with shape ds, with every element’s value as value. Analogous to make-vector.

Examples:

> > (make-array #() 5)
> - : (Array Positive-Byte)
> (array 5)
> > (make-array #(1 2) 'sym)
> - : (Array 'sym)
> (array #[#['sym 'sym]])
> > (make-array #(4 0 2) "Invisible")
> - : (Array String)
> (array #[#[] #[] #[] #[]])

The arrays returned by make-array do not allocate storage for their elements and are strict.

> procedure (build-array ds proc) → (Array A)
> ds : In-Indexes
> proc : (Indexes -> A)

Returns an array with shape ds and procedure proc. Analogous to build-vector.

> procedure (array->mutable-array arr) → (Mutable-Array A)
> arr : (Array A)

Returns a mutable array with the same elements as arr. The result is a copy of arr, even when arr is mutable.

> procedure (mutable-array-copy arr) → (Mutable-Array A)
> arr : (Mutable-Array A)

Like (array->mutable-array arr), but restricted to mutable arrays. It is also faster.

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

Returns an array with shape ds, with each element set to its position in the array.

Examples:

> > (indexes-array #())
> - : (Array Indexes)
> (array '#())
> > (indexes-array #(4))
> - : (Array Indexes)
> (array #['#(0) '#(1) '#(2) '#(3)])
> > (indexes-array #(2 3))
> - : (Array Indexes)
> (array #[#['#(0 0) '#(0 1) '#(0 2)] #['#(1 0) '#(1 1) '#(1 2)]])
> > (indexes-array #(4 0 2))
> - : (Array Indexes)
> (array #[#[] #[] #[] #[]])

The resulting array does not allocate storage for its return value’s elements, and is strict. (It is essentially the identity function for the domain ds.)

> procedure (index-array ds) → (Array Index)
> ds : In-Indexes

Returns an array with shape ds, with each element set to its row-major index in the array.

Examples:

> > (index-array #(2 3))
> - : (Array Index)
> (array #[#[0 1 2] #[3 4 5]])
> > (array-flatten (index-array #(2 3)))
> - : (Array Index)
> (array #[0 1 2 3 4 5])

As with indexes-array, the result does not allocate storage for its elements, and is strict.

> procedure (axis-index-array ds axis) → (Array Index)
> ds : In-Indexes
> axis : Integer

Returns an array with shape ds, with each element set to its position in axis axis. The axis number axis must be nonnegative and less than the number of axes (the length of ds).

Examples:

> > (axis-index-array #(3 3) 0)
> - : (Array Index)
> (array #[#[0 0 0] #[1 1 1] #[2 2 2]])
> > (axis-index-array #(3 3) 1)
> - : (Array Index)
> (array #[#[0 1 2] #[0 1 2] #[0 1 2]])
> > (axis-index-array #() 0)
> axis-index-array: contract violation
> expected: Index < 0
> given: 0
> argument position: 2nd
> other arguments...:
> '#()

As with indexes-array, the result does not allocate storage for its elements, and is strict.

> > procedure
> > (diagonal-array |  | dims |  |  |  |
> > |  | axes-length |  |  |  |
> > |  | on-value |  |  |  |
> > |  | off-value) |  | → |  | (Array A)
> dims : Integer
> axes-length : Integer
> on-value : A
> off-value : A

Returns an array with dims axes, each with length axes-length. (For example, the returned array for dims = 2 is square.) The elements on the diagonal (i.e. at indexes of the form (vector j j ...) for j < axes-length) have the value on-value; the rest have off-value.

Example:

> > (diagonal-array 2 7 1 0)
> - : (Array (U One Zero))
> (array
> #[#[1 0 0 0 0 0 0]
> #[0 1 0 0 0 0 0]
> #[0 0 1 0 0 0 0]
> #[0 0 0 1 0 0 0]
> #[0 0 0 0 1 0 0]
> #[0 0 0 0 0 1 0]
> #[0 0 0 0 0 0 1]])

As with indexes-array, the result does not allocate storage for its elements, and is strict.
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