6.11 Indexing and Slicing

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 arridxs)→(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 #[#[12]#[1020]]))
> (define idxs(array #['#(00)'#(11)]))
> (array-indexes-ref arridxs)

- : #(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 #[1 20])

Implementation-level explanation: (array-indexes-ref arridxs) is equivalent to

> (build-array (array-shape idxs)
(λ: ([js: Indexes ])
(array-ref arr(array-ref idxsjs))))

- : #(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 #[1 20])

but faster.

procedure
( array-indexes-set! arridxsvals)→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 #[#[12]#[1020]]))
> (define idxs(array #['#(00)'#(11)]))
> (array-indexes-set! arridxs(array -1))
> arr

- : #(struct:Mutable-Array

(Indexes

Index

(Boxof Boolean)

(-> Void)

(-> Indexes Integer)

(-> Indexes Integer Void)

(Vectorof Integer))

#<syntax:build/user/8.18/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 arrspecs)→(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! arrspecsvals)→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! arridxsvals))

Examples:

> (define arr(array->mutable-array (axis-index-array #(55)1)))
> (array-slice-set! arr(list (:: 1#f2)(:: ))(array 1))
> arr

- : #(struct:Mutable-Array

(Indexes

Index

(Boxof Boolean)

(-> Void)

(-> Indexes Integer)

(-> Indexes Integer Void)

(Vectorof Integer))

#<syntax:build/user/8.18/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#f2))
(array-scale (array-slice-ref arr(list (:: )(:: 1#f2)))-1))
> arr

- : #(struct:Mutable-Array

(Indexes

Index

(Boxof Boolean)

(-> Void)

(-> Indexes Integer)

(-> Indexes Integer Void)

(Vectorof Integer))

#<syntax:build/user/8.18/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 #fInteger )=#f
(:: startend[step])→Slice
start:(U #fInteger )
end:(U #fInteger )
step:Integer =1

procedure
( slice? v)→Boolean
v:Any

procedure
( slice-start s)→(U #fFixnum )
s:Slice

procedure
( slice-end s)→(U #fFixnum )
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 sdk)→(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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